text: /**
   * clmtrackr library (https://www.github.com/auduno/clmtrackr/)
   *
   * Copyright (c) 2013, Audun Mathias Øygard
   * 
   * Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
   *
   * The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
   *
   * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
   */
  
  "use strict";
  //requires: ccv.js, numeric.js
  
  var clm = {
  	tracker : function(params) {
  		
  		if (!params) params = {};
  		if (params.constantVelocity === undefined) params.constantVelocity = true;
  		if (params.searchWindow === undefined) params.searchWindow = 11;
  		if (params.useWebGL === undefined) params.useWebGL = true;
  		if (params.scoreThreshold === undefined) params.scoreThreshold = 0.30;
  		if (params.stopOnConvergence === undefined) params.stopOnConvergence = false;
  		if (params.weightPoints === undefined) params.weightPoints = undefined;
  		if (params.sharpenResponse === undefined) params.sharpenResponse = false;
  		
  		var numPatches, patchSize, numParameters, patchType;
  		var gaussianPD;
  		var eigenVectors, eigenValues;
  		var sketchCC, sketchW, sketchH, sketchCanvas;
  		var candidate;
  		var weights, model;
  		
  		var currentParameters = [];
  		var currentPositions = [];
  		var previousParameters = [];
  		var previousPositions = [];
  		
  		var patches = [];
  		var responses = [];
  		var meanShape = [];
  		
  		/*
  		It's possible to experiment with the sequence of variances used for the finding the maximum in the KDE.
  		This sequence is pretty arbitrary, but was found to be okay using some manual testing.
  		*/
  		var varianceSeq = [10,5,1];
  		//var varianceSeq = [3,1.5,0.75];
  		//var varianceSeq = [6,3,0.75];
  		var PDMVariance = 0.7;
  		
  		var relaxation = 0.1;
  		
  		var first = true;
  		
  		var convergenceLimit = 0.01;
  		
  		var learningRate = [];
  		var stepParameter = 1.25;
  		var prevCostFunc = []
  		
  		var searchWindow;
  		var modelWidth, modelHeight;
  		var halfSearchWindow, vecProbs, responsePixels;
  		
  		if(typeof Float64Array !== 'undefined') {
  			var updatePosition = new Float64Array(2);
  			var vecpos = new Float64Array(2);
  		} else {
  			var updatePosition = new Array(2);
  			var vecpos = new Array(2);
  		}
  		var pw, pl, pdataLength;
  		
  		var facecheck_count = 0;
  		
  		var webglFi, svmFi, mosseCalc;
  
  		var scoringCanvas = document.createElement('canvas');
  		//document.body.appendChild(scoringCanvas);
  		var scoringContext = scoringCanvas.getContext('2d');
  		var msxmin, msymin, msxmax, msymax;
  		var msmodelwidth, msmodelheight;
  		var scoringWeights, scoringBias;
  		var scoringHistory = [];
  		var meanscore = 0;
  
  		var mossef_lefteye, mossef_righteye, mossef_nose;
  		var right_eye_position = [0.0,0.0];
  		var left_eye_position = [0.0,0.0];
  		var nose_position = [0.0,0.0];
  		var lep, rep, mep;
  		var runnerTimeout, runnerElement, runnerBox;
  		
  		var pointWeights;
  
  		var halfPI = Math.PI/2;
  		
  		/*
  		 *	load model data, initialize filters, etc.
  		 *
  		 *	@param	<Object>	pdm model object
  		 */
  		this.init = function(pdmmodel) {
  			
  			model = pdmmodel;
  			
  			// load from model
  			patchType = model.patchModel.patchType;
  			numPatches = model.patchModel.numPatches;
  			patchSize = model.patchModel.patchSize[0];
  			if (patchType == "MOSSE") {
  				searchWindow = patchSize;
  			} else {
  				searchWindow = params.searchWindow;
  			}
  			numParameters = model.shapeModel.numEvalues;
  			modelWidth = model.patchModel.canvasSize[0];
  			modelHeight = model.patchModel.canvasSize[1];
  			
  			// set up canvas to work on
  			sketchCanvas = document.createElement('canvas');
  			sketchCC = sketchCanvas.getContext('2d');
  
  			sketchW = sketchCanvas.width = modelWidth + (searchWindow-1) + patchSize-1;
  			sketchH = sketchCanvas.height = modelHeight + (searchWindow-1) + patchSize-1;
  			
  			if (model.hints && mosseFilter && left_eye_filter && right_eye_filter && nose_filter) {
  				//var mossef_lefteye = new mosseFilter({drawResponse : document.getElementById('overlay2')});
  				mossef_lefteye = new mosseFilter();
  				mossef_lefteye.load(left_eye_filter);
  				//var mossef_righteye = new mosseFilter({drawResponse : document.getElementById('overlay2')});
  				mossef_righteye = new mosseFilter();
  				mossef_righteye.load(right_eye_filter);
  				//var mossef_nose = new mosseFilter({drawResponse : document.getElementById('overlay2')});
  				mossef_nose = new mosseFilter();
  				mossef_nose.load(nose_filter);
  			} else {
  				console.log("MOSSE filters not found, using rough approximation for initialization.");
  			}
  
  			// load eigenvectors
  			eigenVectors = numeric.rep([numPatches*2,numParameters],0.0);
  			for (var i = 0;i < numPatches*2;i++) {
  				for (var j = 0;j < numParameters;j++) {
  					eigenVectors[i][j] = model.shapeModel.eigenVectors[i][j];
  				}
  			}
  			
  			// load mean shape
  			for (var i = 0; i < numPatches;i++) {
  				meanShape[i] = [model.shapeModel.meanShape[i][0], model.shapeModel.meanShape[i][1]];
  			}
  
  			// get max and mins, width and height of meanshape
  			msxmax = msymax = 0;
  			msxmin = msymin = 1000000;
  			for (var i = 0;i < numPatches;i++) {
  				if (meanShape[i][0] < msxmin) msxmin = meanShape[i][0];
  				if (meanShape[i][1] < msymin) msymin = meanShape[i][1];
  				if (meanShape[i][0] > msxmax) msxmax = meanShape[i][0];
  				if (meanShape[i][1] > msymax) msymax = meanShape[i][1];
  			}
  			msmodelwidth = msxmax-msxmin;
  			msmodelheight = msymax-msymin;
  			
  			// get scoringweights if they exist
  			if (model.scoring) {
  				scoringWeights = new Float64Array(model.scoring.coef);
  				scoringBias = model.scoring.bias;
  				scoringCanvas.width = model.scoring.size[0];
  				scoringCanvas.height = model.scoring.size[1];
  			}
  			
  			// load eigenvalues
  			eigenValues = model.shapeModel.eigenValues;
  			
  			weights = model.patchModel.weights;
  			
  			// precalculate gaussianPriorDiagonal
  			gaussianPD = numeric.rep([numParameters+4, numParameters+4],0);
  			// set values and append manual inverse
  			for (var i = 0;i < numParameters;i++) {
  				if (model.shapeModel.nonRegularizedVectors.indexOf(i) >= 0) {
  					gaussianPD[i+4][i+4] = 1/10000000;
  				} else {
  					gaussianPD[i+4][i+4] = 1/eigenValues[i];
  				}
  			}
  			
  			for (var i = 0;i < numParameters+4;i++) {
  				currentParameters[i] = 0;
  			}
  			
  			if (patchType == "SVM") {
  				var webGLContext;
  				var webGLTestCanvas = document.createElement('canvas');
  				if (window.WebGLRenderingContext) {
  					webGLContext = webGLTestCanvas.getContext('webgl') || webGLTestCanvas.getContext('experimental-webgl');
  					if (!webGLContext || !webGLContext.getExtension('OES_texture_float')) {
  						webGLContext = null;
  					}
  				} 
  				
  				if (webGLContext && params.useWebGL && (typeof(webglFilter) !== "undefined")) {
  					webglFi = new webglFilter();
  					try {
  						webglFi.init(weights, numPatches, searchWindow+patchSize-1, searchWindow+patchSize-1, patchSize, patchSize, true);
  					} 
  					catch(err) {
  						alert("There was a problem setting up webGL programs, falling back to slightly slower javascript version. :(");
  						webglFi = undefined;
  						svmFi = new svmFilter();
  						svmFi.init(weights, numPatches, patchSize, searchWindow);
  					}
  				} else if (typeof(svmFilter) !== "undefined") {
  					// use fft convolution if no webGL is available
  					svmFi = new svmFilter();
  					svmFi.init(weights, numPatches, patchSize, searchWindow);
  				} else {
  					throw "Could not initiate filters, please make sure that svmfilter.js or svmfilter_conv_js.js is loaded."
  				}
  			} else if (patchType == "MOSSE") {
  				mosseCalc = new mosseFilterResponses();
  				mosseCalc.init(weights, numPatches, patchSize, patchSize);
  			}
  			
  			if (patchType == "SVM") {
  				pw = pl = patchSize+searchWindow-1;
  			} else {
  				pw = pl = searchWindow;
  			}
  			pdataLength = pw*pl;
  			halfSearchWindow = (searchWindow-1)/2;
  			responsePixels = searchWindow*searchWindow;
  			if(typeof Float64Array !== 'undefined') {
  				vecProbs = new Float64Array(responsePixels);
  				for (var i = 0;i < numPatches;i++) {
  					patches[i] = new Float64Array(pdataLength);
  				}
  			} else {
  				vecProbs = new Array(responsePixels);
  				for (var i = 0;i < numPatches;i++) {
  					patches[i] = new Array(pdataLength);
  				}
  			}
  			
  			for (var i = 0;i < numPatches;i++) {
  				learningRate[i] = 1.0;
  				prevCostFunc[i] = 0.0;
  			}
  
  			if (params.weightPoints) {
  				// weighting of points 
  				pointWeights = [];
  				for (var i = 0;i < numPatches;i++) {
  					if (i in params.weightPoints) {
  						pointWeights[(i*2)] = params.weightPoints[i];
  						pointWeights[(i*2)+1] = params.weightPoints[i];
  					} else {
  						pointWeights[(i*2)] = 1;
  						pointWeights[(i*2)+1] = 1;
  					}
  				}
  				pointWeights = numeric.diag(pointWeights);
  			}
  		}
  		
  		/*
  		 *	starts the tracker to run on a regular interval
  		 */
  		this.start = function(element, box) {
  			// check if model is initalized, else return false
  			if (typeof(model) === "undefined") {
  				console.log("tracker needs to be initalized before starting to track.");
  				return false;
  			}
  			//check if a runnerelement already exists, if not, use passed parameters
  			if (typeof(runnerElement) === "undefined") {
  				runnerElement = element;
  				runnerBox = box;
  			}
  			// start named timeout function
  			runnerTimeout = requestAnimFrame(runnerFunction);
  		}
  
  		/*
  		 *	stop the running tracker
  		 */
  		this.stop = function() {
  			// stop the running tracker if any exists
  			cancelRequestAnimFrame(runnerTimeout);
  		}
  
  		/*
  		 *  element : canvas or video element
  		 *  TODO: should be able to take img element as well
  		 */
  		this.track = function(element, box) {
  			
  			var scaling, translateX, translateY, rotation;
  			var croppedPatches = [];
  			var ptch, px, py;
  						
  			if (first) {
  				// do viola-jones on canvas to get initial guess, if we don't have any points
  				var gi = getInitialPosition(element, box);
  				if (!gi) {
  					// send an event on no face found
  					var evt = document.createEvent("Event");
  					evt.initEvent("clmtrackrNotFound", true, true);
  					document.dispatchEvent(evt)
  					
  					return false;
  				}
  				scaling = gi[0];
  				rotation = gi[1];
  				translateX = gi[2];
  				translateY = gi[3];
  				
  				first = false;
  			} else {
  				facecheck_count += 1;
  				
  				// TODO : do cross-correlation/correlation-filter or similar to find translation of face
  				if (params.constantVelocity) {
  					// calculate where to get patches via constant velocity prediction
  					if (previousParameters.length >= 2) {
  						for (var i = 0;i < currentParameters.length;i++) {
  							currentParameters[i] = (relaxation)*previousParameters[1][i] + (1-relaxation)*((2*previousParameters[1][i]) - previousParameters[0][i]);
  							//currentParameters[i] = (3*previousParameters[2][i]) - (3*previousParameters[1][i]) + previousParameters[0][i];
  						}
  					}
  				}
  				
  				// change translation, rotation and scale parameters
  				rotation = halfPI - Math.atan((currentParameters[0]+1)/currentParameters[1]);
  				if (rotation > halfPI) {
  					rotation -= Math.PI;
  				}
  				scaling = currentParameters[1] / Math.sin(rotation);
  				translateX = currentParameters[2];
  				translateY = currentParameters[3];
  			}
  			
  			// copy canvas to a new dirty canvas
  			sketchCC.save();
  			
  			// clear canvas
  			sketchCC.clearRect(0, 0, sketchW, sketchH);
  			
  			sketchCC.scale(1/scaling, 1/scaling);
  			sketchCC.rotate(-rotation);
  			sketchCC.translate(-translateX, -translateY);
  			
  			sketchCC.drawImage(element, 0, 0, element.width, element.height);
  			
  			sketchCC.restore();
  			//	get cropped images around new points based on model parameters (not scaled and translated)
  			var patchPositions = calculatePositions(currentParameters, false);
  			
  			// check whether tracking is ok
  			if (scoringWeights && (facecheck_count % 10 == 0)) {
  				if (!checkTracking()) {
  					// reset all parameters
  					first = true;
  					scoringHistory = [];
  					for (var i = 0;i < currentParameters.length;i++) {
  						currentParameters[i] = 0;
  						previousParameters = [];
  					}
  					
  					// send event to signal that tracking was lost
  					var evt = document.createEvent("Event");
  					evt.initEvent("clmtrackrLost", true, true);
  					document.dispatchEvent(evt)
  					
  					return false;
  				}
  			}
  
  
  			var pdata, pmatrix, grayscaleColor;
  			for (var i = 0; i < numPatches; i++) {
  				px = patchPositions[i][0]-(pw/2);
  				py = patchPositions[i][1]-(pl/2);
  				ptch = sketchCC.getImageData(Math.round(px), Math.round(py), pw, pl);
  				pdata = ptch.data;
  				
  				// convert to grayscale
  				pmatrix = patches[i];
  				for (var j = 0;j < pdataLength;j++) {
  					grayscaleColor = pdata[j*4]*0.3 + pdata[(j*4)+1]*0.59 + pdata[(j*4)+2]*0.11;
  					pmatrix[j] = grayscaleColor;
  				}
  			}
  			
  			/*print weights*/
  			/*sketchCC.clearRect(0, 0, sketchW, sketchH);
  			var nuWeights;
  			for (var i = 0;i < numPatches;i++) {
  				nuWeights = weights[i].map(function(x) {return x*2000+127;});
  				drawData(sketchCC, nuWeights, patchSize, patchSize, false, patchPositions[i][0]-(patchSize/2), patchPositions[i][1]-(patchSize/2));
  			}*/
  			
  			// print patches
  			/*sketchCC.clearRect(0, 0, sketchW, sketchH);
  			for (var i = 0;i < numPatches;i++) {
  				if ([27,32,44,50].indexOf(i) > -1) {
  					drawData(sketchCC, patches[i], pw, pl, false, patchPositions[i][0]-(pw/2), patchPositions[i][1]-(pl/2));
  				}
  			}*/
  			
  			if (patchType == "SVM") {
  				if (typeof(webglFi) !== "undefined") {
  					var responses = webglFi.getResponses(patches, true);
  				} else if (typeof(svmFi) !== "undefined"){
  					var responses = svmFi.getResponses(patches);
  				} else {
  					throw "SVM-filters do not seem to be initiated properly."
  				}
  			} else if (patchType == "MOSSE") {
  				var responses = mosseCalc.getResponses(patches);
  			}
  
  			// option to increase sharpness of responses
  			if (params.sharpenResponse) {
  				for (var i = 0;i < numPatches;i++) {
  					for (var j = 0;j < responses[i].length;j++) {
  						responses[i][j] = Math.pow(responses[i][j], params.sharpenResponse);
  					}
  				}
  			}
  
  			// print responses
  			/*sketchCC.clearRect(0, 0, sketchW, sketchH);
  			var nuWeights;
  			for (var i = 0;i < numPatches;i++) {
  		
  				nuWeights = [];
  				for (var j = 0;j < responses[i].length;j++) {
  					nuWeights.push(responses[i][j]*255);
  				}
  				
  				//drawData(sketchCC, nuWeights, searchWindow, searchWindow, false, patchPositions[i][0]-((searchWindow-1)/2), patchPositions[i][1]-((searchWindow-1)/2));
  				if ([27,32,44,50].indexOf(i) > -1) {
  					drawData(sketchCC, nuWeights, searchWindow, searchWindow, false, patchPositions[i][0]-((searchWindow-1)/2), patchPositions[i][1]-((searchWindow-1)/2));
  				}
  			}*/
  			
  			// iterate until convergence or max 10, 20 iterations?:
  			var originalPositions = currentPositions;
  			var jac;
  			var meanshiftVectors = [];
  			
  			for (var i = 0; i < varianceSeq.length; i++) {
  				
  				// calculate jacobian
  				jac = createJacobian(currentParameters, eigenVectors);
  
  				// for debugging
  				//var debugMVs = [];
  				//
  				
  				var opj0, opj1;
  				
  				for (var j = 0;j < numPatches;j++) {
  					opj0 = originalPositions[j][0]-((searchWindow-1)*scaling/2);
  					opj1 = originalPositions[j][1]-((searchWindow-1)*scaling/2);
  					
  					// calculate PI x gaussians
  					var vpsum = gpopt(searchWindow, currentPositions[j], updatePosition, vecProbs, responses, opj0, opj1, j, varianceSeq[i], scaling);
  					
  					// calculate meanshift-vector
  					gpopt2(searchWindow, vecpos, updatePosition, vecProbs, vpsum, opj0, opj1, scaling);
  					
  					// for debugging
  					//var debugMatrixMV = gpopt2(searchWindow, vecpos, updatePosition, vecProbs, vpsum, opj0, opj1);
  					
  					// evaluate here whether to increase/decrease stepSize
  					/*if (vpsum >= prevCostFunc[j]) {
  						learningRate[j] *= stepParameter;
  					} else {
  						learningRate[j] = 1.0;
  					}
  					prevCostFunc[j] = vpsum;*/
  					
  					// compute mean shift vectors
  					// extrapolate meanshiftvectors
  					/*var msv = [];
  					msv[0] = learningRate[j]*(vecpos[0] - currentPositions[j][0]);
  					msv[1] = learningRate[j]*(vecpos[1] - currentPositions[j][1]);
  					meanshiftVectors[j] = msv;*/
  					meanshiftVectors[j] = [vecpos[0] - currentPositions[j][0], vecpos[1] - currentPositions[j][1]];
  					
  					//if (isNaN(msv[0]) || isNaN(msv[1])) debugger;
  					
  					//for debugging
  					//debugMVs[j] = debugMatrixMV;
  					//
  				}
  				
  				// draw meanshiftVector
  				/*sketchCC.clearRect(0, 0, sketchW, sketchH);
  				var nuWeights;
  				for (var npidx = 0;npidx < numPatches;npidx++) {
  					nuWeights = debugMVs[npidx].map(function(x) {return x*255*500;});
  					drawData(sketchCC, nuWeights, searchWindow, searchWindow, false, patchPositions[npidx][0]-((searchWindow-1)/2), patchPositions[npidx][1]-((searchWindow-1)/2));
  				}*/
  				
  				var meanShiftVector = numeric.rep([numPatches*2, 1],0.0);
  				for (var k = 0;k < numPatches;k++) {
  					meanShiftVector[k*2][0] = meanshiftVectors[k][0];
  					meanShiftVector[(k*2)+1][0] = meanshiftVectors[k][1];
  				}
  				
  				// compute pdm parameter update
  				//var prior = numeric.mul(gaussianPD, PDMVariance);
  				var prior = numeric.mul(gaussianPD, varianceSeq[i]);
  				if (params.weightPoints) {
  					var jtj = numeric.dot(numeric.transpose(jac), numeric.dot(pointWeights, jac));
  				} else {
  					var jtj = numeric.dot(numeric.transpose(jac), jac);
  				}
  				var cpMatrix = numeric.rep([numParameters+4, 1],0.0);
  				for (var l = 0;l < (numParameters+4);l++) {
  					cpMatrix[l][0] = currentParameters[l];
  				}
  				var priorP = numeric.dot(prior, cpMatrix);
  				if (params.weightPoints) {
  					var jtv = numeric.dot(numeric.transpose(jac), numeric.dot(pointWeights, meanShiftVector));
  				} else {
  					var jtv = numeric.dot(numeric.transpose(jac), meanShiftVector);
  				}
  				var paramUpdateLeft = numeric.add(prior, jtj);
  				var paramUpdateRight = numeric.sub(priorP, jtv);
  				var paramUpdate = numeric.dot(numeric.inv(paramUpdateLeft), paramUpdateRight);
  				//var paramUpdate = numeric.solve(paramUpdateLeft, paramUpdateRight, true);
  				
  				var oldPositions = currentPositions;
  				
  				// update estimated parameters
  				for (var k = 0;k < numParameters+4;k++) {
  					currentParameters[k] -= paramUpdate[k];
  				}
  				
  				// clipping of parameters if they're too high
  				var clip;
  				for (var k = 0;k < numParameters;k++) {
  					clip = Math.abs(3*Math.sqrt(eigenValues[k]));
  					if (Math.abs(currentParameters[k+4]) > clip) {
  						if (currentParameters[k+4] > 0) {
  							currentParameters[k+4] = clip;
  						} else {
  							currentParameters[k+4] = -clip;
  						}
  					}
  					
  				}
  				
  				// update current coordinates
  				currentPositions = calculatePositions(currentParameters, true);
  				
  				// check if converged
  				// calculate norm of parameterdifference
  				var positionNorm = 0;
  				var pnsq_x, pnsq_y;
  				for (var k = 0;k < currentPositions.length;k++) {
  					pnsq_x = (currentPositions[k][0]-oldPositions[k][0]);
  					pnsq_y = (currentPositions[k][1]-oldPositions[k][1]);
  					positionNorm += ((pnsq_x*pnsq_x) + (pnsq_y*pnsq_y));
  				}
  				//console.log("positionnorm:"+positionNorm);
  				
  				// if norm < limit, then break
  				if (positionNorm < convergenceLimit) {
  					break;
  				}
  			
  			}
  			
  			if (params.constantVelocity) {
  				// add current parameter to array of previous parameters
  				previousParameters.push(currentParameters.slice());
  				previousParameters.splice(0, previousParameters.length == 3 ? 1 : 0);
  			}
  			
  			// store positions, for checking convergence
  			previousPositions.splice(0, previousPositions.length == 10 ? 1 : 0);
  			previousPositions.push(currentPositions.slice(0));
  			
  			// send an event on each iteration
  			var evt = document.createEvent("Event");
  			evt.initEvent("clmtrackrIteration", true, true);
  			document.dispatchEvent(evt)
  			
  			if (this.getConvergence() < 0.5) {
  				if (params.stopOnConvergence) {
  					this.stop();
  				}
  				var evt = document.createEvent("Event");
  				evt.initEvent("clmtrackrConverged", true, true);
  				document.dispatchEvent(evt)
  			}
  			
  			// return new points
  			return currentPositions;
  		}
  
  		/*
  		 *	reset tracking, so that track() will start a new detection
  		 */
  		this.reset = function() {
  			first = true;
  			scoringHistory = [];
  			for (var i = 0;i < currentParameters.length;i++) {
  				currentParameters[i] = 0;
  				previousParameters = [];
  			}
  			runnerElement = undefined;
  			runnerBox = undefined;
  		}
  
  		/*
  		 *	draw model on given canvas
  		 */
  		this.draw = function(canvas, pv, path) {
  			// if no previous points, just draw in the middle of canvas
  			
  			var params;
  			if (pv === undefined) {
  				params = currentParameters.slice(0);
  			} else {
  				params = pv.slice(0);
  			}
  			
  			var cc = canvas.getContext('2d');
  			cc.fillStyle = "rgb(200,200,200)";
  			cc.strokeStyle = "rgb(130,255,50)";
  			//cc.lineWidth = 1;
  			
  			var paths;
  			if (path === undefined) {
  				paths = model.path.normal;
  			} else {
  				paths = model.path[path];
  			}
  
  			for (var i = 0;i < paths.length;i++) {
  				if (typeof(paths[i]) == 'number') {
  					drawPoint(cc, paths[i], params);
  				} else {
  					drawPath(cc, paths[i], params);
  				}
  			}
  		}
  
  		/*
  		 * 	get the score of the current model fit
  		 *	(based on svm of face according to current model)
  		 */
  		this.getScore = function() {
  			return meanscore;
  		}
  
  		/*
  		 *	calculate positions based on parameters
  		 */
  		this.calculatePositions = function(parameters) {
  			return calculatePositions(parameters, true);
  		}
  		
  		/*
  		 *	get coordinates of current model fit
  		 */
  		this.getCurrentPosition = function() {
  			if (first) {
  				return false;
  			} else {
  				return currentPositions;
  			}
  		}
  		
  		/*
  		 *	get parameters of current model fit
  		 */
  		this.getCurrentParameters = function() {
  			return currentParameters;
  		}
  
  		/*
  		 *	Get the average of recent model movements
  		 *	Used for checking whether model fit has converged
  		 */
  		this.getConvergence = function() {
  			if (previousPositions.length < 10) return 999999;
  			
  			var prevX = 0.0;
  			var prevY = 0.0;
  			var currX = 0.0;
  			var currY = 0.0;
  			
  			// average 5 previous positions 
  			for (var i = 0;i < 5;i++) {
  				for (var j = 0;j < numPatches;j++) {
  					prevX += previousPositions[i][j][0];
  					prevY += previousPositions[i][j][1];
  				}
  			}
  			prevX /= 5;
  			prevY /= 5;
  			
  			// average 5 positions before that
  			for (var i = 5;i < 10;i++) {
  				for (var j = 0;j < numPatches;j++) {
  					currX += previousPositions[i][j][0];
  					currY += previousPositions[i][j][1];
  				}
  			}
  			currX /= 5;
  			currY /= 5;
  
  			// calculate difference
  			var diffX = currX-prevX;
  			var diffY = currY-prevY;
  			var msavg = ((diffX*diffX) + (diffY*diffY));
  			msavg /= previousPositions.length
  			return msavg;
  		}
  
  		var runnerFunction = function() {
  			runnerTimeout = requestAnimFrame(runnerFunction);
  			// schedule as many iterations as we can during each request
  			var startTime = (new Date()).getTime();
  			while (((new Date()).getTime() - startTime) < 16) {
  				var tracking = this.track(runnerElement, runnerBox);
  				if (!tracking) continue;
  			}
  		}.bind(this);
  
  		// generates the jacobian matrix used for optimization calculations
  		var createJacobian = function(parameters, eigenVectors) {
  			
  			var jacobian = numeric.rep([2*numPatches, numParameters+4],0.0);
  			var j0,j1;
  			for (var i = 0;i < numPatches;i ++) {
  				// 1
  				j0 = meanShape[i][0];
  				j1 = meanShape[i][1];
  				for (var p = 0;p < numParameters;p++) {
  					j0 += parameters[p+4]*eigenVectors[i*2][p];
  					j1 += parameters[p+4]*eigenVectors[(i*2)+1][p];
  				}
  				jacobian[i*2][0] = j0;
  				jacobian[(i*2)+1][0] = j1;
  				// 2
  				j0 = meanShape[i][1];
  				j1 = meanShape[i][0];
  				for (var p = 0;p < numParameters;p++) {
  					j0 += parameters[p+4]*eigenVectors[(i*2)+1][p];
  					j1 += parameters[p+4]*eigenVectors[i*2][p];
  				}
  				jacobian[i*2][1] = -j0;
  				jacobian[(i*2)+1][1] = j1;
  				// 3
  				jacobian[i*2][2] = 1;
  				jacobian[(i*2)+1][2] = 0;
  				// 4
  				jacobian[i*2][3] = 0;
  				jacobian[(i*2)+1][3] = 1;
  				// the rest
  				for (var j = 0;j < numParameters;j++) {
  					j0 = parameters[0]*eigenVectors[i*2][j] - parameters[1]*eigenVectors[(i*2)+1][j] + eigenVectors[i*2][j];
  					j1 = parameters[0]*eigenVectors[(i*2)+1][j] + parameters[1]*eigenVectors[i*2][j] + eigenVectors[(i*2)+1][j];
  					jacobian[i*2][j+4] = j0;
  					jacobian[(i*2)+1][j+4] = j1;
  				}
  			}
  			
  			return jacobian;
  		}
  		
  		// calculate positions from parameters
  		var calculatePositions = function(parameters, useTransforms) {
  			var x, y, a, b;
  			var numParameters = parameters.length;
  			var positions = [];
  			for (var i = 0;i < numPatches;i++) {
  				x = meanShape[i][0];
  				y = meanShape[i][1];
  				for (var j = 0;j < numParameters-4;j++) {
  					x += model.shapeModel.eigenVectors[(i*2)][j]*parameters[j+4];
  					y += model.shapeModel.eigenVectors[(i*2)+1][j]*parameters[j+4];
  				}
  				if (useTransforms) {
  					a = parameters[0]*x - parameters[1]*y + parameters[2];
  					b = parameters[0]*y + parameters[1]*x + parameters[3];
  					x += a;
  					y += b;
  				}
  				positions[i] = [x,y];
  			}
  			
  			return positions;
  		}
  		
  		// detect position of face on canvas/video element
  		var detectPosition = function(el) {
  			var canvas = document.createElement('canvas');
  			canvas.width = el.width;
  			canvas.height = el.height;
  			var cc = canvas.getContext('2d');
  			cc.drawImage(el, 0, 0, el.width, el.height);
  			
  			// do viola-jones on canvas to get initial guess, if we don't have any points
  			var comp = ccv.detect_objects(
  				ccv.grayscale(canvas), ccv.cascade, 5, 1
  			);
  			
  			//var jf = new jsfeat_face(canvas);
  			//var comp = jf.findFace();
  			
  			if (comp.length > 0) {
  				candidate = comp[0];
  			} else {
  				return false;
  			}
  			
  			for (var i = 1; i < comp.length; i++) {
  				if (comp[i].confidence > candidate.confidence) {
  					candidate = comp[i];
  				}
  			}
  			
  			return candidate;
  		}
  		
  		// part one of meanshift calculation
  		var gpopt = function(responseWidth, currentPositionsj, updatePosition, vecProbs, responses, opj0, opj1, j, variance, scaling) {
  			var pos_idx = 0;
  			var vpsum = 0;
  			var dx, dy;
  			for (var k = 0;k < responseWidth;k++) {
  				updatePosition[1] = opj1+(k*scaling);
  				for (var l = 0;l < responseWidth;l++) {
  					updatePosition[0] = opj0+(l*scaling);
  
  					dx = currentPositionsj[0] - updatePosition[0];
  					dy = currentPositionsj[1] - updatePosition[1];
  					vecProbs[pos_idx] = responses[j][pos_idx] * Math.exp(-0.5*((dx*dx)+(dy*dy))/(variance*scaling));
  					
  					vpsum += vecProbs[pos_idx];
  					pos_idx++;
  				}
  			}
  			
  			return vpsum;
  		}
  		
  		// part two of meanshift calculation
  		var gpopt2 = function(responseWidth, vecpos, updatePosition, vecProbs, vpsum, opj0, opj1, scaling) {
  			//for debugging
  			//var vecmatrix = [];
  			
  			var pos_idx = 0;
  			var vecsum = 0;
  			vecpos[0] = 0;
  			vecpos[1] = 0;
  			for (var k = 0;k < responseWidth;k++) {
  				updatePosition[1] = opj1+(k*scaling);
  				for (var l = 0;l < responseWidth;l++) {
  					updatePosition[0] = opj0+(l*scaling);
  					vecsum = vecProbs[pos_idx]/vpsum;
  					
  					//for debugging
  					//vecmatrix[k*responseWidth + l] = vecsum;
  					
  					vecpos[0] += vecsum*updatePosition[0];
  					vecpos[1] += vecsum*updatePosition[1];
  					pos_idx++;
  				}
  			}
  			// for debugging
  			//return vecmatrix;
  		}
  		
  		// calculate score of current fit
  		var checkTracking = function() {			
  			scoringContext.drawImage(sketchCanvas, Math.round(msxmin), Math.round(msymin), Math.round(msmodelwidth), Math.round(msmodelheight), 0, 0, 20, 22);
  			// getImageData of canvas
  			var imgData = scoringContext.getImageData(0,0,20,22);
  			// convert data to grayscale
  			var scoringData = new Array(20*22);
  			var scdata = imgData.data;
  			var scmax = 0;
  			var scmin = 255;
  			for (var i = 0;i < 20*22;i++) {
  			  scoringData[i] = scdata[i*4]*0.3 + scdata[(i*4)+1]*0.59 + scdata[(i*4)+2]*0.11;
  			  if (scoringData[i] > scmax) scmax = scoringData[i];
  			  if (scoringData[i] < scmin) scmin = scoringData[i];
  			}
  			
  			if (scmax > 0) {
  				// normalize & multiply by svmFilter
  				var score = 0;
  				var newim = scoringContext.createImageData(20,22);
  				var newimdata = newim.data;
  				var scdaata = new Array(20*22);
  				var scdamin = 10000000;
  				var scdamax = -10000000;
  				for (var i = 0;i < 20*22;i++) {
  					scoringData[i] = (scoringData[i]-scmin)/(scmax-scmin);
  					scdaata[i] = scoringData[i]*scoringWeights[i];
  					if (scdaata[scdamin] < i) scdamin = scdaata[i];
  					if (scdaata[i] > scdamax) scdamax = scdaata[i];
  				}
  
  				for (var i = 0;i < 20*22;i++) {
  					var nid = 255*((scdaata[i]-scdamin)/(scdamax-scdamin));
  					newimdata[i*4] = nid;
  					newimdata[(i*4)+1] = nid;
  					newimdata[(i*4)+2] = nid;
  					newimdata[(i*4)+3] = 255;
  				}
  				scoringContext.putImageData(newim,0,0);
  
  				for (var i = 0;i < 20*22;i++) {
  					score += (scoringData[i])*-scoringWeights[i];
  				}
  				score += scoringBias;
  
  				scoringHistory.splice(0, scoringHistory.length == 5 ? 1 : 0);
  				scoringHistory.push(score);
  
  				if (scoringHistory.length > 4) {
  					// get average
  					meanscore = 0;
  					for (var i = 0;i < 5;i++) {
  						meanscore += scoringHistory[i];
  					}
  					meanscore /= 5;
  					// if below threshold, then reset (return false)
  					if (meanscore < params.scoreThreshold) return false;
  				}
  			}
  			return true;
  		}
  		
  		// get initial starting point for model
  		var getInitialPosition = function(element, box) {
  			var translateX, translateY, scaling, rotation;
  			if (box) {
  				candidate = {x : box[0], y : box[1], width : box[2], height : box[3]};
  			} else {
  				var det = detectPosition(element);
  				if (!det) {
  					// if no face found, stop.
  					return false;
  				}
  			}
  			
  			if (model.hints && mosseFilter && left_eye_filter && right_eye_filter && nose_filter) {
  				var noseFilterWidth = candidate.width * 4.5/10;
  				var eyeFilterWidth = candidate.width * 6/10;
  				
  				// detect position of eyes and nose via mosse filter
  				//
  				/*element.pause();
  				
  				var canvasContext = document.getElementById('overlay2').getContext('2d')
  				canvasContext.clearRect(0,0,500,375);
  				canvasContext.strokeRect(candidate.x, candidate.y, candidate.width, candidate.height);*/
  				//
  				
  				var nose_result = mossef_nose.track(element, Math.round(candidate.x+(candidate.width/2)-(noseFilterWidth/2)), Math.round(candidate.y+candidate.height*(5/8)-(noseFilterWidth/2)), noseFilterWidth, noseFilterWidth, false);
  				var right_result = mossef_righteye.track(element, Math.round(candidate.x+(candidate.width*3/4)-(eyeFilterWidth/2)), Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2)), eyeFilterWidth, eyeFilterWidth, false);
  				var left_result = mossef_lefteye.track(element, Math.round(candidate.x+(candidate.width/4)-(eyeFilterWidth/2)), Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2)), eyeFilterWidth, eyeFilterWidth, false);
  				right_eye_position[0] = Math.round(candidate.x+(candidate.width*3/4)-(eyeFilterWidth/2))+right_result[0];
  				right_eye_position[1] = Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2))+right_result[1];
  				left_eye_position[0] = Math.round(candidate.x+(candidate.width/4)-(eyeFilterWidth/2))+left_result[0];
  				left_eye_position[1] = Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2))+left_result[1];
  				nose_position[0] = Math.round(candidate.x+(candidate.width/2)-(noseFilterWidth/2))+nose_result[0];
  				nose_position[1] = Math.round(candidate.y+candidate.height*(5/8)-(noseFilterWidth/2))+nose_result[1];
  				
  				//
  				/*canvasContext.strokeRect(Math.round(candidate.x+(candidate.width*3/4)-(eyeFilterWidth/2)), Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2)), eyeFilterWidth, eyeFilterWidth);
  				canvasContext.strokeRect(Math.round(candidate.x+(candidate.width/4)-(eyeFilterWidth/2)), Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2)), eyeFilterWidth, eyeFilterWidth);
  				//canvasContext.strokeRect(Math.round(candidate.x+(candidate.width/2)-(noseFilterWidth/2)), Math.round(candidate.y+candidate.height*(3/4)-(noseFilterWidth/2)), noseFilterWidth, noseFilterWidth);
  				canvasContext.strokeRect(Math.round(candidate.x+(candidate.width/2)-(noseFilterWidth/2)), Math.round(candidate.y+candidate.height*(5/8)-(noseFilterWidth/2)), noseFilterWidth, noseFilterWidth);
  				
  				canvasContext.fillStyle = "rgb(0,0,250)";
  				canvasContext.beginPath();
  				canvasContext.arc(left_eye_position[0], left_eye_position[1], 3, 0, Math.PI*2, true);
  				canvasContext.closePath();
  				canvasContext.fill();
  				
  				canvasContext.beginPath();
  				canvasContext.arc(right_eye_position[0], right_eye_position[1], 3, 0, Math.PI*2, true);
  				canvasContext.closePath();
  				canvasContext.fill();
  				
  				canvasContext.beginPath();
  				canvasContext.arc(nose_position[0], nose_position[1], 3, 0, Math.PI*2, true);
  				canvasContext.closePath();
  				canvasContext.fill();
  				
  				debugger;
  				element.play()
  				canvasContext.clearRect(0,0,element.width,element.height);*/
  				//
  				
  				// get eye and nose positions of model
  				var lep = model.hints.leftEye;
  				var rep = model.hints.rightEye;
  				var mep = model.hints.nose;
  				
  				// get scaling, rotation, etc. via procrustes analysis
  				var procrustes_params = procrustes([left_eye_position, right_eye_position, nose_position], [lep, rep, mep]);
  				translateX = procrustes_params[0];
  				translateY = procrustes_params[1];
  				scaling = procrustes_params[2];
  				rotation = procrustes_params[3];
  				
  				//element.play();
  				
  				//var maxscale = 1.10;
  				//if ((scaling*modelHeight)/candidate.height < maxscale*0.7) scaling = (maxscale*0.7*candidate.height)/modelHeight;
  				//if ((scaling*modelHeight)/candidate.height > maxscale*1.2) scaling = (maxscale*1.2*candidate.height)/modelHeight;
  				
  				/*var smean = [0,0];
  				smean[0] += lep[0];
  				smean[1] += lep[1];
  				smean[0] += rep[0];
  				smean[1] += rep[1];
  				smean[0] += mep[0];
  				smean[1] += mep[1];
  				smean[0] /= 3;
  				smean[1] /= 3;
  				
  				var nulep = [(lep[0]*scaling*Math.cos(-rotation)+lep[1]*scaling*Math.sin(-rotation))+translateX, (lep[0]*scaling*(-Math.sin(-rotation)) + lep[1]*scaling*Math.cos(-rotation))+translateY];
  				var nurep = [(rep[0]*scaling*Math.cos(-rotation)+rep[1]*scaling*Math.sin(-rotation))+translateX, (rep[0]*scaling*(-Math.sin(-rotation)) + rep[1]*scaling*Math.cos(-rotation))+translateY];
  				var numep = [(mep[0]*scaling*Math.cos(-rotation)+mep[1]*scaling*Math.sin(-rotation))+translateX, (mep[0]*scaling*(-Math.sin(-rotation)) + mep[1]*scaling*Math.cos(-rotation))+translateY];
  				
  				canvasContext.fillStyle = "rgb(200,10,100)";
  				canvasContext.beginPath();
  				canvasContext.arc(nulep[0], nulep[1], 3, 0, Math.PI*2, true);
  				canvasContext.closePath();
  				canvasContext.fill();
  				
  				canvasContext.beginPath();
  				canvasContext.arc(nurep[0], nurep[1], 3, 0, Math.PI*2, true);
  				canvasContext.closePath();
  				canvasContext.fill();
  				
  				canvasContext.beginPath();
  				canvasContext.arc(numep[0], numep[1], 3, 0, Math.PI*2, true);
  				canvasContext.closePath();
  				canvasContext.fill();*/
  				
  				currentParameters[0] = (scaling*Math.cos(rotation))-1;
  				currentParameters[1] = (scaling*Math.sin(rotation));
  				currentParameters[2] = translateX;
  				currentParameters[3] = translateY;
  				
