mathjs/lib/esm/function/arithmetic/multiply.js

import { factory } from '../../utils/factory.js';
import { isMatrix } from '../../utils/is.js';
import { extend } from '../../utils/object.js';
import { arraySize } from '../../utils/array.js';
import { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js';
import { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js';
var name = 'multiply';
var dependencies = ['typed', 'matrix', 'addScalar', 'multiplyScalar', 'equalScalar', 'dot'];
export var createMultiply = /* #__PURE__ */factory(name, dependencies, (_ref) => {
  var {
    typed,
    matrix,
    addScalar,
    multiplyScalar,
    equalScalar,
    dot
  } = _ref;
  var algorithm11 = createAlgorithm11({
    typed,
    equalScalar
  });
  var algorithm14 = createAlgorithm14({
    typed
  });

  function _validateMatrixDimensions(size1, size2) {
    // check left operand dimensions
    switch (size1.length) {
      case 1:
        // check size2
        switch (size2.length) {
          case 1:
            // Vector x Vector
            if (size1[0] !== size2[0]) {
              // throw error
              throw new RangeError('Dimension mismatch in multiplication. Vectors must have the same length');
            }

            break;

          case 2:
            // Vector x Matrix
            if (size1[0] !== size2[0]) {
              // throw error
              throw new RangeError('Dimension mismatch in multiplication. Vector length (' + size1[0] + ') must match Matrix rows (' + size2[0] + ')');
            }

            break;

          default:
            throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix B has ' + size2.length + ' dimensions)');
        }

        break;

      case 2:
        // check size2
        switch (size2.length) {
          case 1:
            // Matrix x Vector
            if (size1[1] !== size2[0]) {
              // throw error
              throw new RangeError('Dimension mismatch in multiplication. Matrix columns (' + size1[1] + ') must match Vector length (' + size2[0] + ')');
            }

            break;

          case 2:
            // Matrix x Matrix
            if (size1[1] !== size2[0]) {
              // throw error
              throw new RangeError('Dimension mismatch in multiplication. Matrix A columns (' + size1[1] + ') must match Matrix B rows (' + size2[0] + ')');
            }

            break;

          default:
            throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix B has ' + size2.length + ' dimensions)');
        }

        break;

      default:
        throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix A has ' + size1.length + ' dimensions)');
    }
  }
  /**
   * C = A * B
   *
   * @param {Matrix} a            Dense Vector   (N)
   * @param {Matrix} b            Dense Vector   (N)
   *
   * @return {number}             Scalar value
   */


  function _multiplyVectorVector(a, b, n) {
    // check empty vector
    if (n === 0) {
      throw new Error('Cannot multiply two empty vectors');
    }

    return dot(a, b);
  }
  /**
   * C = A * B
   *
   * @param {Matrix} a            Dense Vector   (M)
   * @param {Matrix} b            Matrix         (MxN)
   *
   * @return {Matrix}             Dense Vector   (N)
   */


  function _multiplyVectorMatrix(a, b) {
    // process storage
    if (b.storage() !== 'dense') {
      throw new Error('Support for SparseMatrix not implemented');
    }

    return _multiplyVectorDenseMatrix(a, b);
  }
  /**
   * C = A * B
   *
   * @param {Matrix} a            Dense Vector   (M)
   * @param {Matrix} b            Dense Matrix   (MxN)
   *
   * @return {Matrix}             Dense Vector   (N)
   */


  function _multiplyVectorDenseMatrix(a, b) {
    // a dense
    var adata = a._data;
    var asize = a._size;
    var adt = a._datatype; // b dense

    var bdata = b._data;
    var bsize = b._size;
    var bdt = b._datatype; // rows & columns

    var alength = asize[0];
    var bcolumns = bsize[1]; // datatype

    var dt; // addScalar signature to use

    var af = addScalar; // multiplyScalar signature to use

    var mf = multiplyScalar; // process data types

    if (adt && bdt && adt === bdt && typeof adt === 'string') {
      // datatype
      dt = adt; // find signatures that matches (dt, dt)

