PerceptronFHMM-master/edu.cmu.lti.weizh.cda/src/main/java/edu/cmu/lti/weizh/utils/LBFGS.java
package edu.cmu.lti.weizh.utils;

/* LBFGS.java
 * Copyright (C) 1999, Robert Dodier (robert_dodier@yahoo.com)
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of version 2.1 of the GNU Lesser General Public License
 * as published by the Free Software Foundation.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA, 02111-1307, USA,
 * or visit the GNU web site, www.gnu.org.
 */

/**
 * <p>
 * This class contains code for the limited-memory
 * Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm for large-scale
 * multidimensional unconstrained minimization problems. This file is a
 * translation of Fortran code written by Jorge Nocedal. The only modification
 * to the algorithm is the addition of a cache to store the result of the most
 * recent line search. See <tt>solution_cache</tt> below.
 * 
 * Following is a message from Jorge Nocedal:
 * 
 * <pre>
 *   From: Jorge Nocedal [mailto:nocedal@dario.ece.nwu.edu]
 *   Sent: Friday, August 17, 2001 9:09 AM
 *   To: Robert Dodier
 *   Subject: Re: Commercial licensing terms for LBFGS?
 *   
 *   Robert:
 *   The code L-BFGS (for unconstrained problems) is in the public domain.
 *   It can be used in any commercial application.
 *   
 *   The code L-BFGS-B (for bound constrained problems) belongs to
 *   ACM. You need to contact them for a commercial license. It is
 *   algorithm 778.
 *   
 *   Jorge
 * </pre>
 * 
 * <p>
 * This code is derived from the Fortran program <code>lbfgs.f</code>. The Java
 * translation was effected mostly mechanically, with some manual clean-up; in
 * particular, array indices start at 0 instead of 1. Most of the comments from
 * the Fortran code have been pasted in here as well.
 * </p>
 * 
 * <p>
 * Here's some information on the original LBFGS Fortran source code, available
 * at <a href="http://www.netlib.org/opt/lbfgs_um.shar">
 * http://www.netlib.org/opt/lbfgs_um.shar</a>. This info is taken verbatim from
 * the Netlib blurb on the Fortran source.
 * </p>
 * 
 * <pre>
 * 	file    opt/lbfgs_um.shar
 * 	for     unconstrained optimization problems
 * 	alg     limited memory BFGS method
 * 	by      J. Nocedal
 * 	contact nocedal@eecs.nwu.edu
 * 	ref     D. C. Liu and J. Nocedal, ``On the limited memory BFGS method for
 * 	,       large scale optimization methods'' Mathematical Programming 45
 * 	,       (1989), pp. 503-528.
 * 	,       (Postscript file of this paper is available via anonymous ftp
 * 	,       to eecs.nwu.edu in the directory pub/lbfgs/lbfgs_um.)
 * http://www.ece.northwestern.edu/~nocedal/PDFfiles/limited-memory.pdf
 * </pre>
 * 
 * @author Jorge Nocedal: original Fortran version, including comments (July
 *         1990). Robert Dodier: Java translation, August 1997.
 */

public class LBFGS {
	/**
	 * Specialized exception class for LBFGS; contains the <code>iflag</code>
	 * value returned by <code>lbfgs</code>.
	 */

	public static class ExceptionWithIflag extends Exception {
		/**
		 * 
		 */
		private static final long serialVersionUID = 1L;
		public int iflag;

		public ExceptionWithIflag(int i, String s) {
			super(s);
			iflag = i;
		}

		@Override
		public String toString() {
			return getMessage() + " (iflag == " + iflag + ")";
		}
	}

	/**
	 * Controls the accuracy of the line search <code>mcsrch</code>. If the
	 * function and gradient evaluations are inexpensive with respect to the
	 * cost of the iteration (which is sometimes the case when solving very
	 * large problems) it may be advantageous to set <code>gtol</code> to a
	 * small value. A typical small value is 0.1. Restriction: <code>gtol</code>
	 * should be greater than 1e-4.
	 */

	public static double gtol = 0.9;

	/**
	 * Specify lower bound for the step in the line search. The default value is
	 * 1e-20. This value need not be modified unless the exponent is too large
	 * for the machine being used, or unless the problem is extremely badly
	 * scaled (in which case the exponent should be increased).
	 */

	public static double stpmin = 1e-20;