  				//this.draw(document.getElementById('overlay'), currentParameters);
  				
  			} else {
  				scaling = candidate.width/modelheight;
  				//var ccc = document.getElementById('overlay').getContext('2d');
  				//ccc.strokeRect(candidate.x,candidate.y,candidate.width,candidate.height);
  				translateX = candidate.x-(xmin*scaling)+0.1*candidate.width;
  				translateY = candidate.y-(ymin*scaling)+0.25*candidate.height;
  				currentParameters[0] = scaling-1;
  				currentParameters[2] = translateX;
  				currentParameters[3] = translateY;
  			}
  		
  			currentPositions = calculatePositions(currentParameters, true);
  			
  			return [scaling, rotation, translateX, translateY];
  		}
  		
  		// draw a parametrized line on a canvas
  		var drawPath = function(canvasContext, path, dp) {
  			canvasContext.beginPath();
  			var i, x, y, a, b;
  			for (var p = 0;p < path.length;p++) {
  				i = path[p]*2;
  				x = meanShape[i/2][0];
  				y = meanShape[i/2][1];
  				for (var j = 0;j < numParameters;j++) {
  					x += model.shapeModel.eigenVectors[i][j]*dp[j+4];
  					y += model.shapeModel.eigenVectors[i+1][j]*dp[j+4];
  				}
  				a = dp[0]*x - dp[1]*y + dp[2];
  				b = dp[0]*y + dp[1]*x + dp[3];
  				x += a;
  				y += b;
  				
  				if (i == 0) {
  					canvasContext.moveTo(x,y);
  				} else {
  					canvasContext.lineTo(x,y);
  				}
  			}
  			canvasContext.moveTo(0,0);
  			canvasContext.closePath();
  			canvasContext.stroke();
  		}
  		
  		// draw a point on a canvas
  		function drawPoint(canvasContext, point, dp) {
  			var i, x, y, a, b;
  			i = point*2;
  			x = meanShape[i/2][0];
  			y = meanShape[i/2][1];
  			for (var j = 0;j < numParameters;j++) {
  				x += model.shapeModel.eigenVectors[i][j]*dp[j+4];
  				y += model.shapeModel.eigenVectors[i+1][j]*dp[j+4];
  			}
  			a = dp[0]*x - dp[1]*y + dp[2];
  			b = dp[0]*y + dp[1]*x + dp[3];
  			x += a;
  			y += b;
  			canvasContext.beginPath();
  			canvasContext.arc(x, y, 1, 0, Math.PI*2, true);
  			canvasContext.closePath();
  			canvasContext.fill();
  		}
  		
  		// procrustes analysis
  		function procrustes(template, shape) {
  			// assume template and shape is a vector of x,y-coordinates
  			//i.e. template = [[x1,y1], [x2,y2], [x3,y3]];
  			var templateClone = [];
  			var shapeClone = [];
  			for (var i = 0;i < template.length;i++) {
  				templateClone[i] = [template[i][0], template[i][1]];
  			}
  			for (var i = 0;i < shape.length;i++) {
  				shapeClone[i] = [shape[i][0], shape[i][1]];
  			}
  			shape = shapeClone;
  			template = templateClone;
  			
  			// calculate translation
  			var templateMean = [0.0, 0.0];
  			for (var i = 0;i < template.length;i++) {
  				templateMean[0] += template[i][0];
  				templateMean[1] += template[i][1];
  			}
  			templateMean[0] /= template.length;
  			templateMean[1] /= template.length;
  			
  			var shapeMean = [0.0, 0.0];
  			for (var i = 0;i < shape.length;i++) {
  				shapeMean[0] += shape[i][0];
  				shapeMean[1] += shape[i][1];
  			}
  			shapeMean[0] /= shape.length;
  			shapeMean[1] /= shape.length;
  			
  			var translationX = templateMean[0] - shapeMean[0];
  			var translationY = templateMean[1] - shapeMean[1];
  			
  			// centralize
  			for (var i = 0;i < shape.length;i++) {
  				shape[i][0] -= shapeMean[0];
  				shape[i][1] -= shapeMean[1];
  			}
  			for (var i = 0;i < template.length;i++) {
  				template[i][0] -= templateMean[0];
  				template[i][1] -= templateMean[1];
  			}
  			
  			// scaling
  			
  			var scaleS = 0.0;
  			for (var i = 0;i < shape.length;i++) {
  				scaleS += ((shape[i][0])*(shape[i][0]));
  				scaleS += ((shape[i][1])*(shape[i][1]));
  			}
  			scaleS = Math.sqrt(scaleS/shape.length);
  			
  			var scaleT = 0.0;
  			for (var i = 0;i < template.length;i++) {
  				scaleT += ((template[i][0])*(template[i][0]));
  				scaleT += ((template[i][1])*(template[i][1]));
  			}
  			scaleT = Math.sqrt(scaleT/template.length);
  			
  			var scaling = scaleT/scaleS;
  			
  			for (var i = 0;i < shape.length;i++) {
  				shape[i][0] *= scaling;
  				shape[i][1] *= scaling;
  			}
  				
  			// rotation
  			
  			var top = 0.0;
  			var bottom = 0.0;
  			for (var i = 0;i < shape.length;i++) {
  				top += (shape[i][0]*template[i][1] - shape[i][1]*template[i][0]);
  				bottom += (shape[i][0]*template[i][0] + shape[i][1]*template[i][1]);
  			}
  			var rotation = Math.atan(top/bottom);
  			
  			translationX += (shapeMean[0]-(scaling*Math.cos(-rotation)*shapeMean[0])-(scaling*shapeMean[1]*Math.sin(-rotation)));
  			translationY += (shapeMean[1]+(scaling*Math.sin(-rotation)*shapeMean[0])-(scaling*shapeMean[1]*Math.cos(-rotation)));
  			
  			//returns rotation, scaling, transformx and transformx
  			return [translationX, translationY, scaling, rotation];
  		}
  		
  		// function to draw pixeldata on some canvas, only used for debugging
  		var drawData = function(canvasContext, data, width, height, transposed, drawX, drawY) {
  			var psci = canvasContext.createImageData(width, height);
  			var pscidata = psci.data;
  			for (var j = 0;j < width*height;j++) {
  				if (!transposed) {
  					var val = data[(j%width)+((j/width) >> 0)*width];
  				} else {
  					var val = data[(j%height)*height+((j/height) >> 0)];
  				}
  				val = val > 255 ? 255 : val;
  				val = val < 0 ? 0 : val;
  				pscidata[j*4] = val;
  				pscidata[(j*4)+1] = val;
  				pscidata[(j*4)+2] = val;
  				pscidata[(j*4)+3] = 255;
  			}
  			canvasContext.putImageData(psci, drawX, drawY);
  		}
  		
  		var requestAnimFrame = (function() {
  			return window.requestAnimationFrame ||
  			window.webkitRequestAnimationFrame ||
  			window.mozRequestAnimationFrame ||
  			window.oRequestAnimationFrame ||
  			window.msRequestAnimationFrame ||
  			function(/* function FrameRequestCallback */ callback, /* DOMElement Element */ element) {
  				return window.setTimeout(callback, 1000/60);
  			};
  		})();
  		
  		var cancelRequestAnimFrame = (function() {
  			return window.cancelCancelRequestAnimationFrame ||
  				window.webkitCancelRequestAnimationFrame ||
  				window.mozCancelRequestAnimationFrame ||
  				window.oCancelRequestAnimationFrame ||
  				window.msCancelRequestAnimationFrame ||
  				window.clearTimeout;
  		})();
  		
  		return true;
  	}
  }
  "use strict";
  
  var webglFilter = function() {
    var gl, canvas;
    var filterWidth, filterHeight, patchWidth, patchHeight, numPatches, canvasWidth, canvasHeight;
    var patchResponseProgram, patchDrawProgram;
    var fbo, numBlocks, patchTex;
    var first = true;
    var drawRectBuffer, drawLayerBuffer, drawImageBuffer, rttTexture, filters;
    var texCoordBuffer, texCoordLocation, apositionBuffer;
    var newCanvasWidth, newCanvasBlockHeight, newCanvasHeight;
    var drawOutRectangles, drawOutImages, drawOutLayer;
    var patchCells, textureWidth, textureHeight, patchSize, patchArray;
    
    this.init = function(filterVector, nP, pW, pH, fW, fH, drawOut) {
      // we assume filterVector goes from left to right, rowwise, i.e. row-major order
      
      if (fW != fH) {
        alert("filter width and height must be same size!");
        return;
      }
      
      // if filter width is not odd, alert
      if (fW % 2 == 0 || fH % 2 == 0) {
        alert("filters used in svm must be of odd dimensions!");
        return;
      }
      
      filterWidth = fW;
      filterHeight = fH;
      patchWidth = pW;
      patchHeight = pH;
      numPatches = nP;
      numBlocks = Math.floor(numPatches / 4) + Math.ceil(numPatches % 4);
      canvasWidth = patchWidth;
      canvasHeight = patchHeight*numBlocks;
      newCanvasWidth = patchWidth-filterWidth+1;
      newCanvasBlockHeight = patchHeight-filterWidth+1;
      newCanvasHeight = newCanvasBlockHeight*numPatches;
  
      patchResponseFS = [
        "precision mediump float;",
        "",
        "const vec2 u_onePixelPatches = vec2("+(1/patchWidth).toFixed(10)+","+(1/(patchHeight*numBlocks)).toFixed(10)+");",
        "const vec2 u_onePixelFilters = vec2("+(1/filterWidth).toFixed(10)+","+(1/(filterHeight*numBlocks)).toFixed(10)+");",
        "const float u_halffilterwidth = "+((filterWidth-1.0)/2).toFixed(1)+";",
        "const float u_halffilterheight = "+((filterHeight-1.0)/2).toFixed(1)+";",
        "",
        "// our patches",
        "uniform sampler2D u_patches;",
        "// our filters",
        "uniform sampler2D u_filters;",
        "",
        "// the texCoords passed in from the vertex shader.",
        "varying vec2 v_texCoord;",
        "varying vec2 v_texCoordFilters; // this should give us correct filter",
        "",
        "void main() {",
        "  vec4 colorSum = vec4(0.0, 0.0, 0.0, 0.0);",
        "  vec4 maxn = vec4(0.0, 0.0, 0.0, 0.0);",
        "  vec4 minn = vec4(256.0, 256.0, 256.0, 256.0);",
        "  vec4 scale = vec4(0.0, 0.0, 0.0, 0.0);",
        "  vec4 patchValue = vec4(0.0, 0.0, 0.0, 0.0);",
        "  vec4 filterValue = vec4(0.0, 0.0, 0.0, 0.0);",
        "  vec4 filterTemp = vec4(0.0, 0.0, 0.0, 0.0);",
        "  for (int w = 0;w < "+filterWidth+";w++) {",
        "    for (int h = 0;h < "+filterHeight+";h++) {",
        "      patchValue = texture2D(u_patches, v_texCoord + u_onePixelPatches * vec2(float(w)-u_halffilterwidth, float(h)-u_halffilterheight));",
        "      filterValue = texture2D(u_filters, v_texCoordFilters + u_onePixelFilters * vec2(float(w)-u_halffilterwidth, float(h)-u_halffilterheight));",
        "      maxn = max(patchValue, maxn);",
        "      minn = min(patchValue, minn);",
        "      colorSum += patchValue*filterValue;",
        "      filterTemp += filterValue;",
        "    } ",
        "  }",
        "  scale = maxn-minn;",
        "  colorSum = (colorSum-(minn*filterTemp))/scale;",
        "  // logistic transformation",
        "  colorSum = 1.0/(1.0 + exp(- (colorSum-1.0) ));",
        "  gl_FragColor = colorSum;",
        "}"
      ].join('\n');
      
      patchResponseVS = [
        "attribute vec2 a_texCoord;",
        "attribute vec2 a_position;",
        "",
        "const vec2 u_resolution = vec2("+canvasWidth.toFixed(1)+","+canvasHeight.toFixed(1)+");",
        "const float u_patchHeight = "+(1/numBlocks).toFixed(10)+";",
        "const float u_filterHeight = "+(1/numBlocks).toFixed(10)+";",
        "const vec2 u_midpoint = vec2(0.5 ,"+(1/(numBlocks*2)).toFixed(10)+");",
        "",
        "varying vec2 v_texCoord;",
        "varying vec2 v_texCoordFilters;",
        "",
        "void main() {",
        "   // convert the rectangle from pixels to 0.0 to 1.0",
        "   vec2 zeroToOne = a_position / u_resolution;",
        "",
        "   // convert from 0->1 to 0->2",
        "   vec2 zeroToTwo = zeroToOne * 2.0;",
        "",
        "   // convert from 0->2 to -1->+1 (clipspace)",
        "   vec2 clipSpace = zeroToTwo - 1.0;",
        "   ",
        "   // transform coordinates to regular coordinates",
        "   gl_Position = vec4(clipSpace * vec2(1.0, 1.0), 0, 1);",
        " ",
        "   // pass the texCoord to the fragment shader",
        "   v_texCoord = a_texCoord;",
        "   ",
        "   // set the filtertexture coordinate based on number filter to use",
        "   v_texCoordFilters = u_midpoint + vec2(0.0, u_filterHeight * floor(a_texCoord[1]/u_patchHeight));",
        "}"
      ].join('\n');
      
      //create canvas
      canvas = document.createElement('canvas')
      canvas.setAttribute('width', (patchWidth-filterWidth+1)+"px");
      canvas.setAttribute('height', ((patchHeight-filterHeight+1)*numPatches)+"px");
      canvas.setAttribute('id', 'renderCanvas');
      canvas.setAttribute('style', 'display:none;');
      document.body.appendChild(canvas);
      
      // TODO : isolate this library from webgl-util.js
      gl = setupWebGL(canvas, {premultipliedAlpha: false, preserveDrawingBuffer : true, antialias : false});
      
      // check for float textures support and fail if not
      if (!gl.getExtension("OES_texture_float")) {
        alert("Your graphics card does not support floating point textures! :(");
        return;
      }
      
      // calculate position of vertex rectangles to draw out
      var rectangles = [];
      var halfFilter = (filterWidth-1)/2;
      var yOffset;
      
      for (var i = 0;i < numBlocks;i++) {
        yOffset = i*patchHeight;
        //first triangle
        rectangles = rectangles.concat(
          [halfFilter, yOffset+halfFilter, 
          patchWidth-halfFilter, yOffset+halfFilter,
          halfFilter, yOffset+patchHeight-halfFilter]
        );
        //second triangle
        rectangles = rectangles.concat(
          [halfFilter, yOffset+patchHeight-halfFilter, 
          patchWidth-halfFilter, yOffset+halfFilter,
          patchWidth-halfFilter, yOffset+patchHeight-halfFilter]
        );
      }
      rectangles = new Float32Array(rectangles);
      
      // calculate position of image rectangles to draw out
      var irectangles = [];
      for (var i = 0;i < rectangles.length;i++) {
        if (i % 2 == 0) {
          irectangles[i] = rectangles[i]/canvasWidth;
        } else {
          irectangles[i] = rectangles[i]/canvasHeight;
        }
      }
      irectangles = new Float32Array(irectangles);
      
      // setup patchdraw program
      var drVertexShader = loadShader(gl, drawResponsesVS, gl.VERTEX_SHADER);
      var drFragmentShader = loadShader(gl, drawResponsesFS, gl.FRAGMENT_SHADER);
      patchDrawProgram = createProgram(gl, [drVertexShader, drFragmentShader]);
      gl.useProgram(patchDrawProgram);
      
      // set the resolution/dimension of the canvas
      var resolutionLocation = gl.getUniformLocation(patchDrawProgram, "u_resolutiondraw");
      gl.uniform2f(resolutionLocation, newCanvasWidth, newCanvasHeight);
      
      // set u_responses
      var responsesLocation = gl.getUniformLocation(patchDrawProgram, "u_responses");
      gl.uniform1i(responsesLocation, 2);
      
      
      
      
      // setup patchresponse program
      var prVertexShader = loadShader(gl, patchResponseVS, gl.VERTEX_SHADER);
      var prFragmentShader = loadShader(gl, patchResponseFS, gl.FRAGMENT_SHADER);
      patchResponseProgram = createProgram(gl, [prVertexShader, prFragmentShader]);
      gl.useProgram(patchResponseProgram);
      
      // set up vertices with rectangles
      var positionLocation = gl.getAttribLocation(patchResponseProgram, "a_position");
      apositionBuffer = gl.createBuffer();
      gl.bindBuffer(gl.ARRAY_BUFFER, apositionBuffer);
      gl.bufferData(
        gl.ARRAY_BUFFER, 
        rectangles, 
        gl.STATIC_DRAW);
      gl.enableVertexAttribArray(positionLocation);
      gl.vertexAttribPointer(positionLocation, 2, gl.FLOAT, false, 0, 0);
      
      // set up texture positions
      texCoordLocation = gl.getAttribLocation(patchResponseProgram, "a_texCoord");
      // provide texture coordinates for the rectangle.
      texCoordBuffer = gl.createBuffer();
      gl.bindBuffer(gl.ARRAY_BUFFER, texCoordBuffer);
      gl.bufferData(gl.ARRAY_BUFFER, irectangles, gl.STATIC_DRAW);
      gl.enableVertexAttribArray(texCoordLocation);
      gl.vertexAttribPointer(texCoordLocation, 2, gl.FLOAT, false, 0, 0);
      
      // insert filters into float32array and pass to texture via this mechanism:
      // http://stackoverflow.com/questions/7709689/webgl-pass-array-shader
      var filterSize = filterWidth*filterHeight;
      var filterArray = new Float32Array(filterSize*(numBlocks)*4);
      for (var i = 0;i < numBlocks;i++) {
        for (var j = 0;j < filterHeight;j++) {
          for (var k = 0;k < filterWidth;k++) {
            //set r with first filter
            if (i*4 < filterVector.length) {
              filterArray[((filterSize*i) + (j*filterWidth) + k)*4] = filterVector[i*4][(j*filterWidth) + k];
            } else {
              filterArray[((filterSize*i) + (j*filterWidth) + k)*4] = 0;
            }
            //set g with 2nd filter
            if ((i*4 + 1) < filterVector.length) {
              filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 1] = filterVector[(i*4)+1][(j*filterWidth) + k];
            } else {
              filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 1] = 0;
            }
            //set b with 3rd filter
            if ((i*4 + 2) < filterVector.length) {
              filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 2] = filterVector[(i*4)+2][(j*filterWidth) + k];
            } else {
              filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 2] = 0;
            }
            //set a with 4th filter
            if ((i*4 + 3) < filterVector.length) {
              filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 3] = filterVector[(i*4)+3][(j*filterWidth) + k];
            } else {
              filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 3] = 0;
            }
          }
        }
      }
      
      gl.activeTexture(gl.TEXTURE0);
      filters = gl.createTexture();
      gl.bindTexture(gl.TEXTURE_2D, filters);
      gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, filterWidth, filterHeight*numBlocks, 0, gl.RGBA, gl.FLOAT, filterArray);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST);
      gl.uniform1i(gl.getUniformLocation(patchResponseProgram, "u_filters"), 0);
      
      // set up buffer to draw to
      gl.activeTexture(gl.TEXTURE2);
      rttTexture = gl.createTexture();
      gl.bindTexture(gl.TEXTURE_2D, rttTexture);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST);
      gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, patchWidth, patchHeight*numBlocks, 0, gl.RGBA, gl.FLOAT, null);
      
      // set this buffer as framebuffer
      fbo = gl.createFramebuffer();
      gl.bindFramebuffer(gl.FRAMEBUFFER, fbo);
      
      gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, rttTexture, 0);
      
      gl.viewport(0, 0, patchWidth, patchHeight*numBlocks);
      
      // preinitialization of drawOut variables
      
      // drawOutRectangles
      drawOutRectangles = new Float32Array(12*numPatches);
      var yOffset, indexOffset;
      for (var i = 0;i < numPatches;i++) {
        yOffset = i*newCanvasBlockHeight;
        indexOffset = i*12;
        
        //first triangle
        drawOutRectangles[indexOffset] = 0.0;
        drawOutRectangles[indexOffset+1] = yOffset;
        drawOutRectangles[indexOffset+2] = newCanvasWidth;
        drawOutRectangles[indexOffset+3] = yOffset;
        drawOutRectangles[indexOffset+4] = 0.0;
        drawOutRectangles[indexOffset+5] = yOffset+newCanvasBlockHeight;
        
        //second triangle
        drawOutRectangles[indexOffset+6] = 0.0;
        drawOutRectangles[indexOffset+7] = yOffset+newCanvasBlockHeight;
        drawOutRectangles[indexOffset+8] = newCanvasWidth;
        drawOutRectangles[indexOffset+9] = yOffset;
        drawOutRectangles[indexOffset+10] = newCanvasWidth;
        drawOutRectangles[indexOffset+11] = yOffset+newCanvasBlockHeight;
      }
      
      // images
      drawOutImages = new Float32Array(numPatches*12);
      patchCells = (Math.floor(numPatches / 4) + Math.ceil(numPatches % 4));
      var halfFilterWidth = ((filterWidth-1)/2)/patchWidth;
      var halfFilterHeight = ((filterWidth-1)/2)/(patchHeight*patchCells);
      var patchHeightT = patchHeight / (patchHeight*patchCells);
      for (var i = 0;i < numPatches;i++) {
        yOffset = Math.floor(i / 4)*patchHeightT;
        indexOffset = i*12;
        
        //first triangle
        drawOutImages[indexOffset] = halfFilterWidth;
        drawOutImages[indexOffset+1] = yOffset+halfFilterHeight;
        drawOutImages[indexOffset+2] = 1.0-halfFilterWidth;
        drawOutImages[indexOffset+3] = yOffset+halfFilterHeight;
        drawOutImages[indexOffset+4] = halfFilterWidth;
        drawOutImages[indexOffset+5] = yOffset+patchHeightT-halfFilterHeight;
        
        //second triangle
        drawOutImages[indexOffset+6] = halfFilterWidth;
        drawOutImages[indexOffset+7] = yOffset+patchHeightT-halfFilterHeight;
        drawOutImages[indexOffset+8] = 1.0-halfFilterWidth;
        drawOutImages[indexOffset+9] = yOffset+halfFilterHeight;
        drawOutImages[indexOffset+10] = 1.0-halfFilterWidth;
        drawOutImages[indexOffset+11] = yOffset+patchHeightT-halfFilterHeight;
      }
      
      // layer
      drawOutLayer = new Float32Array(numPatches*6);
      var layernum;
      for (var i = 0;i < numPatches;i++) {
        layernum = i % 4;
        indexOffset = i*6;
        drawOutLayer[indexOffset] = layernum;
        drawOutLayer[indexOffset+1] = layernum;
        drawOutLayer[indexOffset+2] = layernum;
        drawOutLayer[indexOffset+3] = layernum;
        drawOutLayer[indexOffset+4] = layernum;
        drawOutLayer[indexOffset+5] = layernum;
      }
      
      // initialize patchvariables
      textureWidth = patchWidth;
      textureHeight = patchHeight*patchCells;
      patchSize = patchWidth*patchHeight;
      patchArray = new Float32Array(patchSize*patchCells*4);
      
    }
  
    this.getResponses = function(patches, drawOut) {
      // TODO: check patches correct length/dimension
      
      // switch to response generation program if we're not already using it
      if (!first) {
        gl.useProgram(patchResponseProgram);
        
        // set up vertices with rectangles
        var positionLocation = gl.getAttribLocation(patchResponseProgram, "a_position");
        gl.bindBuffer(gl.ARRAY_BUFFER, apositionBuffer);
        gl.enableVertexAttribArray(positionLocation);
        gl.vertexAttribPointer(positionLocation, 2, gl.FLOAT, false, 0, 0);
        
        // set up texture positions
        var texCoordLocation = gl.getAttribLocation(patchResponseProgram, "a_texCoord");
        // provide texture coordinates for the rectangle.
        gl.bindBuffer(gl.ARRAY_BUFFER, texCoordBuffer);
        gl.enableVertexAttribArray(texCoordLocation);
        gl.vertexAttribPointer(texCoordLocation, 2, gl.FLOAT, false, 0, 0);
        
        // set framebuffer to the original one if not already using it
        gl.bindFramebuffer(gl.FRAMEBUFFER, fbo);
        
        gl.viewport(0, 0, patchWidth, patchHeight*numBlocks);
      }
      
      // pass patches into texture, each patch in either r, g, b or a
      var patchArrayIndex = 0;
      var patchesIndex1 = 0;
      var patchesIndex2 = 0;
      for (var i = 0;i < patchCells;i++) {
        for (var j = 0;j < patchHeight;j++) {
          for (var k = 0;k < patchWidth;k++) {
            patchesIndex1 = i*4;
            patchesIndex2 = (j*patchWidth) + k;
            patchArrayIndex = ((patchSize*i) + patchesIndex2)*4;
            
            //set r with first patch
            if (patchesIndex1 < numPatches) {
              patchArray[patchArrayIndex] = patches[patchesIndex1][patchesIndex2];
            } else {
              patchArray[patchArrayIndex] = 0;
            }
            //set g with 2nd patch
            if (patchesIndex1+1 < numPatches) {
              patchArray[patchArrayIndex + 1] = patches[patchesIndex1+1][patchesIndex2];
            } else {
              patchArray[patchArrayIndex + 1] = 0;
            }
            //set b with 3rd patch
            if (patchesIndex1+2 < numPatches) {
              patchArray[patchArrayIndex + 2] = patches[patchesIndex1+2][patchesIndex2];
            } else {
              patchArray[patchArrayIndex + 2] = 0;
            }
            //set a with 4th patch
            if (patchesIndex1+3 < numPatches) {
              patchArray[patchArrayIndex + 3] = patches[patchesIndex1+3][patchesIndex2];
            } else {
              patchArray[patchArrayIndex + 3] = 0;
            }
          }
        }
      }
      
      // pass texture into an uniform
      gl.activeTexture(gl.TEXTURE1);
      if (first) {
        patchTex = gl.createTexture();
      }
      gl.bindTexture(gl.TEXTURE_2D, patchTex);
      gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, textureWidth, textureHeight, 0, gl.RGBA, gl.FLOAT, patchArray);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST);
      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST);
      gl.uniform1i(gl.getUniformLocation(patchResponseProgram, "u_patches"), 1);
      
      gl.clearColor(0.0, 0.0, 0.0, 1.0);
      gl.clear(gl.COLOR_BUFFER_BIT|gl.DEPTH_BUFFER)
      
      // draw to framebuffer
      gl.drawArrays(gl.TRIANGLES, 0, patchCells*6);
      
      //gl.finish();
      
      if (drawOut) {
        
        // switch programs
        gl.useProgram(patchDrawProgram);
        
        // bind canvas buffer
        gl.bindFramebuffer(gl.FRAMEBUFFER, null);
        gl.viewport(0, 0, newCanvasWidth, newCanvasHeight);
        
        gl.clearColor(0.0, 0.0, 0.0, 1.0);
        gl.clear(gl.COLOR_BUFFER_BIT|gl.DEPTH_BUFFER)
        
        if (first) {
          drawRectBuffer = gl.createBuffer();
        }
        gl.bindBuffer(gl.ARRAY_BUFFER, drawRectBuffer);
        gl.bufferData(
          gl.ARRAY_BUFFER, 
          drawOutRectangles, 
          gl.STATIC_DRAW);
        var positionLocation = gl.getAttribLocation(patchDrawProgram, "a_position_draw");
        gl.enableVertexAttribArray(positionLocation);
        gl.vertexAttribPointer(positionLocation, 2, gl.FLOAT, false, 0, 0);
        
        if (first) {
          drawImageBuffer = gl.createBuffer();
        }
        gl.bindBuffer(gl.ARRAY_BUFFER, drawImageBuffer);
        gl.bufferData(
          gl.ARRAY_BUFFER, 
          drawOutImages, 
          gl.STATIC_DRAW);
        var textureLocation = gl.getAttribLocation(patchDrawProgram, "a_texCoord_draw");
        gl.enableVertexAttribArray(textureLocation);
        gl.vertexAttribPointer(textureLocation, 2, gl.FLOAT, false, 0, 0);
        
        if (first) {
          drawLayerBuffer = gl.createBuffer();
        }
        gl.bindBuffer(gl.ARRAY_BUFFER, drawLayerBuffer);
        gl.bufferData(
          gl.ARRAY_BUFFER, 
          drawOutLayer, 
          gl.STATIC_DRAW);
        var layerLocation = gl.getAttribLocation(patchDrawProgram, "a_patchChoice_draw");
        gl.enableVertexAttribArray(layerLocation);
        gl.vertexAttribPointer(layerLocation, 1, gl.FLOAT, false, 0, 0);
        
        // draw out
        gl.drawArrays(gl.TRIANGLES, 0, numPatches*6);
      }
  
      var responses = getOutput();
      responses = unpackToFloat(responses);
      
      // split
      responses = splitArray(responses, numPatches);
      
      // normalize responses to lie within [0,1]
      var rl = responses.length;
      
      for (var i = 0;i < rl;i++) {
        responses[i] = normalizeFilterMatrix(responses[i]);
      }
      
      first = false;
      
      return responses;
    }
    
    var splitArray = function(array, parts) {
      var sp = [];
      var al = array.length;
      var splitlength = al/parts;
      var ta = [];
      for (var i = 0;i < al;i++) {
        if (i % splitlength == 0) {
          if (i != 0) {
            sp.push(ta);
          }
          ta = [];
        }
        ta.push(array[i]); 
      }
      sp.push(ta);
      return sp;
    }
    
    var getOutput = function() {
      // get data
      var pixelValues = new Uint8Array(4*canvas.width*canvas.height);
      var data = gl.readPixels(0, 0, canvas.width, canvas.height, gl.RGBA, gl.UNSIGNED_BYTE, pixelValues);
      // return
      return pixelValues;
    }
    
    var unpackToFloat = function(array) {
      // convert packed floats to proper floats : see http://stackoverflow.com/questions/9882716/packing-float-into-vec4-how-does-this-code-work
      var newArray = [];
      var al = array.length;
      for (var i = 0;i < al;i+=4) {
        newArray[(i / 4) >> 0] = ((array[i]/(256*256*256*256))+(array[i+1]/(256*256*256))+(array[i+2]/(256*256))+(array[i+3]/256));
      }
      return newArray;
    }
    
    var normalizeFilterMatrix = function(response) {
      // normalize responses to lie within [0,1]
      var msize = response.length;
      var max = 0;
      var min = 1;
      
      for (var i = 0;i < msize;i++) {
        max = response[i] > max ? response[i] : max;
        min = response[i] < min ? response[i] : min;
      }
      var dist = max-min;
      
      if (dist == 0) {
        console.log("a patchresponse was monotone, causing normalization to fail. Leaving it unchanged.")
        response = response.map(function() {return 1});
      } else {
        for (var i = 0;i < msize;i++) {
          response[i] = (response[i]-min)/dist;
        }
      }
      
      return response
    }
    
    var patchResponseVS;
    var patchResponseFS;
    
    var drawResponsesVS = [
      "attribute vec2 a_texCoord_draw;",
      "attribute vec2 a_position_draw;",
      "attribute float a_patchChoice_draw;",
      "",
      "uniform vec2 u_resolutiondraw;",
      "",
      "varying vec2 v_texCoord;",
      "varying float v_select;",
      "",
      "void main() {",
      "   // convert the rectangle from pixels to 0.0 to 1.0",
      "   vec2 zeroToOne = a_position_draw / u_resolutiondraw;",
      "",
      "   // convert from 0->1 to 0->2",
      "   vec2 zeroToTwo = zeroToOne * 2.0;",
      "",
      "   // convert from 0->2 to -1->+1 (clipspace)",
      "   vec2 clipSpace = zeroToTwo - 1.0;",
      "   ",
      "   // transform coordinates to regular coordinates",
      "   gl_Position = vec4(clipSpace * vec2(1.0, 1.0), 0, 1);",
      "",
      "   // pass the texCoord to the fragment shader",
      "   v_texCoord = a_texCoord_draw;",
      "   ",
      "   v_select = a_patchChoice_draw;",
      "}"
    ].join('\n');
    
    var drawResponsesFS = [
      "precision mediump float;",
      "",
      "// our responses",
      "uniform sampler2D u_responses;",
      "",
      "// the texCoords passed in from the vertex shader.",
      "varying vec2 v_texCoord;",
      "varying float v_select;",
      "",
      "const vec4 bit_shift = vec4(256.0*256.0*256.0, 256.0*256.0, 256.0, 1.0);",
      "const vec4 bit_mask  = vec4(0.0, 1.0/256.0, 1.0/256.0, 1.0/256.0);",
      "",
      "// packing code from here http://stackoverflow.com/questions/9882716/packing-float-into-vec4-how-does-this-code-work",
      "void main() {",
      "  vec4 colorSum = texture2D(u_responses, v_texCoord);",
      "  float value = 0.0;",
      "  if (v_select < 0.1) {",
      "    value = colorSum[0];",
      "  } else if (v_select > 0.9 && v_select < 1.1) {",
      "    value = colorSum[1];",
      "  } else if (v_select > 1.9 && v_select < 2.1) {",
      "    value = colorSum[2];",
      "  } else if (v_select > 2.9 && v_select < 3.1) {",
      "    value = colorSum[3];",
      "  } else {",
      "    value = 1.0;",
      "  }",
      "  ",
      "  vec4 res = fract(value * bit_shift);",
      "  res -= res.xxyz * bit_mask;",
      "  ",
      "  //gl_FragColor = vec4(value, value, value, value);",
      "  //gl_FragColor = vec4(1.0, value, 1.0, 1.0);",
      "  gl_FragColor = res;",
      "}"
    ].join('\n');
  };
  
  // The rest of the code is based on webgl-utils.js authored by Gregg Tavares, license below:
  /*
   * Copyright (c) 2011, Gregg Tavares
   * All rights reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions are
   * met:
   *
   * * Redistributions of source code must retain the above copyright notice,
   *   this list of conditions and the following disclaimer.
   *
   * * Redistributions in binary form must reproduce the above copyright notice,
   *   this list of conditions and the following disclaimer in the documentation
   *   and/or other materials provided with the distribution.
   *
   *  * Neither the name of greggman.com nor the names of its contributors
   *   may be used to endorse or promote products derived from this software
   *   without specific prior written permission.
   *
   * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
   * IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
   * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
   * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
   * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
   * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
   * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
   * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
   * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
   * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
   * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
   */
  
  (function() {
    
    /**
     * Wrapped logging function.
     * @param {string} msg The message to log.
     */
    var log = function(msg) {
      if (window.console && window.console.log) {
        window.console.log(msg);
      }
    };
  
    /**
     * Wrapped logging function.
     * @param {string} msg The message to log.
     */
    var error = function(msg) {
      if (window.console) {
        if (window.console.error) {
          window.console.error(msg);
        }
        else if (window.console.log) {
          window.console.log(msg);
        }
      }
      throw msg;
    };
  
    /**
     * Turn off all logging.
     */
    var loggingOff = function() {
      log = function() {};
      error = function() {};
    };
  
    /**
     * Check if the page is embedded.
     * @return {boolean} True of we are in an iframe
     */
    var isInIFrame = function() {
      return window != window.top;
    };
  
    /**
     * Converts a WebGL enum to a string
     * @param {!WebGLContext} gl The WebGLContext to use.
     * @param {number} value The enum value.
     * @return {string} The enum as a string.
     */
    var glEnumToString = function(gl, value) {
      for (var p in gl) {
        if (gl[p] == value) {
          return p;
        }
      }
      return "0x" + value.toString(16);
    };
  
    /**
     * Creates the HTLM for a failure message
     * @param {string} canvasContainerId id of container of th
     *        canvas.
     * @return {string} The html.
     */
    var makeFailHTML = function(msg) {
      return '' +
        '<table style="background-color: #8CE; width: 100%; height: 100%;"><tr>' +
        '<td align="center">' +
        '<div style="display: table-cell; vertical-align: middle;">' +
        '<div style="">' + msg + '</div>' +
        '</div>' +
        '</td></tr></table>';
    };
  
    /**
     * Mesasge for getting a webgl browser
     * @type {string}
     */
    var GET_A_WEBGL_BROWSER = '' +
      'This page requires a browser that supports WebGL.<br/>' +
      '<a href="http://get.webgl.org">Click here to upgrade your browser.</a>';
  
    /**
     * Mesasge for need better hardware
     * @type {string}
     */
    var OTHER_PROBLEM = '' +
      "It doesn't appear your computer can support WebGL.<br/>" +
      '<a href="http://get.webgl.org/troubleshooting/">Click here for more information.</a>';
  
    /**
     * Creates a webgl context. If creation fails it will
     * change the contents of the container of the <canvas>
     * tag to an error message with the correct links for WebGL.
     * @param {Element} canvas. The canvas element to create a
     *     context from.
     * @param {WebGLContextCreationAttirbutes} opt_attribs Any
     *     creation attributes you want to pass in.
     * @return {WebGLRenderingContext} The created context.
     */
    var setupWebGL = function(canvas, opt_attribs) {
      function showLink(str) {
        var container = canvas.parentNode;
        if (container) {
          container.innerHTML = makeFailHTML(str);
        }
      };
  
      if (!window.WebGLRenderingContext) {
        //showLink(GET_A_WEBGL_BROWSER);
        return null;
      }
  
      var context = create3DContext(canvas, opt_attribs);
      if (!context) {
        //showLink(OTHER_PROBLEM);
        return null;
      }
      return context;
    };
  
    /**
     * Creates a webgl context.
     * @param {!Canvas} canvas The canvas tag to get context
     *     from. If one is not passed in one will be created.
     * @return {!WebGLContext} The created context.
     */
    var create3DContext = function(canvas, opt_attribs) {
      var names = ["webgl", "experimental-webgl"];
      var context = null;
      for (var ii = 0; ii < names.length; ++ii) {
        try {
          context = canvas.getContext(names[ii], opt_attribs);
        } catch(e) {}
        if (context) {
          break;
        }
      }
      return context;
    }
  
    var updateCSSIfInIFrame = function() {
      if (isInIFrame()) {
        document.body.className = "iframe";
      }
    };
  
    /**
     * Gets a WebGL context.
     * makes its backing store the size it is displayed.
     */
    var getWebGLContext = function(canvas) {
      if (isInIFrame()) {
        updateCSSIfInIFrame();
  
        // make the canvas backing store the size it's displayed.
        canvas.width = canvas.clientWidth;
        canvas.height = canvas.clientHeight;
      }
  
      var gl = setupWebGL(canvas);
      return gl;
    };
  
    /**
     * Loads a shader.
     * @param {!WebGLContext} gl The WebGLContext to use.
     * @param {string} shaderSource The shader source.
     * @param {number} shaderType The type of shader.
     * @param {function(string): void) opt_errorCallback callback for errors.
     * @return {!WebGLShader} The created shader.
     */
    var loadShader = function(gl, shaderSource, shaderType, opt_errorCallback) {
      var errFn = opt_errorCallback || error;
      // Create the shader object
      var shader = gl.createShader(shaderType);
  
      // Load the shader source
      gl.shaderSource(shader, shaderSource);
  
      // Compile the shader
      gl.compileShader(shader);
  
      // Check the compile status
      var compiled = gl.getShaderParameter(shader, gl.COMPILE_STATUS);
      if (!compiled) {
        // Something went wrong during compilation; get the error
        var lastError = gl.getShaderInfoLog(shader);
        errFn("*** Error compiling shader '" + shader + "':" + lastError);
        gl.deleteShader(shader);
        return null;
      }
  
      return shader;
    }
  
    /**
     * Creates a program, attaches shaders, binds attrib locations, links the
     * program and calls useProgram.
     * @param {!Array.<!WebGLShader>} shaders The shaders to attach
     * @param {!Array.<string>} opt_attribs The attribs names.
     * @param {!Array.<number>} opt_locations The locations for the attribs.
     */
    var loadProgram = function(gl, shaders, opt_attribs, opt_locations) {
      var program = gl.createProgram();
      for (var ii = 0; ii < shaders.length; ++ii) {
        gl.attachShader(program, shaders[ii]);
      }
      if (opt_attribs) {
        for (var ii = 0; ii < opt_attribs.length; ++ii) {
          gl.bindAttribLocation(
              program,
              opt_locations ? opt_locations[ii] : ii,
              opt_attribs[ii]);
        }
      }
      gl.linkProgram(program);
  