      af = typed.find(addScalar, [dt, dt]);
      mf = typed.find(multiplyScalar, [dt, dt]);
    } // result


    var c = []; // loop matrix columns

    for (var j = 0; j < bcolumns; j++) {
      // sum (do not initialize it with zero)
      var sum = mf(adata[0], bdata[0][j]); // loop vector

      for (var i = 1; i < alength; i++) {
        // multiply & accumulate
        sum = af(sum, mf(adata[i], bdata[i][j]));
      }

      c[j] = sum;
    } // return matrix


    return a.createDenseMatrix({
      data: c,
      size: [bcolumns],
      datatype: dt
    });
  }
  /**
   * C = A * B
   *
   * @param {Matrix} a            Matrix         (MxN)
   * @param {Matrix} b            Dense Vector   (N)
   *
   * @return {Matrix}             Dense Vector   (M)
   */


  var _multiplyMatrixVector = typed('_multiplyMatrixVector', {
    'DenseMatrix, any': _multiplyDenseMatrixVector,
    'SparseMatrix, any': _multiplySparseMatrixVector
  });
  /**
   * C = A * B
   *
   * @param {Matrix} a            Matrix         (MxN)
   * @param {Matrix} b            Matrix         (NxC)
   *
   * @return {Matrix}             Matrix         (MxC)
   */


  var _multiplyMatrixMatrix = typed('_multiplyMatrixMatrix', {
    'DenseMatrix, DenseMatrix': _multiplyDenseMatrixDenseMatrix,
    'DenseMatrix, SparseMatrix': _multiplyDenseMatrixSparseMatrix,
    'SparseMatrix, DenseMatrix': _multiplySparseMatrixDenseMatrix,
    'SparseMatrix, SparseMatrix': _multiplySparseMatrixSparseMatrix
  });
  /**
   * C = A * B
   *
   * @param {Matrix} a            DenseMatrix  (MxN)
   * @param {Matrix} b            Dense Vector (N)
   *
   * @return {Matrix}             Dense Vector (M)
   */


  function _multiplyDenseMatrixVector(a, b) {
    // a dense
    var adata = a._data;
    var asize = a._size;
    var adt = a._datatype; // b dense

    var bdata = b._data;
    var bdt = b._datatype; // rows & columns

    var arows = asize[0];
    var acolumns = asize[1]; // datatype

    var dt; // addScalar signature to use

    var af = addScalar; // multiplyScalar signature to use

    var mf = multiplyScalar; // process data types

    if (adt && bdt && adt === bdt && typeof adt === 'string') {
      // datatype
      dt = adt; // find signatures that matches (dt, dt)

      af = typed.find(addScalar, [dt, dt]);
      mf = typed.find(multiplyScalar, [dt, dt]);
    } // result


    var c = []; // loop matrix a rows

    for (var i = 0; i < arows; i++) {
      // current row
      var row = adata[i]; // sum (do not initialize it with zero)

      var sum = mf(row[0], bdata[0]); // loop matrix a columns

      for (var j = 1; j < acolumns; j++) {
        // multiply & accumulate
        sum = af(sum, mf(row[j], bdata[j]));
      }

      c[i] = sum;
    } // return matrix


    return a.createDenseMatrix({
      data: c,
      size: [arows],
      datatype: dt
    });
  }
  /**
   * C = A * B
   *
   * @param {Matrix} a            DenseMatrix    (MxN)
   * @param {Matrix} b            DenseMatrix    (NxC)
   *
   * @return {Matrix}             DenseMatrix    (MxC)
   */


  function _multiplyDenseMatrixDenseMatrix(a, b) {
    // a dense
    var adata = a._data;
    var asize = a._size;
    var adt = a._datatype; // b dense

    var bdata = b._data;
    var bsize = b._size;
    var bdt = b._datatype; // rows & columns

    var arows = asize[0];
    var acolumns = asize[1];
    var bcolumns = bsize[1]; // datatype

    var dt; // addScalar signature to use

    var af = addScalar; // multiplyScalar signature to use

    var mf = multiplyScalar; // process data types

    if (adt && bdt && adt === bdt && typeof adt === 'string') {
      // datatype
      dt = adt; // find signatures that matches (dt, dt)