	/**
	 * Specify upper bound for the step in the line search. The default value is
	 * 1e20. This value need not be modified unless the exponent is too large
	 * for the machine being used, or unless the problem is extremely badly
	 * scaled (in which case the exponent should be increased).
	 */

	public static double stpmax = 1e20;

	public static int maxfev = 200;

	/**
	 * The solution vector as it was at the end of the most recently completed
	 * line search. This will usually be different from the return value of the
	 * parameter <tt>x</tt> of <tt>lbfgs</tt>, which is modified by line-search
	 * steps. A caller which wants to stop the optimization iterations before
	 * <tt>LBFGS.lbfgs</tt> automatically stops (by reaching a very small
	 * gradient) should copy this vector instead of using <tt>x</tt>. When
	 * <tt>LBFGS.lbfgs</tt> automatically stops, then <tt>x</tt> and
	 * <tt>solution_cache</tt> are the same.
	 */
	public static double[] solution_cache = null;

	private static double gnorm = 0, stp1 = 0, ftol = 0, stp[] = new double[1],
			ys = 0, yy = 0, sq = 0, yr = 0, beta = 0, xnorm = 0;
	private static int iter = 0, nfun = 0, point = 0, ispt = 0, iypt = 0,
			info[] = new int[1], bound = 0, npt = 0, cp = 0, i = 0,
			nfev[] = new int[1], inmc = 0, iycn = 0, iscn = 0;
	private static boolean finish = false;

	private static double[] w = null;

	/**
	 * This method returns the total number of evaluations of the objective
	 * function since the last time LBFGS was restarted. The total number of
	 * function evaluations increases by the number of evaluations required for
	 * the line search; the total is only increased after a successful line
	 * search.
	 */
	public static int nfevaluations() {
		return nfun;
	}