      // Check the link status
      var linked = gl.getProgramParameter(program, gl.LINK_STATUS);
      if (!linked) {
          // something went wrong with the link
          var lastError = gl.getProgramInfoLog (program);
          error("Error in program linking:" + lastError);
          
          gl.deleteProgram(program);
          return null;
      }
      return program;
    };
  
    /**
     * Loads a shader from a script tag.
     * @param {!WebGLContext} gl The WebGLContext to use.
     * @param {string} scriptId The id of the script tag.
     * @param {number} opt_shaderType The type of shader. If not passed in it will
     *     be derived from the type of the script tag.
     * @param {function(string): void) opt_errorCallback callback for errors.
     * @return {!WebGLShader} The created shader.
     */
    var createShaderFromScript = function(
        gl, scriptId, opt_shaderType, opt_errorCallback) {
      var shaderSource = "";
      var shaderType;
      var shaderScript = document.getElementById(scriptId);
      if (!shaderScript) {
        throw("*** Error: unknown script element" + scriptId);
      }
      shaderSource = shaderScript.text;
  
      if (!opt_shaderType) {
        if (shaderScript.type == "x-shader/x-vertex") {
          shaderType = gl.VERTEX_SHADER;
        } else if (shaderScript.type == "x-shader/x-fragment") {
          shaderType = gl.FRAGMENT_SHADER;
        } else if (shaderType != gl.VERTEX_SHADER && shaderType != gl.FRAGMENT_SHADER) {
          throw("*** Error: unknown shader type");
          return null;
        }
      }
  
      return loadShader(
          gl, shaderSource, opt_shaderType ? opt_shaderType : shaderType,
          opt_errorCallback);
    };
  
    /* export functions */
    window.setupWebGL = setupWebGL;
    window.createProgram = loadProgram;
    window.createShaderFromScriptElement = createShaderFromScript;
    window.getWebGLContext = getWebGLContext;
    window.updateCSSIfInIFrame = updateCSSIfInIFrame;
    window.loadShader = loadShader;
  
  }());
  
  "use strict";
  
  var svmFilter = function() {
    
    var _fft, fft_filters, responses;
    var fft_size, filterLength, filter_width, search_width, num_patches;
    var temp_imag_part, temp_real_part;
    
    // fft function
    this.fft_inplace = function(array, _im_part) {
        // in-place
        
        if (typeof _im_part == "undefined") {
          _im_part = temp_imag_part;
        }
        
        for (var i = 0;i < filterLength;i++) {
          _im_part[i] = 0.0;
        }
        
        _fft.real_fft2d(array,_im_part);
        
        return [array, _im_part];
    }
    
    this.ifft = function(rn, cn) {
        // in-place
        _fft.real_ifft2d(rn, cn);
        return rn;
    }
    
    var complex_mult_inplace = function(cn1, cn2) {
        // in-place, cn1 is the one modified
        var temp1, temp2;
        for (var r = 0;r < filterLength;r++) {
            temp1 = (cn1[0][r]*cn2[0][r]) - (cn1[1][r]*cn2[1][r]);
            temp2 = (cn1[0][r]*cn2[1][r]) + (cn1[1][r]*cn2[0][r]);
            cn1[0][r] = temp1;
            cn1[1][r] = temp2;
        }
    }
    
    this.init = function(filter_input, numPatches, filterWidth, searchWidth) {
      
      var temp, fft, offset;
      
      // calculate needed size of fft (has to be power of two)
      fft_size = upperPowerOfTwo(filterWidth-1+searchWidth);
      filterLength = fft_size*fft_size;
      _fft = new FFT();
      _fft.init(fft_size);
      fft_filters = Array(numPatches);
      var fft_filter;
      var edge = (filterWidth-1)/2;
      
      for (var i = 0;i < numPatches;i++) {
        var flar_fi0 = new Float64Array(filterLength);
        var flar_fi1 = new Float64Array(filterLength);
        
        // load filter 
        var xOffset, yOffset;
        for (var j = 0;j < filterWidth;j++) {
          for (var k = 0;k < filterWidth;k++) {
            // TODO : rotate filter
            
            xOffset = k < edge ? (fft_size-edge) : (-edge);
            yOffset = j < edge ? (fft_size-edge) : (-edge);
            flar_fi0[k+xOffset+((j+yOffset)*fft_size)] = filter_input[i][(filterWidth-1-j)+((filterWidth-1-k)*filterWidth)];
            
            /*xOffset = k < edge ? (fft_size-edge) : (-edge);
            yOffset = j < edge ? (fft_size-edge) : (-edge);
            flar_fi0[k+xOffset+((j+yOffset)*fft_size)] = filter_input[i][k+(j*filterWidth)];*/
            
            //console.log(k + ","+ j+":" + (k+xOffset+((j+yOffset)*fft_size)))
          }
        }
  
        // fft it and store
        fft_filter = this.fft_inplace(flar_fi0, flar_fi1);
        fft_filters[i] = fft_filter;
      }
      
      responses = Array(numPatches);
      temp_imag_part = Array(numPatches);
      for (var i = 0;i < numPatches;i++) {
        responses[i] = new Float64Array(searchWidth*searchWidth);
        temp_imag_part[i] = new Float64Array(searchWidth*searchWidth);
      }
      temp_real_part = new Float64Array(filterLength);
      
      num_patches = numPatches;
      filter_width = filterWidth;
      search_width = searchWidth;
    }
    
    this.getResponses = function(patches) {
      var response, temp, edge;
      var patch_width = filter_width-1+search_width;
      for (var i = 0;i < num_patches;i++) {
        // reset zeroes in temp_real_part
        for (var j = 0;j < fft_size*fft_size;j++) {
          temp_real_part[j] = 0.0;
        }
        
        // normalize patches to 0-1
        patches[i] = normalizePatches(patches[i]);
        
        // patch must be padded (with zeroes) to match fft size
        for (var j = 0;j < patch_width;j++) {
          for (var k = 0;k < patch_width;k++) {
            temp_real_part[j + (fft_size*k)] = patches[i][k + (patch_width*j)];
          }
        }
        
        //drawData(document.getElementById('sketch').getContext('2d'), temp_real_part, 32, 32, false, 0, 0);
        
        // fft it
        response = this.fft_inplace(temp_real_part);
        
        // multiply pointwise with filter
        complex_mult_inplace(response, fft_filters[i]);
        
        // inverse fft it
        response = this.ifft(response[0], response[1]);
        
        // crop out edges
        edge = (filter_width-1)/2;
        for (var j = 0;j < search_width;j++) {
          for (var k = 0;k < search_width;k++) {
            responses[i][j + (k*search_width)] = response[edge + k + ((j+edge)*(fft_size))];
          }
        }
        
        // logistic transformation
        responses[i] = logisticResponse(responses[i]);
        
        /*responses[i] = new Float64Array(32*32)
        for (var j = 0;j < 32;j++) {
          for (var k = 0;k < 32;k++) {
            responses[i][k + (j*(32))] = response[k + (j*(32))]
          }
        }*/
        
        // normalization?
        inplaceNormalizeFilterMatrix(responses[i]);
      }
      
      return responses;
    }
    
    var normalizePatches = function(patch) {
      var patch_width = filter_width-1+search_width;
      var max = 0;
      var min = 1000;
      var value;
      for (var j = 0;j < patch_width;j++) {
        for (var k = 0;k < patch_width;k++) {
          value = patch[k + (patch_width*j)]
          if (value < min) {
            min = value;
          }
          if (value > max) {
            max = value;
          }
        }
      }
      var scale = max-min;
      for (var j = 0;j < patch_width;j++) {
        for (var k = 0;k < patch_width;k++) {
          patch[k + (patch_width*j)] = (patch[k + (patch_width*j)]-min)/scale;
        }
      }
      return patch;
    }
    
    var logisticResponse = function(response) {
      // create probability by doing logistic transformation
      for (var j = 0;j < search_width;j++) {
        for (var k = 0;k < search_width;k++) {
          response[j + (k*search_width)] = 1.0/(1.0 + Math.exp(- (response[j + (k*search_width)] - 1.0 )));
        }
      }
      return response
    }
    
    var upperPowerOfTwo = function(x) {
      x--;
      x |= x >> 1;
      x |= x >> 2;
      x |= x >> 4;
      x |= x >> 8;
      x |= x >> 16;
      x++;
      return x;
    }
    
    var inplaceNormalizeFilterMatrix = function(response) {
      // normalize responses to lie within [0,1]
      var msize = response.length;
      var max = 0;
      var min = 1;
      
      for (var i = 0;i < msize;i++) {
        max = response[i] > max ? response[i] : max;
        min = response[i] < min ? response[i] : min;
      }
      var dist = max-min;
      
      if (dist == 0) {
        console.log("a patchresponse was monotone, causing normalization to fail. Leaving it unchanged.")
      } else {
        for (var i = 0;i < msize;i++) {
          response[i] = (response[i]-min)/dist;
        }
      }
    }
  
    /**
     * Fast Fourier Transform
     * 1D-FFT/IFFT, 2D-FFT/IFFT (radix-2)
     * 
     * @author ryo / github.com/wellflat
     * Based on https://github.com/wellflat/javascript-labs with some tiny optimizations
     */
  
    function FFT() {
      
      var _n = 0,          // order
          _bitrev = null,  // bit reversal table
          _cstb = null;    // sin/cos table
      var _tre, _tim;
      
      this.init = function (n) {
        if(n !== 0 && (n & (n - 1)) === 0) {
          _n = n;
          _setVariables();
          _makeBitReversal();
          _makeCosSinTable();
        } else {
          throw new Error("init: radix-2 required");
        }
      }
        
      // 1D-FFT
      this.fft1d = function (re, im) {
        fft(re, im, 1);
      }
        
      // 1D-IFFT
      this.ifft1d = function (re, im) {
        var n = 1/_n;
        fft(re, im, -1);
        for(var i=0; i<_n; i++) {
          re[i] *= n;
          im[i] *= n;
        }
      }
      
      // 2D-FFT
      this.fft2d = function (re, im) {
        var i = 0;
        // x-axis
        for(var y=0; y<_n; y++) {
          i = y*_n;
          for(var x1=0; x1<_n; x1++) {
            _tre[x1] = re[x1 + i];
            _tim[x1] = im[x1 + i];
          }
          this.fft1d(_tre, _tim);
          for(var x2=0; x2<_n; x2++) {
            re[x2 + i] = _tre[x2];
            im[x2 + i] = _tim[x2];
          }
        }
        
        // y-axis
        for(var x=0; x<_n; x++) {
          for(var y1=0; y1<_n; y1++) {
            i = x + y1*_n;
            _tre[y1] = re[i];
            _tim[y1] = im[i];
          }
          this.fft1d(_tre, _tim);
          for(var y2=0; y2<_n; y2++) {
            i = x + y2*_n;
            re[i] = _tre[y2];
            im[i] = _tim[y2];
          }
        }
      }
      
      // 2D-IFFT
      this.ifft2d = function (re, im) {
        var i = 0;
        // x-axis
        for(var y=0; y<_n; y++) {
          i = y*_n;
          for(var x1=0; x1<_n; x1++) {
            _tre[x1] = re[x1 + i];
            _tim[x1] = im[x1 + i];
          }
          this.ifft1d(_tre, _tim);
          for(var x2=0; x2<_n; x2++) {
            re[x2 + i] = _tre[x2];
            im[x2 + i] = _tim[x2];
          }
        }
        // y-axis
        for(var x=0; x<_n; x++) {
          for(var y1=0; y1<_n; y1++) {
            i = x + y1*_n;
            _tre[y1] = re[i];
            _tim[y1] = im[i];
          }
          this.ifft1d(_tre, _tim);
          for(var y2=0; y2<_n; y2++) {
            i = x + y2*_n;
            re[i] = _tre[y2];
            im[i] = _tim[y2];
          }
        }
      }
      
      // 2D-IFFT, real-valued
      // only outputs the real valued part
      this.real_ifft2d = function (re, im) {
        var i2;
        var i = 0;
        // x-axis
        for(var y=0; y<_n; y++) {
          i = y*_n;
          for(var x1=0; x1<_n; x1++) {
            _tre[x1] = re[x1 + i];
            _tim[x1] = im[x1 + i];
          }
          this.ifft1d(_tre, _tim);
          for(var x2=0; x2<_n; x2++) {
            re[x2 + i] = _tre[x2];
            im[x2 + i] = _tim[x2];
          }
        }
        // y-axis
        var halfn = _n/2;
        var rowIdx = 0;
        for(var x=0; x<_n; x+=2) {
          //untangle
          i = x;
          i2 = x+1;
          _tre[0] = re[0 + i];
          _tim[0] = re[0 + i2];
          _tre[_n/2] = re[(halfn*_n) + i];
          _tim[_n/2] = re[(halfn*_n) + i2];
          for (var x2=1;x2<halfn;x2++) {
            rowIdx = x2*_n
            _tre[x2] = re[rowIdx+i] - im[rowIdx + i2];
            _tre[_n - x2] = re[rowIdx+i] + im[rowIdx + i2];
            _tim[x2] = im[rowIdx+i] + re[rowIdx+i2];
            _tim[_n - x2] = re[rowIdx+i2] - im[rowIdx+i];
          }
          this.ifft1d(_tre, _tim);
          for(var y2=0; y2<_n; y2++) {
            i = x + y2*_n;
            i2 = (x + 1) + y2*_n;
            re[i] = _tre[y2];
            re[i2] = _tim[y2];
          }
        }
      }
      
      // 2D-FFT, real-valued only
      // ignores the imaginary input
      //   see:
      // http://www.inf.fu-berlin.de/lehre/SS12/SP-Par/download/fft1.pdf
      // http://cnx.org/content/m12021/latest/
      // http://images.apple.com/acg/pdf/g4fft.pdf
      // http://www.ti.com/lit/an/spra291/spra291.pdf
      this.real_fft2d = function (re, im) {
        var i = 0, i2 = 0;
        var fftlen = (_n*_n)-1;
        // x-axis
        for(var y=0; y<_n; y += 2) {
          i = y*_n;
          i2 = (y+1)*_n;
          // tangle
          for(var x1=0; x1<_n; x1++) {
            _tre[x1] = re[x1 + i];
            _tim[x1] = re[x1 + i2];
          }
          this.fft1d(_tre, _tim);
          // untangle
          re[0 + i] = _tre[0];
          re[0 + i2] = _tim[0];
          im[0 + i] = 0;
          im[0 + i2] = 0;
          re[_n/2 + i] = _tre[_n/2];
          re[_n/2 + i2] = _tim[_n/2];
          im[_n/2 + i] = 0;
          im[_n/2 + i2] = 0;
          for(var x2=1;x2<(_n/2);x2++) {
            re[x2 + i] = 0.5 * (_tre[x2] + _tre[_n - x2]);
            im[x2 + i] = 0.5 * (_tim[x2] - _tim[_n - x2]);
            re[x2 + i2] = 0.5 * (_tim[x2] + _tim[_n - x2]);
            im[x2 + i2] = -0.5 * (_tre[x2] - _tre[_n - x2]);
            re[(_n-x2) + i] = re[x2 + i];
            im[(_n-x2) + i] = -im[x2 + i];
            re[(_n-x2) + i2] = re[x2 + i2];
            im[(_n-x2) + i2] = -im[x2 + i2];
          }
        }
        // y-axis
        for(var x=0; x<_n; x++) {
          for(var y1=0; y1<_n; y1++) {
            i = x + y1*_n;
            _tre[y1] = re[i];
            _tim[y1] = im[i];
          }
          this.fft1d(_tre, _tim);
          for(var y2=0; y2<_n; y2++) {
            i = x + y2*_n;
            re[i] = _tre[y2];
            im[i] = _tim[y2];
          }
        }
      }
      
      // core operation of FFT
      function fft(re, im, inv) {
        var d, h, ik, m, tmp, wr, wi, xr, xi,
            n4 = _n >> 2;
        // bit reversal
        for(var l=0; l<_n; l++) {
          m = _bitrev[l];
          if(l < m) {
            tmp = re[l];
            re[l] = re[m];
            re[m] = tmp;
            tmp = im[l];
            im[l] = im[m];
            im[m] = tmp;
          }
        }
        // butterfly operation
        //butfly(re,im,inv,n4);
        for(var k=1; k<_n; k<<=1) {
          h = 0;
          d = _n/(k << 1);
          for(var j=0; j<k; j++) {
            wr = _cstb[h + n4];
            wi = inv*_cstb[h];
            for(var i=j; i<_n; i+=(k<<1)) {
              ik = i + k;
              xr = wr*re[ik] + wi*im[ik];
              xi = wr*im[ik] - wi*re[ik];
              re[ik] = re[i] - xr;
              re[i] += xr;
              im[ik] = im[i] - xi;
              im[i] += xi;
            }
            h += d;
          }
        }
      }
      
      function butfly(re, im, inv, n4) {
        var h,d,wr,wi,ik,xr,xi;
        for(var k=1; k<_n; k<<=1) {
          h = 0;
          d = _n/(k << 1);
          for(var j=0; j<k; j++) {
            wr = _cstb[h + n4];
            wi = inv*_cstb[h];
            for(var i=j; i<_n; i+=(k<<1)) {
              ik = i + k;
              xr = wr*re[ik] + wi*im[ik];
              xi = wr*im[ik] - wi*re[ik];
              re[ik] = re[i] - xr;
              re[i] += xr;
              im[ik] = im[i] - xi;
              im[i] += xi;
            }
            h += d;
          }
        }
      }
      
      // set variables
      function _setVariables() {
        if(typeof Uint8Array !== 'undefined') {
          _bitrev = new Uint8Array(_n);
        } else {
          _bitrev = new Array(_n);
        }
        if(typeof Float64Array !== 'undefined') {
          _cstb = new Float64Array(_n*1.25);
          _tre = new Float64Array(_n);
          _tim = new Float64Array(_n);
        } else {
          _cstb = new Array(_n*1.25);
          _tre = new Array(_n);
          _tim = new Array(_n);
        }
      }
      
      // make bit reversal table
      function _makeBitReversal() {
        var i = 0,
            j = 0,
            k = 0;
        _bitrev[0] = 0;
        while(++i < _n) {
          k = _n >> 1;
          while(k <= j) {
            j -= k;
            k >>= 1;
          }
          j += k;
          _bitrev[i] = j;
        }
      }
      
      // make trigonometric function table
      function _makeCosSinTable() {
        var n2 = _n >> 1,
            n4 = _n >> 2,
            n8 = _n >> 3,
            n2p4 = n2 + n4,
            t = Math.sin(Math.PI/_n),
            dc = 2*t*t,
            ds = Math.sqrt(dc*(2 - dc)),
            c = _cstb[n4] = 1,
            s = _cstb[0] = 0;
        t = 2*dc;
        for(var i=1; i<n8; i++) {
          c -= dc;
          dc += t*c;
          s += ds;
          ds -= t*s;
          _cstb[i] = s;
          _cstb[n4 - i] = c;
        }
        if(n8 !== 0) {
          _cstb[n8] = Math.sqrt(0.5);
        }
        for(var j=0; j<n4; j++) {
          _cstb[n2 - j]  = _cstb[j];
        }
        for(var k=0; k<n2p4; k++) {
          _cstb[k + n2] = -_cstb[k];
        }
      }
    }
  }
  
  // requires mosse.js
  
  var mosseFilterResponses = function() {
    
    var filters = [];
    var responses = [];
    var num_Patches = 0;
    
    this.init = function(filter_input, numPatches, filterWidth, filterHeight) {
      // load filters, make fft ready
      
      for (var i = 0;i < numPatches;i++) {
        var temp = {};
        temp.width = filterWidth;
        temp.height = filterHeight;
        var filterLength = filterWidth*filterHeight
        var flar_fi0 = new Float64Array(filterLength);
        var flar_fi1 = new Float64Array(filterLength);
        for (var j = 0;j < filterLength;j++) {
          flar_fi0[j] = filter_input[i][0][j];
          flar_fi1[j] = filter_input[i][1][j];
        }
        temp.real = flar_fi0;
        temp.imag = flar_fi1;
        filters[i] = new mosseFilter();
        filters[i].load(temp);
      }
      
      num_Patches = numPatches;
    }
    
    this.getResponses = function(patches) {
      for (var i = 0;i < num_Patches;i++) {
        responses[i] = filters[i].getResponse(patches[i]);
        //responses[i] = logisticResponse(responses[i]);
        responses[i] = normalizeFilterMatrix(responses[i]);
      }
      
      return responses;
    }
    
    var logisticResponse = function(response) {
      // create probability by doing logistic transformation
      var filter_size = response.length;
      for (var j = 0;j < filter_size;j++) {
        response[j] = 1.0/(1.0 + Math.exp(- (response[j]-1.0) ));
      }
      return response;
    }
    
    var normalizeFilterMatrix = function(response) {
      // normalize responses to lie within [0,1]
      var msize = response.length;
      var max = 0;
      var min = 1;
      
      for (var i = 0;i < msize;i++) {
        max = response[i] > max ? response[i] : max;
        min = response[i] < min ? response[i] : min;
      }
      var dist = max-min;
      
      if (dist == 0) {
        console.log("a patchresponse was monotone, causing normalization to fail. Leaving it unchanged.")
        response = response.map(function() {return 1});
      } else {
        for (var i = 0;i < msize;i++) {
          response[i] = (response[i]-min)/dist;
        }
      }
      
      return response
    }
  }
  
  var left_eye_filter = {"real": [1.5419219943717721, 0.40010880110578706, -0.79043641265342957, -1.2685464969238938, 0.39878117336167285, -1.0673489992245377, -0.079880838229404019, -0.45374680224191505, -0.043474097938900787, -0.31125662385352687, 0.17092430376098702, -0.29613086164846153, 0.5616469648110296, -1.559786848789493, 0.64513037997492662, -1.2899747976234162, 1.1761667998175334, -1.2899747976233551, 0.64513037997490474, -1.5597868487894897, 0.56164696481102505, -0.29613086164845964, 0.17092430376099094, -0.31125662385352959, -0.043474097938900787, -0.45374680224191177, -0.079880838229404658, -1.0673489992245357, 0.39878117336167307, -1.2685464969238942, -0.79043641265343012, 0.40010880110578717, -1.3820969331049027, 0.069560471269205768, -1.9786339579213206, -1.9807415717551982, -0.78667274410450883, -1.2217002325587256, -0.19150029104902774, -0.35131617290773243, -0.17646388464205803, -0.16672095020503441, -0.092298612924566523, -0.028899376452253527, -0.1314555696102146, -0.32892265898101813, -0.40987148655061206, 0.11741827111366547, -0.67254330182605138, -0.46007833291519956, -0.67215259521101001, -0.44871907432473013, -0.034749316729184583, 0.0055639281302433969, -0.17675902360981591, -0.26196208085032191, -0.36301254306387037, -0.33546767337818123, -0.6458889740799838, -1.1981932989987978, 0.12372650763830917, -1.4996172161865935, -2.4084298023013888, -2.0505291279591722, -1.7249706159518585, -2.277646289702639, -3.1259631743419591, -2.9656385065342015, -2.8480835086962011, -1.4260964500310189, -0.61792590829173544, -0.2611655301498782, -0.38519889843539723, -0.17511899827006483, -0.32808050503227176, 0.0076800871037463036, -0.18710828510427668, 0.1976534820339281, -0.55444453100465052, 0.14583567590328381, -0.69844971117515287, -0.90188577233526623, -0.53500016384583371, -0.044420751861669799, 0.014727914354086128, -0.28084584584371913, -0.29890408748685848, -0.39431380149336548, -0.39569215798819307, -0.74351999988258299, -0.82502198370631752, -1.851491897104155, -0.74302378668934244, 0.21156442062863762, -3.3061472495599986, -1.7990472945779568, -2.2193764251732282, -2.3438802466919251, -3.3615971067123311, -3.5383249085863708, -2.2639673745086588, -2.0271757806780748, -0.75242583405872232, -0.30143411016839378, -0.3625272253546275, -0.25489431004647689, -0.18928491561467081, -0.1179891518538482, 0.027920290231533224, -0.035472107498143821, -0.29008721857562259, -0.3604588674139817, -0.39156143807433802, -0.82222257402876564, -0.44979914971695928, -0.098136330355476253, 0.065628582466229365, -0.33607304327303128, -0.32161201323497779, -0.41856090178723965, -0.64028425429629054, -0.7766428172010218, -1.3946448661671447, -2.2603422126144683, -0.38769722219534525, -0.95341593939478653, -1.412952994959813, -2.3602336858020432, -1.2756392437278019, -2.0983496132652038, -2.5682454610054268, -2.8791053946930378, -2.1809972632688095, -0.84281293847776861, -0.75998936793718697, -0.18584599820380068, -0.30105748355308259, -0.16098142942852958, -0.13792125740417191, -0.089790022871128708, -0.12321821342876504, -0.1128661923016878, -0.3924098378001975, -0.5780902167586397, -0.48685989567066695, -0.53565359443296234, -0.051036689850526382, -0.0068547033925117689, -0.18963405157839419, -0.22514761090777807, -0.35555823460888908, -0.46670603976585517, -0.56179541485257889, -0.7495095888115163, -1.4772075422260349, -1.5836466114968029, -2.3846549454186694, -1.4884613952536236, -1.8237453905245253, -1.6712324532934877, -1.5169157844507295, -1.6930052820597281, -2.1023566589276004, -2.2062031109308458, -1.7945281756942255, -0.26457398838912649, 0.22038139379151148, -0.43479836723775234, -0.19830827357221226, -0.18018565146479498, -0.097060879184795737, -0.10088329756370379, -0.063069709957272527, -0.17970932516041177, -0.1943040732581543, -0.37970560392277619, -0.47302301606251812, -0.30366967948052181, -0.064732391018915397, -0.08902516330269715, -0.082000200083027344, -0.22965854401457736, -0.32035624605031326, -0.31836783196552437, -0.40132058236311119, -0.65601747033470859, -0.59040483751417483, -1.8503084663080034, -1.8694842425148914, -1.9326778896298584, -1.6301578422923519, -1.4332006785118301, -1.305707665299106, -1.364200787821644, -1.5357935460809622, -1.6161992336951241, -0.74003518668370516, -0.29423824173210689, 0.025934598230976654, -0.043349004411304674, -0.25408021803022468, -0.066965686484977499, -0.075717498698635255, 0.007057189465364498, -0.042171356658338113, -0.036938315661768008, -0.34221561581756049, -0.20400167508805764, -0.37417116097079772, -0.25039909487805356, -0.070874531394524931, -0.0569972852039487, -0.067238206950403182, -0.17397285212300442, -0.20428337307808273, -0.23651154356493315, -0.33356498933276568, -0.07339749754226077, -0.70367959806681601, -0.82403680021595049, -1.6058616381755235, -1.6192427030685497, -1.5705638815427956, -1.4659201063980019, -0.95504179549951018, -0.97237526162739873, -1.0460191987834688, 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-0.55610134656922283, 0.40792084439497267, 1.0440547633891391, -0.23916839371037832, 0.2750333919575636, 0.62135646441400449, -0.21110858701983135, -0.81615985313544015, 0.14589390394899499, 0.32406742573949032, 0.74952192547288177, -0.32511669967392071, -0.48825453192442569, 0.36648156701751228, 1.0443697855595189, -0.22841081726546683, -1.4950174056034862, 6.4644843028741308, 2.9904131431626397, -13.820343051841599, 1.9854594697574315, -13.304182061875386, -6.3352095159572039, 0.3195679261341049, 0.22665765093840967, 0.19533791786523994, 0.21778449617622839, 0.69288180199640803, 0.084400039832664031, -0.31425797573231284, -0.31479155143425158, 0.078939183973069621, -0.58294801786464789, 0.46161406526582016, 0.41846754429722727, 0.79801858694486438, 0.43858849762191948, 0.23788459440435036, -1.2725586605629382, -0.75720231383362191, -0.29841298969258917, 0.14587335963051393, -0.16753374785242225, -0.21612918483653495, 0.53597221218340851, 0.69495683349647419, -1.0539667118389073, 0.87617222540110107, 4.3629732153958827, -8.0952123464619206, -7.414834109374171, 7.5311386138631651, -44.041788084316849, 22.050605310259897, 5.1510032561702142, -5.6601916863792514, 8.4367427775736488, 1.5703737430868991, -0.83895281997413862, 0.19212817740850727, 0.39792121836056477, -0.14922819541222082, -0.047770712409500753, -0.2908510034609289, -0.015061212014133111, 0.32646574432385927, 0.77395352504545112, -0.16614591312540627, 0.36806371804963284, -0.097634295479077288, 0.091330331747514912, -0.24450075339721231, -0.029095718259234932, 0.16613612027343472, 0.28240974426972948, -0.18044316667269469, -0.48074766055651602, -0.36626836712779753, 3.4507560855810189, -1.9317197634824488, -11.789513877445398, 17.692027714058376, 32.190550839656112, -28.446155418037584, 65.634374404237818, -24.878800155519698, -2.0570987009734387, -3.2997425925449106, -11.516126179313863, 12.372184270457085, 4.9611285532463585, 0.86391702025516592, 0.16530865667454706, -0.46079094226119116, -0.1732663636027687, -0.25470104821282824, -0.43031399471588622, -0.041501479859297648, -0.54386217024143224, 0.81683568275167029, 0.097089152898783726, -0.13744024889929929, -0.095619359707603865, 0.098626184449285684, -0.63036999033225893, -0.18311714867083492, -0.07372642556981146, -0.19104942819406445, 0.075862266735016198, 3.0325028906240856, -9.0326984830007238, -11.815798616251362, 36.620593610799446, 10.636065931319884, -38.68839724466217, 45.716174186409333, -314.74785574475044, 197.27075321520152, 337.61540934331566, 21.930976284520245, -28.837963587037731, -13.475211488788421, 9.5917712473092944, 1.5250850436867665, -1.5545017016282761, -0.64667209976974838, 0.44513357712322837, 0.056507066939540815, -0.23461588343644407, -0.26011219704759359, 0.8042712968338912, 0.30779007494077798, 0.77483290182744469, -0.65133332546861145, -0.18908937081392915, -0.50446476014305819, -0.0074294169071514489, -0.43833208591156614, 0.3383874374890965, 1.0227323524080993, -0.18896973496668346, -8.9206630611282982, -3.6862817789376785, 19.35920062861366, -44.579795546563581, 57.025448777424586, 360.31891091191056, 8.8001261891013822, 1526.2181503116453, 45.053807917762221, -140.68826246910882, 254.89688572081207, -61.967816961200398, -4.5083476182968329, 11.964107143689583, 3.7790359077733431, -1.9045345605049631, -1.7624207728132955, -0.01261576384946491, 0.19558932994062728, -0.30219131214854072, 0.4699644624025669, -0.91230383136372128, 0.36883118795348824, -0.13682839189736087, 0.66713893962058779, -0.25989055470659439, -0.44968314290067052, -1.2882353738829488, -0.76755040332110314, 0.21593130161202181, 1.7124190510555817, 0.6346191100738432, -2.3593378023079388, -10.295701682078779, -39.603849315110132, 54.052681314235315, 182.3786468306393, -282.18880697804133, 735.50774046161428, -423.76919790180091, 46.72930747865378, 744.09540667092074, 65.421023262373566, -26.998515460375824, -110.68919188818332, 1.7026644231740455, 8.6847068298461902, -3.6812627646537122, -1.4462870038602713, 0.66403014974352648, 0.98268640942926089, -0.10353485266764806, -1.1704253870693322, 0.47609558693405896, -0.63809937787576798, 1.9145243520823476, 0.11088180406502474, 0.082864627703299776, -0.36254455317814699, -0.74689297610786809, -0.69551673309504447, -0.24508893173895085, 4.773352510756971, -0.034376983736587929, -18.791248861451901, 0.26732768536914786, 52.084914641107339, -48.782690015656009, -267.77827954485792, 730.15551768721207, 777.49072200787191, 9988.2725309741272, 2608.4519239039569, -953.38531885843202, 570.34935164465708, -262.60583525697274, -86.61832325668658, -42.569555354666946, 2.6532766677526505, 7.1796038797667014, -2.7868839636562561, -0.37842412015855753, 2.0950938638350354, 0.042260514128576405, -0.56850457149086808, -0.90990468751900622, 0.4779279337996068, -1.7872556824974217, 2.239357916267509, 1.748611490859272, 1.4553261209412682, -0.72663987403827102, -2.6646257572640879, 0.50817475490745234, 1.8456273678139588, -1.3367261976572486, 1.0587560944122603, 22.259718007212488, -10.499004391497355, -376.50689706328382, 153.72085790515695, 213.86760970710961, 5000.8757444384837, 12998.804313286144, 3077.5993672243935, -814.38538391702389, -589.84188198577237, 52.443377241039045, -203.58844824671809, -68.764375920932238, 24.893726268864992, 6.7517210150420599, -0.13350548988021724, -0.12421201224142447, -0.33273215463053935, -0.74767454410310241, -2.6325944160953538, 0.19923279402974362, -1.8330278968089646, 1.4063404110660558, 0.33462283171345686, 1.8114765667849764, -0.030361957750053889, -0.81638586337482577, 0.82869028871127859, -0.22176027695649836, 1.260192177948489, -13.167070698799225, -23.742310304940538, 82.499903393484416, 67.213502175129648, -232.07891937634469, -387.93265499317204, 1281.4742181751474, 7140.8743305075477, 19170.83401144094, 6565.2013915603166, -266.59769699529113, 524.55810593663034, -105.08267177765569, 68.939947660481323, -65.513717323045299, -7.7366224074036598, 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  /**
   * Numeric Javascript
   * Copyright (C) 2011 by Sébastien Loisel
   *
   * Permission is hereby granted, free of charge, to any person obtaining a copy
   * of this software and associated documentation files (the "Software"), to deal
   * in the Software without restriction, including without limitation the rights
   * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
   * copies of the Software, and to permit persons to whom the Software is
   * furnished to do so, subject to the following conditions:
   *
   * The above copyright notice and this permission notice shall be included in
   * all copies or substantial portions of the Software.
   *
   * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
   * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
   * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
   * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
   * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
   * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
   * THE SOFTWARE.
   */
  
  "use strict";
  
  var numeric = (typeof exports === "undefined")?(function numeric() {}):(exports);
  if(typeof global !== "undefined") { global.numeric = numeric; }
  
  numeric.version = "1.2.6";
  
  // 1. Utility functions
  numeric.bench = function bench (f,interval) {
      var t1,t2,n,i;
      if(typeof interval === "undefined") { interval = 15; }
      n = 0.5;
      t1 = new Date();
      while(1) {
          n*=2;
          for(i=n;i>3;i-=4) { f(); f(); f(); f(); }
          while(i>0) { f(); i--; }
          t2 = new Date();
          if(t2-t1 > interval) break;
      }
      for(i=n;i>3;i-=4) { f(); f(); f(); f(); }
      while(i>0) { f(); i--; }
      t2 = new Date();
      return 1000*(3*n-1)/(t2-t1);
  }
  
  numeric._myIndexOf = (function _myIndexOf(w) {
      var n = this.length,k;
      for(k=0;k<n;++k) if(this[k]===w) return k;
      return -1;
  });
  numeric.myIndexOf = (Array.prototype.indexOf)?Array.prototype.indexOf:numeric._myIndexOf;
  
  numeric.Function = Function;
  numeric.precision = 4;
  numeric.largeArray = 50;
  
  numeric.prettyPrint = function prettyPrint(x) {
      function fmtnum(x) {
          if(x === 0) { return '0'; }
          if(isNaN(x)) { return 'NaN'; }
          if(x<0) { return '-'+fmtnum(-x); }
          if(isFinite(x)) {
              var scale = Math.floor(Math.log(x) / Math.log(10));
              var normalized = x / Math.pow(10,scale);
              var basic = normalized.toPrecision(numeric.precision);
              if(parseFloat(basic) === 10) { scale++; normalized = 1; basic = normalized.toPrecision(numeric.precision); }
              return parseFloat(basic).toString()+'e'+scale.toString();
          }
          return 'Infinity';
      }
      var ret = [];
      function foo(x) {
          var k;
          if(typeof x === "undefined") { ret.push(Array(numeric.precision+8).join(' ')); return false; }
          if(typeof x === "string") { ret.push('"'+x+'"'); return false; }
          if(typeof x === "boolean") { ret.push(x.toString()); return false; }
          if(typeof x === "number") {
              var a = fmtnum(x);
              var b = x.toPrecision(numeric.precision);
              var c = parseFloat(x.toString()).toString();
              var d = [a,b,c,parseFloat(b).toString(),parseFloat(c).toString()];
              for(k=1;k<d.length;k++) { if(d[k].length < a.length) a = d[k]; }
              ret.push(Array(numeric.precision+8-a.length).join(' ')+a);
              return false;
          }
          if(x === null) { ret.push("null"); return false; }
          if(typeof x === "function") { 
              ret.push(x.toString());
              var flag = false;
              for(k in x) { if(x.hasOwnProperty(k)) { 
                  if(flag) ret.push(',\n');
                  else ret.push('\n{');
                  flag = true; 
                  ret.push(k); 
                  ret.push(': \n'); 
                  foo(x[k]); 
              } }
              if(flag) ret.push('}\n');
              return true;
          }
          if(x instanceof Array) {
              if(x.length > numeric.largeArray) { ret.push('...Large Array...'); return true; }
              var flag = false;
              ret.push('[');
              for(k=0;k<x.length;k++) { if(k>0) { ret.push(','); if(flag) ret.push('\n '); } flag = foo(x[k]); }
              ret.push(']');
              return true;
          }
          ret.push('{');
          var flag = false;
          for(k in x) { if(x.hasOwnProperty(k)) { if(flag) ret.push(',\n'); flag = true; ret.push(k); ret.push(': \n'); foo(x[k]); } }
          ret.push('}');
          return true;
      }
      foo(x);
      return ret.join('');
  }
  
  numeric.parseDate = function parseDate(d) {
      function foo(d) {
          if(typeof d === 'string') { return Date.parse(d.replace(/-/g,'/')); }
          if(!(d instanceof Array)) { throw new Error("parseDate: parameter must be arrays of strings"); }
          var ret = [],k;
          for(k=0;k<d.length;k++) { ret[k] = foo(d[k]); }
          return ret;
      }
      return foo(d);
  }
  
  numeric.parseFloat = function parseFloat_(d) {
      function foo(d) {
          if(typeof d === 'string') { return parseFloat(d); }
          if(!(d instanceof Array)) { throw new Error("parseFloat: parameter must be arrays of strings"); }
          var ret = [],k;
          for(k=0;k<d.length;k++) { ret[k] = foo(d[k]); }
          return ret;
      }
      return foo(d);
  }
  
  numeric.parseCSV = function parseCSV(t) {
      var foo = t.split('\n');
      var j,k;
      var ret = [];
      var pat = /(([^'",]*)|('[^']*')|("[^"]*")),/g;
      var patnum = /^\s*(([+-]?[0-9]+(\.[0-9]*)?(e[+-]?[0-9]+)?)|([+-]?[0-9]*(\.[0-9]+)?(e[+-]?[0-9]+)?))\s*$/;
      var stripper = function(n) { return n.substr(0,n.length-1); }
      var count = 0;
      for(k=0;k<foo.length;k++) {
        var bar = (foo[k]+",").match(pat),baz;
        if(bar.length>0) {
            ret[count] = [];
            for(j=0;j<bar.length;j++) {
                baz = stripper(bar[j]);
                if(patnum.test(baz)) { ret[count][j] = parseFloat(baz); }
                else ret[count][j] = baz;
            }
            count++;
        }
      }
      return ret;
  }
  
  numeric.toCSV = function toCSV(A) {
      var s = numeric.dim(A);
      var i,j,m,n,row,ret;
      m = s[0];
      n = s[1];
      ret = [];
      for(i=0;i<m;i++) {
          row = [];
          for(j=0;j<m;j++) { row[j] = A[i][j].toString(); }
          ret[i] = row.join(', ');
      }
      return ret.join('\n')+'\n';
  }
  
  numeric.getURL = function getURL(url) {
      var client = new XMLHttpRequest();
      client.open("GET",url,false);
      client.send();
      return client;
  }
  