      af = typed.find(addScalar, [dt, dt]);
      mf = typed.find(multiplyScalar, [dt, dt]);
    } // result


    var c = []; // loop matrix a rows

    for (var i = 0; i < arows; i++) {
      // current row
      var row = adata[i]; // initialize row array

      c[i] = []; // loop matrix b columns

      for (var j = 0; j < bcolumns; j++) {
        // sum (avoid initializing sum to zero)
        var sum = mf(row[0], bdata[0][j]); // loop matrix a columns

        for (var x = 1; x < acolumns; x++) {
          // multiply & accumulate
          sum = af(sum, mf(row[x], bdata[x][j]));
        }

        c[i][j] = sum;
      }
    } // return matrix


    return a.createDenseMatrix({
      data: c,
      size: [arows, bcolumns],
      datatype: dt
    });
  }
  /**
   * C = A * B
   *
   * @param {Matrix} a            DenseMatrix    (MxN)
   * @param {Matrix} b            SparseMatrix   (NxC)
   *
   * @return {Matrix}             SparseMatrix   (MxC)
   */


  function _multiplyDenseMatrixSparseMatrix(a, b) {
    // a dense
    var adata = a._data;
    var asize = a._size;
    var adt = a._datatype; // b sparse

    var bvalues = b._values;
    var bindex = b._index;
    var bptr = b._ptr;
    var bsize = b._size;
    var bdt = b._datatype; // validate b matrix

    if (!bvalues) {
      throw new Error('Cannot multiply Dense Matrix times Pattern only Matrix');
    } // rows & columns


    var arows = asize[0];
    var bcolumns = bsize[1]; // datatype

    var dt; // addScalar signature to use

    var af = addScalar; // multiplyScalar signature to use

    var mf = multiplyScalar; // equalScalar signature to use

    var eq = equalScalar; // zero value

    var zero = 0; // process data types

    if (adt && bdt && adt === bdt && typeof adt === 'string') {
      // datatype
      dt = adt; // find signatures that matches (dt, dt)

      af = typed.find(addScalar, [dt, dt]);
      mf = typed.find(multiplyScalar, [dt, dt]);
      eq = typed.find(equalScalar, [dt, dt]); // convert 0 to the same datatype

      zero = typed.convert(0, dt);
    } // result


    var cvalues = [];
    var cindex = [];
    var cptr = []; // c matrix

    var c = b.createSparseMatrix({
      values: cvalues,
      index: cindex,
      ptr: cptr,
      size: [arows, bcolumns],
      datatype: dt
    }); // loop b columns

    for (var jb = 0; jb < bcolumns; jb++) {
      // update ptr
      cptr[jb] = cindex.length; // indeces in column jb

      var kb0 = bptr[jb];
      var kb1 = bptr[jb + 1]; // do not process column jb if no data exists

      if (kb1 > kb0) {
        // last row mark processed
        var last = 0; // loop a rows

        for (var i = 0; i < arows; i++) {
          // column mark
          var mark = i + 1; // C[i, jb]

          var cij = void 0; // values in b column j

          for (var kb = kb0; kb < kb1; kb++) {
            // row
            var ib = bindex[kb]; // check value has been initialized

            if (last !== mark) {
              // first value in column jb
              cij = mf(adata[i][ib], bvalues[kb]); // update mark

              last = mark;
            } else {
              // accumulate value
              cij = af(cij, mf(adata[i][ib], bvalues[kb]));
            }
          } // check column has been processed and value != 0


          if (last === mark && !eq(cij, zero)) {
            // push row & value
            cindex.push(i);
            cvalues.push(cij);
          }
        }
      }
    } // update ptr


    cptr[bcolumns] = cindex.length; // return sparse matrix

    return c;
  }
  /**
   * C = A * B
   *
   * @param {Matrix} a            SparseMatrix    (MxN)
   * @param {Matrix} b            Dense Vector (N)
   *
   * @return {Matrix}             SparseMatrix    (M, 1)
   */