	/**
	 * This subroutine solves the unconstrained minimization problem
	 * 
	 * <pre>
	 *     min f(x),    x = (x1,x2,...,x_n),
	 * </pre>
	 * 
	 * using the limited-memory BFGS method. The routine is especially effective
	 * on problems involving a large number of variables. In a typical iteration
	 * of this method an approximation <code>Hk</code> to the inverse of the
	 * Hessian is obtained by applying <code>m</code> BFGS updates to a diagonal
	 * matrix <code>Hk0</code>, using information from the previous M steps. The
	 * user specifies the number <code>m</code>, which determines the amount of
	 * storage required by the routine. The user may also provide the diagonal
	 * matrices <code>Hk0</code> if not satisfied with the default choice. The
	 * algorithm is described in "On the limited memory BFGS method for large
	 * scale optimization", by D. Liu and J. Nocedal, Mathematical Programming B
	 * 45 (1989) 503-528.
	 * 
	 * The user is required to calculate the function value <code>f</code> and
	 * its gradient <code>g</code>. In order to allow the user complete control
	 * over these computations, reverse communication is used. The routine must
	 * be called repeatedly under the control of the parameter
	 * <code>iflag</code>.
	 * 
	 * The steplength is determined at each iteration by means of the line
	 * search routine <code>mcsrch</code>, which is a slight modification of the
	 * routine <code>CSRCH</code> written by More' and Thuente.
	 * 
	 * The only variables that are machine-dependent are <code>xtol</code>,
	 * <code>stpmin</code> and <code>stpmax</code>.
	 * 
	 * Progress messages and non-fatal error messages are printed to
	 * <code>System.err</code>. Fatal errors cause exception to be thrown, as
	 * listed below.
	 * 
	 * @param n
	 *            The number of variables in the minimization problem.
	 *            Restriction: <code>n &gt; 0</code>.
	 * 
	 * @param m
	 *            The number of corrections used in the BFGS update. Values of
	 *            <code>m</code> less than 3 are not recommended; large values
	 *            of <code>m</code> will result in excessive computing time.
	 *            <code>3 &lt;= m &lt;= 7</code> is recommended. Restriction:
	 *            <code>m &gt; 0</code>.
	 * 
	 * @param x
	 *            On initial entry this must be set by the user to the values of
	 *            the initial estimate of the solution vector. On exit with
	 *            <code>iflag = 0</code>, it contains the values of the
	 *            variables at the best point found (usually a solution).
	 * 
	 * @param f
	 *            Before initial entry and on a re-entry with
	 *            <code>iflag = 1</code>, it must be set by the user to contain
	 *            the value of the function <code>f</code> at the point
	 *            <code>x</code>.
	 * 
	 * @param g
	 *            Before initial entry and on a re-entry with
	 *            <code>iflag = 1</code>, it must be set by the user to contain
	 *            the components of the gradient <code>g</code> at the point
	 *            <code>x</code>.
	 * 
	 * @param diagco
	 *            Set this to <code>true</code> if the user wishes to provide
	 *            the diagonal matrix <code>Hk0</code> at each iteration.
	 *            Otherwise it should be set to <code>false</code> in which case
	 *            <code>lbfgs</code> will use a default value described below.
	 *            If <code>diagco</code> is set to <code>true</code> the routine
	 *            will return at each iteration of the algorithm with
	 *            <code>iflag = 2</code>, and the diagonal matrix
	 *            <code>Hk0</code> must be provided in the array
	 *            <code>diag</code>.
	 * 
	 * @param diag
	 *            If <code>diagco = true</code>, then on initial entry or on
	 *            re-entry with <code>iflag = 2</code>, <code>diag</code> must
	 *            be set by the user to contain the values of the diagonal
	 *            matrix <code>Hk0</code>. Restriction: all elements of
	 *            <code>diag</code> must be positive.
	 * 
	 * @param iprint
	 *            Specifies output generated by <code>lbfgs</code>.
	 *            <code>iprint[0]</code> specifies the frequency of the output:
	 *            <ul>
	 *            <li> <code>iprint[0] &lt; 0</code>: no output is generated,
	 *            <li> <code>iprint[0] = 0</code>: output only at first and last
	 *            iteration,
	 *            <li> <code>iprint[0] &gt; 0</code>: output every
	 *            <code>iprint[0]</code> iterations.
	 *            </ul>
	 * 
	 *            <code>iprint[1]</code> specifies the type of output generated:
	 *            <ul>
	 *            <li> <code>iprint[1] = 0</code>: iteration count, number of
	 *            function evaluations, function value, norm of the gradient,
	 *            and steplength,
	 *            <li> <code>iprint[1] = 1</code>: same as
	 *            <code>iprint[1]=0</code>, plus vector of variables and
	 *            gradient vector at the initial point,
	 *            <li> <code>iprint[1] = 2</code>: same as
	 *            <code>iprint[1]=1</code>, plus vector of variables,
	 *            <li> <code>iprint[1] = 3</code>: same as
	 *            <code>iprint[1]=2</code>, plus gradient vector.
	 *            </ul>
	 * 
	 * @param eps
	 *            Determines the accuracy with which the solution is to be
	 *            found. The subroutine terminates when
	 * 
	 *            <pre>
	 *            ||G|| &lt; EPS max(1,||X||),
	 * </pre>
	 * 
	 *            where <code>||.||</code> denotes the Euclidean norm.
	 * 
	 * @param xtol
	 *            An estimate of the machine precision (e.g. 10e-16 on a SUN
	 *            station 3/60). The line search routine will terminate if the
	 *            relative width of the interval of uncertainty is less than
	 *            <code>xtol</code>.
	 * 
	 * @param iflag
	 *            This must be set to 0 on initial entry to <code>lbfgs</code>.
	 *            A return with <code>iflag &lt; 0</code> indicates an error,
	 *            and <code>iflag = 0</code> indicates that the routine has
	 *            terminated without detecting errors. On a return with
	 *            <code>iflag = 1</code>, the user must evaluate the function
	 *            <code>f</code> and gradient <code>g</code>. On a return with
	 *            <code>iflag = 2</code>, the user must provide the diagonal
	 *            matrix <code>Hk0</code>.
	 * 
	 *            The following negative values of <code>iflag</code>, detecting
	 *            an error, are possible:
	 *            <ul>
	 *            <li> <code>iflag = -1</code> The line search routine
	 *            <code>mcsrch</code> failed. One of the following messages is
	 *            printed:
	 *            <ul>
	 *            <li>Improper input parameters.
	 *            <li>Relative width of the interval of uncertainty is at most
	 *            <code>xtol</code>.
	 *            <li>More than 20 function evaluations were required at the
	 *            present iteration.
	 *            <li>The step is too small.
	 *            <li>The step is too large.
	 *            <li>Rounding errors prevent further progress. There may not be
	 *            a step which satisfies the sufficient decrease and curvature
	 *            conditions. Tolerances may be too small.
	 *            </ul>
	 *            <li><code>iflag = -2</code> The i-th diagonal element of the
	 *            diagonal inverse Hessian approximation, given in DIAG, is not
	 *            positive.
	 *            <li><code>iflag = -3</code> Improper input parameters for
	 *            LBFGS (<code>n</code> or <code>m</code> are not positive).
	 *            </ul>
	 * 
	 * @throws LBFGS.ExceptionWithIflag
	 */