  numeric.imageURL = function imageURL(img) {
      function base64(A) {
          var n = A.length, i,x,y,z,p,q,r,s;
          var key = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=";
          var ret = "";
          for(i=0;i<n;i+=3) {
              x = A[i];
              y = A[i+1];
              z = A[i+2];
              p = x >> 2;
              q = ((x & 3) << 4) + (y >> 4);
              r = ((y & 15) << 2) + (z >> 6);
              s = z & 63;
              if(i+1>=n) { r = s = 64; }
              else if(i+2>=n) { s = 64; }
              ret += key.charAt(p) + key.charAt(q) + key.charAt(r) + key.charAt(s);
              }
          return ret;
      }
      function crc32Array (a,from,to) {
          if(typeof from === "undefined") { from = 0; }
          if(typeof to === "undefined") { to = a.length; }
          var table = [0x00000000, 0x77073096, 0xEE0E612C, 0x990951BA, 0x076DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3,
                       0x0EDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988, 0x09B64C2B, 0x7EB17CBD, 0xE7B82D07, 0x90BF1D91, 
                       0x1DB71064, 0x6AB020F2, 0xF3B97148, 0x84BE41DE, 0x1ADAD47D, 0x6DDDE4EB, 0xF4D4B551, 0x83D385C7,
                       0x136C9856, 0x646BA8C0, 0xFD62F97A, 0x8A65C9EC, 0x14015C4F, 0x63066CD9, 0xFA0F3D63, 0x8D080DF5, 
                       0x3B6E20C8, 0x4C69105E, 0xD56041E4, 0xA2677172, 0x3C03E4D1, 0x4B04D447, 0xD20D85FD, 0xA50AB56B, 
                       0x35B5A8FA, 0x42B2986C, 0xDBBBC9D6, 0xACBCF940, 0x32D86CE3, 0x45DF5C75, 0xDCD60DCF, 0xABD13D59, 
                       0x26D930AC, 0x51DE003A, 0xC8D75180, 0xBFD06116, 0x21B4F4B5, 0x56B3C423, 0xCFBA9599, 0xB8BDA50F,
                       0x2802B89E, 0x5F058808, 0xC60CD9B2, 0xB10BE924, 0x2F6F7C87, 0x58684C11, 0xC1611DAB, 0xB6662D3D,
                       0x76DC4190, 0x01DB7106, 0x98D220BC, 0xEFD5102A, 0x71B18589, 0x06B6B51F, 0x9FBFE4A5, 0xE8B8D433,
                       0x7807C9A2, 0x0F00F934, 0x9609A88E, 0xE10E9818, 0x7F6A0DBB, 0x086D3D2D, 0x91646C97, 0xE6635C01, 
                       0x6B6B51F4, 0x1C6C6162, 0x856530D8, 0xF262004E, 0x6C0695ED, 0x1B01A57B, 0x8208F4C1, 0xF50FC457, 
                       0x65B0D9C6, 0x12B7E950, 0x8BBEB8EA, 0xFCB9887C, 0x62DD1DDF, 0x15DA2D49, 0x8CD37CF3, 0xFBD44C65, 
                       0x4DB26158, 0x3AB551CE, 0xA3BC0074, 0xD4BB30E2, 0x4ADFA541, 0x3DD895D7, 0xA4D1C46D, 0xD3D6F4FB, 
                       0x4369E96A, 0x346ED9FC, 0xAD678846, 0xDA60B8D0, 0x44042D73, 0x33031DE5, 0xAA0A4C5F, 0xDD0D7CC9, 
                       0x5005713C, 0x270241AA, 0xBE0B1010, 0xC90C2086, 0x5768B525, 0x206F85B3, 0xB966D409, 0xCE61E49F, 
                       0x5EDEF90E, 0x29D9C998, 0xB0D09822, 0xC7D7A8B4, 0x59B33D17, 0x2EB40D81, 0xB7BD5C3B, 0xC0BA6CAD, 
                       0xEDB88320, 0x9ABFB3B6, 0x03B6E20C, 0x74B1D29A, 0xEAD54739, 0x9DD277AF, 0x04DB2615, 0x73DC1683, 
                       0xE3630B12, 0x94643B84, 0x0D6D6A3E, 0x7A6A5AA8, 0xE40ECF0B, 0x9309FF9D, 0x0A00AE27, 0x7D079EB1, 
                       0xF00F9344, 0x8708A3D2, 0x1E01F268, 0x6906C2FE, 0xF762575D, 0x806567CB, 0x196C3671, 0x6E6B06E7, 
                       0xFED41B76, 0x89D32BE0, 0x10DA7A5A, 0x67DD4ACC, 0xF9B9DF6F, 0x8EBEEFF9, 0x17B7BE43, 0x60B08ED5, 
                       0xD6D6A3E8, 0xA1D1937E, 0x38D8C2C4, 0x4FDFF252, 0xD1BB67F1, 0xA6BC5767, 0x3FB506DD, 0x48B2364B, 
                       0xD80D2BDA, 0xAF0A1B4C, 0x36034AF6, 0x41047A60, 0xDF60EFC3, 0xA867DF55, 0x316E8EEF, 0x4669BE79, 
                       0xCB61B38C, 0xBC66831A, 0x256FD2A0, 0x5268E236, 0xCC0C7795, 0xBB0B4703, 0x220216B9, 0x5505262F, 
                       0xC5BA3BBE, 0xB2BD0B28, 0x2BB45A92, 0x5CB36A04, 0xC2D7FFA7, 0xB5D0CF31, 0x2CD99E8B, 0x5BDEAE1D, 
                       0x9B64C2B0, 0xEC63F226, 0x756AA39C, 0x026D930A, 0x9C0906A9, 0xEB0E363F, 0x72076785, 0x05005713, 
                       0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0x0CB61B38, 0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0x0BDBDF21, 
                       0x86D3D2D4, 0xF1D4E242, 0x68DDB3F8, 0x1FDA836E, 0x81BE16CD, 0xF6B9265B, 0x6FB077E1, 0x18B74777, 
                       0x88085AE6, 0xFF0F6A70, 0x66063BCA, 0x11010B5C, 0x8F659EFF, 0xF862AE69, 0x616BFFD3, 0x166CCF45, 
                       0xA00AE278, 0xD70DD2EE, 0x4E048354, 0x3903B3C2, 0xA7672661, 0xD06016F7, 0x4969474D, 0x3E6E77DB, 
                       0xAED16A4A, 0xD9D65ADC, 0x40DF0B66, 0x37D83BF0, 0xA9BCAE53, 0xDEBB9EC5, 0x47B2CF7F, 0x30B5FFE9, 
                       0xBDBDF21C, 0xCABAC28A, 0x53B39330, 0x24B4A3A6, 0xBAD03605, 0xCDD70693, 0x54DE5729, 0x23D967BF, 
                       0xB3667A2E, 0xC4614AB8, 0x5D681B02, 0x2A6F2B94, 0xB40BBE37, 0xC30C8EA1, 0x5A05DF1B, 0x2D02EF8D];
       
          var crc = -1, y = 0, n = a.length,i;
  
          for (i = from; i < to; i++) {
              y = (crc ^ a[i]) & 0xFF;
              crc = (crc >>> 8) ^ table[y];
          }
       
          return crc ^ (-1);
      }
  
      var h = img[0].length, w = img[0][0].length, s1, s2, next,k,length,a,b,i,j,adler32,crc32;
      var stream = [
                    137, 80, 78, 71, 13, 10, 26, 10,                           //  0: PNG signature
                    0,0,0,13,                                                  //  8: IHDR Chunk length
                    73, 72, 68, 82,                                            // 12: "IHDR" 
                    (w >> 24) & 255, (w >> 16) & 255, (w >> 8) & 255, w&255,   // 16: Width
                    (h >> 24) & 255, (h >> 16) & 255, (h >> 8) & 255, h&255,   // 20: Height
                    8,                                                         // 24: bit depth
                    2,                                                         // 25: RGB
                    0,                                                         // 26: deflate
                    0,                                                         // 27: no filter
                    0,                                                         // 28: no interlace
                    -1,-2,-3,-4,                                               // 29: CRC
                    -5,-6,-7,-8,                                               // 33: IDAT Chunk length
                    73, 68, 65, 84,                                            // 37: "IDAT"
                    // RFC 1950 header starts here
                    8,                                                         // 41: RFC1950 CMF
                    29                                                         // 42: RFC1950 FLG
                    ];
      crc32 = crc32Array(stream,12,29);
      stream[29] = (crc32>>24)&255;
      stream[30] = (crc32>>16)&255;
      stream[31] = (crc32>>8)&255;
      stream[32] = (crc32)&255;
      s1 = 1;
      s2 = 0;
      for(i=0;i<h;i++) {
          if(i<h-1) { stream.push(0); }
          else { stream.push(1); }
          a = (3*w+1+(i===0))&255; b = ((3*w+1+(i===0))>>8)&255;
          stream.push(a); stream.push(b);
          stream.push((~a)&255); stream.push((~b)&255);
          if(i===0) stream.push(0);
          for(j=0;j<w;j++) {
              for(k=0;k<3;k++) {
                  a = img[k][i][j];
                  if(a>255) a = 255;
                  else if(a<0) a=0;
                  else a = Math.round(a);
                  s1 = (s1 + a )%65521;
                  s2 = (s2 + s1)%65521;
                  stream.push(a);
              }
          }
          stream.push(0);
      }
      adler32 = (s2<<16)+s1;
      stream.push((adler32>>24)&255);
      stream.push((adler32>>16)&255);
      stream.push((adler32>>8)&255);
      stream.push((adler32)&255);
      length = stream.length - 41;
      stream[33] = (length>>24)&255;
      stream[34] = (length>>16)&255;
      stream[35] = (length>>8)&255;
      stream[36] = (length)&255;
      crc32 = crc32Array(stream,37);
      stream.push((crc32>>24)&255);
      stream.push((crc32>>16)&255);
      stream.push((crc32>>8)&255);
      stream.push((crc32)&255);
      stream.push(0);
      stream.push(0);
      stream.push(0);
      stream.push(0);
  //    a = stream.length;
      stream.push(73);  // I
      stream.push(69);  // E
      stream.push(78);  // N
      stream.push(68);  // D
      stream.push(174); // CRC1
      stream.push(66);  // CRC2
      stream.push(96);  // CRC3
      stream.push(130); // CRC4
      return 'data:image/png;base64,'+base64(stream);
  }
  
  // 2. Linear algebra with Arrays.
  numeric._dim = function _dim(x) {
      var ret = [];
      while(typeof x === "object") { ret.push(x.length); x = x[0]; }
      return ret;
  }
  
  numeric.dim = function dim(x) {
      var y,z;
      if(typeof x === "object") {
          y = x[0];
          if(typeof y === "object") {
              z = y[0];
              if(typeof z === "object") {
                  return numeric._dim(x);
              }
              return [x.length,y.length];
          }
          return [x.length];
      }
      return [];
  }
  
  numeric.mapreduce = function mapreduce(body,init) {
      return Function('x','accum','_s','_k',
              'if(typeof accum === "undefined") accum = '+init+';\n'+
              'if(typeof x === "number") { var xi = x; '+body+'; return accum; }\n'+
              'if(typeof _s === "undefined") _s = numeric.dim(x);\n'+
              'if(typeof _k === "undefined") _k = 0;\n'+
              'var _n = _s[_k];\n'+
              'var i,xi;\n'+
              'if(_k < _s.length-1) {\n'+
              '    for(i=_n-1;i>=0;i--) {\n'+
              '        accum = arguments.callee(x[i],accum,_s,_k+1);\n'+
              '    }'+
              '    return accum;\n'+
              '}\n'+
              'for(i=_n-1;i>=1;i-=2) { \n'+
              '    xi = x[i];\n'+
              '    '+body+';\n'+
              '    xi = x[i-1];\n'+
              '    '+body+';\n'+
              '}\n'+
              'if(i === 0) {\n'+
              '    xi = x[i];\n'+
              '    '+body+'\n'+
              '}\n'+
              'return accum;'
              );
  }
  numeric.mapreduce2 = function mapreduce2(body,setup) {
      return Function('x',
              'var n = x.length;\n'+
              'var i,xi;\n'+setup+';\n'+
              'for(i=n-1;i!==-1;--i) { \n'+
              '    xi = x[i];\n'+
              '    '+body+';\n'+
              '}\n'+
              'return accum;'
              );
  }
  
  
  numeric.same = function same(x,y) {
      var i,n;
      if(!(x instanceof Array) || !(y instanceof Array)) { return false; }
      n = x.length;
      if(n !== y.length) { return false; }
      for(i=0;i<n;i++) {
          if(x[i] === y[i]) { continue; }
          if(typeof x[i] === "object") { if(!same(x[i],y[i])) return false; }
          else { return false; }
      }
      return true;
  }
  
  numeric.rep = function rep(s,v,k) {
      if(typeof k === "undefined") { k=0; }
      var n = s[k], ret = Array(n), i;
      if(k === s.length-1) {
          for(i=n-2;i>=0;i-=2) { ret[i+1] = v; ret[i] = v; }
          if(i===-1) { ret[0] = v; }
          return ret;
      }
      for(i=n-1;i>=0;i--) { ret[i] = numeric.rep(s,v,k+1); }
      return ret;
  }
  
  
  numeric.dotMMsmall = function dotMMsmall(x,y) {
      var i,j,k,p,q,r,ret,foo,bar,woo,i0,k0,p0,r0;
      p = x.length; q = y.length; r = y[0].length;
      ret = Array(p);
      for(i=p-1;i>=0;i--) {
          foo = Array(r);
          bar = x[i];
          for(k=r-1;k>=0;k--) {
              woo = bar[q-1]*y[q-1][k];
              for(j=q-2;j>=1;j-=2) {
                  i0 = j-1;
                  woo += bar[j]*y[j][k] + bar[i0]*y[i0][k];
              }
              if(j===0) { woo += bar[0]*y[0][k]; }
              foo[k] = woo;
          }
          ret[i] = foo;
      }
      return ret;
  }
  numeric._getCol = function _getCol(A,j,x) {
      var n = A.length, i;
      for(i=n-1;i>0;--i) {
          x[i] = A[i][j];
          --i;
          x[i] = A[i][j];
      }
      if(i===0) x[0] = A[0][j];
  }
  numeric.dotMMbig = function dotMMbig(x,y){
      var gc = numeric._getCol, p = y.length, v = Array(p);
      var m = x.length, n = y[0].length, A = new Array(m), xj;
      var VV = numeric.dotVV;
      var i,j,k,z;
      --p;
      --m;
      for(i=m;i!==-1;--i) A[i] = Array(n);
      --n;
      for(i=n;i!==-1;--i) {
          gc(y,i,v);
          for(j=m;j!==-1;--j) {
              z=0;
              xj = x[j];
              A[j][i] = VV(xj,v);
          }
      }
      return A;
  }
  
  numeric.dotMV = function dotMV(x,y) {
      var p = x.length, q = y.length,i;
      var ret = Array(p), dotVV = numeric.dotVV;
      for(i=p-1;i>=0;i--) { ret[i] = dotVV(x[i],y); }
      return ret;
  }
  
  numeric.dotVM = function dotVM(x,y) {
      var i,j,k,p,q,r,ret,foo,bar,woo,i0,k0,p0,r0,s1,s2,s3,baz,accum;
      p = x.length; q = y[0].length;
      ret = Array(q);
      for(k=q-1;k>=0;k--) {
          woo = x[p-1]*y[p-1][k];
          for(j=p-2;j>=1;j-=2) {
              i0 = j-1;
              woo += x[j]*y[j][k] + x[i0]*y[i0][k];
          }
          if(j===0) { woo += x[0]*y[0][k]; }
          ret[k] = woo;
      }
      return ret;
  }
  
  numeric.dotVV = function dotVV(x,y) {
      var i,n=x.length,i1,ret = x[n-1]*y[n-1];
      for(i=n-2;i>=1;i-=2) {
          i1 = i-1;
          ret += x[i]*y[i] + x[i1]*y[i1];
      }
      if(i===0) { ret += x[0]*y[0]; }
      return ret;
  }
  
  numeric.dot = function dot(x,y) {
      var d = numeric.dim;
      switch(d(x).length*1000+d(y).length) {
      case 2002:
          if(y.length < 10) return numeric.dotMMsmall(x,y);
          else return numeric.dotMMbig(x,y);
      case 2001: return numeric.dotMV(x,y);
      case 1002: return numeric.dotVM(x,y);
      case 1001: return numeric.dotVV(x,y);
      case 1000: return numeric.mulVS(x,y);
      case 1: return numeric.mulSV(x,y);
      case 0: return x*y;
      default: throw new Error('numeric.dot only works on vectors and matrices');
      }
  }
  
  numeric.diag = function diag(d) {
      var i,i1,j,n = d.length, A = Array(n), Ai;
      for(i=n-1;i>=0;i--) {
          Ai = Array(n);
          i1 = i+2;
          for(j=n-1;j>=i1;j-=2) {
              Ai[j] = 0;
              Ai[j-1] = 0;
          }
          if(j>i) { Ai[j] = 0; }
          Ai[i] = d[i];
          for(j=i-1;j>=1;j-=2) {
              Ai[j] = 0;
              Ai[j-1] = 0;
          }
          if(j===0) { Ai[0] = 0; }
          A[i] = Ai;
      }
      return A;
  }
  numeric.getDiag = function(A) {
      var n = Math.min(A.length,A[0].length),i,ret = Array(n);
      for(i=n-1;i>=1;--i) {
          ret[i] = A[i][i];
          --i;
          ret[i] = A[i][i];
      }
      if(i===0) {
          ret[0] = A[0][0];
      }
      return ret;
  }
  
  numeric.identity = function identity(n) { return numeric.diag(numeric.rep([n],1)); }
  numeric.pointwise = function pointwise(params,body,setup) {
      if(typeof setup === "undefined") { setup = ""; }
      var fun = [];
      var k;
      var avec = /\[i\]$/,p,thevec = '';
      var haveret = false;
      for(k=0;k<params.length;k++) {
          if(avec.test(params[k])) {
              p = params[k].substring(0,params[k].length-3);
              thevec = p;
          } else { p = params[k]; }
          if(p==='ret') haveret = true;
          fun.push(p);
      }
      fun[params.length] = '_s';
      fun[params.length+1] = '_k';
      fun[params.length+2] = (
              'if(typeof _s === "undefined") _s = numeric.dim('+thevec+');\n'+
              'if(typeof _k === "undefined") _k = 0;\n'+
              'var _n = _s[_k];\n'+
              'var i'+(haveret?'':', ret = Array(_n)')+';\n'+
              'if(_k < _s.length-1) {\n'+
              '    for(i=_n-1;i>=0;i--) ret[i] = arguments.callee('+params.join(',')+',_s,_k+1);\n'+
              '    return ret;\n'+
              '}\n'+
              setup+'\n'+
              'for(i=_n-1;i!==-1;--i) {\n'+
              '    '+body+'\n'+
              '}\n'+
              'return ret;'
              );
      return Function.apply(null,fun);
  }
  numeric.pointwise2 = function pointwise2(params,body,setup) {
      if(typeof setup === "undefined") { setup = ""; }
      var fun = [];
      var k;
      var avec = /\[i\]$/,p,thevec = '';
      var haveret = false;
      for(k=0;k<params.length;k++) {
          if(avec.test(params[k])) {
              p = params[k].substring(0,params[k].length-3);
              thevec = p;
          } else { p = params[k]; }
          if(p==='ret') haveret = true;
          fun.push(p);
      }
      fun[params.length] = (
              'var _n = '+thevec+'.length;\n'+
              'var i'+(haveret?'':', ret = Array(_n)')+';\n'+
              setup+'\n'+
              'for(i=_n-1;i!==-1;--i) {\n'+
              body+'\n'+
              '}\n'+
              'return ret;'
              );
      return Function.apply(null,fun);
  }
  numeric._biforeach = (function _biforeach(x,y,s,k,f) {
      if(k === s.length-1) { f(x,y); return; }
      var i,n=s[k];
      for(i=n-1;i>=0;i--) { _biforeach(typeof x==="object"?x[i]:x,typeof y==="object"?y[i]:y,s,k+1,f); }
  });
  numeric._biforeach2 = (function _biforeach2(x,y,s,k,f) {
      if(k === s.length-1) { return f(x,y); }
      var i,n=s[k],ret = Array(n);
      for(i=n-1;i>=0;--i) { ret[i] = _biforeach2(typeof x==="object"?x[i]:x,typeof y==="object"?y[i]:y,s,k+1,f); }
      return ret;
  });
  numeric._foreach = (function _foreach(x,s,k,f) {
      if(k === s.length-1) { f(x); return; }
      var i,n=s[k];
      for(i=n-1;i>=0;i--) { _foreach(x[i],s,k+1,f); }
  });
  numeric._foreach2 = (function _foreach2(x,s,k,f) {
      if(k === s.length-1) { return f(x); }
      var i,n=s[k], ret = Array(n);
      for(i=n-1;i>=0;i--) { ret[i] = _foreach2(x[i],s,k+1,f); }
      return ret;
  });
  
  /*numeric.anyV = numeric.mapreduce('if(xi) return true;','false');
  numeric.allV = numeric.mapreduce('if(!xi) return false;','true');
  numeric.any = function(x) { if(typeof x.length === "undefined") return x; return numeric.anyV(x); }
  numeric.all = function(x) { if(typeof x.length === "undefined") return x; return numeric.allV(x); }*/
  
  numeric.ops2 = {
          add: '+',
          sub: '-',
          mul: '*',
          div: '/',
          mod: '%',
          and: '&&',
          or:  '||',
          eq:  '===',
          neq: '!==',
          lt:  '<',
          gt:  '>',
          leq: '<=',
          geq: '>=',
          band: '&',
          bor: '|',
          bxor: '^',
          lshift: '<<',
          rshift: '>>',
          rrshift: '>>>'
  };
  numeric.opseq = {
          addeq: '+=',
          subeq: '-=',
          muleq: '*=',
          diveq: '/=',
          modeq: '%=',
          lshifteq: '<<=',
          rshifteq: '>>=',
          rrshifteq: '>>>=',
          bandeq: '&=',
          boreq: '|=',
          bxoreq: '^='
  };
  numeric.mathfuns = ['abs','acos','asin','atan','ceil','cos',
                      'exp','floor','log','round','sin','sqrt','tan',
                      'isNaN','isFinite'];
  numeric.mathfuns2 = ['atan2','pow','max','min'];
  numeric.ops1 = {
          neg: '-',
          not: '!',
          bnot: '~',
          clone: ''
  };
  numeric.mapreducers = {
          any: ['if(xi) return true;','var accum = false;'],
          all: ['if(!xi) return false;','var accum = true;'],
          sum: ['accum += xi;','var accum = 0;'],
          prod: ['accum *= xi;','var accum = 1;'],
          norm2Squared: ['accum += xi*xi;','var accum = 0;'],
          norminf: ['accum = max(accum,abs(xi));','var accum = 0, max = Math.max, abs = Math.abs;'],
          norm1: ['accum += abs(xi)','var accum = 0, abs = Math.abs;'],
          sup: ['accum = max(accum,xi);','var accum = -Infinity, max = Math.max;'],
          inf: ['accum = min(accum,xi);','var accum = Infinity, min = Math.min;']
  };
  
  (function () {
      var i,o;
      for(i=0;i<numeric.mathfuns2.length;++i) {
          o = numeric.mathfuns2[i];
          numeric.ops2[o] = o;
      }
      for(i in numeric.ops2) {
          if(numeric.ops2.hasOwnProperty(i)) {
              o = numeric.ops2[i];
              var code, codeeq, setup = '';
              if(numeric.myIndexOf.call(numeric.mathfuns2,i)!==-1) {
                  setup = 'var '+o+' = Math.'+o+';\n';
                  code = function(r,x,y) { return r+' = '+o+'('+x+','+y+')'; };
                  codeeq = function(x,y) { return x+' = '+o+'('+x+','+y+')'; };
              } else {
                  code = function(r,x,y) { return r+' = '+x+' '+o+' '+y; };
                  if(numeric.opseq.hasOwnProperty(i+'eq')) {
                      codeeq = function(x,y) { return x+' '+o+'= '+y; };
                  } else {
                      codeeq = function(x,y) { return x+' = '+x+' '+o+' '+y; };                    
                  }
              }
              numeric[i+'VV'] = numeric.pointwise2(['x[i]','y[i]'],code('ret[i]','x[i]','y[i]'),setup);
              numeric[i+'SV'] = numeric.pointwise2(['x','y[i]'],code('ret[i]','x','y[i]'),setup);
              numeric[i+'VS'] = numeric.pointwise2(['x[i]','y'],code('ret[i]','x[i]','y'),setup);
              numeric[i] = Function(
                      'var n = arguments.length, i, x = arguments[0], y;\n'+
                      'var VV = numeric.'+i+'VV, VS = numeric.'+i+'VS, SV = numeric.'+i+'SV;\n'+
                      'var dim = numeric.dim;\n'+
                      'for(i=1;i!==n;++i) { \n'+
                      '  y = arguments[i];\n'+
                      '  if(typeof x === "object") {\n'+
                      '      if(typeof y === "object") x = numeric._biforeach2(x,y,dim(x),0,VV);\n'+
                      '      else x = numeric._biforeach2(x,y,dim(x),0,VS);\n'+
                      '  } else if(typeof y === "object") x = numeric._biforeach2(x,y,dim(y),0,SV);\n'+
                      '  else '+codeeq('x','y')+'\n'+
                      '}\nreturn x;\n');
              numeric[o] = numeric[i];
              numeric[i+'eqV'] = numeric.pointwise2(['ret[i]','x[i]'], codeeq('ret[i]','x[i]'),setup);
              numeric[i+'eqS'] = numeric.pointwise2(['ret[i]','x'], codeeq('ret[i]','x'),setup);
              numeric[i+'eq'] = Function(
                      'var n = arguments.length, i, x = arguments[0], y;\n'+
                      'var V = numeric.'+i+'eqV, S = numeric.'+i+'eqS\n'+
                      'var s = numeric.dim(x);\n'+
                      'for(i=1;i!==n;++i) { \n'+
                      '  y = arguments[i];\n'+
                      '  if(typeof y === "object") numeric._biforeach(x,y,s,0,V);\n'+
                      '  else numeric._biforeach(x,y,s,0,S);\n'+
                      '}\nreturn x;\n');
          }
      }
      for(i=0;i<numeric.mathfuns2.length;++i) {
          o = numeric.mathfuns2[i];
          delete numeric.ops2[o];
      }
      for(i=0;i<numeric.mathfuns.length;++i) {
          o = numeric.mathfuns[i];
          numeric.ops1[o] = o;
      }
      for(i in numeric.ops1) {
          if(numeric.ops1.hasOwnProperty(i)) {
              setup = '';
              o = numeric.ops1[i];
              if(numeric.myIndexOf.call(numeric.mathfuns,i)!==-1) {
                  if(Math.hasOwnProperty(o)) setup = 'var '+o+' = Math.'+o+';\n';
              }
              numeric[i+'eqV'] = numeric.pointwise2(['ret[i]'],'ret[i] = '+o+'(ret[i]);',setup);
              numeric[i+'eq'] = Function('x',
                      'if(typeof x !== "object") return '+o+'x\n'+
                      'var i;\n'+
                      'var V = numeric.'+i+'eqV;\n'+
                      'var s = numeric.dim(x);\n'+
                      'numeric._foreach(x,s,0,V);\n'+
                      'return x;\n');
              numeric[i+'V'] = numeric.pointwise2(['x[i]'],'ret[i] = '+o+'(x[i]);',setup);
              numeric[i] = Function('x',
                      'if(typeof x !== "object") return '+o+'(x)\n'+
                      'var i;\n'+
                      'var V = numeric.'+i+'V;\n'+
                      'var s = numeric.dim(x);\n'+
                      'return numeric._foreach2(x,s,0,V);\n');
          }
      }
      for(i=0;i<numeric.mathfuns.length;++i) {
          o = numeric.mathfuns[i];
          delete numeric.ops1[o];
      }
      for(i in numeric.mapreducers) {
          if(numeric.mapreducers.hasOwnProperty(i)) {
              o = numeric.mapreducers[i];
              numeric[i+'V'] = numeric.mapreduce2(o[0],o[1]);
              numeric[i] = Function('x','s','k',
                      o[1]+
                      'if(typeof x !== "object") {'+
                      '    xi = x;\n'+
                      o[0]+';\n'+
                      '    return accum;\n'+
                      '}'+
                      'if(typeof s === "undefined") s = numeric.dim(x);\n'+
                      'if(typeof k === "undefined") k = 0;\n'+
                      'if(k === s.length-1) return numeric.'+i+'V(x);\n'+
                      'var xi;\n'+
                      'var n = x.length, i;\n'+
                      'for(i=n-1;i!==-1;--i) {\n'+
                      '   xi = arguments.callee(x[i]);\n'+
                      o[0]+';\n'+
                      '}\n'+
                      'return accum;\n');
          }
      }
  }());
  
  numeric.truncVV = numeric.pointwise(['x[i]','y[i]'],'ret[i] = round(x[i]/y[i])*y[i];','var round = Math.round;');
  numeric.truncVS = numeric.pointwise(['x[i]','y'],'ret[i] = round(x[i]/y)*y;','var round = Math.round;');
  numeric.truncSV = numeric.pointwise(['x','y[i]'],'ret[i] = round(x/y[i])*y[i];','var round = Math.round;');
  numeric.trunc = function trunc(x,y) {
      if(typeof x === "object") {
          if(typeof y === "object") return numeric.truncVV(x,y);
          return numeric.truncVS(x,y);
      }
      if (typeof y === "object") return numeric.truncSV(x,y);
      return Math.round(x/y)*y;
  }
  
  numeric.inv = function inv(x) {
      var s = numeric.dim(x), abs = Math.abs, m = s[0], n = s[1];
      var A = numeric.clone(x), Ai, Aj;
      var I = numeric.identity(m), Ii, Ij;
      var i,j,k,x;
      for(j=0;j<n;++j) {
          var i0 = -1;
          var v0 = -1;
          for(i=j;i!==m;++i) { k = abs(A[i][j]); if(k>v0) { i0 = i; v0 = k; } }
          Aj = A[i0]; A[i0] = A[j]; A[j] = Aj;
          Ij = I[i0]; I[i0] = I[j]; I[j] = Ij;
          x = Aj[j];
          for(k=j;k!==n;++k)    Aj[k] /= x; 
          for(k=n-1;k!==-1;--k) Ij[k] /= x;
          for(i=m-1;i!==-1;--i) {
              if(i!==j) {
                  Ai = A[i];
                  Ii = I[i];
                  x = Ai[j];
                  for(k=j+1;k!==n;++k)  Ai[k] -= Aj[k]*x;
                  for(k=n-1;k>0;--k) { Ii[k] -= Ij[k]*x; --k; Ii[k] -= Ij[k]*x; }
                  if(k===0) Ii[0] -= Ij[0]*x;
              }
          }
      }
      return I;
  }
  
  numeric.det = function det(x) {
      var s = numeric.dim(x);
      if(s.length !== 2 || s[0] !== s[1]) { throw new Error('numeric: det() only works on square matrices'); }
      var n = s[0], ret = 1,i,j,k,A = numeric.clone(x),Aj,Ai,alpha,temp,k1,k2,k3;
      for(j=0;j<n-1;j++) {
          k=j;
          for(i=j+1;i<n;i++) { if(Math.abs(A[i][j]) > Math.abs(A[k][j])) { k = i; } }
          if(k !== j) {
              temp = A[k]; A[k] = A[j]; A[j] = temp;
              ret *= -1;
          }
          Aj = A[j];
          for(i=j+1;i<n;i++) {
              Ai = A[i];
              alpha = Ai[j]/Aj[j];
              for(k=j+1;k<n-1;k+=2) {
                  k1 = k+1;
                  Ai[k] -= Aj[k]*alpha;
                  Ai[k1] -= Aj[k1]*alpha;
              }
              if(k!==n) { Ai[k] -= Aj[k]*alpha; }
          }
          if(Aj[j] === 0) { return 0; }
          ret *= Aj[j];
      }
      return ret*A[j][j];
  }
  
  numeric.transpose = function transpose(x) {
      var i,j,m = x.length,n = x[0].length, ret=Array(n),A0,A1,Bj;
      for(j=0;j<n;j++) ret[j] = Array(m);
      for(i=m-1;i>=1;i-=2) {
          A1 = x[i];
          A0 = x[i-1];
          for(j=n-1;j>=1;--j) {
              Bj = ret[j]; Bj[i] = A1[j]; Bj[i-1] = A0[j];
              --j;
              Bj = ret[j]; Bj[i] = A1[j]; Bj[i-1] = A0[j];
          }
          if(j===0) {
              Bj = ret[0]; Bj[i] = A1[0]; Bj[i-1] = A0[0];
          }
      }
      if(i===0) {
          A0 = x[0];
          for(j=n-1;j>=1;--j) {
              ret[j][0] = A0[j];
              --j;
              ret[j][0] = A0[j];
          }
          if(j===0) { ret[0][0] = A0[0]; }
      }
      return ret;
  }
  numeric.negtranspose = function negtranspose(x) {
      var i,j,m = x.length,n = x[0].length, ret=Array(n),A0,A1,Bj;
      for(j=0;j<n;j++) ret[j] = Array(m);
      for(i=m-1;i>=1;i-=2) {
          A1 = x[i];
          A0 = x[i-1];
          for(j=n-1;j>=1;--j) {
              Bj = ret[j]; Bj[i] = -A1[j]; Bj[i-1] = -A0[j];
              --j;
              Bj = ret[j]; Bj[i] = -A1[j]; Bj[i-1] = -A0[j];
          }
          if(j===0) {
              Bj = ret[0]; Bj[i] = -A1[0]; Bj[i-1] = -A0[0];
          }
      }
      if(i===0) {
          A0 = x[0];
          for(j=n-1;j>=1;--j) {
              ret[j][0] = -A0[j];
              --j;
              ret[j][0] = -A0[j];
          }
          if(j===0) { ret[0][0] = -A0[0]; }
      }
      return ret;
  }
  
  numeric._random = function _random(s,k) {
      var i,n=s[k],ret=Array(n), rnd;
      if(k === s.length-1) {
          rnd = Math.random;
          for(i=n-1;i>=1;i-=2) {
              ret[i] = rnd();
              ret[i-1] = rnd();
          }
          if(i===0) { ret[0] = rnd(); }
          return ret;
      }
      for(i=n-1;i>=0;i--) ret[i] = _random(s,k+1);
      return ret;
  }
  numeric.random = function random(s) { return numeric._random(s,0); }
  
  numeric.norm2 = function norm2(x) { return Math.sqrt(numeric.norm2Squared(x)); }
  
  numeric.linspace = function linspace(a,b,n) {
      if(typeof n === "undefined") n = Math.max(Math.round(b-a)+1,1);
      if(n<2) { return n===1?[a]:[]; }
      var i,ret = Array(n);
      n--;
      for(i=n;i>=0;i--) { ret[i] = (i*b+(n-i)*a)/n; }
      return ret;
  }
  
  numeric.getBlock = function getBlock(x,from,to) {
      var s = numeric.dim(x);
      function foo(x,k) {
          var i,a = from[k], n = to[k]-a, ret = Array(n);
          if(k === s.length-1) {
              for(i=n;i>=0;i--) { ret[i] = x[i+a]; }
              return ret;
          }
          for(i=n;i>=0;i--) { ret[i] = foo(x[i+a],k+1); }
          return ret;
      }
      return foo(x,0);
  }
  
  numeric.setBlock = function setBlock(x,from,to,B) {
      var s = numeric.dim(x);
      function foo(x,y,k) {
          var i,a = from[k], n = to[k]-a;
          if(k === s.length-1) { for(i=n;i>=0;i--) { x[i+a] = y[i]; } }
          for(i=n;i>=0;i--) { foo(x[i+a],y[i],k+1); }
      }
      foo(x,B,0);
      return x;
  }
  
  numeric.getRange = function getRange(A,I,J) {
      var m = I.length, n = J.length;
      var i,j;
      var B = Array(m), Bi, AI;
      for(i=m-1;i!==-1;--i) {
          B[i] = Array(n);
          Bi = B[i];
          AI = A[I[i]];
          for(j=n-1;j!==-1;--j) Bi[j] = AI[J[j]];
      }
      return B;
  }
  
  numeric.blockMatrix = function blockMatrix(X) {
      var s = numeric.dim(X);
      if(s.length<4) return numeric.blockMatrix([X]);
      var m=s[0],n=s[1],M,N,i,j,Xij;
      M = 0; N = 0;
      for(i=0;i<m;++i) M+=X[i][0].length;
      for(j=0;j<n;++j) N+=X[0][j][0].length;
      var Z = Array(M);
      for(i=0;i<M;++i) Z[i] = Array(N);
      var I=0,J,ZI,k,l,Xijk;
      for(i=0;i<m;++i) {
          J=N;
          for(j=n-1;j!==-1;--j) {
              Xij = X[i][j];
              J -= Xij[0].length;
              for(k=Xij.length-1;k!==-1;--k) {
                  Xijk = Xij[k];
                  ZI = Z[I+k];
                  for(l = Xijk.length-1;l!==-1;--l) ZI[J+l] = Xijk[l];
              }
          }
          I += X[i][0].length;
      }
      return Z;
  }
  
  numeric.tensor = function tensor(x,y) {
      if(typeof x === "number" || typeof y === "number") return numeric.mul(x,y);
      var s1 = numeric.dim(x), s2 = numeric.dim(y);
      if(s1.length !== 1 || s2.length !== 1) {
          throw new Error('numeric: tensor product is only defined for vectors');
      }
      var m = s1[0], n = s2[0], A = Array(m), Ai, i,j,xi;
      for(i=m-1;i>=0;i--) {
          Ai = Array(n);
          xi = x[i];
          for(j=n-1;j>=3;--j) {
              Ai[j] = xi * y[j];
              --j;
              Ai[j] = xi * y[j];
              --j;
              Ai[j] = xi * y[j];
              --j;
              Ai[j] = xi * y[j];
          }
          while(j>=0) { Ai[j] = xi * y[j]; --j; }
          A[i] = Ai;
      }
      return A;
  }
  
