text: import { factory } from '../../../utils/factory.js';
  import { createSolveValidation } from './utils/solveValidation.js';
  var name = 'lsolve';
  var dependencies = ['typed', 'matrix', 'divideScalar', 'multiplyScalar', 'subtract', 'equalScalar', 'DenseMatrix'];
  export var createLsolve = /* #__PURE__ */factory(name, dependencies, _ref => {
    var {
      typed,
      matrix,
      divideScalar,
      multiplyScalar,
      subtract,
      equalScalar,
      DenseMatrix
    } = _ref;
    var solveValidation = createSolveValidation({
      DenseMatrix
    });
    /**
     * Finds one solution of a linear equation system by forwards substitution. Matrix must be a lower triangular matrix. Throws an error if there's no solution.
     *
     * `L * x = b`
     *
     * Syntax:
     *
     *    math.lsolve(L, b)
     *
     * Examples:
     *
     *    const a = [[-2, 3], [2, 1]]
     *    const b = [11, 9]
     *    const x = lsolve(a, b)  // [[-5.5], [20]]
     *
     * See also:
     *
     *    lsolveAll, lup, slu, usolve, lusolve
     *
     * @param {Matrix, Array} L       A N x N matrix or array (L)
     * @param {Matrix, Array} b       A column vector with the b values
     *
     * @return {DenseMatrix | Array}  A column vector with the linear system solution (x)
     */
  
    return typed(name, {
      'SparseMatrix, Array | Matrix': function SparseMatrixArrayMatrix(m, b) {
        return _sparseForwardSubstitution(m, b);
      },
      'DenseMatrix, Array | Matrix': function DenseMatrixArrayMatrix(m, b) {
        return _denseForwardSubstitution(m, b);
      },
      'Array, Array | Matrix': function ArrayArrayMatrix(a, b) {
        var m = matrix(a);
  
        var r = _denseForwardSubstitution(m, b);
  
        return r.valueOf();
      }
    });
  
    function _denseForwardSubstitution(m, b) {
      // validate matrix and vector, return copy of column vector b
      b = solveValidation(m, b, true);
      var bdata = b._data;
      var rows = m._size[0];
      var columns = m._size[1]; // result
  
      var x = [];
      var mdata = m._data; // loop columns
  
      for (var j = 0; j < columns; j++) {
        var bj = bdata[j][0] || 0;
        var xj = void 0;
  
        if (!equalScalar(bj, 0)) {
          // non-degenerate row, find solution
          var vjj = mdata[j][j];
  
          if (equalScalar(vjj, 0)) {
            throw new Error('Linear system cannot be solved since matrix is singular');
          }
  
          xj = divideScalar(bj, vjj); // loop rows
  
          for (var i = j + 1; i < rows; i++) {
            bdata[i] = [subtract(bdata[i][0] || 0, multiplyScalar(xj, mdata[i][j]))];
          }
        } else {
          // degenerate row, we can choose any value
          xj = 0;
        }
  
        x[j] = [xj];
      }
  
      return new DenseMatrix({
        data: x,
        size: [rows, 1]
      });
    }
  
    function _sparseForwardSubstitution(m, b) {
      // validate matrix and vector, return copy of column vector b
      b = solveValidation(m, b, true);
      var bdata = b._data;
      var rows = m._size[0];
      var columns = m._size[1];
      var values = m._values;
      var index = m._index;
      var ptr = m._ptr; // result
  
      var x = []; // loop columns
  
      for (var j = 0; j < columns; j++) {
        var bj = bdata[j][0] || 0;
  
        if (!equalScalar(bj, 0)) {
          // non-degenerate row, find solution
          var vjj = 0; // matrix values & indices (column j)
  
          var jValues = [];
          var jIndices = []; // first and last index in the column
  
          var firstIndex = ptr[j];
          var lastIndex = ptr[j + 1]; // values in column, find value at [j, j]
  
          for (var k = firstIndex; k < lastIndex; k++) {
            var i = index[k]; // check row (rows are not sorted!)
  
            if (i === j) {
              vjj = values[k];
            } else if (i > j) {
              // store lower triangular
              jValues.push(values[k]);
              jIndices.push(i);
            }
          } // at this point we must have a value in vjj
  
  
          if (equalScalar(vjj, 0)) {
            throw new Error('Linear system cannot be solved since matrix is singular');
          }
  
          var xj = divideScalar(bj, vjj);
  
          for (var _k = 0, l = jIndices.length; _k < l; _k++) {
            var _i = jIndices[_k];
            bdata[_i] = [subtract(bdata[_i][0] || 0, multiplyScalar(xj, jValues[_k]))];
          }
  
          x[j] = [xj];
        } else {
          // degenerate row, we can choose any value
          x[j] = [0];
        }
      }
  
      return new DenseMatrix({
        data: x,
        size: [rows, 1]
      });
    }
  });