	public static void lbfgs(int n, int m, double[] x, double f, double[] g,
			boolean diagco, double[] diag, int[] iprint, double eps,
			double xtol, int[] iflag) throws ExceptionWithIflag {
		boolean execute_entire_while_loop = false;

		if (w == null || w.length != n * (2 * m + 1) + 2 * m) {
			w = new double[n * (2 * m + 1) + 2 * m];
		}

		if (iflag[0] == 0) {
			// Initialize.

			solution_cache = new double[n];
			System.arraycopy(x, 0, solution_cache, 0, n);

			iter = 0;

			if (n <= 0 || m <= 0) {
				iflag[0] = -3;
				throw new ExceptionWithIflag(iflag[0],
						"Improper input parameters  (n or m are not positive.)");
			}

			if (gtol <= 0.0001) {
				System.err
						.println("LBFGS.lbfgs: gtol is less than or equal to 0.0001. It has been reset to 0.9.");
				gtol = 0.9;
			}

			nfun = 1;
			point = 0;
			finish = false;

			if (diagco) {
				for (i = 1; i <= n; i += 1) {
					if (diag[i - 1] <= 0) {
						iflag[0] = -2;
						throw new ExceptionWithIflag(
								iflag[0],
								"The "
										+ i
										+ "-th diagonal element of the inverse hessian approximation is not positive.");
					}
				}
			} else {
				for (i = 1; i <= n; i += 1) {
					diag[i - 1] = 1;
				}
			}
			ispt = n + 2 * m;
			iypt = ispt + n * m;

			for (i = 1; i <= n; i += 1) {
				w[ispt + i - 1] = -g[i - 1] * diag[i - 1];
				if (badNum(w[ispt + i - 1]))
					System.err.println("w1 " + g[i - 1] + " " + diag[i - 1]);
			}

			gnorm = Math.sqrt(ddot(n, g, 0, 1, g, 0, 1));
			stp1 = 1 / gnorm;
			ftol = 0.0001;

			if (iprint[1 - 1] >= 0)
				lb1(iprint, iter, nfun, gnorm, n, m, x, f, g, stp, finish);

			execute_entire_while_loop = true;
		}

		while (true) {
			if (execute_entire_while_loop) {
				iter = iter + 1;
				info[0] = 0;
				bound = iter - 1;
				if (iter != 1) {
					if (iter > m)
						bound = m;
					ys = ddot(n, w, iypt + npt, 1, w, ispt + npt, 1);
					if (!diagco) {
						yy = ddot(n, w, iypt + npt, 1, w, iypt + npt, 1);

						for (i = 1; i <= n; i += 1) {
							diag[i - 1] = safeDiv(ys , yy);
						}
					} else {
						iflag[0] = 2;
						return;
					}
				}
			}

			if (execute_entire_while_loop || iflag[0] == 2) {
				if (iter != 1) {
					if (diagco) {
						for (i = 1; i <= n; i += 1) {
							if (diag[i - 1] <= 0) {
								iflag[0] = -2;
								throw new ExceptionWithIflag(
										iflag[0],
										"The "
												+ i
												+ "-th diagonal element of the inverse hessian approximation is not positive.");
							}
						}
					}
					cp = point;
					if (point == 0)
						cp = m;
					w[n + cp - 1] = 1 / ys;
					if (badNum(w[n + cp - 1]))
						System.err.println("w2 " + ys);

					for (i = 1; i <= n; i += 1) {
						w[i - 1] = -g[i - 1];
						if (badNum(w[i - 1]))
							throw new IllegalArgumentException(i + " "
									+ g[i - 1]);
					}

					cp = point;

					for (i = 1; i <= bound; i += 1) {
						cp = cp - 1;
						if (cp == -1)
							cp = m - 1;
						sq = ddot(n, w, ispt + cp * n, 1, w, 0, 1);
						inmc = n + m + cp + 1;
						iycn = iypt + cp * n;
						w[inmc - 1] = w[n + cp] * sq;
						if (badNum(w[inmc - 1])) {
							System.err.println("w3 " + w[n + cp] + " " + sq);
							lb1(iprint, iter, nfun, gnorm, n, m, x, f, g, stp,
									finish);
						}
						daxpy(n, -w[inmc - 1], w, iycn, 1, w, 0, 1);
					}