  // 3. The Tensor type T
  numeric.T = function T(x,y) { this.x = x; this.y = y; }
  numeric.t = function t(x,y) { return new numeric.T(x,y); }
  
  numeric.Tbinop = function Tbinop(rr,rc,cr,cc,setup) {
      var io = numeric.indexOf;
      if(typeof setup !== "string") {
          var k;
          setup = '';
          for(k in numeric) {
              if(numeric.hasOwnProperty(k) && (rr.indexOf(k)>=0 || rc.indexOf(k)>=0 || cr.indexOf(k)>=0 || cc.indexOf(k)>=0) && k.length>1) {
                  setup += 'var '+k+' = numeric.'+k+';\n';
              }
          }
      }
      return Function(['y'],
              'var x = this;\n'+
              'if(!(y instanceof numeric.T)) { y = new numeric.T(y); }\n'+
              setup+'\n'+
              'if(x.y) {'+
              '  if(y.y) {'+
              '    return new numeric.T('+cc+');\n'+
              '  }\n'+
              '  return new numeric.T('+cr+');\n'+
              '}\n'+
              'if(y.y) {\n'+
              '  return new numeric.T('+rc+');\n'+
              '}\n'+
              'return new numeric.T('+rr+');\n'
      );
  }
  
  numeric.T.prototype.add = numeric.Tbinop(
          'add(x.x,y.x)',
          'add(x.x,y.x),y.y',
          'add(x.x,y.x),x.y',
          'add(x.x,y.x),add(x.y,y.y)');
  numeric.T.prototype.sub = numeric.Tbinop(
          'sub(x.x,y.x)',
          'sub(x.x,y.x),neg(y.y)',
          'sub(x.x,y.x),x.y',
          'sub(x.x,y.x),sub(x.y,y.y)');
  numeric.T.prototype.mul = numeric.Tbinop(
          'mul(x.x,y.x)',
          'mul(x.x,y.x),mul(x.x,y.y)',
          'mul(x.x,y.x),mul(x.y,y.x)',
          'sub(mul(x.x,y.x),mul(x.y,y.y)),add(mul(x.x,y.y),mul(x.y,y.x))');
  
  numeric.T.prototype.reciprocal = function reciprocal() {
      var mul = numeric.mul, div = numeric.div;
      if(this.y) {
          var d = numeric.add(mul(this.x,this.x),mul(this.y,this.y));
          return new numeric.T(div(this.x,d),div(numeric.neg(this.y),d));
      }
      return new T(div(1,this.x));
  }
  numeric.T.prototype.div = function div(y) {
      if(!(y instanceof numeric.T)) y = new numeric.T(y);
      if(y.y) { return this.mul(y.reciprocal()); }
      var div = numeric.div;
      if(this.y) { return new numeric.T(div(this.x,y.x),div(this.y,y.x)); }
      return new numeric.T(div(this.x,y.x));
  }
  numeric.T.prototype.dot = numeric.Tbinop(
          'dot(x.x,y.x)',
          'dot(x.x,y.x),dot(x.x,y.y)',
          'dot(x.x,y.x),dot(x.y,y.x)',
          'sub(dot(x.x,y.x),dot(x.y,y.y)),add(dot(x.x,y.y),dot(x.y,y.x))'
          );
  numeric.T.prototype.transpose = function transpose() {
      var t = numeric.transpose, x = this.x, y = this.y;
      if(y) { return new numeric.T(t(x),t(y)); }
      return new numeric.T(t(x));
  }
  numeric.T.prototype.transjugate = function transjugate() {
      var t = numeric.transpose, x = this.x, y = this.y;
      if(y) { return new numeric.T(t(x),numeric.negtranspose(y)); }
      return new numeric.T(t(x));
  }
  numeric.Tunop = function Tunop(r,c,s) {
      if(typeof s !== "string") { s = ''; }
      return Function(
              'var x = this;\n'+
              s+'\n'+
              'if(x.y) {'+
              '  '+c+';\n'+
              '}\n'+
              r+';\n'
      );
  }
  
  numeric.T.prototype.exp = numeric.Tunop(
          'return new numeric.T(ex)',
          'return new numeric.T(mul(cos(x.y),ex),mul(sin(x.y),ex))',
          'var ex = numeric.exp(x.x), cos = numeric.cos, sin = numeric.sin, mul = numeric.mul;');
  numeric.T.prototype.conj = numeric.Tunop(
          'return new numeric.T(x.x);',
          'return new numeric.T(x.x,numeric.neg(x.y));');
  numeric.T.prototype.neg = numeric.Tunop(
          'return new numeric.T(neg(x.x));',
          'return new numeric.T(neg(x.x),neg(x.y));',
          'var neg = numeric.neg;');
  numeric.T.prototype.sin = numeric.Tunop(
          'return new numeric.T(numeric.sin(x.x))',
          'return x.exp().sub(x.neg().exp()).div(new numeric.T(0,2));');
  numeric.T.prototype.cos = numeric.Tunop(
          'return new numeric.T(numeric.cos(x.x))',
          'return x.exp().add(x.neg().exp()).div(2);');
  numeric.T.prototype.abs = numeric.Tunop(
          'return new numeric.T(numeric.abs(x.x));',
          'return new numeric.T(numeric.sqrt(numeric.add(mul(x.x,x.x),mul(x.y,x.y))));',
          'var mul = numeric.mul;');
  numeric.T.prototype.log = numeric.Tunop(
          'return new numeric.T(numeric.log(x.x));',
          'var theta = new numeric.T(numeric.atan2(x.y,x.x)), r = x.abs();\n'+
          'return new numeric.T(numeric.log(r.x),theta.x);');
  numeric.T.prototype.norm2 = numeric.Tunop(
          'return numeric.norm2(x.x);',
          'var f = numeric.norm2Squared;\n'+
          'return Math.sqrt(f(x.x)+f(x.y));');
  numeric.T.prototype.inv = function inv() {
      var A = this;
      if(typeof A.y === "undefined") { return new numeric.T(numeric.inv(A.x)); }
      var n = A.x.length, i, j, k;
      var Rx = numeric.identity(n),Ry = numeric.rep([n,n],0);
      var Ax = numeric.clone(A.x), Ay = numeric.clone(A.y);
      var Aix, Aiy, Ajx, Ajy, Rix, Riy, Rjx, Rjy;
      var i,j,k,d,d1,ax,ay,bx,by,temp;
      for(i=0;i<n;i++) {
          ax = Ax[i][i]; ay = Ay[i][i];
          d = ax*ax+ay*ay;
          k = i;
          for(j=i+1;j<n;j++) {
              ax = Ax[j][i]; ay = Ay[j][i];
              d1 = ax*ax+ay*ay;
              if(d1 > d) { k=j; d = d1; }
          }
          if(k!==i) {
              temp = Ax[i]; Ax[i] = Ax[k]; Ax[k] = temp;
              temp = Ay[i]; Ay[i] = Ay[k]; Ay[k] = temp;
              temp = Rx[i]; Rx[i] = Rx[k]; Rx[k] = temp;
              temp = Ry[i]; Ry[i] = Ry[k]; Ry[k] = temp;
          }
          Aix = Ax[i]; Aiy = Ay[i];
          Rix = Rx[i]; Riy = Ry[i];
          ax = Aix[i]; ay = Aiy[i];
          for(j=i+1;j<n;j++) {
              bx = Aix[j]; by = Aiy[j];
              Aix[j] = (bx*ax+by*ay)/d;
              Aiy[j] = (by*ax-bx*ay)/d;
          }
          for(j=0;j<n;j++) {
              bx = Rix[j]; by = Riy[j];
              Rix[j] = (bx*ax+by*ay)/d;
              Riy[j] = (by*ax-bx*ay)/d;
          }
          for(j=i+1;j<n;j++) {
              Ajx = Ax[j]; Ajy = Ay[j];
              Rjx = Rx[j]; Rjy = Ry[j];
              ax = Ajx[i]; ay = Ajy[i];
              for(k=i+1;k<n;k++) {
                  bx = Aix[k]; by = Aiy[k];
                  Ajx[k] -= bx*ax-by*ay;
                  Ajy[k] -= by*ax+bx*ay;
              }
              for(k=0;k<n;k++) {
                  bx = Rix[k]; by = Riy[k];
                  Rjx[k] -= bx*ax-by*ay;
                  Rjy[k] -= by*ax+bx*ay;
              }
          }
      }
      for(i=n-1;i>0;i--) {
          Rix = Rx[i]; Riy = Ry[i];
          for(j=i-1;j>=0;j--) {
              Rjx = Rx[j]; Rjy = Ry[j];
              ax = Ax[j][i]; ay = Ay[j][i];
              for(k=n-1;k>=0;k--) {
                  bx = Rix[k]; by = Riy[k];
                  Rjx[k] -= ax*bx - ay*by;
                  Rjy[k] -= ax*by + ay*bx;
              }
          }
      }
      return new numeric.T(Rx,Ry);
  }
  numeric.T.prototype.get = function get(i) {
      var x = this.x, y = this.y, k = 0, ik, n = i.length;
      if(y) {
          while(k<n) {
              ik = i[k];
              x = x[ik];
              y = y[ik];
              k++;
          }
          return new numeric.T(x,y);
      }
      while(k<n) {
          ik = i[k];
          x = x[ik];
          k++;
      }
      return new numeric.T(x);
  }
  numeric.T.prototype.set = function set(i,v) {
      var x = this.x, y = this.y, k = 0, ik, n = i.length, vx = v.x, vy = v.y;
      if(n===0) {
          if(vy) { this.y = vy; }
          else if(y) { this.y = undefined; }
          this.x = x;
          return this;
      }
      if(vy) {
          if(y) { /* ok */ }
          else {
              y = numeric.rep(numeric.dim(x),0);
              this.y = y;
          }
          while(k<n-1) {
              ik = i[k];
              x = x[ik];
              y = y[ik];
              k++;
          }
          ik = i[k];
          x[ik] = vx;
          y[ik] = vy;
          return this;
      }
      if(y) {
          while(k<n-1) {
              ik = i[k];
              x = x[ik];
              y = y[ik];
              k++;
          }
          ik = i[k];
          x[ik] = vx;
          if(vx instanceof Array) y[ik] = numeric.rep(numeric.dim(vx),0);
          else y[ik] = 0;
          return this;
      }
      while(k<n-1) {
          ik = i[k];
          x = x[ik];
          k++;
      }
      ik = i[k];
      x[ik] = vx;
      return this;
  }
  numeric.T.prototype.getRows = function getRows(i0,i1) {
      var n = i1-i0+1, j;
      var rx = Array(n), ry, x = this.x, y = this.y;
      for(j=i0;j<=i1;j++) { rx[j-i0] = x[j]; }
      if(y) {
          ry = Array(n);
          for(j=i0;j<=i1;j++) { ry[j-i0] = y[j]; }
          return new numeric.T(rx,ry);
      }
      return new numeric.T(rx);
  }
  numeric.T.prototype.setRows = function setRows(i0,i1,A) {
      var j;
      var rx = this.x, ry = this.y, x = A.x, y = A.y;
      for(j=i0;j<=i1;j++) { rx[j] = x[j-i0]; }
      if(y) {
          if(!ry) { ry = numeric.rep(numeric.dim(rx),0); this.y = ry; }
          for(j=i0;j<=i1;j++) { ry[j] = y[j-i0]; }
      } else if(ry) {
          for(j=i0;j<=i1;j++) { ry[j] = numeric.rep([x[j-i0].length],0); }
      }
      return this;
  }
  numeric.T.prototype.getRow = function getRow(k) {
      var x = this.x, y = this.y;
      if(y) { return new numeric.T(x[k],y[k]); }
      return new numeric.T(x[k]);
  }
  numeric.T.prototype.setRow = function setRow(i,v) {
      var rx = this.x, ry = this.y, x = v.x, y = v.y;
      rx[i] = x;
      if(y) {
          if(!ry) { ry = numeric.rep(numeric.dim(rx),0); this.y = ry; }
          ry[i] = y;
      } else if(ry) {
          ry = numeric.rep([x.length],0);
      }
      return this;
  }
  
  numeric.T.prototype.getBlock = function getBlock(from,to) {
      var x = this.x, y = this.y, b = numeric.getBlock;
      if(y) { return new numeric.T(b(x,from,to),b(y,from,to)); }
      return new numeric.T(b(x,from,to));
  }
  numeric.T.prototype.setBlock = function setBlock(from,to,A) {
      if(!(A instanceof numeric.T)) A = new numeric.T(A);
      var x = this.x, y = this.y, b = numeric.setBlock, Ax = A.x, Ay = A.y;
      if(Ay) {
          if(!y) { this.y = numeric.rep(numeric.dim(this),0); y = this.y; }
          b(x,from,to,Ax);
          b(y,from,to,Ay);
          return this;
      }
      b(x,from,to,Ax);
      if(y) b(y,from,to,numeric.rep(numeric.dim(Ax),0));
  }
  numeric.T.rep = function rep(s,v) {
      var T = numeric.T;
      if(!(v instanceof T)) v = new T(v);
      var x = v.x, y = v.y, r = numeric.rep;
      if(y) return new T(r(s,x),r(s,y));
      return new T(r(s,x));
  }
  numeric.T.diag = function diag(d) {
      if(!(d instanceof numeric.T)) d = new numeric.T(d);
      var x = d.x, y = d.y, diag = numeric.diag;
      if(y) return new numeric.T(diag(x),diag(y));
      return new numeric.T(diag(x));
  }
  numeric.T.eig = function eig() {
      if(this.y) { throw new Error('eig: not implemented for complex matrices.'); }
      return numeric.eig(this.x);
  }
  numeric.T.identity = function identity(n) { return new numeric.T(numeric.identity(n)); }
  numeric.T.prototype.getDiag = function getDiag() {
      var n = numeric;
      var x = this.x, y = this.y;
      if(y) { return new n.T(n.getDiag(x),n.getDiag(y)); }
      return new n.T(n.getDiag(x));
  }
  
  // 4. Eigenvalues of real matrices
  
  numeric.house = function house(x) {
      var v = numeric.clone(x);
      var s = x[0] >= 0 ? 1 : -1;
      var alpha = s*numeric.norm2(x);
      v[0] += alpha;
      var foo = numeric.norm2(v);
      if(foo === 0) { /* this should not happen */ throw new Error('eig: internal error'); }
      return numeric.div(v,foo);
  }
  
  numeric.toUpperHessenberg = function toUpperHessenberg(me) {
      var s = numeric.dim(me);
      if(s.length !== 2 || s[0] !== s[1]) { throw new Error('numeric: toUpperHessenberg() only works on square matrices'); }
      var m = s[0], i,j,k,x,v,A = numeric.clone(me),B,C,Ai,Ci,Q = numeric.identity(m),Qi;
      for(j=0;j<m-2;j++) {
          x = Array(m-j-1);
          for(i=j+1;i<m;i++) { x[i-j-1] = A[i][j]; }
          if(numeric.norm2(x)>0) {
              v = numeric.house(x);
              B = numeric.getBlock(A,[j+1,j],[m-1,m-1]);
              C = numeric.tensor(v,numeric.dot(v,B));
              for(i=j+1;i<m;i++) { Ai = A[i]; Ci = C[i-j-1]; for(k=j;k<m;k++) Ai[k] -= 2*Ci[k-j]; }
              B = numeric.getBlock(A,[0,j+1],[m-1,m-1]);
              C = numeric.tensor(numeric.dot(B,v),v);
              for(i=0;i<m;i++) { Ai = A[i]; Ci = C[i]; for(k=j+1;k<m;k++) Ai[k] -= 2*Ci[k-j-1]; }
              B = Array(m-j-1);
              for(i=j+1;i<m;i++) B[i-j-1] = Q[i];
              C = numeric.tensor(v,numeric.dot(v,B));
              for(i=j+1;i<m;i++) { Qi = Q[i]; Ci = C[i-j-1]; for(k=0;k<m;k++) Qi[k] -= 2*Ci[k]; }
          }
      }
      return {H:A, Q:Q};
  }
  
  numeric.epsilon = 2.220446049250313e-16;
  
  numeric.QRFrancis = function(H,maxiter) {
      if(typeof maxiter === "undefined") { maxiter = 10000; }
      H = numeric.clone(H);
      var H0 = numeric.clone(H);
      var s = numeric.dim(H),m=s[0],x,v,a,b,c,d,det,tr, Hloc, Q = numeric.identity(m), Qi, Hi, B, C, Ci,i,j,k,iter;
      if(m<3) { return {Q:Q, B:[ [0,m-1] ]}; }
      var epsilon = numeric.epsilon;
      for(iter=0;iter<maxiter;iter++) {
          for(j=0;j<m-1;j++) {
              if(Math.abs(H[j+1][j]) < epsilon*(Math.abs(H[j][j])+Math.abs(H[j+1][j+1]))) {
                  var QH1 = numeric.QRFrancis(numeric.getBlock(H,[0,0],[j,j]),maxiter);
                  var QH2 = numeric.QRFrancis(numeric.getBlock(H,[j+1,j+1],[m-1,m-1]),maxiter);
                  B = Array(j+1);
                  for(i=0;i<=j;i++) { B[i] = Q[i]; }
                  C = numeric.dot(QH1.Q,B);
                  for(i=0;i<=j;i++) { Q[i] = C[i]; }
                  B = Array(m-j-1);
                  for(i=j+1;i<m;i++) { B[i-j-1] = Q[i]; }
                  C = numeric.dot(QH2.Q,B);
                  for(i=j+1;i<m;i++) { Q[i] = C[i-j-1]; }
                  return {Q:Q,B:QH1.B.concat(numeric.add(QH2.B,j+1))};
              }
          }
          a = H[m-2][m-2]; b = H[m-2][m-1];
          c = H[m-1][m-2]; d = H[m-1][m-1];
          tr = a+d;
          det = (a*d-b*c);
          Hloc = numeric.getBlock(H, [0,0], [2,2]);
          if(tr*tr>=4*det) {
              var s1,s2;
              s1 = 0.5*(tr+Math.sqrt(tr*tr-4*det));
              s2 = 0.5*(tr-Math.sqrt(tr*tr-4*det));
              Hloc = numeric.add(numeric.sub(numeric.dot(Hloc,Hloc),
                                             numeric.mul(Hloc,s1+s2)),
                                 numeric.diag(numeric.rep([3],s1*s2)));
          } else {
              Hloc = numeric.add(numeric.sub(numeric.dot(Hloc,Hloc),
                                             numeric.mul(Hloc,tr)),
                                 numeric.diag(numeric.rep([3],det)));
          }
          x = [Hloc[0][0],Hloc[1][0],Hloc[2][0]];
          v = numeric.house(x);
          B = [H[0],H[1],H[2]];
          C = numeric.tensor(v,numeric.dot(v,B));
          for(i=0;i<3;i++) { Hi = H[i]; Ci = C[i]; for(k=0;k<m;k++) Hi[k] -= 2*Ci[k]; }
          B = numeric.getBlock(H, [0,0],[m-1,2]);
          C = numeric.tensor(numeric.dot(B,v),v);
          for(i=0;i<m;i++) { Hi = H[i]; Ci = C[i]; for(k=0;k<3;k++) Hi[k] -= 2*Ci[k]; }
          B = [Q[0],Q[1],Q[2]];
          C = numeric.tensor(v,numeric.dot(v,B));
          for(i=0;i<3;i++) { Qi = Q[i]; Ci = C[i]; for(k=0;k<m;k++) Qi[k] -= 2*Ci[k]; }
          var J;
          for(j=0;j<m-2;j++) {
              for(k=j;k<=j+1;k++) {
                  if(Math.abs(H[k+1][k]) < epsilon*(Math.abs(H[k][k])+Math.abs(H[k+1][k+1]))) {
                      var QH1 = numeric.QRFrancis(numeric.getBlock(H,[0,0],[k,k]),maxiter);
                      var QH2 = numeric.QRFrancis(numeric.getBlock(H,[k+1,k+1],[m-1,m-1]),maxiter);
                      B = Array(k+1);
                      for(i=0;i<=k;i++) { B[i] = Q[i]; }
                      C = numeric.dot(QH1.Q,B);
                      for(i=0;i<=k;i++) { Q[i] = C[i]; }
                      B = Array(m-k-1);
                      for(i=k+1;i<m;i++) { B[i-k-1] = Q[i]; }
                      C = numeric.dot(QH2.Q,B);
                      for(i=k+1;i<m;i++) { Q[i] = C[i-k-1]; }
                      return {Q:Q,B:QH1.B.concat(numeric.add(QH2.B,k+1))};
                  }
              }
              J = Math.min(m-1,j+3);
              x = Array(J-j);
              for(i=j+1;i<=J;i++) { x[i-j-1] = H[i][j]; }
              v = numeric.house(x);
              B = numeric.getBlock(H, [j+1,j],[J,m-1]);
              C = numeric.tensor(v,numeric.dot(v,B));
              for(i=j+1;i<=J;i++) { Hi = H[i]; Ci = C[i-j-1]; for(k=j;k<m;k++) Hi[k] -= 2*Ci[k-j]; }
              B = numeric.getBlock(H, [0,j+1],[m-1,J]);
              C = numeric.tensor(numeric.dot(B,v),v);
              for(i=0;i<m;i++) { Hi = H[i]; Ci = C[i]; for(k=j+1;k<=J;k++) Hi[k] -= 2*Ci[k-j-1]; }
              B = Array(J-j);
              for(i=j+1;i<=J;i++) B[i-j-1] = Q[i];
              C = numeric.tensor(v,numeric.dot(v,B));
              for(i=j+1;i<=J;i++) { Qi = Q[i]; Ci = C[i-j-1]; for(k=0;k<m;k++) Qi[k] -= 2*Ci[k]; }
          }
      }
      throw new Error('numeric: eigenvalue iteration does not converge -- increase maxiter?');
  }
  
  numeric.eig = function eig(A,maxiter) {
      var QH = numeric.toUpperHessenberg(A);
      var QB = numeric.QRFrancis(QH.H,maxiter);
      var T = numeric.T;
      var n = A.length,i,k,flag = false,B = QB.B,H = numeric.dot(QB.Q,numeric.dot(QH.H,numeric.transpose(QB.Q)));
      var Q = new T(numeric.dot(QB.Q,QH.Q)),Q0;
      var m = B.length,j;
      var a,b,c,d,p1,p2,disc,x,y,p,q,n1,n2;
      var sqrt = Math.sqrt;
      for(k=0;k<m;k++) {
          i = B[k][0];
          if(i === B[k][1]) {
              // nothing
          } else {
              j = i+1;
              a = H[i][i];
              b = H[i][j];
              c = H[j][i];
              d = H[j][j];
              if(b === 0 && c === 0) continue;
              p1 = -a-d;
              p2 = a*d-b*c;
              disc = p1*p1-4*p2;
              if(disc>=0) {
                  if(p1<0) x = -0.5*(p1-sqrt(disc));
                  else     x = -0.5*(p1+sqrt(disc));
                  n1 = (a-x)*(a-x)+b*b;
                  n2 = c*c+(d-x)*(d-x);
                  if(n1>n2) {
                      n1 = sqrt(n1);
                      p = (a-x)/n1;
                      q = b/n1;
                  } else {
                      n2 = sqrt(n2);
                      p = c/n2;
                      q = (d-x)/n2;
                  }
                  Q0 = new T([[q,-p],[p,q]]);
                  Q.setRows(i,j,Q0.dot(Q.getRows(i,j)));
              } else {
                  x = -0.5*p1;
                  y = 0.5*sqrt(-disc);
                  n1 = (a-x)*(a-x)+b*b;
                  n2 = c*c+(d-x)*(d-x);
                  if(n1>n2) {
                      n1 = sqrt(n1+y*y);
                      p = (a-x)/n1;
                      q = b/n1;
                      x = 0;
                      y /= n1;
                  } else {
                      n2 = sqrt(n2+y*y);
                      p = c/n2;
                      q = (d-x)/n2;
                      x = y/n2;
                      y = 0;
                  }
                  Q0 = new T([[q,-p],[p,q]],[[x,y],[y,-x]]);
                  Q.setRows(i,j,Q0.dot(Q.getRows(i,j)));
              }
          }
      }
      var R = Q.dot(A).dot(Q.transjugate()), n = A.length, E = numeric.T.identity(n);
      for(j=0;j<n;j++) {
          if(j>0) {
              for(k=j-1;k>=0;k--) {
                  var Rk = R.get([k,k]), Rj = R.get([j,j]);
                  if(numeric.neq(Rk.x,Rj.x) || numeric.neq(Rk.y,Rj.y)) {
                      x = R.getRow(k).getBlock([k],[j-1]);
                      y = E.getRow(j).getBlock([k],[j-1]);
                      E.set([j,k],(R.get([k,j]).neg().sub(x.dot(y))).div(Rk.sub(Rj)));
                  } else {
                      E.setRow(j,E.getRow(k));
                      continue;
                  }
              }
          }
      }
      for(j=0;j<n;j++) {
          x = E.getRow(j);
          E.setRow(j,x.div(x.norm2()));
      }
      E = E.transpose();
      E = Q.transjugate().dot(E);
      return { lambda:R.getDiag(), E:E };
  };
  
  // 5. Compressed Column Storage matrices
  numeric.ccsSparse = function ccsSparse(A) {
      var m = A.length,n,foo, i,j, counts = [];
      for(i=m-1;i!==-1;--i) {
          foo = A[i];
          for(j in foo) {
              j = parseInt(j);
              while(j>=counts.length) counts[counts.length] = 0;
              if(foo[j]!==0) counts[j]++;
          }
      }
      var n = counts.length;
      var Ai = Array(n+1);
      Ai[0] = 0;
      for(i=0;i<n;++i) Ai[i+1] = Ai[i] + counts[i];
      var Aj = Array(Ai[n]), Av = Array(Ai[n]);
      for(i=m-1;i!==-1;--i) {
          foo = A[i];
          for(j in foo) {
              if(foo[j]!==0) {
                  counts[j]--;
                  Aj[Ai[j]+counts[j]] = i;
                  Av[Ai[j]+counts[j]] = foo[j];
              }
          }
      }
      return [Ai,Aj,Av];
  }
  numeric.ccsFull = function ccsFull(A) {
      var Ai = A[0], Aj = A[1], Av = A[2], s = numeric.ccsDim(A), m = s[0], n = s[1], i,j,j0,j1,k;
      var B = numeric.rep([m,n],0);
      for(i=0;i<n;i++) {
          j0 = Ai[i];
          j1 = Ai[i+1];
          for(j=j0;j<j1;++j) { B[Aj[j]][i] = Av[j]; }
      }
      return B;
  }
  numeric.ccsTSolve = function ccsTSolve(A,b,x,bj,xj) {
      var Ai = A[0], Aj = A[1], Av = A[2],m = Ai.length-1, max = Math.max,n=0;
      if(typeof bj === "undefined") x = numeric.rep([m],0);
      if(typeof bj === "undefined") bj = numeric.linspace(0,x.length-1);
      if(typeof xj === "undefined") xj = [];
      function dfs(j) {
          var k;
          if(x[j] !== 0) return;
          x[j] = 1;
          for(k=Ai[j];k<Ai[j+1];++k) dfs(Aj[k]);
          xj[n] = j;
          ++n;
      }
      var i,j,j0,j1,k,l,l0,l1,a;
      for(i=bj.length-1;i!==-1;--i) { dfs(bj[i]); }
      xj.length = n;
      for(i=xj.length-1;i!==-1;--i) { x[xj[i]] = 0; }
      for(i=bj.length-1;i!==-1;--i) { j = bj[i]; x[j] = b[j]; }
      for(i=xj.length-1;i!==-1;--i) {
          j = xj[i];
          j0 = Ai[j];
          j1 = max(Ai[j+1],j0);
          for(k=j0;k!==j1;++k) { if(Aj[k] === j) { x[j] /= Av[k]; break; } }
          a = x[j];
          for(k=j0;k!==j1;++k) {
              l = Aj[k];
              if(l !== j) x[l] -= a*Av[k];
          }
      }
      return x;
  }
  numeric.ccsDFS = function ccsDFS(n) {
      this.k = Array(n);
      this.k1 = Array(n);
      this.j = Array(n);
  }
  numeric.ccsDFS.prototype.dfs = function dfs(J,Ai,Aj,x,xj,Pinv) {
      var m = 0,foo,n=xj.length;
      var k = this.k, k1 = this.k1, j = this.j,km,k11;
      if(x[J]!==0) return;
      x[J] = 1;
      j[0] = J;
      k[0] = km = Ai[J];
      k1[0] = k11 = Ai[J+1];
      while(1) {
          if(km >= k11) {
              xj[n] = j[m];
              if(m===0) return;
              ++n;
              --m;
              km = k[m];
              k11 = k1[m];
          } else {
              foo = Pinv[Aj[km]];
              if(x[foo] === 0) {
                  x[foo] = 1;
                  k[m] = km;
                  ++m;
                  j[m] = foo;
                  km = Ai[foo];
                  k1[m] = k11 = Ai[foo+1];
              } else ++km;
          }
      }
  }
  numeric.ccsLPSolve = function ccsLPSolve(A,B,x,xj,I,Pinv,dfs) {
      var Ai = A[0], Aj = A[1], Av = A[2],m = Ai.length-1, n=0;
      var Bi = B[0], Bj = B[1], Bv = B[2];
      
      var i,i0,i1,j,J,j0,j1,k,l,l0,l1,a;
      i0 = Bi[I];
      i1 = Bi[I+1];
      xj.length = 0;
      for(i=i0;i<i1;++i) { dfs.dfs(Pinv[Bj[i]],Ai,Aj,x,xj,Pinv); }
      for(i=xj.length-1;i!==-1;--i) { x[xj[i]] = 0; }
      for(i=i0;i!==i1;++i) { j = Pinv[Bj[i]]; x[j] = Bv[i]; }
      for(i=xj.length-1;i!==-1;--i) {
          j = xj[i];
          j0 = Ai[j];
          j1 = Ai[j+1];
          for(k=j0;k<j1;++k) { if(Pinv[Aj[k]] === j) { x[j] /= Av[k]; break; } }
          a = x[j];
          for(k=j0;k<j1;++k) {
              l = Pinv[Aj[k]];
              if(l !== j) x[l] -= a*Av[k];
          }
      }
      return x;
  }
  numeric.ccsLUP1 = function ccsLUP1(A,threshold) {
      var m = A[0].length-1;
      var L = [numeric.rep([m+1],0),[],[]], U = [numeric.rep([m+1], 0),[],[]];
      var Li = L[0], Lj = L[1], Lv = L[2], Ui = U[0], Uj = U[1], Uv = U[2];
      var x = numeric.rep([m],0), xj = numeric.rep([m],0);
      var i,j,k,j0,j1,a,e,c,d,K;
      var sol = numeric.ccsLPSolve, max = Math.max, abs = Math.abs;
      var P = numeric.linspace(0,m-1),Pinv = numeric.linspace(0,m-1);
      var dfs = new numeric.ccsDFS(m);
      if(typeof threshold === "undefined") { threshold = 1; }
      for(i=0;i<m;++i) {
          sol(L,A,x,xj,i,Pinv,dfs);
          a = -1;
          e = -1;
          for(j=xj.length-1;j!==-1;--j) {
              k = xj[j];
              if(k <= i) continue;
              c = abs(x[k]);
              if(c > a) { e = k; a = c; }
          }
          if(abs(x[i])<threshold*a) {
              j = P[i];
              a = P[e];
              P[i] = a; Pinv[a] = i;
              P[e] = j; Pinv[j] = e;
              a = x[i]; x[i] = x[e]; x[e] = a;
          }
          a = Li[i];
          e = Ui[i];
          d = x[i];
          Lj[a] = P[i];
          Lv[a] = 1;
          ++a;
          for(j=xj.length-1;j!==-1;--j) {
              k = xj[j];
              c = x[k];
              xj[j] = 0;
              x[k] = 0;
              if(k<=i) { Uj[e] = k; Uv[e] = c;   ++e; }
              else     { Lj[a] = P[k]; Lv[a] = c/d; ++a; }
          }
          Li[i+1] = a;
          Ui[i+1] = e;
      }
      for(j=Lj.length-1;j!==-1;--j) { Lj[j] = Pinv[Lj[j]]; }
      return {L:L, U:U, P:P, Pinv:Pinv};
  }
  numeric.ccsDFS0 = function ccsDFS0(n) {
      this.k = Array(n);
      this.k1 = Array(n);
      this.j = Array(n);
  }
  numeric.ccsDFS0.prototype.dfs = function dfs(J,Ai,Aj,x,xj,Pinv,P) {
      var m = 0,foo,n=xj.length;
      var k = this.k, k1 = this.k1, j = this.j,km,k11;
      if(x[J]!==0) return;
      x[J] = 1;
      j[0] = J;
      k[0] = km = Ai[Pinv[J]];
      k1[0] = k11 = Ai[Pinv[J]+1];
      while(1) {
          if(isNaN(km)) throw new Error("Ow!");
          if(km >= k11) {
              xj[n] = Pinv[j[m]];
              if(m===0) return;
              ++n;
              --m;
              km = k[m];
              k11 = k1[m];
          } else {
              foo = Aj[km];
              if(x[foo] === 0) {
                  x[foo] = 1;
                  k[m] = km;
                  ++m;
                  j[m] = foo;
                  foo = Pinv[foo];
                  km = Ai[foo];
                  k1[m] = k11 = Ai[foo+1];
              } else ++km;
          }
      }
  }
  numeric.ccsLPSolve0 = function ccsLPSolve0(A,B,y,xj,I,Pinv,P,dfs) {
      var Ai = A[0], Aj = A[1], Av = A[2],m = Ai.length-1, n=0;
      var Bi = B[0], Bj = B[1], Bv = B[2];
      
      var i,i0,i1,j,J,j0,j1,k,l,l0,l1,a;
      i0 = Bi[I];
      i1 = Bi[I+1];
      xj.length = 0;
      for(i=i0;i<i1;++i) { dfs.dfs(Bj[i],Ai,Aj,y,xj,Pinv,P); }
      for(i=xj.length-1;i!==-1;--i) { j = xj[i]; y[P[j]] = 0; }
      for(i=i0;i!==i1;++i) { j = Bj[i]; y[j] = Bv[i]; }
      for(i=xj.length-1;i!==-1;--i) {
          j = xj[i];
          l = P[j];
          j0 = Ai[j];
          j1 = Ai[j+1];
          for(k=j0;k<j1;++k) { if(Aj[k] === l) { y[l] /= Av[k]; break; } }
          a = y[l];
          for(k=j0;k<j1;++k) y[Aj[k]] -= a*Av[k];
          y[l] = a;
      }
  }
  numeric.ccsLUP0 = function ccsLUP0(A,threshold) {
      var m = A[0].length-1;
      var L = [numeric.rep([m+1],0),[],[]], U = [numeric.rep([m+1], 0),[],[]];
      var Li = L[0], Lj = L[1], Lv = L[2], Ui = U[0], Uj = U[1], Uv = U[2];
      var y = numeric.rep([m],0), xj = numeric.rep([m],0);
      var i,j,k,j0,j1,a,e,c,d,K;
      var sol = numeric.ccsLPSolve0, max = Math.max, abs = Math.abs;
      var P = numeric.linspace(0,m-1),Pinv = numeric.linspace(0,m-1);
      var dfs = new numeric.ccsDFS0(m);
      if(typeof threshold === "undefined") { threshold = 1; }
      for(i=0;i<m;++i) {
          sol(L,A,y,xj,i,Pinv,P,dfs);
          a = -1;
          e = -1;
          for(j=xj.length-1;j!==-1;--j) {
              k = xj[j];
              if(k <= i) continue;
              c = abs(y[P[k]]);
              if(c > a) { e = k; a = c; }
          }
          if(abs(y[P[i]])<threshold*a) {
              j = P[i];
              a = P[e];
              P[i] = a; Pinv[a] = i;
              P[e] = j; Pinv[j] = e;
          }
          a = Li[i];
          e = Ui[i];
          d = y[P[i]];
          Lj[a] = P[i];
          Lv[a] = 1;
          ++a;
          for(j=xj.length-1;j!==-1;--j) {
              k = xj[j];
              c = y[P[k]];
              xj[j] = 0;
              y[P[k]] = 0;
              if(k<=i) { Uj[e] = k; Uv[e] = c;   ++e; }
              else     { Lj[a] = P[k]; Lv[a] = c/d; ++a; }
          }
          Li[i+1] = a;
          Ui[i+1] = e;
      }
      for(j=Lj.length-1;j!==-1;--j) { Lj[j] = Pinv[Lj[j]]; }
      return {L:L, U:U, P:P, Pinv:Pinv};
  }
  numeric.ccsLUP = numeric.ccsLUP0;
  
  numeric.ccsDim = function ccsDim(A) { return [numeric.sup(A[1])+1,A[0].length-1]; }
  numeric.ccsGetBlock = function ccsGetBlock(A,i,j) {
      var s = numeric.ccsDim(A),m=s[0],n=s[1];
      if(typeof i === "undefined") { i = numeric.linspace(0,m-1); }
      else if(typeof i === "number") { i = [i]; }
      if(typeof j === "undefined") { j = numeric.linspace(0,n-1); }
      else if(typeof j === "number") { j = [j]; }
      var p,p0,p1,P = i.length,q,Q = j.length,r,jq,ip;
      var Bi = numeric.rep([n],0), Bj=[], Bv=[], B = [Bi,Bj,Bv];
      var Ai = A[0], Aj = A[1], Av = A[2];
      var x = numeric.rep([m],0),count=0,flags = numeric.rep([m],0);
      for(q=0;q<Q;++q) {
          jq = j[q];
          var q0 = Ai[jq];
          var q1 = Ai[jq+1];
          for(p=q0;p<q1;++p) {
              r = Aj[p];
              flags[r] = 1;
              x[r] = Av[p];
          }
          for(p=0;p<P;++p) {
              ip = i[p];
              if(flags[ip]) {
                  Bj[count] = p;
                  Bv[count] = x[i[p]];
                  ++count;
              }
          }
          for(p=q0;p<q1;++p) {
              r = Aj[p];
              flags[r] = 0;
          }
          Bi[q+1] = count;
      }
      return B;
  }
  
  numeric.ccsDot = function ccsDot(A,B) {
      var Ai = A[0], Aj = A[1], Av = A[2];
      var Bi = B[0], Bj = B[1], Bv = B[2];
      var sA = numeric.ccsDim(A), sB = numeric.ccsDim(B);
      var m = sA[0], n = sA[1], o = sB[1];
      var x = numeric.rep([m],0), flags = numeric.rep([m],0), xj = Array(m);
      var Ci = numeric.rep([o],0), Cj = [], Cv = [], C = [Ci,Cj,Cv];
      var i,j,k,j0,j1,i0,i1,l,p,a,b;
      for(k=0;k!==o;++k) {
          j0 = Bi[k];
          j1 = Bi[k+1];
          p = 0;
          for(j=j0;j<j1;++j) {
              a = Bj[j];
              b = Bv[j];
              i0 = Ai[a];
              i1 = Ai[a+1];
              for(i=i0;i<i1;++i) {
                  l = Aj[i];
                  if(flags[l]===0) {
                      xj[p] = l;
                      flags[l] = 1;
                      p = p+1;
                  }
                  x[l] = x[l] + Av[i]*b;
              }
          }
          j0 = Ci[k];
          j1 = j0+p;
          Ci[k+1] = j1;
          for(j=p-1;j!==-1;--j) {
              b = j0+j;
              i = xj[j];
              Cj[b] = i;
              Cv[b] = x[i];
              flags[i] = 0;
              x[i] = 0;
          }
          Ci[k+1] = Ci[k]+p;
      }
      return C;
  }
  
  numeric.ccsLUPSolve = function ccsLUPSolve(LUP,B) {
      var L = LUP.L, U = LUP.U, P = LUP.P;
      var Bi = B[0];
      var flag = false;
      if(typeof Bi !== "object") { B = [[0,B.length],numeric.linspace(0,B.length-1),B]; Bi = B[0]; flag = true; }
      var Bj = B[1], Bv = B[2];
      var n = L[0].length-1, m = Bi.length-1;
      var x = numeric.rep([n],0), xj = Array(n);
      var b = numeric.rep([n],0), bj = Array(n);
      var Xi = numeric.rep([m+1],0), Xj = [], Xv = [];
      var sol = numeric.ccsTSolve;
      var i,j,j0,j1,k,J,N=0;
      for(i=0;i<m;++i) {
          k = 0;
          j0 = Bi[i];
          j1 = Bi[i+1];
          for(j=j0;j<j1;++j) { 
              J = LUP.Pinv[Bj[j]];
              bj[k] = J;
              b[J] = Bv[j];
              ++k;
          }
          bj.length = k;
          sol(L,b,x,bj,xj);
          for(j=bj.length-1;j!==-1;--j) b[bj[j]] = 0;
          sol(U,x,b,xj,bj);
          if(flag) return b;
          for(j=xj.length-1;j!==-1;--j) x[xj[j]] = 0;
          for(j=bj.length-1;j!==-1;--j) {
              J = bj[j];
              Xj[N] = J;
              Xv[N] = b[J];
              b[J] = 0;
              ++N;
          }
          Xi[i+1] = N;
      }
      return [Xi,Xj,Xv];
  }
  
  numeric.ccsbinop = function ccsbinop(body,setup) {
      if(typeof setup === "undefined") setup='';
      return Function('X','Y',
              'var Xi = X[0], Xj = X[1], Xv = X[2];\n'+
              'var Yi = Y[0], Yj = Y[1], Yv = Y[2];\n'+
              'var n = Xi.length-1,m = Math.max(numeric.sup(Xj),numeric.sup(Yj))+1;\n'+
              'var Zi = numeric.rep([n+1],0), Zj = [], Zv = [];\n'+
              'var x = numeric.rep([m],0),y = numeric.rep([m],0);\n'+
              'var xk,yk,zk;\n'+
              'var i,j,j0,j1,k,p=0;\n'+
              setup+
              'for(i=0;i<n;++i) {\n'+
              '  j0 = Xi[i]; j1 = Xi[i+1];\n'+
              '  for(j=j0;j!==j1;++j) {\n'+
              '    k = Xj[j];\n'+
              '    x[k] = 1;\n'+
              '    Zj[p] = k;\n'+
              '    ++p;\n'+
              '  }\n'+
              '  j0 = Yi[i]; j1 = Yi[i+1];\n'+
              '  for(j=j0;j!==j1;++j) {\n'+
              '    k = Yj[j];\n'+
              '    y[k] = Yv[j];\n'+
              '    if(x[k] === 0) {\n'+
              '      Zj[p] = k;\n'+
              '      ++p;\n'+
              '    }\n'+
              '  }\n'+
              '  Zi[i+1] = p;\n'+
              '  j0 = Xi[i]; j1 = Xi[i+1];\n'+
              '  for(j=j0;j!==j1;++j) x[Xj[j]] = Xv[j];\n'+
              '  j0 = Zi[i]; j1 = Zi[i+1];\n'+
              '  for(j=j0;j!==j1;++j) {\n'+
              '    k = Zj[j];\n'+
              '    xk = x[k];\n'+
              '    yk = y[k];\n'+
              body+'\n'+
              '    Zv[j] = zk;\n'+
              '  }\n'+
              '  j0 = Xi[i]; j1 = Xi[i+1];\n'+
              '  for(j=j0;j!==j1;++j) x[Xj[j]] = 0;\n'+
              '  j0 = Yi[i]; j1 = Yi[i+1];\n'+
              '  for(j=j0;j!==j1;++j) y[Yj[j]] = 0;\n'+
              '}\n'+
              'return [Zi,Zj,Zv];'
              );
  };
  