  function _multiplySparseMatrixVector(a, b) {
    // a sparse
    var avalues = a._values;
    var aindex = a._index;
    var aptr = a._ptr;
    var adt = a._datatype; // validate a matrix

    if (!avalues) {
      throw new Error('Cannot multiply Pattern only Matrix times Dense Matrix');
    } // b dense


    var bdata = b._data;
    var bdt = b._datatype; // rows & columns

    var arows = a._size[0];
    var brows = b._size[0]; // result

    var cvalues = [];
    var cindex = [];
    var cptr = []; // datatype

    var dt; // addScalar signature to use

    var af = addScalar; // multiplyScalar signature to use

    var mf = multiplyScalar; // equalScalar signature to use

    var eq = equalScalar; // zero value

    var zero = 0; // process data types

    if (adt && bdt && adt === bdt && typeof adt === 'string') {
      // datatype
      dt = adt; // find signatures that matches (dt, dt)

      af = typed.find(addScalar, [dt, dt]);
      mf = typed.find(multiplyScalar, [dt, dt]);
      eq = typed.find(equalScalar, [dt, dt]); // convert 0 to the same datatype

      zero = typed.convert(0, dt);
    } // workspace


    var x = []; // vector with marks indicating a value x[i] exists in a given column

    var w = []; // update ptr

    cptr[0] = 0; // rows in b

    for (var ib = 0; ib < brows; ib++) {
      // b[ib]
      var vbi = bdata[ib]; // check b[ib] != 0, avoid loops

      if (!eq(vbi, zero)) {
        // A values & index in ib column
        for (var ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {
          // a row
          var ia = aindex[ka]; // check value exists in current j

          if (!w[ia]) {
            // ia is new entry in j
            w[ia] = true; // add i to pattern of C

            cindex.push(ia); // x(ia) = A

            x[ia] = mf(vbi, avalues[ka]);
          } else {
            // i exists in C already
            x[ia] = af(x[ia], mf(vbi, avalues[ka]));
          }
        }
      }
    } // copy values from x to column jb of c


    for (var p1 = cindex.length, p = 0; p < p1; p++) {
      // row
      var ic = cindex[p]; // copy value

      cvalues[p] = x[ic];
    } // update ptr


    cptr[1] = cindex.length; // return sparse matrix

    return a.createSparseMatrix({
      values: cvalues,
      index: cindex,
      ptr: cptr,
      size: [arows, 1],
      datatype: dt
    });
  }
  /**
   * C = A * B
   *
   * @param {Matrix} a            SparseMatrix      (MxN)
   * @param {Matrix} b            DenseMatrix       (NxC)
   *
   * @return {Matrix}             SparseMatrix      (MxC)
   */


  function _multiplySparseMatrixDenseMatrix(a, b) {
    // a sparse
    var avalues = a._values;
    var aindex = a._index;
    var aptr = a._ptr;
    var adt = a._datatype; // validate a matrix

    if (!avalues) {
      throw new Error('Cannot multiply Pattern only Matrix times Dense Matrix');
    } // b dense


    var bdata = b._data;
    var bdt = b._datatype; // rows & columns

    var arows = a._size[0];
    var brows = b._size[0];
    var bcolumns = b._size[1]; // datatype

    var dt; // addScalar signature to use

    var af = addScalar; // multiplyScalar signature to use

    var mf = multiplyScalar; // equalScalar signature to use

    var eq = equalScalar; // zero value

    var zero = 0; // process data types

    if (adt && bdt && adt === bdt && typeof adt === 'string') {
      // datatype
      dt = adt; // find signatures that matches (dt, dt)

      af = typed.find(addScalar, [dt, dt]);
      mf = typed.find(multiplyScalar, [dt, dt]);
      eq = typed.find(equalScalar, [dt, dt]); // convert 0 to the same datatype

      zero = typed.convert(0, dt);
    } // result


    var cvalues = [];
    var cindex = [];
    var cptr = []; // c matrix

    var c = a.createSparseMatrix({
      values: cvalues,
      index: cindex,
      ptr: cptr,
      size: [arows, bcolumns],
      datatype: dt
    }); // workspace