					for (i = 1; i <= n; i += 1) {
						w[i - 1] *= diag[i - 1];
						if (badNum(w[i - 1]))
							System.err.println("w4 " + diag[i - 1]);
					}

					for (i = 1; i <= bound; i += 1) {
						yr = ddot(n, w, iypt + cp * n, 1, w, 0, 1);
						beta = safeMult(w[n + cp] , yr);
						inmc = n + m + cp + 1;
						beta = w[inmc - 1] - beta;
						if (badNum(beta)) {
								throw new IllegalArgumentException(w[inmc - 1]+" "+safeMult(w[n + cp] , yr));
						}
						iscn = ispt + cp * n;
						daxpy(n, beta, w, iscn, 1, w, 0, 1);
						cp = cp + 1;
						if (cp == m)
							cp = 0;
					}

					for (i = 1; i <= n; i += 1) {
						w[ispt + point * n + i - 1] = w[i - 1];
						if (badNum(w[ispt + point * n + i - 1]))
							System.err.println("w5 " + w[i - 1]);
					}
				}

				nfev[0] = 0;
				Mcsrch.setSTP(stp, iter == 1 && stp1 < 1 ? stp1 : 1);

				for (i = 1; i <= n; i += 1) {
					w[i - 1] = g[i - 1];
					if (badNum(w[i - 1]))
						System.err.println("w6 " + g[i - 1]);
				}
			}
			double MY_MAX_STEP = 1;
			double directionMag = ddot(n, w, ispt + point * n, 1, w, ispt
					+ point * n, 1);
			double effectiveStep = stp[0] * directionMag;
			if (effectiveStep > MY_MAX_STEP) {
				if (iprint[0] > 0)
					System.err.println("reducing step: " + stp[0] + " => "
							+ (MY_MAX_STEP / directionMag));
				// stpmax = MY_MAX_STEP / directionMag;
			} else
				stpmax = 1e20;

			// if (iprint[1 - 1] >= 0)
			// lb1(iprint, iter, nfun, gnorm, n, m, x, f, g, stp, finish);

			Mcsrch.mcsrch(n, x, f, g, w, ispt + point * n, stp, ftol, xtol,
					maxfev, info, nfev, diag, iprint);

			if (info[0] == -1) {
				iflag[0] = 1;
				return;
			}

			if (iprint[0] > 0)
				System.err.println("msrch return = nfev=" + nfev[0] + " nfun="
						+ nfun + " info=" + info[0] + " bestx=" + Mcsrch.stx[0]
						+ " farx=" + Mcsrch.sty[0] + " brackt="
						+ Mcsrch.brackt[0] + " stp=" + stp[0] + " gnorm="
						+ Math.sqrt(ddot(n, g, 0, 1, g, 0, 1)) + " xnorm="
						+ Math.sqrt(ddot(n, x, 0, 1, x, 0, 1)));

			if (info[0] != 1) {
				iflag[0] = -1;
				throw new ExceptionWithIflag(
						iflag[0],
						"Line search failed. See documentation of routine mcsrch. Error return of line search: info = "
								+ info[0]
								+ " Possible causes: function or gradient are incorrect, or incorrect tolerances.");
			}

			nfun += nfev[0];
			npt = point * n;

			for (i = 1; i <= n; i += 1) {
				w[ispt + npt + i - 1] *= stp[0];
				if (badNum(w[ispt + npt + i - 1]))
					System.err.println("w6 " + stp[0]);
				w[iypt + npt + i - 1] = g[i - 1] - w[i - 1];
				if (badNum(w[iypt + npt + i - 1]))
					System.err.println("w7 " + g[i - 1] + " " + w[i - 1]);
			}

			point++;
			if (point == m)
				point = 0;

			gnorm = Math.sqrt(ddot(n, g, 0, 1, g, 0, 1));
			xnorm = Math.sqrt(ddot(n, x, 0, 1, x, 0, 1));
			xnorm = Math.max(1.0, xnorm);

			if (gnorm / xnorm <= eps)
				finish = true;

			if (iprint[1 - 1] >= 0)
				lb1(iprint, iter, nfun, gnorm, n, m, x, f, g, stp, finish);