  (function() {
      var k,A,B,C;
      for(k in numeric.ops2) {
          if(isFinite(eval('1'+numeric.ops2[k]+'0'))) A = '[Y[0],Y[1],numeric.'+k+'(X,Y[2])]';
          else A = 'NaN';
          if(isFinite(eval('0'+numeric.ops2[k]+'1'))) B = '[X[0],X[1],numeric.'+k+'(X[2],Y)]';
          else B = 'NaN';
          if(isFinite(eval('1'+numeric.ops2[k]+'0')) && isFinite(eval('0'+numeric.ops2[k]+'1'))) C = 'numeric.ccs'+k+'MM(X,Y)';
          else C = 'NaN';
          numeric['ccs'+k+'MM'] = numeric.ccsbinop('zk = xk '+numeric.ops2[k]+'yk;');
          numeric['ccs'+k] = Function('X','Y',
                  'if(typeof X === "number") return '+A+';\n'+
                  'if(typeof Y === "number") return '+B+';\n'+
                  'return '+C+';\n'
                  );
      }
  }());
  
  numeric.ccsScatter = function ccsScatter(A) {
      var Ai = A[0], Aj = A[1], Av = A[2];
      var n = numeric.sup(Aj)+1,m=Ai.length;
      var Ri = numeric.rep([n],0),Rj=Array(m), Rv = Array(m);
      var counts = numeric.rep([n],0),i;
      for(i=0;i<m;++i) counts[Aj[i]]++;
      for(i=0;i<n;++i) Ri[i+1] = Ri[i] + counts[i];
      var ptr = Ri.slice(0),k,Aii;
      for(i=0;i<m;++i) {
          Aii = Aj[i];
          k = ptr[Aii];
          Rj[k] = Ai[i];
          Rv[k] = Av[i];
          ptr[Aii]=ptr[Aii]+1;
      }
      return [Ri,Rj,Rv];
  }
  
  numeric.ccsGather = function ccsGather(A) {
      var Ai = A[0], Aj = A[1], Av = A[2];
      var n = Ai.length-1,m = Aj.length;
      var Ri = Array(m), Rj = Array(m), Rv = Array(m);
      var i,j,j0,j1,p;
      p=0;
      for(i=0;i<n;++i) {
          j0 = Ai[i];
          j1 = Ai[i+1];
          for(j=j0;j!==j1;++j) {
              Rj[p] = i;
              Ri[p] = Aj[j];
              Rv[p] = Av[j];
              ++p;
          }
      }
      return [Ri,Rj,Rv];
  }
  
  // The following sparse linear algebra routines are deprecated.
  
  numeric.sdim = function dim(A,ret,k) {
      if(typeof ret === "undefined") { ret = []; }
      if(typeof A !== "object") return ret;
      if(typeof k === "undefined") { k=0; }
      if(!(k in ret)) { ret[k] = 0; }
      if(A.length > ret[k]) ret[k] = A.length;
      var i;
      for(i in A) {
          if(A.hasOwnProperty(i)) dim(A[i],ret,k+1);
      }
      return ret;
  };
  
  numeric.sclone = function clone(A,k,n) {
      if(typeof k === "undefined") { k=0; }
      if(typeof n === "undefined") { n = numeric.sdim(A).length; }
      var i,ret = Array(A.length);
      if(k === n-1) {
          for(i in A) { if(A.hasOwnProperty(i)) ret[i] = A[i]; }
          return ret;
      }
      for(i in A) {
          if(A.hasOwnProperty(i)) ret[i] = clone(A[i],k+1,n);
      }
      return ret;
  }
  
  numeric.sdiag = function diag(d) {
      var n = d.length,i,ret = Array(n),i1,i2,i3;
      for(i=n-1;i>=1;i-=2) {
          i1 = i-1;
          ret[i] = []; ret[i][i] = d[i];
          ret[i1] = []; ret[i1][i1] = d[i1];
      }
      if(i===0) { ret[0] = []; ret[0][0] = d[i]; }
      return ret;
  }
  
  numeric.sidentity = function identity(n) { return numeric.sdiag(numeric.rep([n],1)); }
  
  numeric.stranspose = function transpose(A) {
      var ret = [], n = A.length, i,j,Ai;
      for(i in A) {
          if(!(A.hasOwnProperty(i))) continue;
          Ai = A[i];
          for(j in Ai) {
              if(!(Ai.hasOwnProperty(j))) continue;
              if(typeof ret[j] !== "object") { ret[j] = []; }
              ret[j][i] = Ai[j];
          }
      }
      return ret;
  }
  
  numeric.sLUP = function LUP(A,tol) {
      throw new Error("The function numeric.sLUP had a bug in it and has been removed. Please use the new numeric.ccsLUP function instead.");
  };
  
  numeric.sdotMM = function dotMM(A,B) {
      var p = A.length, q = B.length, BT = numeric.stranspose(B), r = BT.length, Ai, BTk;
      var i,j,k,accum;
      var ret = Array(p),reti;
      for(i=p-1;i>=0;i--) {
          reti = [];
          Ai = A[i];
          for(k=r-1;k>=0;k--) {
              accum = 0;
              BTk = BT[k];
              for(j in Ai) {
                  if(!(Ai.hasOwnProperty(j))) continue;
                  if(j in BTk) { accum += Ai[j]*BTk[j]; }
              }
              if(accum) reti[k] = accum;
          }
          ret[i] = reti;
      }
      return ret;
  }
  
  numeric.sdotMV = function dotMV(A,x) {
      var p = A.length, Ai, i,j;
      var ret = Array(p), accum;
      for(i=p-1;i>=0;i--) {
          Ai = A[i];
          accum = 0;
          for(j in Ai) {
              if(!(Ai.hasOwnProperty(j))) continue;
              if(x[j]) accum += Ai[j]*x[j];
          }
          if(accum) ret[i] = accum;
      }
      return ret;
  }
  
  numeric.sdotVM = function dotMV(x,A) {
      var i,j,Ai,alpha;
      var ret = [], accum;
      for(i in x) {
          if(!x.hasOwnProperty(i)) continue;
          Ai = A[i];
          alpha = x[i];
          for(j in Ai) {
              if(!Ai.hasOwnProperty(j)) continue;
              if(!ret[j]) { ret[j] = 0; }
              ret[j] += alpha*Ai[j];
          }
      }
      return ret;
  }
  
  numeric.sdotVV = function dotVV(x,y) {
      var i,ret=0;
      for(i in x) { if(x[i] && y[i]) ret+= x[i]*y[i]; }
      return ret;
  }
  
  numeric.sdot = function dot(A,B) {
      var m = numeric.sdim(A).length, n = numeric.sdim(B).length;
      var k = m*1000+n;
      switch(k) {
      case 0: return A*B;
      case 1001: return numeric.sdotVV(A,B);
      case 2001: return numeric.sdotMV(A,B);
      case 1002: return numeric.sdotVM(A,B);
      case 2002: return numeric.sdotMM(A,B);
      default: throw new Error('numeric.sdot not implemented for tensors of order '+m+' and '+n);
      }
  }
  
  numeric.sscatter = function scatter(V) {
      var n = V[0].length, Vij, i, j, m = V.length, A = [], Aj;
      for(i=n-1;i>=0;--i) {
          if(!V[m-1][i]) continue;
          Aj = A;
          for(j=0;j<m-2;j++) {
              Vij = V[j][i];
              if(!Aj[Vij]) Aj[Vij] = [];
              Aj = Aj[Vij];
          }
          Aj[V[j][i]] = V[j+1][i];
      }
      return A;
  }
  
  numeric.sgather = function gather(A,ret,k) {
      if(typeof ret === "undefined") ret = [];
      if(typeof k === "undefined") k = [];
      var n,i,Ai;
      n = k.length;
      for(i in A) {
          if(A.hasOwnProperty(i)) {
              k[n] = parseInt(i);
              Ai = A[i];
              if(typeof Ai === "number") {
                  if(Ai) {
                      if(ret.length === 0) {
                          for(i=n+1;i>=0;--i) ret[i] = [];
                      }
                      for(i=n;i>=0;--i) ret[i].push(k[i]);
                      ret[n+1].push(Ai);
                  }
              } else gather(Ai,ret,k);
          }
      }
      if(k.length>n) k.pop();
      return ret;
  }
  
  // 6. Coordinate matrices
  numeric.cLU = function LU(A) {
      var I = A[0], J = A[1], V = A[2];
      var p = I.length, m=0, i,j,k,a,b,c;
      for(i=0;i<p;i++) if(I[i]>m) m=I[i];
      m++;
      var L = Array(m), U = Array(m), left = numeric.rep([m],Infinity), right = numeric.rep([m],-Infinity);
      var Ui, Uj,alpha;
      for(k=0;k<p;k++) {
          i = I[k];
          j = J[k];
          if(j<left[i]) left[i] = j;
          if(j>right[i]) right[i] = j;
      }
      for(i=0;i<m-1;i++) { if(right[i] > right[i+1]) right[i+1] = right[i]; }
      for(i=m-1;i>=1;i--) { if(left[i]<left[i-1]) left[i-1] = left[i]; }
      var countL = 0, countU = 0;
      for(i=0;i<m;i++) {
          U[i] = numeric.rep([right[i]-left[i]+1],0);
          L[i] = numeric.rep([i-left[i]],0);
          countL += i-left[i]+1;
          countU += right[i]-i+1;
      }
      for(k=0;k<p;k++) { i = I[k]; U[i][J[k]-left[i]] = V[k]; }
      for(i=0;i<m-1;i++) {
          a = i-left[i];
          Ui = U[i];
          for(j=i+1;left[j]<=i && j<m;j++) {
              b = i-left[j];
              c = right[i]-i;
              Uj = U[j];
              alpha = Uj[b]/Ui[a];
              if(alpha) {
                  for(k=1;k<=c;k++) { Uj[k+b] -= alpha*Ui[k+a]; }
                  L[j][i-left[j]] = alpha;
              }
          }
      }
      var Ui = [], Uj = [], Uv = [], Li = [], Lj = [], Lv = [];
      var p,q,foo;
      p=0; q=0;
      for(i=0;i<m;i++) {
          a = left[i];
          b = right[i];
          foo = U[i];
          for(j=i;j<=b;j++) {
              if(foo[j-a]) {
                  Ui[p] = i;
                  Uj[p] = j;
                  Uv[p] = foo[j-a];
                  p++;
              }
          }
          foo = L[i];
          for(j=a;j<i;j++) {
              if(foo[j-a]) {
                  Li[q] = i;
                  Lj[q] = j;
                  Lv[q] = foo[j-a];
                  q++;
              }
          }
          Li[q] = i;
          Lj[q] = i;
          Lv[q] = 1;
          q++;
      }
      return {U:[Ui,Uj,Uv], L:[Li,Lj,Lv]};
  };
  
  numeric.cLUsolve = function LUsolve(lu,b) {
      var L = lu.L, U = lu.U, ret = numeric.clone(b);
      var Li = L[0], Lj = L[1], Lv = L[2];
      var Ui = U[0], Uj = U[1], Uv = U[2];
      var p = Ui.length, q = Li.length;
      var m = ret.length,i,j,k;
      k = 0;
      for(i=0;i<m;i++) {
          while(Lj[k] < i) {
              ret[i] -= Lv[k]*ret[Lj[k]];
              k++;
          }
          k++;
      }
      k = p-1;
      for(i=m-1;i>=0;i--) {
          while(Uj[k] > i) {
              ret[i] -= Uv[k]*ret[Uj[k]];
              k--;
          }
          ret[i] /= Uv[k];
          k--;
      }
      return ret;
  };
  
  numeric.cgrid = function grid(n,shape) {
      if(typeof n === "number") n = [n,n];
      var ret = numeric.rep(n,-1);
      var i,j,count;
      if(typeof shape !== "function") {
          switch(shape) {
          case 'L':
              shape = function(i,j) { return (i>=n[0]/2 || j<n[1]/2); }
              break;
          default:
              shape = function(i,j) { return true; };
              break;
          }
      }
      count=0;
      for(i=1;i<n[0]-1;i++) for(j=1;j<n[1]-1;j++) 
          if(shape(i,j)) {
              ret[i][j] = count;
              count++;
          }
      return ret;
  }
  
  numeric.cdelsq = function delsq(g) {
      var dir = [[-1,0],[0,-1],[0,1],[1,0]];
      var s = numeric.dim(g), m = s[0], n = s[1], i,j,k,p,q;
      var Li = [], Lj = [], Lv = [];
      for(i=1;i<m-1;i++) for(j=1;j<n-1;j++) {
          if(g[i][j]<0) continue;
          for(k=0;k<4;k++) {
              p = i+dir[k][0];
              q = j+dir[k][1];
              if(g[p][q]<0) continue;
              Li.push(g[i][j]);
              Lj.push(g[p][q]);
              Lv.push(-1);
          }
          Li.push(g[i][j]);
          Lj.push(g[i][j]);
          Lv.push(4);
      }
      return [Li,Lj,Lv];
  }
  
  numeric.cdotMV = function dotMV(A,x) {
      var ret, Ai = A[0], Aj = A[1], Av = A[2],k,p=Ai.length,N;
      N=0;
      for(k=0;k<p;k++) { if(Ai[k]>N) N = Ai[k]; }
      N++;
      ret = numeric.rep([N],0);
      for(k=0;k<p;k++) { ret[Ai[k]]+=Av[k]*x[Aj[k]]; }
      return ret;
  }
  
  // 7. Splines
  
  numeric.Spline = function Spline(x,yl,yr,kl,kr) { this.x = x; this.yl = yl; this.yr = yr; this.kl = kl; this.kr = kr; }
  numeric.Spline.prototype._at = function _at(x1,p) {
      var x = this.x;
      var yl = this.yl;
      var yr = this.yr;
      var kl = this.kl;
      var kr = this.kr;
      var x1,a,b,t;
      var add = numeric.add, sub = numeric.sub, mul = numeric.mul;
      a = sub(mul(kl[p],x[p+1]-x[p]),sub(yr[p+1],yl[p]));
      b = add(mul(kr[p+1],x[p]-x[p+1]),sub(yr[p+1],yl[p]));
      t = (x1-x[p])/(x[p+1]-x[p]);
      var s = t*(1-t);
      return add(add(add(mul(1-t,yl[p]),mul(t,yr[p+1])),mul(a,s*(1-t))),mul(b,s*t));
  }
  numeric.Spline.prototype.at = function at(x0) {
      if(typeof x0 === "number") {
          var x = this.x;
          var n = x.length;
          var p,q,mid,floor = Math.floor,a,b,t;
          p = 0;
          q = n-1;
          while(q-p>1) {
              mid = floor((p+q)/2);
              if(x[mid] <= x0) p = mid;
              else q = mid;
          }
          return this._at(x0,p);
      }
      var n = x0.length, i, ret = Array(n);
      for(i=n-1;i!==-1;--i) ret[i] = this.at(x0[i]);
      return ret;
  }
  numeric.Spline.prototype.diff = function diff() {
      var x = this.x;
      var yl = this.yl;
      var yr = this.yr;
      var kl = this.kl;
      var kr = this.kr;
      var n = yl.length;
      var i,dx,dy;
      var zl = kl, zr = kr, pl = Array(n), pr = Array(n);
      var add = numeric.add, mul = numeric.mul, div = numeric.div, sub = numeric.sub;
      for(i=n-1;i!==-1;--i) {
          dx = x[i+1]-x[i];
          dy = sub(yr[i+1],yl[i]);
          pl[i] = div(add(mul(dy, 6),mul(kl[i],-4*dx),mul(kr[i+1],-2*dx)),dx*dx);
          pr[i+1] = div(add(mul(dy,-6),mul(kl[i], 2*dx),mul(kr[i+1], 4*dx)),dx*dx);
      }
      return new numeric.Spline(x,zl,zr,pl,pr);
  }
  numeric.Spline.prototype.roots = function roots() {
      function sqr(x) { return x*x; }
      function heval(y0,y1,k0,k1,x) {
          var A = k0*2-(y1-y0);
          var B = -k1*2+(y1-y0);
          var t = (x+1)*0.5;
          var s = t*(1-t);
          return (1-t)*y0+t*y1+A*s*(1-t)+B*s*t;
      }
      var ret = [];
      var x = this.x, yl = this.yl, yr = this.yr, kl = this.kl, kr = this.kr;
      if(typeof yl[0] === "number") {
          yl = [yl];
          yr = [yr];
          kl = [kl];
          kr = [kr];
      }
      var m = yl.length,n=x.length-1,i,j,k,y,s,t;
      var ai,bi,ci,di, ret = Array(m),ri,k0,k1,y0,y1,A,B,D,dx,cx,stops,z0,z1,zm,t0,t1,tm;
      var sqrt = Math.sqrt;
      for(i=0;i!==m;++i) {
          ai = yl[i];
          bi = yr[i];
          ci = kl[i];
          di = kr[i];
          ri = [];
          for(j=0;j!==n;j++) {
              if(j>0 && bi[j]*ai[j]<0) ri.push(x[j]);
              dx = (x[j+1]-x[j]);
              cx = x[j];
              y0 = ai[j];
              y1 = bi[j+1];
              k0 = ci[j]/dx;
              k1 = di[j+1]/dx;
              D = sqr(k0-k1+3*(y0-y1)) + 12*k1*y0;
              A = k1+3*y0+2*k0-3*y1;
              B = 3*(k1+k0+2*(y0-y1));
              if(D<=0) {
                  z0 = A/B;
                  if(z0>x[j] && z0<x[j+1]) stops = [x[j],z0,x[j+1]];
                  else stops = [x[j],x[j+1]];
              } else {
                  z0 = (A-sqrt(D))/B;
                  z1 = (A+sqrt(D))/B;
                  stops = [x[j]];
                  if(z0>x[j] && z0<x[j+1]) stops.push(z0);
                  if(z1>x[j] && z1<x[j+1]) stops.push(z1);
                  stops.push(x[j+1]);
              }
              t0 = stops[0];
              z0 = this._at(t0,j);
              for(k=0;k<stops.length-1;k++) {
                  t1 = stops[k+1];
                  z1 = this._at(t1,j);
                  if(z0 === 0) {
                      ri.push(t0); 
                      t0 = t1;
                      z0 = z1;
                      continue;
                  }
                  if(z1 === 0 || z0*z1>0) {
                      t0 = t1;
                      z0 = z1;
                      continue;
                  }
                  var side = 0;
                  while(1) {
                      tm = (z0*t1-z1*t0)/(z0-z1);
                      if(tm <= t0 || tm >= t1) { break; }
                      zm = this._at(tm,j);
                      if(zm*z1>0) {
                          t1 = tm;
                          z1 = zm;
                          if(side === -1) z0*=0.5;
                          side = -1;
                      } else if(zm*z0>0) {
                          t0 = tm;
                          z0 = zm;
                          if(side === 1) z1*=0.5;
                          side = 1;
                      } else break;
                  }
                  ri.push(tm);
                  t0 = stops[k+1];
                  z0 = this._at(t0, j);
              }
              if(z1 === 0) ri.push(t1);
          }
          ret[i] = ri;
      }
      if(typeof this.yl[0] === "number") return ret[0];
      return ret;
  }
  numeric.spline = function spline(x,y,k1,kn) {
      var n = x.length, b = [], dx = [], dy = [];
      var i;
      var sub = numeric.sub,mul = numeric.mul,add = numeric.add;
      for(i=n-2;i>=0;i--) { dx[i] = x[i+1]-x[i]; dy[i] = sub(y[i+1],y[i]); }
      if(typeof k1 === "string" || typeof kn === "string") { 
          k1 = kn = "periodic";
      }
      // Build sparse tridiagonal system
      var T = [[],[],[]];
      switch(typeof k1) {
      case "undefined":
          b[0] = mul(3/(dx[0]*dx[0]),dy[0]);
          T[0].push(0,0);
          T[1].push(0,1);
          T[2].push(2/dx[0],1/dx[0]);
          break;
      case "string":
          b[0] = add(mul(3/(dx[n-2]*dx[n-2]),dy[n-2]),mul(3/(dx[0]*dx[0]),dy[0]));
          T[0].push(0,0,0);
          T[1].push(n-2,0,1);
          T[2].push(1/dx[n-2],2/dx[n-2]+2/dx[0],1/dx[0]);
          break;
      default:
          b[0] = k1;
          T[0].push(0);
          T[1].push(0);
          T[2].push(1);
          break;
      }
      for(i=1;i<n-1;i++) {
          b[i] = add(mul(3/(dx[i-1]*dx[i-1]),dy[i-1]),mul(3/(dx[i]*dx[i]),dy[i]));
          T[0].push(i,i,i);
          T[1].push(i-1,i,i+1);
          T[2].push(1/dx[i-1],2/dx[i-1]+2/dx[i],1/dx[i]);
      }
      switch(typeof kn) {
      case "undefined":
          b[n-1] = mul(3/(dx[n-2]*dx[n-2]),dy[n-2]);
          T[0].push(n-1,n-1);
          T[1].push(n-2,n-1);
          T[2].push(1/dx[n-2],2/dx[n-2]);
          break;
      case "string":
          T[1][T[1].length-1] = 0;
          break;
      default:
          b[n-1] = kn;
          T[0].push(n-1);
          T[1].push(n-1);
          T[2].push(1);
          break;
      }
      if(typeof b[0] !== "number") b = numeric.transpose(b);
      else b = [b];
      var k = Array(b.length);
      if(typeof k1 === "string") {
          for(i=k.length-1;i!==-1;--i) {
              k[i] = numeric.ccsLUPSolve(numeric.ccsLUP(numeric.ccsScatter(T)),b[i]);
              k[i][n-1] = k[i][0];
          }
      } else {
          for(i=k.length-1;i!==-1;--i) {
              k[i] = numeric.cLUsolve(numeric.cLU(T),b[i]);
          }
      }
      if(typeof y[0] === "number") k = k[0];
      else k = numeric.transpose(k);
      return new numeric.Spline(x,y,y,k,k);
  }
  
  // 8. FFT
  numeric.fftpow2 = function fftpow2(x,y) {
      var n = x.length;
      if(n === 1) return;
      var cos = Math.cos, sin = Math.sin, i,j;
      var xe = Array(n/2), ye = Array(n/2), xo = Array(n/2), yo = Array(n/2);
      j = n/2;
      for(i=n-1;i!==-1;--i) {
          --j;
          xo[j] = x[i];
          yo[j] = y[i];
          --i;
          xe[j] = x[i];
          ye[j] = y[i];
      }
      fftpow2(xe,ye);
      fftpow2(xo,yo);
      j = n/2;
      var t,k = (-6.2831853071795864769252867665590057683943387987502116419/n),ci,si;
      for(i=n-1;i!==-1;--i) {
          --j;
          if(j === -1) j = n/2-1;
          t = k*i;
          ci = cos(t);
          si = sin(t);
          x[i] = xe[j] + ci*xo[j] - si*yo[j];
          y[i] = ye[j] + ci*yo[j] + si*xo[j];
      }
  }
  numeric._ifftpow2 = function _ifftpow2(x,y) {
      var n = x.length;
      if(n === 1) return;
      var cos = Math.cos, sin = Math.sin, i,j;
      var xe = Array(n/2), ye = Array(n/2), xo = Array(n/2), yo = Array(n/2);
      j = n/2;
      for(i=n-1;i!==-1;--i) {
          --j;
          xo[j] = x[i];
          yo[j] = y[i];
          --i;
          xe[j] = x[i];
          ye[j] = y[i];
      }
      _ifftpow2(xe,ye);
      _ifftpow2(xo,yo);
      j = n/2;
      var t,k = (6.2831853071795864769252867665590057683943387987502116419/n),ci,si;
      for(i=n-1;i!==-1;--i) {
          --j;
          if(j === -1) j = n/2-1;
          t = k*i;
          ci = cos(t);
          si = sin(t);
          x[i] = xe[j] + ci*xo[j] - si*yo[j];
          y[i] = ye[j] + ci*yo[j] + si*xo[j];
      }
  }
  numeric.ifftpow2 = function ifftpow2(x,y) {
      numeric._ifftpow2(x,y);
      numeric.diveq(x,x.length);
      numeric.diveq(y,y.length);
  }
  numeric.convpow2 = function convpow2(ax,ay,bx,by) {
      numeric.fftpow2(ax,ay);
      numeric.fftpow2(bx,by);
      var i,n = ax.length,axi,bxi,ayi,byi;
      for(i=n-1;i!==-1;--i) {
          axi = ax[i]; ayi = ay[i]; bxi = bx[i]; byi = by[i];
          ax[i] = axi*bxi-ayi*byi;
          ay[i] = axi*byi+ayi*bxi;
      }
      numeric.ifftpow2(ax,ay);
  }
  numeric.T.prototype.fft = function fft() {
      var x = this.x, y = this.y;
      var n = x.length, log = Math.log, log2 = log(2),
          p = Math.ceil(log(2*n-1)/log2), m = Math.pow(2,p);
      var cx = numeric.rep([m],0), cy = numeric.rep([m],0), cos = Math.cos, sin = Math.sin;
      var k, c = (-3.141592653589793238462643383279502884197169399375105820/n),t;
      var a = numeric.rep([m],0), b = numeric.rep([m],0),nhalf = Math.floor(n/2);
      for(k=0;k<n;k++) a[k] = x[k];
      if(typeof y !== "undefined") for(k=0;k<n;k++) b[k] = y[k];
      cx[0] = 1;
      for(k=1;k<=m/2;k++) {
          t = c*k*k;
          cx[k] = cos(t);
          cy[k] = sin(t);
          cx[m-k] = cos(t);
          cy[m-k] = sin(t)
      }
      var X = new numeric.T(a,b), Y = new numeric.T(cx,cy);
      X = X.mul(Y);
      numeric.convpow2(X.x,X.y,numeric.clone(Y.x),numeric.neg(Y.y));
      X = X.mul(Y);
      X.x.length = n;
      X.y.length = n;
      return X;
  }
  numeric.T.prototype.ifft = function ifft() {
      var x = this.x, y = this.y;
      var n = x.length, log = Math.log, log2 = log(2),
          p = Math.ceil(log(2*n-1)/log2), m = Math.pow(2,p);
      var cx = numeric.rep([m],0), cy = numeric.rep([m],0), cos = Math.cos, sin = Math.sin;
      var k, c = (3.141592653589793238462643383279502884197169399375105820/n),t;
      var a = numeric.rep([m],0), b = numeric.rep([m],0),nhalf = Math.floor(n/2);
      for(k=0;k<n;k++) a[k] = x[k];
      if(typeof y !== "undefined") for(k=0;k<n;k++) b[k] = y[k];
      cx[0] = 1;
      for(k=1;k<=m/2;k++) {
          t = c*k*k;
          cx[k] = cos(t);
          cy[k] = sin(t);
          cx[m-k] = cos(t);
          cy[m-k] = sin(t)
      }
      var X = new numeric.T(a,b), Y = new numeric.T(cx,cy);
      X = X.mul(Y);
      numeric.convpow2(X.x,X.y,numeric.clone(Y.x),numeric.neg(Y.y));
      X = X.mul(Y);
      X.x.length = n;
      X.y.length = n;
      return X.div(n);
  }
  
  //9. Unconstrained optimization
  numeric.gradient = function gradient(f,x) {
      var n = x.length;
      var f0 = f(x);
      if(isNaN(f0)) throw new Error('gradient: f(x) is a NaN!');
      var max = Math.max;
      var i,x0 = numeric.clone(x),f1,f2, J = Array(n);
      var div = numeric.div, sub = numeric.sub,errest,roundoff,max = Math.max,eps = 1e-3,abs = Math.abs, min = Math.min;
      var t0,t1,t2,it=0,d1,d2,N;
      for(i=0;i<n;i++) {
          var h = max(1e-6*f0,1e-8);
          while(1) {
              ++it;
              if(it>20) { throw new Error("Numerical gradient fails"); }
              x0[i] = x[i]+h;
              f1 = f(x0);
              x0[i] = x[i]-h;
              f2 = f(x0);
              x0[i] = x[i];
              if(isNaN(f1) || isNaN(f2)) { h/=16; continue; }
              J[i] = (f1-f2)/(2*h);
              t0 = x[i]-h;
              t1 = x[i];
              t2 = x[i]+h;
              d1 = (f1-f0)/h;
              d2 = (f0-f2)/h;
              N = max(abs(J[i]),abs(f0),abs(f1),abs(f2),abs(t0),abs(t1),abs(t2),1e-8);
              errest = min(max(abs(d1-J[i]),abs(d2-J[i]),abs(d1-d2))/N,h/N);
              if(errest>eps) { h/=16; }
              else break;
              }
      }
      return J;
  }
  
  numeric.uncmin = function uncmin(f,x0,tol,gradient,maxit,callback,options) {
      var grad = numeric.gradient;
      if(typeof options === "undefined") { options = {}; }
      if(typeof tol === "undefined") { tol = 1e-8; }
      if(typeof gradient === "undefined") { gradient = function(x) { return grad(f,x); }; }
      if(typeof maxit === "undefined") maxit = 1000;
      x0 = numeric.clone(x0);
      var n = x0.length;
      var f0 = f(x0),f1,df0;
      if(isNaN(f0)) throw new Error('uncmin: f(x0) is a NaN!');
      var max = Math.max, norm2 = numeric.norm2;
      tol = max(tol,numeric.epsilon);
      var step,g0,g1,H1 = options.Hinv || numeric.identity(n);
      var dot = numeric.dot, inv = numeric.inv, sub = numeric.sub, add = numeric.add, ten = numeric.tensor, div = numeric.div, mul = numeric.mul;
      var all = numeric.all, isfinite = numeric.isFinite, neg = numeric.neg;
      var it=0,i,s,x1,y,Hy,Hs,ys,i0,t,nstep,t1,t2;
      var msg = "";
      g0 = gradient(x0);
      while(it<maxit) {
          if(typeof callback === "function") { if(callback(it,x0,f0,g0,H1)) { msg = "Callback returned true"; break; } }
          if(!all(isfinite(g0))) { msg = "Gradient has Infinity or NaN"; break; }
          step = neg(dot(H1,g0));
          if(!all(isfinite(step))) { msg = "Search direction has Infinity or NaN"; break; }
          nstep = norm2(step);
          if(nstep < tol) { msg="Newton step smaller than tol"; break; }
          t = 1;
          df0 = dot(g0,step);
          // line search
          x1 = x0;
          while(it < maxit) {
              if(t*nstep < tol) { break; }
              s = mul(step,t);
              x1 = add(x0,s);
              f1 = f(x1);
              if(f1-f0 >= 0.1*t*df0 || isNaN(f1)) {
                  t *= 0.5;
                  ++it;
                  continue;
              }
              break;
          }
          if(t*nstep < tol) { msg = "Line search step size smaller than tol"; break; }
          if(it === maxit) { msg = "maxit reached during line search"; break; }
          g1 = gradient(x1);
          y = sub(g1,g0);
          ys = dot(y,s);
          Hy = dot(H1,y);
          H1 = sub(add(H1,
                  mul(
                          (ys+dot(y,Hy))/(ys*ys),
                          ten(s,s)    )),
                  div(add(ten(Hy,s),ten(s,Hy)),ys));
          x0 = x1;
          f0 = f1;
          g0 = g1;
          ++it;
      }
      return {solution: x0, f: f0, gradient: g0, invHessian: H1, iterations:it, message: msg};
  }
  
  // 10. Ode solver (Dormand-Prince)
  numeric.Dopri = function Dopri(x,y,f,ymid,iterations,msg,events) {
      this.x = x;
      this.y = y;
      this.f = f;
      this.ymid = ymid;
      this.iterations = iterations;
      this.events = events;
      this.message = msg;
  }
  numeric.Dopri.prototype._at = function _at(xi,j) {
      function sqr(x) { return x*x; }
      var sol = this;
      var xs = sol.x;
      var ys = sol.y;
      var k1 = sol.f;
      var ymid = sol.ymid;
      var n = xs.length;
      var x0,x1,xh,y0,y1,yh,xi;
      var floor = Math.floor,h;
      var c = 0.5;
      var add = numeric.add, mul = numeric.mul,sub = numeric.sub, p,q,w;
      x0 = xs[j];
      x1 = xs[j+1];
      y0 = ys[j];
      y1 = ys[j+1];
      h  = x1-x0;
      xh = x0+c*h;
      yh = ymid[j];
      p = sub(k1[j  ],mul(y0,1/(x0-xh)+2/(x0-x1)));
      q = sub(k1[j+1],mul(y1,1/(x1-xh)+2/(x1-x0)));
      w = [sqr(xi - x1) * (xi - xh) / sqr(x0 - x1) / (x0 - xh),
           sqr(xi - x0) * sqr(xi - x1) / sqr(x0 - xh) / sqr(x1 - xh),
           sqr(xi - x0) * (xi - xh) / sqr(x1 - x0) / (x1 - xh),
           (xi - x0) * sqr(xi - x1) * (xi - xh) / sqr(x0-x1) / (x0 - xh),
           (xi - x1) * sqr(xi - x0) * (xi - xh) / sqr(x0-x1) / (x1 - xh)];
      return add(add(add(add(mul(y0,w[0]),
                             mul(yh,w[1])),
                             mul(y1,w[2])),
                             mul( p,w[3])),
                             mul( q,w[4]));
  }
  numeric.Dopri.prototype.at = function at(x) {
      var i,j,k,floor = Math.floor;
      if(typeof x !== "number") {
          var n = x.length, ret = Array(n);
          for(i=n-1;i!==-1;--i) {
              ret[i] = this.at(x[i]);
          }
          return ret;
      }
      var x0 = this.x;
      i = 0; j = x0.length-1;
      while(j-i>1) {
          k = floor(0.5*(i+j));
          if(x0[k] <= x) i = k;
          else j = k;
      }
      return this._at(x,i);
  }
  
  numeric.dopri = function dopri(x0,x1,y0,f,tol,maxit,event) {
      if(typeof tol === "undefined") { tol = 1e-6; }
      if(typeof maxit === "undefined") { maxit = 1000; }
      var xs = [x0], ys = [y0], k1 = [f(x0,y0)], k2,k3,k4,k5,k6,k7, ymid = [];
      var A2 = 1/5;
      var A3 = [3/40,9/40];
      var A4 = [44/45,-56/15,32/9];
      var A5 = [19372/6561,-25360/2187,64448/6561,-212/729];
      var A6 = [9017/3168,-355/33,46732/5247,49/176,-5103/18656];
      var b = [35/384,0,500/1113,125/192,-2187/6784,11/84];
      var bm = [0.5*6025192743/30085553152,
                0,
                0.5*51252292925/65400821598,
                0.5*-2691868925/45128329728,
                0.5*187940372067/1594534317056,
                0.5*-1776094331/19743644256,
                0.5*11237099/235043384];
      var c = [1/5,3/10,4/5,8/9,1,1];
      var e = [-71/57600,0,71/16695,-71/1920,17253/339200,-22/525,1/40];
      var i = 0,er,j;
      var h = (x1-x0)/10;
      var it = 0;
      var add = numeric.add, mul = numeric.mul, y1,erinf;
      var max = Math.max, min = Math.min, abs = Math.abs, norminf = numeric.norminf,pow = Math.pow;
      var any = numeric.any, lt = numeric.lt, and = numeric.and, sub = numeric.sub;
      var e0, e1, ev;
      var ret = new numeric.Dopri(xs,ys,k1,ymid,-1,"");
      if(typeof event === "function") e0 = event(x0,y0);
      while(x0<x1 && it<maxit) {
          ++it;
          if(x0+h>x1) h = x1-x0;
          k2 = f(x0+c[0]*h,                add(y0,mul(   A2*h,k1[i])));
          k3 = f(x0+c[1]*h,            add(add(y0,mul(A3[0]*h,k1[i])),mul(A3[1]*h,k2)));
          k4 = f(x0+c[2]*h,        add(add(add(y0,mul(A4[0]*h,k1[i])),mul(A4[1]*h,k2)),mul(A4[2]*h,k3)));
          k5 = f(x0+c[3]*h,    add(add(add(add(y0,mul(A5[0]*h,k1[i])),mul(A5[1]*h,k2)),mul(A5[2]*h,k3)),mul(A5[3]*h,k4)));
          k6 = f(x0+c[4]*h,add(add(add(add(add(y0,mul(A6[0]*h,k1[i])),mul(A6[1]*h,k2)),mul(A6[2]*h,k3)),mul(A6[3]*h,k4)),mul(A6[4]*h,k5)));
          y1 = add(add(add(add(add(y0,mul(k1[i],h*b[0])),mul(k3,h*b[2])),mul(k4,h*b[3])),mul(k5,h*b[4])),mul(k6,h*b[5]));
          k7 = f(x0+h,y1);
          er = add(add(add(add(add(mul(k1[i],h*e[0]),mul(k3,h*e[2])),mul(k4,h*e[3])),mul(k5,h*e[4])),mul(k6,h*e[5])),mul(k7,h*e[6]));
          if(typeof er === "number") erinf = abs(er);
          else erinf = norminf(er);
          if(erinf > tol) { // reject
              h = 0.2*h*pow(tol/erinf,0.25);
              if(x0+h === x0) {
                  ret.msg = "Step size became too small";
                  break;
              }
              continue;
          }
          ymid[i] = add(add(add(add(add(add(y0,
                  mul(k1[i],h*bm[0])),
                  mul(k3   ,h*bm[2])),
                  mul(k4   ,h*bm[3])),
                  mul(k5   ,h*bm[4])),
                  mul(k6   ,h*bm[5])),
                  mul(k7   ,h*bm[6]));
          ++i;
          xs[i] = x0+h;
          ys[i] = y1;
          k1[i] = k7;
          if(typeof event === "function") {
              var yi,xl = x0,xr = x0+0.5*h,xi;
              e1 = event(xr,ymid[i-1]);
              ev = and(lt(e0,0),lt(0,e1));
              if(!any(ev)) { xl = xr; xr = x0+h; e0 = e1; e1 = event(xr,y1); ev = and(lt(e0,0),lt(0,e1)); }
              if(any(ev)) {
                  var xc, yc, en,ei;
                  var side=0, sl = 1.0, sr = 1.0;
                  while(1) {
                      if(typeof e0 === "number") xi = (sr*e1*xl-sl*e0*xr)/(sr*e1-sl*e0);
                      else {
                          xi = xr;
                          for(j=e0.length-1;j!==-1;--j) {
                              if(e0[j]<0 && e1[j]>0) xi = min(xi,(sr*e1[j]*xl-sl*e0[j]*xr)/(sr*e1[j]-sl*e0[j]));
                          }
                      }
                      if(xi <= xl || xi >= xr) break;
                      yi = ret._at(xi, i-1);
                      ei = event(xi,yi);
                      en = and(lt(e0,0),lt(0,ei));
                      if(any(en)) {
                          xr = xi;
                          e1 = ei;
                          ev = en;
                          sr = 1.0;
                          if(side === -1) sl *= 0.5;
                          else sl = 1.0;
                          side = -1;
                      } else {
                          xl = xi;
                          e0 = ei;
                          sl = 1.0;
                          if(side === 1) sr *= 0.5;
                          else sr = 1.0;
                          side = 1;
                      }
                  }
                  y1 = ret._at(0.5*(x0+xi),i-1);
                  ret.f[i] = f(xi,yi);
                  ret.x[i] = xi;
                  ret.y[i] = yi;
                  ret.ymid[i-1] = y1;
                  ret.events = ev;
                  ret.iterations = it;
                  return ret;
              }
          }
          x0 += h;
          y0 = y1;
          e0 = e1;
          h = min(0.8*h*pow(tol/erinf,0.25),4*h);
      }
      ret.iterations = it;
      return ret;
  }
  
  // 11. Ax = b
  numeric.LU = function(A, fast) {
    fast = fast || false;
  
    var abs = Math.abs;
    var i, j, k, absAjk, Akk, Ak, Pk, Ai;
    var max;
    var n = A.length, n1 = n-1;
    var P = new Array(n);
    if(!fast) A = numeric.clone(A);
  
    for (k = 0; k < n; ++k) {
      Pk = k;
      Ak = A[k];
      max = abs(Ak[k]);
      for (j = k + 1; j < n; ++j) {
        absAjk = abs(A[j][k]);
        if (max < absAjk) {
          max = absAjk;
          Pk = j;
        }
      }
      P[k] = Pk;
  
      if (Pk != k) {
        A[k] = A[Pk];
        A[Pk] = Ak;
        Ak = A[k];
      }
  
      Akk = Ak[k];
  
      for (i = k + 1; i < n; ++i) {
        A[i][k] /= Akk;
      }
  
      for (i = k + 1; i < n; ++i) {
        Ai = A[i];
        for (j = k + 1; j < n1; ++j) {
          Ai[j] -= Ai[k] * Ak[j];
          ++j;
          Ai[j] -= Ai[k] * Ak[j];
        }
        if(j===n1) Ai[j] -= Ai[k] * Ak[j];
      }
    }
  
    return {
      LU: A,
      P:  P
    };
  }
  
  numeric.LUsolve = function LUsolve(LUP, b) {
    var i, j;
    var LU = LUP.LU;
    var n   = LU.length;
    var x = numeric.clone(b);
    var P   = LUP.P;
    var Pi, LUi, LUii, tmp;
  
    for (i=n-1;i!==-1;--i) x[i] = b[i];
    for (i = 0; i < n; ++i) {
      Pi = P[i];
      if (P[i] !== i) {
        tmp = x[i];
        x[i] = x[Pi];
        x[Pi] = tmp;
      }
  
      LUi = LU[i];
      for (j = 0; j < i; ++j) {
        x[i] -= x[j] * LUi[j];
      }
    }
  
    for (i = n - 1; i >= 0; --i) {
      LUi = LU[i];
      for (j = i + 1; j < n; ++j) {
        x[i] -= x[j] * LUi[j];
      }
  
      x[i] /= LUi[i];
    }
  
    return x;
  }
  
  numeric.solve = function solve(A,b,fast) { return numeric.LUsolve(numeric.LU(A,fast), b); }
  