    var x = []; // vector with marks indicating a value x[i] exists in a given column

    var w = []; // loop b columns

    for (var jb = 0; jb < bcolumns; jb++) {
      // update ptr
      cptr[jb] = cindex.length; // mark in workspace for current column

      var mark = jb + 1; // rows in jb

      for (var ib = 0; ib < brows; ib++) {
        // b[ib, jb]
        var vbij = bdata[ib][jb]; // check b[ib, jb] != 0, avoid loops

        if (!eq(vbij, zero)) {
          // A values & index in ib column
          for (var ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {
            // a row
            var ia = aindex[ka]; // check value exists in current j

            if (w[ia] !== mark) {
              // ia is new entry in j
              w[ia] = mark; // add i to pattern of C

              cindex.push(ia); // x(ia) = A

              x[ia] = mf(vbij, avalues[ka]);
            } else {
              // i exists in C already
              x[ia] = af(x[ia], mf(vbij, avalues[ka]));
            }
          }
        }
      } // copy values from x to column jb of c


      for (var p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {
        // row
        var ic = cindex[p]; // copy value

        cvalues[p] = x[ic];
      }
    } // update ptr


    cptr[bcolumns] = cindex.length; // return sparse matrix

    return c;
  }
  /**
   * C = A * B
   *
   * @param {Matrix} a            SparseMatrix      (MxN)
   * @param {Matrix} b            SparseMatrix      (NxC)
   *
   * @return {Matrix}             SparseMatrix      (MxC)
   */


  function _multiplySparseMatrixSparseMatrix(a, b) {
    // a sparse
    var avalues = a._values;
    var aindex = a._index;
    var aptr = a._ptr;
    var adt = a._datatype; // b sparse

    var bvalues = b._values;
    var bindex = b._index;
    var bptr = b._ptr;
    var bdt = b._datatype; // rows & columns

    var arows = a._size[0];
    var bcolumns = b._size[1]; // flag indicating both matrices (a & b) contain data

    var values = avalues && bvalues; // datatype

    var dt; // addScalar signature to use

    var af = addScalar; // multiplyScalar signature to use

    var mf = multiplyScalar; // process data types

    if (adt && bdt && adt === bdt && typeof adt === 'string') {
      // datatype
      dt = adt; // find signatures that matches (dt, dt)

      af = typed.find(addScalar, [dt, dt]);
      mf = typed.find(multiplyScalar, [dt, dt]);
    } // result


    var cvalues = values ? [] : undefined;
    var cindex = [];
    var cptr = []; // c matrix

    var c = a.createSparseMatrix({
      values: cvalues,
      index: cindex,
      ptr: cptr,
      size: [arows, bcolumns],
      datatype: dt
    }); // workspace

    var x = values ? [] : undefined; // vector with marks indicating a value x[i] exists in a given column

    var w = []; // variables

    var ka, ka0, ka1, kb, kb0, kb1, ia, ib; // loop b columns

    for (var jb = 0; jb < bcolumns; jb++) {
      // update ptr
      cptr[jb] = cindex.length; // mark in workspace for current column

      var mark = jb + 1; // B values & index in j

      for (kb0 = bptr[jb], kb1 = bptr[jb + 1], kb = kb0; kb < kb1; kb++) {
        // b row
        ib = bindex[kb]; // check we need to process values

        if (values) {
          // loop values in a[:,ib]
          for (ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {
            // row
            ia = aindex[ka]; // check value exists in current j

            if (w[ia] !== mark) {
              // ia is new entry in j
              w[ia] = mark; // add i to pattern of C

              cindex.push(ia); // x(ia) = A

              x[ia] = mf(bvalues[kb], avalues[ka]);
            } else {
              // i exists in C already
              x[ia] = af(x[ia], mf(bvalues[kb], avalues[ka]));
            }
          }
        } else {
          // loop values in a[:,ib]
          for (ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {
            // row
            ia = aindex[ka]; // check value exists in current j

            if (w[ia] !== mark) {
              // ia is new entry in j
              w[ia] = mark; // add i to pattern of C