			// Cache the current solution vector. Due to the spaghetti-like
			// nature of this code, it's not possible to quit here and return;
			// we need to go back to the top of the loop, and eventually call
			// mcsrch one more time -- but that will modify the solution vector.
			// So we need to keep a copy of the solution vector as it was at
			// the completion (info[0]==1) of the most recent line search.
			System.arraycopy(x, 0, solution_cache, 0, n);

			if (finish) {
				iflag[0] = 0;
				return;
			}

			execute_entire_while_loop = true; // from now on, execute whole loop
		}
	}

	/**
	 * Print debugging and status messages for <code>lbfgs</code>. Depending on
	 * the parameter <code>iprint</code>, this can include number of function
	 * evaluations, current function value, etc. The messages are output to
	 * <code>System.err</code>.
	 * 
	 * @param iprint
	 *            Specifies output generated by <code>lbfgs</code>.
	 *            <p>
	 *            <code>iprint[0]</code> specifies the frequency of the output:
	 *            <ul>
	 *            <li> <code>iprint[0] &lt; 0</code>: no output is generated,
	 *            <li> <code>iprint[0] = 0</code>: output only at first and last
	 *            iteration,
	 *            <li> <code>iprint[0] &gt; 0</code>: output every
	 *            <code>iprint[0]</code> iterations.
	 *            </ul>
	 *            <p>
	 * 
	 *            <code>iprint[1]</code> specifies the type of output generated:
	 *            <ul>
	 *            <li> <code>iprint[1] = 0</code>: iteration count, number of
	 *            function evaluations, function value, norm of the gradient,
	 *            and steplength,
	 *            <li> <code>iprint[1] = 1</code>: same as
	 *            <code>iprint[1]=0</code>, plus vector of variables and
	 *            gradient vector at the initial point,
	 *            <li> <code>iprint[1] = 2</code>: same as
	 *            <code>iprint[1]=1</code>, plus vector of variables,
	 *            <li> <code>iprint[1] = 3</code>: same as
	 *            <code>iprint[1]=2</code>, plus gradient vector.
	 *            </ul>
	 * @param iter1
	 *            Number of iterations so far.
	 * @param nfun1
	 *            Number of function evaluations so far.
	 * @param gnorm1
	 *            Norm of gradient at current solution <code>x</code>.
	 * @param n
	 *            Number of free parameters.
	 * @param m
	 *            Number of corrections kept.
	 * @param x
	 *            Current solution.
	 * @param f
	 *            Function value at current solution.
	 * @param g
	 *            Gradient at current solution <code>x</code>.
	 * @param stp11
	 *            Current stepsize.
	 * @param finish1
	 *            Whether this method should print the ``we're done'' message.
	 */
	public static void lb1(int[] iprint, int iter1, int nfun1, double gnorm1,
			int n, int m, double[] x, double f, double[] g, double[] stp11,
			boolean finish1) {
		String heading = "\ti\tnfn\tfunc\t\t\tgnorm\t\t\tsteplength";
		int i1;

		if (iter1 == 0) {
			System.err
					.println("*************************************************");
			System.err.println("  n = " + n + "   number of corrections = " + m
					+ "\n       initial values");
			System.err.println(" f =  " + f + "   gnorm =  " + gnorm1);
			if (iprint[2 - 1] >= 1) {
				System.err.print(" vector x =");
				for (i1 = 1; i1 <= n; i1++)
					System.err.print("  " + x[i1 - 1]);
				System.err.println("");

				System.err.print(" gradient vector g =");
				for (i1 = 1; i1 <= n; i1++)
					System.err.print("  " + g[i1 - 1]);
				System.err.println("");
			}
			System.err
					.println("*************************************************");
			System.err.println(heading);
		} else {
			if ((iprint[1 - 1] == 0) && (iter1 != 1 && !finish1))
				return;
			if (iprint[1 - 1] != 0) {
				if ((iter1 - 1) % iprint[1 - 1] == 0 || finish1) {
					if (iprint[2 - 1] > 1 && iter1 > 1)
						System.err.println(heading);
					System.err.println("\t" + iter1 + "\t" + nfun1 + "\t" + f
							+ "\t" + gnorm1 + "\t" + stp11[0]);
				} else {
					return;
				}
			} else {
				if (iprint[2 - 1] > 1 && finish1)
					System.err.println(heading);
				System.err.println("\t" + iter1 + "\t" + nfun1 + "\t" + f
						+ "\t" + gnorm1 + "\t" + stp11[0]);
			}
			if (iprint[2 - 1] == 2 || iprint[2 - 1] == 3) {
				if (finish1) {
					System.err.print(" final point x =");
				} else {
					System.err.print(" vector x =  ");
				}
				for (i1 = 1; i1 <= n; i1++)
					System.err.print("  " + x[i1 - 1]);
				System.err.println("");
				if (iprint[2 - 1] == 3) {
					System.err.print(" gradient vector g =");
					for (i1 = 1; i1 <= n; i1++)
						System.err.print("  " + g[i1 - 1]);
					System.err.println("");
				}
			}
			if (finish1)
				System.err
						.println(" The minimization terminated without detecting errors. iflag = 0");
		}
		return;
	}