  // 12. Linear programming
  numeric.echelonize = function echelonize(A) {
      var s = numeric.dim(A), m = s[0], n = s[1];
      var I = numeric.identity(m);
      var P = Array(m);
      var i,j,k,l,Ai,Ii,Z,a;
      var abs = Math.abs;
      var diveq = numeric.diveq;
      A = numeric.clone(A);
      for(i=0;i<m;++i) {
          k = 0;
          Ai = A[i];
          Ii = I[i];
          for(j=1;j<n;++j) if(abs(Ai[k])<abs(Ai[j])) k=j;
          P[i] = k;
          diveq(Ii,Ai[k]);
          diveq(Ai,Ai[k]);
          for(j=0;j<m;++j) if(j!==i) {
              Z = A[j]; a = Z[k];
              for(l=n-1;l!==-1;--l) Z[l] -= Ai[l]*a;
              Z = I[j];
              for(l=m-1;l!==-1;--l) Z[l] -= Ii[l]*a;
          }
      }
      return {I:I, A:A, P:P};
  }
  
  numeric.__solveLP = function __solveLP(c,A,b,tol,maxit,x,flag) {
      var sum = numeric.sum, log = numeric.log, mul = numeric.mul, sub = numeric.sub, dot = numeric.dot, div = numeric.div, add = numeric.add;
      var m = c.length, n = b.length,y;
      var unbounded = false, cb,i0=0;
      var alpha = 1.0;
      var f0,df0,AT = numeric.transpose(A), svd = numeric.svd,transpose = numeric.transpose,leq = numeric.leq, sqrt = Math.sqrt, abs = Math.abs;
      var muleq = numeric.muleq;
      var norm = numeric.norminf, any = numeric.any,min = Math.min;
      var all = numeric.all, gt = numeric.gt;
      var p = Array(m), A0 = Array(n),e=numeric.rep([n],1), H;
      var solve = numeric.solve, z = sub(b,dot(A,x)),count;
      var dotcc = dot(c,c);
      var g;
      for(count=i0;count<maxit;++count) {
          var i,j,d;
          for(i=n-1;i!==-1;--i) A0[i] = div(A[i],z[i]);
          var A1 = transpose(A0);
          for(i=m-1;i!==-1;--i) p[i] = (/*x[i]+*/sum(A1[i]));
          alpha = 0.25*abs(dotcc/dot(c,p));
          var a1 = 100*sqrt(dotcc/dot(p,p));
          if(!isFinite(alpha) || alpha>a1) alpha = a1;
          g = add(c,mul(alpha,p));
          H = dot(A1,A0);
          for(i=m-1;i!==-1;--i) H[i][i] += 1;
          d = solve(H,div(g,alpha),true);
          var t0 = div(z,dot(A,d));
          var t = 1.0;
          for(i=n-1;i!==-1;--i) if(t0[i]<0) t = min(t,-0.999*t0[i]);
          y = sub(x,mul(d,t));
          z = sub(b,dot(A,y));
          if(!all(gt(z,0))) return { solution: x, message: "", iterations: count };
          x = y;
          if(alpha<tol) return { solution: y, message: "", iterations: count };
          if(flag) {
              var s = dot(c,g), Ag = dot(A,g);
              unbounded = true;
              for(i=n-1;i!==-1;--i) if(s*Ag[i]<0) { unbounded = false; break; }
          } else {
              if(x[m-1]>=0) unbounded = false;
              else unbounded = true;
          }
          if(unbounded) return { solution: y, message: "Unbounded", iterations: count };
      }
      return { solution: x, message: "maximum iteration count exceeded", iterations:count };
  }
  
  numeric._solveLP = function _solveLP(c,A,b,tol,maxit) {
      var m = c.length, n = b.length,y;
      var sum = numeric.sum, log = numeric.log, mul = numeric.mul, sub = numeric.sub, dot = numeric.dot, div = numeric.div, add = numeric.add;
      var c0 = numeric.rep([m],0).concat([1]);
      var J = numeric.rep([n,1],-1);
      var A0 = numeric.blockMatrix([[A                   ,   J  ]]);
      var b0 = b;
      var y = numeric.rep([m],0).concat(Math.max(0,numeric.sup(numeric.neg(b)))+1);
      var x0 = numeric.__solveLP(c0,A0,b0,tol,maxit,y,false);
      var x = numeric.clone(x0.solution);
      x.length = m;
      var foo = numeric.inf(sub(b,dot(A,x)));
      if(foo<0) { return { solution: NaN, message: "Infeasible", iterations: x0.iterations }; }
      var ret = numeric.__solveLP(c, A, b, tol, maxit-x0.iterations, x, true);
      ret.iterations += x0.iterations;
      return ret;
  };
  
  numeric.solveLP = function solveLP(c,A,b,Aeq,beq,tol,maxit) {
      if(typeof maxit === "undefined") maxit = 1000;
      if(typeof tol === "undefined") tol = numeric.epsilon;
      if(typeof Aeq === "undefined") return numeric._solveLP(c,A,b,tol,maxit);
      var m = Aeq.length, n = Aeq[0].length, o = A.length;
      var B = numeric.echelonize(Aeq);
      var flags = numeric.rep([n],0);
      var P = B.P;
      var Q = [];
      var i;
      for(i=P.length-1;i!==-1;--i) flags[P[i]] = 1;
      for(i=n-1;i!==-1;--i) if(flags[i]===0) Q.push(i);
      var g = numeric.getRange;
      var I = numeric.linspace(0,m-1), J = numeric.linspace(0,o-1);
      var Aeq2 = g(Aeq,I,Q), A1 = g(A,J,P), A2 = g(A,J,Q), dot = numeric.dot, sub = numeric.sub;
      var A3 = dot(A1,B.I);
      var A4 = sub(A2,dot(A3,Aeq2)), b4 = sub(b,dot(A3,beq));
      var c1 = Array(P.length), c2 = Array(Q.length);
      for(i=P.length-1;i!==-1;--i) c1[i] = c[P[i]];
      for(i=Q.length-1;i!==-1;--i) c2[i] = c[Q[i]];
      var c4 = sub(c2,dot(c1,dot(B.I,Aeq2)));
      var S = numeric._solveLP(c4,A4,b4,tol,maxit);
      var x2 = S.solution;
      if(x2!==x2) return S;
      var x1 = dot(B.I,sub(beq,dot(Aeq2,x2)));
      var x = Array(c.length);
      for(i=P.length-1;i!==-1;--i) x[P[i]] = x1[i];
      for(i=Q.length-1;i!==-1;--i) x[Q[i]] = x2[i];
      return { solution: x, message:S.message, iterations: S.iterations };
  }
  
  numeric.MPStoLP = function MPStoLP(MPS) {
      if(MPS instanceof String) { MPS.split('\n'); }
      var state = 0;
      var states = ['Initial state','NAME','ROWS','COLUMNS','RHS','BOUNDS','ENDATA'];
      var n = MPS.length;
      var i,j,z,N=0,rows = {}, sign = [], rl = 0, vars = {}, nv = 0;
      var name;
      var c = [], A = [], b = [];
      function err(e) { throw new Error('MPStoLP: '+e+'\nLine '+i+': '+MPS[i]+'\nCurrent state: '+states[state]+'\n'); }
      for(i=0;i<n;++i) {
          z = MPS[i];
          var w0 = z.match(/\S*/g);
          var w = [];
          for(j=0;j<w0.length;++j) if(w0[j]!=="") w.push(w0[j]);
          if(w.length === 0) continue;
          for(j=0;j<states.length;++j) if(z.substr(0,states[j].length) === states[j]) break;
          if(j<states.length) {
              state = j;
              if(j===1) { name = w[1]; }
              if(j===6) return { name:name, c:c, A:numeric.transpose(A), b:b, rows:rows, vars:vars };
              continue;
          }
          switch(state) {
          case 0: case 1: err('Unexpected line');
          case 2: 
              switch(w[0]) {
              case 'N': if(N===0) N = w[1]; else err('Two or more N rows'); break;
              case 'L': rows[w[1]] = rl; sign[rl] = 1; b[rl] = 0; ++rl; break;
              case 'G': rows[w[1]] = rl; sign[rl] = -1;b[rl] = 0; ++rl; break;
              case 'E': rows[w[1]] = rl; sign[rl] = 0;b[rl] = 0; ++rl; break;
              default: err('Parse error '+numeric.prettyPrint(w));
              }
              break;
          case 3:
              if(!vars.hasOwnProperty(w[0])) { vars[w[0]] = nv; c[nv] = 0; A[nv] = numeric.rep([rl],0); ++nv; }
              var p = vars[w[0]];
              for(j=1;j<w.length;j+=2) {
                  if(w[j] === N) { c[p] = parseFloat(w[j+1]); continue; }
                  var q = rows[w[j]];
                  A[p][q] = (sign[q]<0?-1:1)*parseFloat(w[j+1]);
              }
              break;
          case 4:
              for(j=1;j<w.length;j+=2) b[rows[w[j]]] = (sign[rows[w[j]]]<0?-1:1)*parseFloat(w[j+1]);
              break;
          case 5: /*FIXME*/ break;
          case 6: err('Internal error');
          }
      }
      err('Reached end of file without ENDATA');
  }
  // seedrandom.js version 2.0.
  // Author: David Bau 4/2/2011
  //
  // Defines a method Math.seedrandom() that, when called, substitutes
  // an explicitly seeded RC4-based algorithm for Math.random().  Also
  // supports automatic seeding from local or network sources of entropy.
  //
  // Usage:
  //
  //   <script src=http://davidbau.com/encode/seedrandom-min.js></script>
  //
  //   Math.seedrandom('yipee'); Sets Math.random to a function that is
  //                             initialized using the given explicit seed.
  //
  //   Math.seedrandom();        Sets Math.random to a function that is
  //                             seeded using the current time, dom state,
  //                             and other accumulated local entropy.
  //                             The generated seed string is returned.
  //
  //   Math.seedrandom('yowza', true);
  //                             Seeds using the given explicit seed mixed
  //                             together with accumulated entropy.
  //
  //   <script src="http://bit.ly/srandom-512"></script>
  //                             Seeds using physical random bits downloaded
  //                             from random.org.
  //
  //   <script src="https://jsonlib.appspot.com/urandom?callback=Math.seedrandom">
  //   </script>                 Seeds using urandom bits from call.jsonlib.com,
  //                             which is faster than random.org.
  //
  // Examples:
  //
  //   Math.seedrandom("hello");            // Use "hello" as the seed.
  //   document.write(Math.random());       // Always 0.5463663768140734
  //   document.write(Math.random());       // Always 0.43973793770592234
  //   var rng1 = Math.random;              // Remember the current prng.
  //
  //   var autoseed = Math.seedrandom();    // New prng with an automatic seed.
  //   document.write(Math.random());       // Pretty much unpredictable.
  //
  //   Math.random = rng1;                  // Continue "hello" prng sequence.
  //   document.write(Math.random());       // Always 0.554769432473455
  //
  //   Math.seedrandom(autoseed);           // Restart at the previous seed.
  //   document.write(Math.random());       // Repeat the 'unpredictable' value.
  //
  // Notes:
  //
  // Each time seedrandom('arg') is called, entropy from the passed seed
  // is accumulated in a pool to help generate future seeds for the
  // zero-argument form of Math.seedrandom, so entropy can be injected over
  // time by calling seedrandom with explicit data repeatedly.
  //
  // On speed - This javascript implementation of Math.random() is about
  // 3-10x slower than the built-in Math.random() because it is not native
  // code, but this is typically fast enough anyway.  Seeding is more expensive,
  // especially if you use auto-seeding.  Some details (timings on Chrome 4):
  //
  // Our Math.random()            - avg less than 0.002 milliseconds per call
  // seedrandom('explicit')       - avg less than 0.5 milliseconds per call
  // seedrandom('explicit', true) - avg less than 2 milliseconds per call
  // seedrandom()                 - avg about 38 milliseconds per call
  //
  // LICENSE (BSD):
  //
  // Copyright 2010 David Bau, all rights reserved.
  //
  // Redistribution and use in source and binary forms, with or without
  // modification, are permitted provided that the following conditions are met:
  // 
  //   1. Redistributions of source code must retain the above copyright
  //      notice, this list of conditions and the following disclaimer.
  //
  //   2. Redistributions in binary form must reproduce the above copyright
  //      notice, this list of conditions and the following disclaimer in the
  //      documentation and/or other materials provided with the distribution.
  // 
  //   3. Neither the name of this module nor the names of its contributors may
  //      be used to endorse or promote products derived from this software
  //      without specific prior written permission.
  // 
  // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
  // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
  // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
  // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  //
  /**
   * All code is in an anonymous closure to keep the global namespace clean.
   *
   * @param {number=} overflow 
   * @param {number=} startdenom
   */
  
  // Patched by Seb so that seedrandom.js does not pollute the Math object.
  // My tests suggest that doing Math.trouble = 1 makes Math lookups about 5%
  // slower.
  numeric.seedrandom = { pow:Math.pow, random:Math.random };
  
  (function (pool, math, width, chunks, significance, overflow, startdenom) {
  
  
  //
  // seedrandom()
  // This is the seedrandom function described above.
  //
  math['seedrandom'] = function seedrandom(seed, use_entropy) {
    var key = [];
    var arc4;
  
    // Flatten the seed string or build one from local entropy if needed.
    seed = mixkey(flatten(
      use_entropy ? [seed, pool] :
      arguments.length ? seed :
      [new Date().getTime(), pool, window], 3), key);
  
    // Use the seed to initialize an ARC4 generator.
    arc4 = new ARC4(key);
  
    // Mix the randomness into accumulated entropy.
    mixkey(arc4.S, pool);
  
    // Override Math.random
  
    // This function returns a random double in [0, 1) that contains
    // randomness in every bit of the mantissa of the IEEE 754 value.
  
    math['random'] = function random() {  // Closure to return a random double:
      var n = arc4.g(chunks);             // Start with a numerator n < 2 ^ 48
      var d = startdenom;                 //   and denominator d = 2 ^ 48.
      var x = 0;                          //   and no 'extra last byte'.
      while (n < significance) {          // Fill up all significant digits by
        n = (n + x) * width;              //   shifting numerator and
        d *= width;                       //   denominator and generating a
        x = arc4.g(1);                    //   new least-significant-byte.
      }
      while (n >= overflow) {             // To avoid rounding up, before adding
        n /= 2;                           //   last byte, shift everything
        d /= 2;                           //   right using integer math until
        x >>>= 1;                         //   we have exactly the desired bits.
      }
      return (n + x) / d;                 // Form the number within [0, 1).
    };
  
    // Return the seed that was used
    return seed;
  };
  
  //
  // ARC4
  //
  // An ARC4 implementation.  The constructor takes a key in the form of
  // an array of at most (width) integers that should be 0 <= x < (width).
  //
  // The g(count) method returns a pseudorandom integer that concatenates
  // the next (count) outputs from ARC4.  Its return value is a number x
  // that is in the range 0 <= x < (width ^ count).
  //
  /** @constructor */
  function ARC4(key) {
    var t, u, me = this, keylen = key.length;
    var i = 0, j = me.i = me.j = me.m = 0;
    me.S = [];
    me.c = [];
  
    // The empty key [] is treated as [0].
    if (!keylen) { key = [keylen++]; }
  
    // Set up S using the standard key scheduling algorithm.
    while (i < width) { me.S[i] = i++; }
    for (i = 0; i < width; i++) {
      t = me.S[i];
      j = lowbits(j + t + key[i % keylen]);
      u = me.S[j];
      me.S[i] = u;
      me.S[j] = t;
    }
  
    // The "g" method returns the next (count) outputs as one number.
    me.g = function getnext(count) {
      var s = me.S;
      var i = lowbits(me.i + 1); var t = s[i];
      var j = lowbits(me.j + t); var u = s[j];
      s[i] = u;
      s[j] = t;
      var r = s[lowbits(t + u)];
      while (--count) {
        i = lowbits(i + 1); t = s[i];
        j = lowbits(j + t); u = s[j];
        s[i] = u;
        s[j] = t;
        r = r * width + s[lowbits(t + u)];
      }
      me.i = i;
      me.j = j;
      return r;
    };
    // For robust unpredictability discard an initial batch of values.
    // See http://www.rsa.com/rsalabs/node.asp?id=2009
    me.g(width);
  }
  
  //
  // flatten()
  // Converts an object tree to nested arrays of strings.
  //
  /** @param {Object=} result 
    * @param {string=} prop
    * @param {string=} typ */
  function flatten(obj, depth, result, prop, typ) {
    result = [];
    typ = typeof(obj);
    if (depth && typ == 'object') {
      for (prop in obj) {
        if (prop.indexOf('S') < 5) {    // Avoid FF3 bug (local/sessionStorage)
          try { result.push(flatten(obj[prop], depth - 1)); } catch (e) {}
        }
      }
    }
    return (result.length ? result : obj + (typ != 'string' ? '\0' : ''));
  }
  
  //
  // mixkey()
  // Mixes a string seed into a key that is an array of integers, and
  // returns a shortened string seed that is equivalent to the result key.
  //
  /** @param {number=} smear 
    * @param {number=} j */
  function mixkey(seed, key, smear, j) {
    seed += '';                         // Ensure the seed is a string
    smear = 0;
    for (j = 0; j < seed.length; j++) {
      key[lowbits(j)] =
        lowbits((smear ^= key[lowbits(j)] * 19) + seed.charCodeAt(j));
    }
    seed = '';
    for (j in key) { seed += String.fromCharCode(key[j]); }
    return seed;
  }
  
  //
  // lowbits()
  // A quick "n mod width" for width a power of 2.
  //
  function lowbits(n) { return n & (width - 1); }
  
  //
  // The following constants are related to IEEE 754 limits.
  //
  startdenom = math.pow(width, chunks);
  significance = math.pow(2, significance);
  overflow = significance * 2;
  
  //
  // When seedrandom.js is loaded, we immediately mix a few bits
  // from the built-in RNG into the entropy pool.  Because we do
  // not want to intefere with determinstic PRNG state later,
  // seedrandom will not call math.random on its own again after
  // initialization.
  //
  mixkey(math.random(), pool);
  
  // End anonymous scope, and pass initial values.
  }(
    [],   // pool: entropy pool starts empty
    numeric.seedrandom, // math: package containing random, pow, and seedrandom
    256,  // width: each RC4 output is 0 <= x < 256
    6,    // chunks: at least six RC4 outputs for each double
    52    // significance: there are 52 significant digits in a double
    ));
  /* This file is a slightly modified version of quadprog.js from Alberto Santini.
   * It has been slightly modified by SÃ©bastien Loisel to make sure that it handles
   * 0-based Arrays instead of 1-based Arrays.
   * License is in resources/LICENSE.quadprog */
  (function(exports) {
  
  function base0to1(A) {
      if(typeof A !== "object") { return A; }
      var ret = [], i,n=A.length;
      for(i=0;i<n;i++) ret[i+1] = base0to1(A[i]);
      return ret;
  }
  function base1to0(A) {
      if(typeof A !== "object") { return A; }
      var ret = [], i,n=A.length;
      for(i=1;i<n;i++) ret[i-1] = base1to0(A[i]);
      return ret;
  }
  
  function dpori(a, lda, n) {
      var i, j, k, kp1, t;
  
      for (k = 1; k <= n; k = k + 1) {
          a[k][k] = 1 / a[k][k];
          t = -a[k][k];
          //~ dscal(k - 1, t, a[1][k], 1);
          for (i = 1; i < k; i = i + 1) {
              a[i][k] = t * a[i][k];
          }
  
          kp1 = k + 1;
          if (n < kp1) {
              break;
          }
          for (j = kp1; j <= n; j = j + 1) {
              t = a[k][j];
              a[k][j] = 0;
              //~ daxpy(k, t, a[1][k], 1, a[1][j], 1);
              for (i = 1; i <= k; i = i + 1) {
                  a[i][j] = a[i][j] + (t * a[i][k]);
              }
          }
      }
  
  }
  
  function dposl(a, lda, n, b) {
      var i, k, kb, t;
  
      for (k = 1; k <= n; k = k + 1) {
          //~ t = ddot(k - 1, a[1][k], 1, b[1], 1);
          t = 0;
          for (i = 1; i < k; i = i + 1) {
              t = t + (a[i][k] * b[i]);
          }
  
          b[k] = (b[k] - t) / a[k][k];
      }
  
      for (kb = 1; kb <= n; kb = kb + 1) {
          k = n + 1 - kb;
          b[k] = b[k] / a[k][k];
          t = -b[k];
          //~ daxpy(k - 1, t, a[1][k], 1, b[1], 1);
          for (i = 1; i < k; i = i + 1) {
              b[i] = b[i] + (t * a[i][k]);
          }
      }
  }
  
  function dpofa(a, lda, n, info) {
      var i, j, jm1, k, t, s;
  
      for (j = 1; j <= n; j = j + 1) {
          info[1] = j;
          s = 0;
          jm1 = j - 1;
          if (jm1 < 1) {
              s = a[j][j] - s;
              if (s <= 0) {
                  break;
              }
              a[j][j] = Math.sqrt(s);
          } else {
              for (k = 1; k <= jm1; k = k + 1) {
                  //~ t = a[k][j] - ddot(k - 1, a[1][k], 1, a[1][j], 1);
                  t = a[k][j];
                  for (i = 1; i < k; i = i + 1) {
                      t = t - (a[i][j] * a[i][k]);
                  }
                  t = t / a[k][k];
                  a[k][j] = t;
                  s = s + t * t;
              }
              s = a[j][j] - s;
              if (s <= 0) {
                  break;
              }
              a[j][j] = Math.sqrt(s);
          }
          info[1] = 0;
      }
  }
  
  function qpgen2(dmat, dvec, fddmat, n, sol, crval, amat,
      bvec, fdamat, q, meq, iact, nact, iter, work, ierr) {
  
      var i, j, l, l1, info, it1, iwzv, iwrv, iwrm, iwsv, iwuv, nvl, r, iwnbv,
          temp, sum, t1, tt, gc, gs, nu,
          t1inf, t2min,
          vsmall, tmpa, tmpb,
          go;
  
      r = Math.min(n, q);
      l = 2 * n + (r * (r + 5)) / 2 + 2 * q + 1;
  
      vsmall = 1.0e-60;
      do {
          vsmall = vsmall + vsmall;
          tmpa = 1 + 0.1 * vsmall;
          tmpb = 1 + 0.2 * vsmall;
      } while (tmpa <= 1 || tmpb <= 1);
  
      for (i = 1; i <= n; i = i + 1) {
          work[i] = dvec[i];
      }
      for (i = n + 1; i <= l; i = i + 1) {
          work[i] = 0;
      }
      for (i = 1; i <= q; i = i + 1) {
          iact[i] = 0;
      }
  
      info = [];
  
      if (ierr[1] === 0) {
          dpofa(dmat, fddmat, n, info);
          if (info[1] !== 0) {
              ierr[1] = 2;
              return;
          }
          dposl(dmat, fddmat, n, dvec);
          dpori(dmat, fddmat, n);
      } else {
          for (j = 1; j <= n; j = j + 1) {
              sol[j] = 0;
              for (i = 1; i <= j; i = i + 1) {
                  sol[j] = sol[j] + dmat[i][j] * dvec[i];
              }
          }
          for (j = 1; j <= n; j = j + 1) {
              dvec[j] = 0;
              for (i = j; i <= n; i = i + 1) {
                  dvec[j] = dvec[j] + dmat[j][i] * sol[i];
              }
          }
      }
  
      crval[1] = 0;
      for (j = 1; j <= n; j = j + 1) {
          sol[j] = dvec[j];
          crval[1] = crval[1] + work[j] * sol[j];
          work[j] = 0;
          for (i = j + 1; i <= n; i = i + 1) {
              dmat[i][j] = 0;
          }
      }
      crval[1] = -crval[1] / 2;
      ierr[1] = 0;
  
      iwzv = n;
      iwrv = iwzv + n;
      iwuv = iwrv + r;
      iwrm = iwuv + r + 1;
      iwsv = iwrm + (r * (r + 1)) / 2;
      iwnbv = iwsv + q;
  
      for (i = 1; i <= q; i = i + 1) {
          sum = 0;
          for (j = 1; j <= n; j = j + 1) {
              sum = sum + amat[j][i] * amat[j][i];
          }
          work[iwnbv + i] = Math.sqrt(sum);
      }
      nact = 0;
      iter[1] = 0;
      iter[2] = 0;
  
      function fn_goto_50() {
          iter[1] = iter[1] + 1;
  
          l = iwsv;
          for (i = 1; i <= q; i = i + 1) {
              l = l + 1;
              sum = -bvec[i];
              for (j = 1; j <= n; j = j + 1) {
                  sum = sum + amat[j][i] * sol[j];
              }
              if (Math.abs(sum) < vsmall) {
                  sum = 0;
              }
              if (i > meq) {
                  work[l] = sum;
              } else {
                  work[l] = -Math.abs(sum);
                  if (sum > 0) {
                      for (j = 1; j <= n; j = j + 1) {
                          amat[j][i] = -amat[j][i];
                      }
                      bvec[i] = -bvec[i];
                  }
              }
          }
  
          for (i = 1; i <= nact; i = i + 1) {
              work[iwsv + iact[i]] = 0;
          }
  
          nvl = 0;
          temp = 0;
          for (i = 1; i <= q; i = i + 1) {
              if (work[iwsv + i] < temp * work[iwnbv + i]) {
                  nvl = i;
                  temp = work[iwsv + i] / work[iwnbv + i];
              }
          }
          if (nvl === 0) {
              return 999;
          }
  
          return 0;
      }
  
      function fn_goto_55() {
          for (i = 1; i <= n; i = i + 1) {
              sum = 0;
              for (j = 1; j <= n; j = j + 1) {
                  sum = sum + dmat[j][i] * amat[j][nvl];
              }
              work[i] = sum;
          }
  
          l1 = iwzv;
          for (i = 1; i <= n; i = i + 1) {
              work[l1 + i] = 0;
          }
          for (j = nact + 1; j <= n; j = j + 1) {
              for (i = 1; i <= n; i = i + 1) {
                  work[l1 + i] = work[l1 + i] + dmat[i][j] * work[j];
              }
          }
  
          t1inf = true;
          for (i = nact; i >= 1; i = i - 1) {
              sum = work[i];
              l = iwrm + (i * (i + 3)) / 2;
              l1 = l - i;
              for (j = i + 1; j <= nact; j = j + 1) {
                  sum = sum - work[l] * work[iwrv + j];
                  l = l + j;
              }
              sum = sum / work[l1];
              work[iwrv + i] = sum;
              if (iact[i] < meq) {
                  // continue;
                  break;
              }
              if (sum < 0) {
                  // continue;
                  break;
              }
              t1inf = false;
              it1 = i;
          }
  
          if (!t1inf) {
              t1 = work[iwuv + it1] / work[iwrv + it1];
              for (i = 1; i <= nact; i = i + 1) {
                  if (iact[i] < meq) {
                      // continue;
                      break;
                  }
                  if (work[iwrv + i] < 0) {
                      // continue;
                      break;
                  }
                  temp = work[iwuv + i] / work[iwrv + i];
                  if (temp < t1) {
                      t1 = temp;
                      it1 = i;
                  }
              }
          }
  
          sum = 0;
          for (i = iwzv + 1; i <= iwzv + n; i = i + 1) {
              sum = sum + work[i] * work[i];
          }
          if (Math.abs(sum) <= vsmall) {
              if (t1inf) {
                  ierr[1] = 1;
                  // GOTO 999
                  return 999;
              } else {
                  for (i = 1; i <= nact; i = i + 1) {
                      work[iwuv + i] = work[iwuv + i] - t1 * work[iwrv + i];
                  }
                  work[iwuv + nact + 1] = work[iwuv + nact + 1] + t1;
                  // GOTO 700
                  return 700;
              }
          } else {
              sum = 0;
              for (i = 1; i <= n; i = i + 1) {
                  sum = sum + work[iwzv + i] * amat[i][nvl];
              }
              tt = -work[iwsv + nvl] / sum;
              t2min = true;
              if (!t1inf) {
                  if (t1 < tt) {
                      tt = t1;
                      t2min = false;
                  }
              }
  
              for (i = 1; i <= n; i = i + 1) {
                  sol[i] = sol[i] + tt * work[iwzv + i];
                  if (Math.abs(sol[i]) < vsmall) {
                      sol[i] = 0;
                  }
              }
  
              crval[1] = crval[1] + tt * sum * (tt / 2 + work[iwuv + nact + 1]);
              for (i = 1; i <= nact; i = i + 1) {
                  work[iwuv + i] = work[iwuv + i] - tt * work[iwrv + i];
              }
              work[iwuv + nact + 1] = work[iwuv + nact + 1] + tt;
  
              if (t2min) {
                  nact = nact + 1;
                  iact[nact] = nvl;
  
                  l = iwrm + ((nact - 1) * nact) / 2 + 1;
                  for (i = 1; i <= nact - 1; i = i + 1) {
                      work[l] = work[i];
                      l = l + 1;
                  }
  
                  if (nact === n) {
                      work[l] = work[n];
                  } else {
                      for (i = n; i >= nact + 1; i = i - 1) {
                          if (work[i] === 0) {
                              // continue;
                              break;
                          }
                          gc = Math.max(Math.abs(work[i - 1]), Math.abs(work[i]));
                          gs = Math.min(Math.abs(work[i - 1]), Math.abs(work[i]));
                          if (work[i - 1] >= 0) {
                              temp = Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
                          } else {
                              temp = -Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
                          }
                          gc = work[i - 1] / temp;
                          gs = work[i] / temp;
  
                          if (gc === 1) {
                              // continue;
                              break;
                          }
                          if (gc === 0) {
                              work[i - 1] = gs * temp;
                              for (j = 1; j <= n; j = j + 1) {
                                  temp = dmat[j][i - 1];
                                  dmat[j][i - 1] = dmat[j][i];
                                  dmat[j][i] = temp;
                              }
                          } else {
                              work[i - 1] = temp;
                              nu = gs / (1 + gc);
                              for (j = 1; j <= n; j = j + 1) {
                                  temp = gc * dmat[j][i - 1] + gs * dmat[j][i];
                                  dmat[j][i] = nu * (dmat[j][i - 1] + temp) - dmat[j][i];
                                  dmat[j][i - 1] = temp;
  
                              }
                          }
                      }
                      work[l] = work[nact];
                  }
              } else {
                  sum = -bvec[nvl];
                  for (j = 1; j <= n; j = j + 1) {
                      sum = sum + sol[j] * amat[j][nvl];
                  }
                  if (nvl > meq) {
                      work[iwsv + nvl] = sum;
                  } else {
                      work[iwsv + nvl] = -Math.abs(sum);
                      if (sum > 0) {
                          for (j = 1; j <= n; j = j + 1) {
                              amat[j][nvl] = -amat[j][nvl];
                          }
                          bvec[nvl] = -bvec[nvl];
                      }
                  }
                  // GOTO 700
                  return 700;
              }
          }
  
          return 0;
      }
  
      function fn_goto_797() {
          l = iwrm + (it1 * (it1 + 1)) / 2 + 1;
          l1 = l + it1;
          if (work[l1] === 0) {
              // GOTO 798
              return 798;
          }
          gc = Math.max(Math.abs(work[l1 - 1]), Math.abs(work[l1]));
          gs = Math.min(Math.abs(work[l1 - 1]), Math.abs(work[l1]));
          if (work[l1 - 1] >= 0) {
              temp = Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
          } else {
              temp = -Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
          }
          gc = work[l1 - 1] / temp;
          gs = work[l1] / temp;
  
          if (gc === 1) {
              // GOTO 798
              return 798;
          }
          if (gc === 0) {
              for (i = it1 + 1; i <= nact; i = i + 1) {
                  temp = work[l1 - 1];
                  work[l1 - 1] = work[l1];
                  work[l1] = temp;
                  l1 = l1 + i;
              }
              for (i = 1; i <= n; i = i + 1) {
                  temp = dmat[i][it1];
                  dmat[i][it1] = dmat[i][it1 + 1];
                  dmat[i][it1 + 1] = temp;
              }
          } else {
              nu = gs / (1 + gc);
              for (i = it1 + 1; i <= nact; i = i + 1) {
                  temp = gc * work[l1 - 1] + gs * work[l1];
                  work[l1] = nu * (work[l1 - 1] + temp) - work[l1];
                  work[l1 - 1] = temp;
                  l1 = l1 + i;
              }
              for (i = 1; i <= n; i = i + 1) {
                  temp = gc * dmat[i][it1] + gs * dmat[i][it1 + 1];
                  dmat[i][it1 + 1] = nu * (dmat[i][it1] + temp) - dmat[i][it1 + 1];
                  dmat[i][it1] = temp;
              }
          }
  
          return 0;
      }
  
      function fn_goto_798() {
          l1 = l - it1;
          for (i = 1; i <= it1; i = i + 1) {
              work[l1] = work[l];
              l = l + 1;
              l1 = l1 + 1;
          }
  
          work[iwuv + it1] = work[iwuv + it1 + 1];
          iact[it1] = iact[it1 + 1];
          it1 = it1 + 1;
          if (it1 < nact) {
              // GOTO 797
              return 797;
          }
  
          return 0;
      }
  
      function fn_goto_799() {
          work[iwuv + nact] = work[iwuv + nact + 1];
          work[iwuv + nact + 1] = 0;
          iact[nact] = 0;
          nact = nact - 1;
          iter[2] = iter[2] + 1;
  
          return 0;
      }
  
      go = 0;
      while (true) {
          go = fn_goto_50();
          if (go === 999) {
              return;
          }
          while (true) {
              go = fn_goto_55();
              if (go === 0) {
                  break;
              }
              if (go === 999) {
                  return;
              }
              if (go === 700) {
                  if (it1 === nact) {
                      fn_goto_799();
                  } else {
                      while (true) {
                          fn_goto_797();
                          go = fn_goto_798();
                          if (go !== 797) {
                              break;
                          }
                      }
                      fn_goto_799();
                  }
              }
          }
      }
  
  }
  
  function solveQP(Dmat, dvec, Amat, bvec, meq, factorized) {
      Dmat = base0to1(Dmat);
      dvec = base0to1(dvec);
      Amat = base0to1(Amat);
      var i, n, q,
          nact, r,
          crval = [], iact = [], sol = [], work = [], iter = [],
          message;
  
      meq = meq || 0;
      factorized = factorized ? base0to1(factorized) : [undefined, 0];
      bvec = bvec ? base0to1(bvec) : [];
  
      // In Fortran the array index starts from 1
      n = Dmat.length - 1;
      q = Amat[1].length - 1;
  
      if (!bvec) {
          for (i = 1; i <= q; i = i + 1) {
              bvec[i] = 0;
          }
      }
      for (i = 1; i <= q; i = i + 1) {
          iact[i] = 0;
      }
      nact = 0;
      r = Math.min(n, q);
      for (i = 1; i <= n; i = i + 1) {
          sol[i] = 0;
      }
      crval[1] = 0;
      for (i = 1; i <= (2 * n + (r * (r + 5)) / 2 + 2 * q + 1); i = i + 1) {
          work[i] = 0;
      }
      for (i = 1; i <= 2; i = i + 1) {
          iter[i] = 0;
      }
  
      qpgen2(Dmat, dvec, n, n, sol, crval, Amat,
          bvec, n, q, meq, iact, nact, iter, work, factorized);
  
      message = "";
      if (factorized[1] === 1) {
          message = "constraints are inconsistent, no solution!";
      }
      if (factorized[1] === 2) {
          message = "matrix D in quadratic function is not positive definite!";
      }
  
      return {
          solution: base1to0(sol),
          value: base1to0(crval),
          unconstrained_solution: base1to0(dvec),
          iterations: base1to0(iter),
          iact: base1to0(iact),
          message: message
      };
  }
  exports.solveQP = solveQP;
  }(numeric));
  /*
  Shanti Rao sent me this routine by private email. I had to modify it
  slightly to work on Arrays instead of using a Matrix object.
  It is apparently translated from http://stitchpanorama.sourceforge.net/Python/svd.py
  */
  
  numeric.svd= function svd(A) {
      var temp;
  //Compute the thin SVD from G. H. Golub and C. Reinsch, Numer. Math. 14, 403-420 (1970)
  	var prec= numeric.epsilon; //Math.pow(2,-52) // assumes double prec
  	var tolerance= 1.e-64/prec;
  	var itmax= 50;
  	var c=0;
  	var i=0;
  	var j=0;
  	var k=0;
  	var l=0;
  	
  	var u= numeric.clone(A);
  	var m= u.length;
  	
  	var n= u[0].length;
  	
  	if (m < n) throw "Need more rows than columns"
  	
  	var e = new Array(n);
  	var q = new Array(n);
  	for (i=0; i<n; i++) e[i] = q[i] = 0.0;
  	var v = numeric.rep([n,n],0);
  //	v.zero();
  	
   	function pythag(a,b)
   	{
  		a = Math.abs(a)
  		b = Math.abs(b)
  		if (a > b)
  			return a*Math.sqrt(1.0+(b*b/a/a))
  		else if (b == 0.0) 
  			return a
  		return b*Math.sqrt(1.0+(a*a/b/b))
  	}
  
  	//Householder's reduction to bidiagonal form
  
  	var f= 0.0;
  	var g= 0.0;
  	var h= 0.0;
  	var x= 0.0;
  	var y= 0.0;
  	var z= 0.0;
  	var s= 0.0;
  	
  	for (i=0; i < n; i++)
  	{	
  		e[i]= g;
  		s= 0.0;
  		l= i+1;
  		for (j=i; j < m; j++) 
  			s += (u[j][i]*u[j][i]);
  		if (s <= tolerance)
  			g= 0.0;
  		else
  		{	
  			f= u[i][i];
  			g= Math.sqrt(s);
  			if (f >= 0.0) g= -g;
  			h= f*g-s
  			u[i][i]=f-g;
  			for (j=l; j < n; j++)
  			{
  				s= 0.0
  				for (k=i; k < m; k++) 
  					s += u[k][i]*u[k][j]
  				f= s/h
  				for (k=i; k < m; k++) 
  					u[k][j]+=f*u[k][i]
  			}
  		}
  		q[i]= g
  		s= 0.0
  		for (j=l; j < n; j++) 
  			s= s + u[i][j]*u[i][j]
  		if (s <= tolerance)
  			g= 0.0
  		else
  		{	
  			f= u[i][i+1]
  			g= Math.sqrt(s)
  			if (f >= 0.0) g= -g
  			h= f*g - s
  			u[i][i+1] = f-g;
  			for (j=l; j < n; j++) e[j]= u[i][j]/h
  			for (j=l; j < m; j++)
  			{	
  				s=0.0
  				for (k=l; k < n; k++) 
  					s += (u[j][k]*u[i][k])
  				for (k=l; k < n; k++) 
  					u[j][k]+=s*e[k]
  			}	
  		}
  		y= Math.abs(q[i])+Math.abs(e[i])
  		if (y>x) 
  			x=y
  	}
  	
  	// accumulation of right hand gtransformations
  	for (i=n-1; i != -1; i+= -1)
  	{	
  		if (g != 0.0)
  		{
  		 	h= g*u[i][i+1]
  			for (j=l; j < n; j++) 
  				v[j][i]=u[i][j]/h
  			for (j=l; j < n; j++)
  			{	
  				s=0.0
  				for (k=l; k < n; k++) 
  					s += u[i][k]*v[k][j]
  				for (k=l; k < n; k++) 
  					v[k][j]+=(s*v[k][i])
  			}	
  		}
  		for (j=l; j < n; j++)
  		{
  			v[i][j] = 0;
  			v[j][i] = 0;
  		}
  		v[i][i] = 1;
  		g= e[i]
  		l= i
  	}
  	
  	// accumulation of left hand transformations
  	for (i=n-1; i != -1; i+= -1)
  	{	
  		l= i+1
  		g= q[i]
  		for (j=l; j < n; j++) 
  			u[i][j] = 0;
  		if (g != 0.0)
  		{
  			h= u[i][i]*g
  			for (j=l; j < n; j++)
  			{
  				s=0.0
  				for (k=l; k < m; k++) s += u[k][i]*u[k][j];
  				f= s/h
  				for (k=i; k < m; k++) u[k][j]+=f*u[k][i];
  			}
  			for (j=i; j < m; j++) u[j][i] = u[j][i]/g;
  		}
  		else
  			for (j=i; j < m; j++) u[j][i] = 0;
  		u[i][i] += 1;
  	}
  	