              cindex.push(ia);
            }
          }
        }
      } // check we need to process matrix values (pattern matrix)


      if (values) {
        // copy values from x to column jb of c
        for (var p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {
          // row
          var ic = cindex[p]; // copy value

          cvalues[p] = x[ic];
        }
      }
    } // update ptr


    cptr[bcolumns] = cindex.length; // return sparse matrix

    return c;
  }
  /**
   * Multiply two or more values, `x * y`.
   * For matrices, the matrix product is calculated.
   *
   * Syntax:
   *
   *    math.multiply(x, y)
   *    math.multiply(x, y, z, ...)
   *
   * Examples:
   *
   *    math.multiply(4, 5.2)        // returns number 20.8
   *    math.multiply(2, 3, 4)       // returns number 24
   *
   *    const a = math.complex(2, 3)
   *    const b = math.complex(4, 1)
   *    math.multiply(a, b)          // returns Complex 5 + 14i
   *
   *    const c = [[1, 2], [4, 3]]
   *    const d = [[1, 2, 3], [3, -4, 7]]
   *    math.multiply(c, d)          // returns Array [[7, -6, 17], [13, -4, 33]]
   *
   *    const e = math.unit('2.1 km')
   *    math.multiply(3, e)          // returns Unit 6.3 km
   *
   * See also:
   *
   *    divide, prod, cross, dot
   *
   * @param  {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x First value to multiply
   * @param  {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Second value to multiply
   * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Multiplication of `x` and `y`
   */


  return typed(name, extend({
    // we extend the signatures of multiplyScalar with signatures dealing with matrices
    'Array, Array': function ArrayArray(x, y) {
      // check dimensions
      _validateMatrixDimensions(arraySize(x), arraySize(y)); // use dense matrix implementation


      var m = this(matrix(x), matrix(y)); // return array or scalar

      return isMatrix(m) ? m.valueOf() : m;
    },
    'Matrix, Matrix': function MatrixMatrix(x, y) {
      // dimensions
      var xsize = x.size();
      var ysize = y.size(); // check dimensions

      _validateMatrixDimensions(xsize, ysize); // process dimensions


      if (xsize.length === 1) {
        // process y dimensions
        if (ysize.length === 1) {
          // Vector * Vector
          return _multiplyVectorVector(x, y, xsize[0]);
        } // Vector * Matrix


        return _multiplyVectorMatrix(x, y);
      } // process y dimensions


      if (ysize.length === 1) {
        // Matrix * Vector
        return _multiplyMatrixVector(x, y);
      } // Matrix * Matrix


      return _multiplyMatrixMatrix(x, y);
    },
    'Matrix, Array': function MatrixArray(x, y) {
      // use Matrix * Matrix implementation
      return this(x, matrix(y));
    },
    'Array, Matrix': function ArrayMatrix(x, y) {
      // use Matrix * Matrix implementation
      return this(matrix(x, y.storage()), y);
    },
    'SparseMatrix, any': function SparseMatrixAny(x, y) {
      return algorithm11(x, y, multiplyScalar, false);
    },
    'DenseMatrix, any': function DenseMatrixAny(x, y) {
      return algorithm14(x, y, multiplyScalar, false);
    },
    'any, SparseMatrix': function anySparseMatrix(x, y) {
      return algorithm11(y, x, multiplyScalar, true);
    },
    'any, DenseMatrix': function anyDenseMatrix(x, y) {
      return algorithm14(y, x, multiplyScalar, true);
    },
    'Array, any': function ArrayAny(x, y) {
      // use matrix implementation
      return algorithm14(matrix(x), y, multiplyScalar, false).valueOf();
    },
    'any, Array': function anyArray(x, y) {
      // use matrix implementation
      return algorithm14(matrix(y), x, multiplyScalar, true).valueOf();
    },
    'any, any': multiplyScalar,
    'any, any, ...any': function anyAnyAny(x, y, rest) {
      var result = this(x, y);

      for (var i = 0; i < rest.length; i++) {
        result = this(result, rest[i]);
      }

      return result;
    }
  }, multiplyScalar.signatures));
});