	/**
	 * Compute the sum of a vector times a scalara plus another vector. Adapted
	 * from the subroutine <code>daxpy</code> in <code>lbfgs.f</code>. There
	 * could well be faster ways to carry out this operation; this code is a
	 * straight translation from the Fortran.
	 */
	public static void daxpy(int n, double da, double[] dx, int ix0, int incx,
			double[] dy, int iy0, int incy) {
		int i1, ix, iy;// , m, mp1;

		if (n <= 0)
			return;

		if (da == 0)
			return;

		// if (!(incx == 1 && incy == 1)) {
		ix = 1;
		iy = 1;

		if (incx < 0)
			ix = (-n + 1) * incx + 1;
		if (incy < 0)
			iy = (-n + 1) * incy + 1;

		for (i1 = 1; i1 <= n; i1 += 1) {
			dy[iy0 + iy - 1] += safeMult(da , dx[ix0 + ix - 1]);
			ix = ix + incx;
			iy = iy + incy;
		}

		return;
		// }

		// m = n % 4;
		// if (m != 0) {
		// for (i1 = 1; i1 <= m; i1 += 1) {
		// dy[iy0 + i1 - 1] += da * dx[ix0 + i1 - 1];
		// if (badNum(dy[iy0 + i1 - 1]))
		// throw new IllegalArgumentException(da + " " + dx[ix0 + i1 - 1]);
		// }
		//
		// if (n < 4)
		// return;
		// }
		//
		// mp1 = m + 1;
		// for (i1 = mp1; i1 <= n; i1 += 4) {
		// dy[iy0 + i1 - 1] = dy[iy0 + i1 - 1] + da * dx[ix0 + i1 - 1];
		// dy[iy0 + i1 ] = dy[iy0 + i1 ] + da
		// * dx[ix0 + i1 ];
		// dy[iy0 + i1 + 1] = dy[iy0 + i1 + 1] + da
		// * dx[ix0 + i1 + 1];
		// dy[iy0 + i1 + 3 - 1] = dy[iy0 + i1 + 3 - 1] + da
		// * dx[ix0 + i1 + 3 - 1];
		// }
		// return;
	}

	/**
	 * Compute the dot product of two vectors. Adapted from the subroutine
	 * <code>ddot</code> in <code>lbfgs.f</code>. There could well be faster
	 * ways to carry out this operation; this code is a straight translation
	 * from the Fortran.
	 */
	static double ddot(int n, double[] dx, int ix0, int incx, double[] dy,
			int iy0, int incy) {
		double result = 0;
		for (int in = 0, ix = ix0, iy = iy0; in < n; in++, ix += incx, iy += incy) {
			result += safeMult(dx[ix], dy[iy]);
		}
		return result;
	}

	static boolean badNum(double n) {
		return Double.isNaN(n) || Double.isInfinite(n);
	}

	static double safeMult(double n1, double n2) {
		double result = n1 * n2;
		if (badNum(result)) {
			if (n1 == 0 || n2 == 0) {
				result = 0;
			} else {
				throw new IllegalArgumentException(n1 + " " + n2);
			}
		}
		return result;
	}

	static double safeDiv(double n1, double n2) {
		double result = n1 / n2;
		if (badNum(result)) {
			if (n1 == 0 && n2 == 0) {
				result = 1;
			} else {
				throw new IllegalArgumentException(n1 + " " + n2);
			}
		}
		return result;
	}

//	public static double[] subArray(double[] a, int start, int end) {
//		assert start <= end;
//		assert end <= a.length;
//		double[] result = new double[end - start];
//		System.arraycopy(a, start, result, 0, end - start);
//		return result;
//	}
}