  	// diagonalization of the bidiagonal form
  	prec= prec*x
  	for (k=n-1; k != -1; k+= -1)
  	{
  		for (var iteration=0; iteration < itmax; iteration++)
  		{	// test f splitting
  			var test_convergence = false
  			for (l=k; l != -1; l+= -1)
  			{	
  				if (Math.abs(e[l]) <= prec)
  				{	test_convergence= true
  					break 
  				}
  				if (Math.abs(q[l-1]) <= prec)
  					break 
  			}
  			if (!test_convergence)
  			{	// cancellation of e[l] if l>0
  				c= 0.0
  				s= 1.0
  				var l1= l-1
  				for (i =l; i<k+1; i++)
  				{	
  					f= s*e[i]
  					e[i]= c*e[i]
  					if (Math.abs(f) <= prec)
  						break
  					g= q[i]
  					h= pythag(f,g)
  					q[i]= h
  					c= g/h
  					s= -f/h
  					for (j=0; j < m; j++)
  					{	
  						y= u[j][l1]
  						z= u[j][i]
  						u[j][l1] =  y*c+(z*s)
  						u[j][i] = -y*s+(z*c)
  					} 
  				}	
  			}
  			// test f convergence
  			z= q[k]
  			if (l== k)
  			{	//convergence
  				if (z<0.0)
  				{	//q[k] is made non-negative
  					q[k]= -z
  					for (j=0; j < n; j++)
  						v[j][k] = -v[j][k]
  				}
  				break  //break out of iteration loop and move on to next k value
  			}
  			if (iteration >= itmax-1)
  				throw 'Error: no convergence.'
  			// shift from bottom 2x2 minor
  			x= q[l]
  			y= q[k-1]
  			g= e[k-1]
  			h= e[k]
  			f= ((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y)
  			g= pythag(f,1.0)
  			if (f < 0.0)
  				f= ((x-z)*(x+z)+h*(y/(f-g)-h))/x
  			else
  				f= ((x-z)*(x+z)+h*(y/(f+g)-h))/x
  			// next QR transformation
  			c= 1.0
  			s= 1.0
  			for (i=l+1; i< k+1; i++)
  			{	
  				g= e[i]
  				y= q[i]
  				h= s*g
  				g= c*g
  				z= pythag(f,h)
  				e[i-1]= z
  				c= f/z
  				s= h/z
  				f= x*c+g*s
  				g= -x*s+g*c
  				h= y*s
  				y= y*c
  				for (j=0; j < n; j++)
  				{	
  					x= v[j][i-1]
  					z= v[j][i]
  					v[j][i-1] = x*c+z*s
  					v[j][i] = -x*s+z*c
  				}
  				z= pythag(f,h)
  				q[i-1]= z
  				c= f/z
  				s= h/z
  				f= c*g+s*y
  				x= -s*g+c*y
  				for (j=0; j < m; j++)
  				{
  					y= u[j][i-1]
  					z= u[j][i]
  					u[j][i-1] = y*c+z*s
  					u[j][i] = -y*s+z*c
  				}
  			}
  			e[l]= 0.0
  			e[k]= f
  			q[k]= x
  		} 
  	}
  		
  	//vt= transpose(v)
  	//return (u,q,vt)
  	for (i=0;i<q.length; i++) 
  	  if (q[i] < prec) q[i] = 0
  	  
  	//sort eigenvalues	
  	for (i=0; i< n; i++)
  	{	 
  	//writeln(q)
  	 for (j=i-1; j >= 0; j--)
  	 {
  	  if (q[j] < q[i])
  	  {
  	//  writeln(i,'-',j)
  	   c = q[j]
  	   q[j] = q[i]
  	   q[i] = c
  	   for(k=0;k<u.length;k++) { temp = u[k][i]; u[k][i] = u[k][j]; u[k][j] = temp; }
  	   for(k=0;k<v.length;k++) { temp = v[k][i]; v[k][i] = v[k][j]; v[k][j] = temp; }
  //	   u.swapCols(i,j)
  //	   v.swapCols(i,j)
  	   i = j	   
  	  }
  	 }	
  	}
  	
  	return {U:u,S:q,V:v}
  };
  
  /**
   * Viola-Jones-like face detection algorithm
   * Some explanation here: http://liuliu.me/eyes/javascript-face-detection-explained/
   *
   * @author Liu Liu / github.com/liuliu
   *
   * Copyright (c) 2010, Liu Liu
   * All rights reserved.
   *
   * Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
   *
   * * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
   * * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
   * * Neither the name of the authors nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
   *
   * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
   *
   */
  
  var ccv = {};
  
  ccv.grayscale = function (canvas) {
    /* detect_objects requires gray-scale image */
    var ctx = canvas.getContext("2d");
    var imageData = ctx.getImageData(0, 0, canvas.width, canvas.height);
    var data = imageData.data;
    var pix1, pix2, pix = canvas.width * canvas.height * 4;
    while (pix > 0)
      data[pix -= 4] = data[pix1 = pix + 1] = data[pix2 = pix + 2] = (data[pix] * 0.3 + data[pix1] * 0.59 + data[pix2] * 0.11);
    ctx.putImageData(imageData, 0, 0);
    return canvas;
  };
  
  ccv.array_group = function (seq, gfunc) {
    var i, j;
    var node = new Array(seq.length);
    for (i = 0; i < seq.length; i++)
      node[i] = {"parent" : -1,
             "element" : seq[i],
             "rank" : 0};
    for (i = 0; i < seq.length; i++)
    {
      if (!node[i].element)
        continue;
      var root = i;
      while (node[root].parent != -1)
        root = node[root].parent;
      for (j = 0; j < seq.length; j++)
      {
        if( i != j && node[j].element && gfunc(node[i].element, node[j].element))
        {
          var root2 = j;
  
          while (node[root2].parent != -1)
            root2 = node[root2].parent;
  
          if(root2 != root)
          {
            if(node[root].rank > node[root2].rank)
              node[root2].parent = root;
            else
            {
              node[root].parent = root2;
              if (node[root].rank == node[root2].rank)
              node[root2].rank++;
              root = root2;
            }
  
            /* compress path from node2 to the root: */
            var temp, node2 = j;
            while (node[node2].parent != -1)
            {
              temp = node2;
              node2 = node[node2].parent;
              node[temp].parent = root;
            }
  
            /* compress path from node to the root: */
            node2 = i;
            while (node[node2].parent != -1)
            {
              temp = node2;
              node2 = node[node2].parent;
              node[temp].parent = root;
            }
          }
        }
      }
    }
    var idx = new Array(seq.length);
    var class_idx = 0;
    for(i = 0; i < seq.length; i++)
    {
      j = -1;
      var node1 = i;
      if(node[node1].element)
      {
        while (node[node1].parent != -1)
          node1 = node[node1].parent;
        if(node[node1].rank >= 0)
          node[node1].rank = ~class_idx++;
        j = ~node[node1].rank;
      }
      idx[i] = j;
    }
    return {"index" : idx, "cat" : class_idx};
  };
  
  ccv.detect_objects = function (canvas, cascade, interval, min_neighbors) {
    var scale = Math.pow(2, 1 / (interval + 1));
    var next = interval + 1;
    var scale_upto = Math.floor(Math.log(Math.min(cascade.width, cascade.height)) / Math.log(scale));
    var pyr = new Array((scale_upto + next * 2) * 4);
    pyr[0] = canvas;
    pyr[0].data = pyr[0].getContext("2d").getImageData(0, 0, pyr[0].width, pyr[0].height).data;
    var i, j, k, x, y, q;
    for (i = 1; i <= interval; i++) {
      pyr[i * 4] = document.createElement("canvas");
      pyr[i * 4].width = Math.floor(pyr[0].width / Math.pow(scale, i));
      pyr[i * 4].height = Math.floor(pyr[0].height / Math.pow(scale, i));
      pyr[i * 4].getContext("2d").drawImage(pyr[0], 0, 0, pyr[0].width, pyr[0].height, 0, 0, pyr[i * 4].width, pyr[i * 4].height);
      pyr[i * 4].data = pyr[i * 4].getContext("2d").getImageData(0, 0, pyr[i * 4].width, pyr[i * 4].height).data;
    }
    for (i = next; i < scale_upto + next * 2; i++) {
      pyr[i * 4] = document.createElement("canvas");
      pyr[i * 4].width = Math.floor(pyr[i * 4 - next * 4].width / 2);
      pyr[i * 4].height = Math.floor(pyr[i * 4 - next * 4].height / 2);
      pyr[i * 4].getContext("2d").drawImage(pyr[i * 4 - next * 4], 0, 0, pyr[i * 4 - next * 4].width, pyr[i * 4 - next * 4].height, 0, 0, pyr[i * 4].width, pyr[i * 4].height);
      pyr[i * 4].data = pyr[i * 4].getContext("2d").getImageData(0, 0, pyr[i * 4].width, pyr[i * 4].height).data;
    }
    for (i = next * 2; i < scale_upto + next * 2; i++) {
      pyr[i * 4 + 1] = document.createElement("canvas");
      pyr[i * 4 + 1].width = Math.floor(pyr[i * 4 - next * 4].width / 2);
      pyr[i * 4 + 1].height = Math.floor(pyr[i * 4 - next * 4].height / 2);
      pyr[i * 4 + 1].getContext("2d").drawImage(pyr[i * 4 - next * 4], 1, 0, pyr[i * 4 - next * 4].width - 1, pyr[i * 4 - next * 4].height, 0, 0, pyr[i * 4 + 1].width - 2, pyr[i * 4 + 1].height);
      pyr[i * 4 + 1].data = pyr[i * 4 + 1].getContext("2d").getImageData(0, 0, pyr[i * 4 + 1].width, pyr[i * 4 + 1].height).data;
      pyr[i * 4 + 2] = document.createElement("canvas");
      pyr[i * 4 + 2].width = Math.floor(pyr[i * 4 - next * 4].width / 2);
      pyr[i * 4 + 2].height = Math.floor(pyr[i * 4 - next * 4].height / 2);
      pyr[i * 4 + 2].getContext("2d").drawImage(pyr[i * 4 - next * 4], 0, 1, pyr[i * 4 - next * 4].width, pyr[i * 4 - next * 4].height - 1, 0, 0, pyr[i * 4 + 2].width, pyr[i * 4 + 2].height - 2);
      pyr[i * 4 + 2].data = pyr[i * 4 + 2].getContext("2d").getImageData(0, 0, pyr[i * 4 + 2].width, pyr[i * 4 + 2].height).data;
      pyr[i * 4 + 3] = document.createElement("canvas");
      pyr[i * 4 + 3].width = Math.floor(pyr[i * 4 - next * 4].width / 2);
      pyr[i * 4 + 3].height = Math.floor(pyr[i * 4 - next * 4].height / 2);
      pyr[i * 4 + 3].getContext("2d").drawImage(pyr[i * 4 - next * 4], 1, 1, pyr[i * 4 - next * 4].width - 1, pyr[i * 4 - next * 4].height - 1, 0, 0, pyr[i * 4 + 3].width - 2, pyr[i * 4 + 3].height - 2);
      pyr[i * 4 + 3].data = pyr[i * 4 + 3].getContext("2d").getImageData(0, 0, pyr[i * 4 + 3].width, pyr[i * 4 + 3].height).data;
    }
    for (j = 0; j < cascade.stage_classifier.length; j++)
      cascade.stage_classifier[j].orig_feature = cascade.stage_classifier[j].feature;
    var scale_x = 1, scale_y = 1;
    var dx = [0, 1, 0, 1];
    var dy = [0, 0, 1, 1];
    var seq = [];
    for (i = 0; i < scale_upto; i++) {
      var qw = pyr[i * 4 + next * 8].width - Math.floor(cascade.width / 4);
      var qh = pyr[i * 4 + next * 8].height - Math.floor(cascade.height / 4);
      var step = [pyr[i * 4].width * 4, pyr[i * 4 + next * 4].width * 4, pyr[i * 4 + next * 8].width * 4];
      var paddings = [pyr[i * 4].width * 16 - qw * 16,
              pyr[i * 4 + next * 4].width * 8 - qw * 8,
              pyr[i * 4 + next * 8].width * 4 - qw * 4];
      for (j = 0; j < cascade.stage_classifier.length; j++) {
        var orig_feature = cascade.stage_classifier[j].orig_feature;
        var feature = cascade.stage_classifier[j].feature = new Array(cascade.stage_classifier[j].count);
        for (k = 0; k < cascade.stage_classifier[j].count; k++) {
          feature[k] = {"size" : orig_feature[k].size,
                  "px" : new Array(orig_feature[k].size),
                  "pz" : new Array(orig_feature[k].size),
                  "nx" : new Array(orig_feature[k].size),
                  "nz" : new Array(orig_feature[k].size)};
          for (q = 0; q < orig_feature[k].size; q++) {
            feature[k].px[q] = orig_feature[k].px[q] * 4 + orig_feature[k].py[q] * step[orig_feature[k].pz[q]];
            feature[k].pz[q] = orig_feature[k].pz[q];
            feature[k].nx[q] = orig_feature[k].nx[q] * 4 + orig_feature[k].ny[q] * step[orig_feature[k].nz[q]];
            feature[k].nz[q] = orig_feature[k].nz[q];
          }
        }
      }
      for (q = 0; q < 4; q++) {
        var u8 = [pyr[i * 4].data, pyr[i * 4 + next * 4].data, pyr[i * 4 + next * 8 + q].data];
        var u8o = [dx[q] * 8 + dy[q] * pyr[i * 4].width * 8, dx[q] * 4 + dy[q] * pyr[i * 4 + next * 4].width * 4, 0];
        for (y = 0; y < qh; y++) {
          for (x = 0; x < qw; x++) {
            var sum = 0;
            var flag = true;
            for (j = 0; j < cascade.stage_classifier.length; j++) {
              sum = 0;
              var alpha = cascade.stage_classifier[j].alpha;
              var feature = cascade.stage_classifier[j].feature;
              for (k = 0; k < cascade.stage_classifier[j].count; k++) {
                var feature_k = feature[k];
                var p, pmin = u8[feature_k.pz[0]][u8o[feature_k.pz[0]] + feature_k.px[0]];
                var n, nmax = u8[feature_k.nz[0]][u8o[feature_k.nz[0]] + feature_k.nx[0]];
                if (pmin <= nmax) {
                  sum += alpha[k * 2];
                } else {
                  var f, shortcut = true;
                  for (f = 0; f < feature_k.size; f++) {
                    if (feature_k.pz[f] >= 0) {
                      p = u8[feature_k.pz[f]][u8o[feature_k.pz[f]] + feature_k.px[f]];
                      if (p < pmin) {
                        if (p <= nmax) {
                          shortcut = false;
                          break;
                        }
                        pmin = p;
                      }
                    }
                    if (feature_k.nz[f] >= 0) {
                      n = u8[feature_k.nz[f]][u8o[feature_k.nz[f]] + feature_k.nx[f]];
                      if (n > nmax) {
                        if (pmin <= n) {
                          shortcut = false;
                          break;
                        }
                        nmax = n;
                      }
                    }
                  }
                  sum += (shortcut) ? alpha[k * 2 + 1] : alpha[k * 2];
                }
              }
              if (sum < cascade.stage_classifier[j].threshold) {
                flag = false;
                break;
              }
            }
            if (flag) {
              seq.push({"x" : (x * 4 + dx[q] * 2) * scale_x,
                    "y" : (y * 4 + dy[q] * 2) * scale_y,
                    "width" : cascade.width * scale_x,
                    "height" : cascade.height * scale_y,
                    "neighbor" : 1,
                    "confidence" : sum});
            }
            u8o[0] += 16;
            u8o[1] += 8;
            u8o[2] += 4;
          }
          u8o[0] += paddings[0];
          u8o[1] += paddings[1];
          u8o[2] += paddings[2];
        }
      }
      scale_x *= scale;
      scale_y *= scale;
    }
    for (j = 0; j < cascade.stage_classifier.length; j++)
      cascade.stage_classifier[j].feature = cascade.stage_classifier[j].orig_feature;
    if (!(min_neighbors > 0))
      return seq;
    else {
      var result = ccv.array_group(seq, function (r1, r2) {
        var distance = Math.floor(r1.width * 0.25 + 0.5);
  
        return r2.x <= r1.x + distance &&
             r2.x >= r1.x - distance &&
             r2.y <= r1.y + distance &&
             r2.y >= r1.y - distance &&
             r2.width <= Math.floor(r1.width * 1.5 + 0.5) &&
             Math.floor(r2.width * 1.5 + 0.5) >= r1.width;
      });
      var ncomp = result.cat;
      var idx_seq = result.index;
      var comps = new Array(ncomp + 1);
      for (i = 0; i < comps.length; i++)
        comps[i] = {"neighbors" : 0,
              "x" : 0,
              "y" : 0,
              "width" : 0,
              "height" : 0,
              "confidence" : 0};
  
      // count number of neighbors
      for(i = 0; i < seq.length; i++)
      {
        var r1 = seq[i];
        var idx = idx_seq[i];
  
        if (comps[idx].neighbors == 0)
          comps[idx].confidence = r1.confidence;
  
        ++comps[idx].neighbors;
  
        comps[idx].x += r1.x;
        comps[idx].y += r1.y;
        comps[idx].width += r1.width;
        comps[idx].height += r1.height;
        comps[idx].confidence = Math.max(comps[idx].confidence, r1.confidence);
      }
  
      var seq2 = [];
      // calculate average bounding box
      for(i = 0; i < ncomp; i++)
      {
        var n = comps[i].neighbors;
        if (n >= min_neighbors)
          seq2.push({"x" : (comps[i].x * 2 + n) / (2 * n),
                 "y" : (comps[i].y * 2 + n) / (2 * n),
                 "width" : (comps[i].width * 2 + n) / (2 * n),
                 "height" : (comps[i].height * 2 + n) / (2 * n),
                 "neighbors" : comps[i].neighbors,
                 "confidence" : comps[i].confidence});
      }
  
      var result_seq = [];
      // filter out small face rectangles inside large face rectangles
      for(i = 0; i < seq2.length; i++)
      {
        var r1 = seq2[i];
        var flag = true;
        for(j = 0; j < seq2.length; j++)
        {
          var r2 = seq2[j];
          var distance = Math.floor(r2.width * 0.25 + 0.5);
  
          if(i != j &&
             r1.x >= r2.x - distance &&
             r1.y >= r2.y - distance &&
             r1.x + r1.width <= r2.x + r2.width + distance &&
             r1.y + r1.height <= r2.y + r2.height + distance &&
             (r2.neighbors > Math.max(3, r1.neighbors) || r1.neighbors < 3))
          {
            flag = false;
            break;
          }
        }
  
        if(flag)
          result_seq.push(r1);
      }
      return result_seq;
    }
  };
  
  /**
   * Data for ccv facedetection
   *
   * @author Liu Liu / github.com/liuliu
   *
   * Copyright (c) 2010, Liu Liu
   * All rights reserved.
   *
   * Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
   *
   * * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
   * * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
   * * Neither the name of the authors nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
   *
   * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
   *
   */
  
  ccv.cascade = {"count" : 16, "width" : 24, "height" : 24, "stage_classifier" : 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 
  "use strict";
  /*
   * MOSSE correlation filter
   *
   * Optional parameters to constructor:
   *   drawResponse {canvasElement} : draws the correlation filter output on the given canvas element (default is none)
   *   psrThreshold {number} : peak-to-sidelobe-ratio threshold to use when updating filter while tracking (default is 10)
   *   eta {number} : adjusts how much new input affects the mosse filter, when updating filter while tracking
   *     number should be between 0 and 1 (default is 0.1)
   *   convertToGrayscale {boolean} : whether to convert canvas output to grayscale (default is true)
   *     if this is set to false, we assume all channels are equal and only grab values from red channel
   *
   * @author auduno / github.com/auduno
   */ 
  
  function mosseFilter(params) {
      
      var _filter, _top, _bottom;
      var _fft;
      var _w,_h;
      var _im_part;
      var _arrlen;
      var _cc;
      var _image_array;
      
      this.psr_prev = undefined;
      this.peak_prev = undefined;
      var peak = 0.0;
      var updateable = false;
      
      if (!params) params = {};
      // setup of canvas for drawing responses, if given
      if (params.drawResponse === undefined) {
          params.drawResponse = false;
      } else {
          if (params.drawResponse.tagName != 'CANVAS') {
              params.drawResponse = false;
          } else {
              var responseContext = params.drawResponse.getContext('2d');
          }
      }
      if (params.psrThreshold === undefined) params.psrThreshold = 10;
      if (params.eta === undefined) params.eta = 0.10;
      if (params.convertToGrayscale === undefined) params.convertToGrayscale = true;
      
      this.load = function(filter) {
          // initialize filter width and height
          _w = filter.width;
          _h = filter.height;
          _arrlen = _w*_h;
          _filter = [filter.real, filter.imag];
          // handling top and bottom when they're not present
          if (filter.top && filter.bottom) {
            updateable = true;
            _top = [filter.top.real, filter.top.imag];
            _bottom = [filter.bottom.real, filter.bottom.imag];
          }
          
          // initialize fft to given width
          _fft = new FFT();
          _fft.init(filter.width);
          
          // set up temporary variables
          if(typeof Float64Array !== 'undefined') {
              _im_part = new Float64Array(_arrlen);
              _image_array = new Float64Array(_arrlen);
          } else {
              _im_part = new Array(_arrlen);
              _image_array = new Array(_arrlen);
          }
          var canvas = document.createElement("canvas");
          canvas.setAttribute('width', _w);
          canvas.setAttribute('height', _h);
          _cc = canvas.getContext('2d');
      }
      
      this.init = function(w,h) {
          // initialize filter width and height for a blank filter
          _w = w;
          _h = h;
          _arrlen = _w*_h;
          
          _filter = [[],[]];
          _top = [[],[]];
          _bottom = [[],[]];
          for (var i = 0;i < _arrlen;i++) {
              _filter[0][i] = 0;
              _filter[1][i] = 0;
              _top[0][i] = 0;
              _top[1][i] = 0;
              _bottom[0][i] = 0;
              _bottom[1][i] = 0;
          }
          updateable = true;
          
          // initialize fft to given width
          _fft = new FFT();
          _fft.init(w);
          
          // set up temporary variables
          if(typeof Float64Array !== 'undefined') {
              _im_part = new Float64Array(_arrlen);
          } else {
              _im_part = new Array(_arrlen);
          }
          var canvas = document.createElement("canvas");
          canvas.setAttribute('width', _w);
          canvas.setAttribute('height', _h);
          _cc = canvas.getContext('2d');
      }
      
      // fft function
      this.fft = function(array) {
          // not in-place
          
          var cn = new Array(_arrlen);
          for (var i = 0;i < _arrlen;i++) {
            cn[i] = 0.0;
          }
          
          _fft.fft2d(array,cn)
          return [array, cn];
      }
      
      // fft function
      this.fft_inplace = function(array) {
          // in-place
          
          for (var i = 0;i < _arrlen;i++) {
            _im_part[i] = 0.0;
          }
          
          _fft.fft2d(array,_im_part)
          return [array, _im_part];
      }
      
      this.ifft = function(rn, cn) {
          // in-place
          _fft.ifft2d(rn, cn);
          return rn;
      }
  
      // peak to sidelobe ratio function (optional)
      this.psr = function(array) {
          // proper
          var sum = 0;
          var max = 0;
          var maxpos = [];
          var sdo = 0;
          var val;
          for (var x = 0;x < _w;x++) {
              for (var y = 0;y < _h;y++) {
                  val = array[(y*_w)+x];
                  sum += val;
                  sdo += (val*val);
                  if (max < val) {
                      max = val;
                      maxpos = [x,y];
                  }
              }
          }
          
          // subtract values around peak
          for (var x = -5;x < 6;x++) {
              for (var y = -5;y < 6;y++) {
                  if (Math.sqrt(x*x+y*y) < 5) {
                      val = array[((maxpos[1]+y)*_w)+(maxpos[0]+x)]
                      sdo -= (val*val);
                      sum -= val;
                  }
              }
          }
          
          var mean = sum/array.length;
          var sd = Math.sqrt((sdo/array.length)-(mean*mean));
          
          // get mean/variance of output around peak
          var psr = (max-mean)/sd;
          return psr;
      }
      
      this.getResponse = function(imageData) {
          // in-place
          
          // preprocess
          var prepImage = preprocess(imageData);
          prepImage = cosine_window(prepImage);
          
          // filter
          var res = this.fft_inplace(prepImage);
          
          // elementwise multiplication with filter
          complex_mult_inplace(res, _filter);
          
          // do inverse 2d fft
          var filtered = this.ifft(res[0],res[1]);
          return filtered;
      }
      
      this.track = function(input, left, top, width, height, updateFilter, gaussianPrior, calcPSR) {
          // finds position of filter in input image
          
          if (!_filter) {
              console.log("Mosse-filter needs to be initialized or trained before starting tracking.");
              return false;
          }
          
          if (input.tagName == "VIDEO" || input.tagName == "IMG") {
              // scale selection according to original source image
              var videoLeft = Math.round((left/input.width)*input.videoWidth);
              var videoTop = Math.round((top/input.height)*input.videoHeight);
              var videoWidth = Math.round((width/input.width)*input.videoWidth);
              var videoHeight = Math.round((height/input.height)*input.videoHeight);
              _cc.drawImage(input, videoLeft, videoTop, videoWidth, videoHeight, 0, 0, _w, _h);
          } else if (input.tagName == "CANVAS") {
              _cc.drawImage(input, left, top, width, height, 0, 0, _w, _h);
          }
          
          var image = _cc.getImageData(0,0,_w,_h);
          var id = image.data;
          
          if (params.convertToGrayscale) {
              // convert to grayscale
              for (var i = 0;i < _arrlen;i++) {
                  _image_array[i] = id[(4*i)]*0.3;
                  _image_array[i] += id[(4*i)+1]*0.59;
                  _image_array[i] += id[(4*i)+2]*0.11;
              } 
          } else {
              // use only one channel
              for (var i = 0;i < _arrlen;i++) {
                  _image_array[i] = id[(4*i)];
              } 
          }
          
          // preprocess
          var prepImage = preprocess(_image_array);
          prepImage = cosine_window(prepImage);
          
          // filter
          var res = this.fft_inplace(prepImage);
          // elementwise multiplication with filter
          var nures = complex_mult(res, _filter);
          // do inverse 2d fft
          var filtered = this.ifft(nures[0],nures[1]);
          
          // find max and min
          var max = 0;
          var min = 0;
          var maxpos = [];
          
          //method using centered gaussian prior
          if (gaussianPrior) {
              var prior, dx, dy;
              var variance = 128;
              for (var x = 0;x < _w;x++) {
                  for (var y = 0;y < _h;y++) {
                      dx = x - _w/2;
                      dy = y - _h/2;
                      prior = Math.exp(-0.5*((dx*dx)+(dy*dy))/variance)
                      if ((filtered[(y*_w)+x]*prior) > max) {
                          max = filtered[(y*_w)+x]*prior;
                          maxpos = [x,y];
                      }
                      if (filtered[(y*_w)+x] < min) {
                          min = filtered[(y*_w)+x];
                      }
                  }
              }
          } else {
              for (var x = 0;x < _w;x++) {
                  for (var y = 0;y < _h;y++) {
                      if (filtered[(y*_w)+x] > max) {
                          max = filtered[(y*_w)+x];
                          maxpos = [x,y];
                      }
                      if (filtered[(y*_w)+x] < min) {
                          min = filtered[(y*_w)+x];
                      }
                  }
              }
          }
          this.peak_prev = max;
          
          if (params.drawResponse) {
              // draw response
              var diff = max-min;
              var dc = document.createElement('canvas');
              dc.setAttribute('width', 32);
              dc.setAttribute('height', 32);
              var dcc = dc.getContext('2d');
              var psci = dcc.createImageData(32, 32);
              var pscidata = psci.data;
              for (var j = 0;j < 32*32;j++) {
                  //draw with priors
                  //var val = filtered[j]*Math.exp(-0.5*(((j%_w - _w/2)*(j%_w -_w/2))+((Math.floor(j/_h)-(_h/2))*(Math.floor(j/_h)-(_h/2))))/128);
                  var val = filtered[j];
                  val = Math.round((val+Math.abs(min))*(255/diff));
                  pscidata[j*4] = val;
                  pscidata[(j*4)+1] = val;
                  pscidata[(j*4)+2] = val;
                  pscidata[(j*4)+3] = 255;
              }
              dcc.putImageData(psci, 0, 0);
              responseContext.drawImage(dc, left, top, width, width);
          }
          
          if (calcPSR) {
            this.psr_prev = this.psr(filtered);
          }
          
          if (updateFilter) {
              if (!updateable) {
                  console.log("The loaded filter does not support updating. Ignoring parameter 'updateFilter'.");
              } else {
                  if (calcPSR) {
                    var psr = this.psr_prev;
                  } else {
                    var psr = this.psr(filtered);
                  }
                  
                  if (psr > params.psrThreshold) {
                      // create target
                      var target = [];
                      var nux = maxpos[0];
                      var nuy = maxpos[1];
                      for (var x = 0;x < _w;x++) {
                          for (var y = 0;y < _h;y++) {
                              target[(y*_w)+x] = Math.exp(-(((x-nux)*(x-nux))+((y-nuy)*(y-nuy)))/(2*2));
                          }
                      }
                      
                      //fft target
                      target = this.fft(target);
                      
                      // create filter
                      var res_conj = complex_conj(res);
                      var fuTop = complex_mult(target,res_conj);
                      var fuBottom = complex_mult(res,res_conj);
                      
                      // add up
                      var eta = params.eta;
                      for (var i = 0;i < _arrlen;i++) {
                          _top[0][i] = eta*fuTop[0][i] + (1-eta)*_top[0][i];
                          _top[1][i] = eta*fuTop[1][i] + (1-eta)*_top[1][i];
                          _bottom[0][i] = eta*fuBottom[0][i] + (1-eta)*_bottom[0][i];
                          _bottom[1][i] = eta*fuBottom[1][i] + (1-eta)*_bottom[1][i];
                      }
                      
                      _filter = complex_div(_top,_bottom);
                  }
              }
          }
          
          /*if (psr < 5) {
            maxpos = [_w/2,_h/2]; 
          }*/
          
          maxpos[0] = maxpos[0]*(width/_w);
          maxpos[1] = maxpos[1]*(width/_h);
          
          // check if output is strong enough
          // if not, return false?
          if (max < 0) {
            return false;
          } else {
            return maxpos;
          }
      }
      
      this.train = function(input, left, top, width, height) {
          
          if (!updateable) {
            console.log("The loaded filter does not support updating. Unable to do training.");
            return false;
          }
          
          if (input.tagName == "VIDEO" || input.tagName == "IMG") {
              // scale selection according to original source image
              var videoLeft = Math.round((left/input.width)*input.videoWidth);
              var videoTop = Math.round((top/input.height)*input.videoHeight);
              var videoWidth = Math.round((width/input.width)*input.videoWidth);
              var videoHeight = Math.round((height/input.height)*input.videoHeight);
              _cc.drawImage(input, videoLeft, videoTop, videoWidth, videoHeight, 0, 0, _w, _h);
          } else if (input.tagName == "CANVAS") {
              _cc.drawImage(input, left, top, width, height, 0, 0, _w, _h);
          }
          
          var image = _cc.getImageData(0,0,_w,_h);
          var id = image.data;
           
          // convert to grayscale
          for (var i = 0;i < _arrlen;i++) {
              _image_array[i] = id[(4*i)]*0.3;
              _image_array[i] += id[(4*i)+1]*0.59;
              _image_array[i] += id[(4*i)+2]*0.11;
          }
          
          // preprocess
          var prepImage = preprocess(_image_array);
          prepImage = cosine_window(prepImage);
          
          // create target
          var target = [];
          var nux = _w/2;
          var nuy = _h/2;
          for (var x = 0;x < _w;x++) {
              for (var y = 0;y < _h;y++) {
                  target[(y*_w)+x] = Math.exp(-(((x-nux)*(x-nux))+((y-nuy)*(y-nuy)))/(2*2));
              }
          }
          
          //fft target
          target = this.fft(target);
          
          // filter
          var res = this.fft(prepImage);
          // create filter
          var res_conj = complex_conj(res);
          var fuTop = complex_mult(target,res_conj);
          var fuBottom = complex_mult(res,res_conj);
          
          // add up
          var eta = params.eta;
          for (var i = 0;i < _arrlen;i++) {
              _top[0][i] = eta*fuTop[0][i] + (1-eta)*_top[0][i];
              _top[1][i] = eta*fuTop[1][i] + (1-eta)*_top[1][i];
              _bottom[0][i] = eta*fuBottom[0][i] + (1-eta)*_bottom[0][i];
              _bottom[1][i] = eta*fuBottom[1][i] + (1-eta)*_bottom[1][i];
          }
          
          _filter = complex_div(_top,_bottom);
          
          return true;
      }
      
      var preprocess = function(array) {
          // in-place
          
          // log adjusting
          for (var i = 0;i < _arrlen;i++) {
            array[i] = Math.log(array[i]+1);
          }
          
          // normalize to mean 0 and norm 1
          var mean = 0;
          for (var i = 0;i < _arrlen;i++) {
            mean += array[i];
          }
          mean /= _arrlen;
          
          for (var i = 0;i < _arrlen;i++) {
            array[i] -= mean;
          }
          var norm = 0.0;
          for (var i = 0;i < _arrlen;i++) {
            norm += (array[i]*array[i]);
          }
          norm = Math.sqrt(norm);
          for (var i = 0;i < _arrlen;i++) {
            array[i] /= norm;
          }
          
          return array;
      }
      
      var cosine_window = function(array) {
          // calculate rect cosine window (in-place)
          var pos = 0;
          for (var i = 0;i < _w;i++) {
              for (var j = 0;j < _h;j++) {
                  //pos = (i%_w)+(j*_w);
                  var cww = Math.sin((Math.PI*i)/(_w-1))
                  var cwh = Math.sin((Math.PI*j)/(_h-1))
                  array[pos] = Math.min(cww,cwh)*array[pos];
                  pos++;
              }
          }
          
          return array;
      }
      
      var complex_mult = function(cn1, cn2) {
          // not in-place
          var re_part = new Array(_w);
          var im_part = new Array(_w);
          var nucn = [re_part, im_part];
          for (var r = 0;r < _arrlen;r++) {
              nucn[0][r] = (cn1[0][r]*cn2[0][r]) - (cn1[1][r]*cn2[1][r]);
              nucn[1][r] = (cn1[0][r]*cn2[1][r]) + (cn1[1][r]*cn2[0][r]);
          }
          return nucn;
      }
      
      var complex_mult_inplace = function(cn1, cn2) {
          // in-place
          var temp1, temp2;
          for (var r = 0;r < _arrlen;r++) {
              temp1 = (cn1[0][r]*cn2[0][r]) - (cn1[1][r]*cn2[1][r]);
              temp2 = (cn1[0][r]*cn2[1][r]) + (cn1[1][r]*cn2[0][r]);
              cn1[0][r] = temp1;
              cn1[1][r] = temp2;
          }
      }
      
      var complex_conj = function(cn) {
          // not in-place (TODO)
          var nucn = [[],[]];
          for (var i = 0;i < _arrlen;i++) {
              nucn[0][i] = cn[0][i]
              nucn[1][i] = -cn[1][i];
          }
          return nucn;
      }
      
      var complex_div = function(cn1, cn2) {
          // not in-place (TODO)
          var nucn = [[],[]];
          for (var r = 0;r < _arrlen;r++) {
              nucn[0][r] = ((cn1[0][r]*cn2[0][r])+(cn1[1][r]*cn2[1][r])) / ((cn2[0][r]*cn2[0][r]) + (cn2[1][r]*cn2[1][r]));
              nucn[1][r] = ((cn1[1][r]*cn2[0][r])-(cn1[0][r]*cn2[1][r])) / ((cn2[0][r]*cn2[0][r]) + (cn2[1][r]*cn2[1][r]));
          }
          return nucn;
      }
  }
  
  /**
   * Fast Fourier Transform
   * 1D-FFT/IFFT, 2D-FFT/IFFT (radix-2)
   * 
   * @author ryo / github.com/wellflat
   * Based on https://github.com/wellflat/jslib with some tiny optimizations
   */
  
  function FFT() {
    
    var _n = 0,          // order
        _bitrev = null,  // bit reversal table
        _cstb = null;    // sin/cos table
    var _tre, _tim;
    
    this.init = function (n) {
      if(n !== 0 && (n & (n - 1)) === 0) {
        _n = n;
        _setVariables();
        _makeBitReversal();
        _makeCosSinTable();
      } else {
        throw new Error("init: radix-2 required");
      }
    }
      
    // 1D-FFT
    this.fft1d = function (re, im) {
      fft(re, im, 1);
    }
      
    // 1D-IFFT
    this.ifft1d = function (re, im) {
      var n = 1/_n;
      fft(re, im, -1);
      for(var i=0; i<_n; i++) {
        re[i] *= n;
        im[i] *= n;
      }
    }
    
    // 2D-FFT
    this.fft2d = function (re, im) {
      var i = 0;
      // x-axis
      for(var y=0; y<_n; y++) {
        i = y*_n;
        for(var x1=0; x1<_n; x1++) {
          _tre[x1] = re[x1 + i];
          _tim[x1] = im[x1 + i];
        }
        this.fft1d(_tre, _tim);
        for(var x2=0; x2<_n; x2++) {
          re[x2 + i] = _tre[x2];
          im[x2 + i] = _tim[x2];
        }
      }
      // y-axis
      for(var x=0; x<_n; x++) {
        for(var y1=0; y1<_n; y1++) {
          i = x + y1*_n;
          _tre[y1] = re[i];
          _tim[y1] = im[i];
        }
        this.fft1d(_tre, _tim);
        for(var y2=0; y2<_n; y2++) {
          i = x + y2*_n;
          re[i] = _tre[y2];
          im[i] = _tim[y2];
        }
      }
    }
    
    // 2D-IFFT
    this.ifft2d = function (re, im) {
      var i = 0;
      // x-axis
      for(var y=0; y<_n; y++) {
        i = y*_n;
        for(var x1=0; x1<_n; x1++) {
          _tre[x1] = re[x1 + i];
          _tim[x1] = im[x1 + i];
        }
        this.ifft1d(_tre, _tim);
        for(var x2=0; x2<_n; x2++) {
          re[x2 + i] = _tre[x2];
          im[x2 + i] = _tim[x2];
        }
      }
      // y-axis
      for(var x=0; x<_n; x++) {
        for(var y1=0; y1<_n; y1++) {
          i = x + y1*_n;
          _tre[y1] = re[i];
          _tim[y1] = im[i];
        }
        this.ifft1d(_tre, _tim);
        for(var y2=0; y2<_n; y2++) {
          i = x + y2*_n;
          re[i] = _tre[y2];
          im[i] = _tim[y2];
        }
      }
    }
    
    // core operation of FFT
    function fft(re, im, inv) {
      var d, h, ik, m, tmp, wr, wi, xr, xi,
          n4 = _n >> 2;
      // bit reversal
      for(var l=0; l<_n; l++) {
        m = _bitrev[l];
        if(l < m) {
          tmp = re[l];
          re[l] = re[m];
          re[m] = tmp;
          tmp = im[l];
          im[l] = im[m];
          im[m] = tmp;
        }
      }
      // butterfly operation
      for(var k=1; k<_n; k<<=1) {
        h = 0;
        d = _n/(k << 1);
        for(var j=0; j<k; j++) {
          wr = _cstb[h + n4];
          wi = inv*_cstb[h];
          for(var i=j; i<_n; i+=(k<<1)) {
            ik = i + k;
            xr = wr*re[ik] + wi*im[ik];
            xi = wr*im[ik] - wi*re[ik];
            re[ik] = re[i] - xr;
            re[i] += xr;
            im[ik] = im[i] - xi;
            im[i] += xi;
          }
          h += d;
        }
      }
    }
    
    // set variables
    function _setVariables() {
      if(typeof Uint8Array !== 'undefined') {
        _bitrev = new Uint8Array(_n);
      } else {
        _bitrev = new Array(_n);
      }
      if(typeof Float64Array !== 'undefined') {
        _cstb = new Float64Array(_n*1.25);
        _tre = new Float64Array(_n*_n);
        _tim = new Float64Array(_n*_n);
      } else {
        _cstb = new Array(_n*1.25);
        _tre = new Array(_n*_n);
        _tim = new Array(_n*_n);
      }
    }
    
    // make bit reversal table
    function _makeBitReversal() {
      var i = 0,
          j = 0,
          k = 0;
      _bitrev[0] = 0;
      while(++i < _n) {
        k = _n >> 1;
        while(k <= j) {
          j -= k;
          k >>= 1;
        }
        j += k;
        _bitrev[i] = j;
      }
    }
    
    // make trigonometric function table
    function _makeCosSinTable() {
      var n2 = _n >> 1,
          n4 = _n >> 2,
          n8 = _n >> 3,
          n2p4 = n2 + n4,
          t = Math.sin(Math.PI/_n),
          dc = 2*t*t,
          ds = Math.sqrt(dc*(2 - dc)),
          c = _cstb[n4] = 1,
          s = _cstb[0] = 0;
      t = 2*dc;
      for(var i=1; i<n8; i++) {
        c -= dc;
        dc += t*c;
        s += ds;
        ds -= t*s;
        _cstb[i] = s;
        _cstb[n4 - i] = c;
      }
      if(n8 !== 0) {
        _cstb[n8] = Math.sqrt(0.5);
      }
      for(var j=0; j<n4; j++) {
        _cstb[n2 - j]  = _cstb[j];
      }
      for(var k=0; k<n2p4; k++) {
        _cstb[k + n2] = -_cstb[k];
      }
    }
  }
  