import { factory } from '../../utils/factory.js'

import { isMatrix } from '../../utils/is.js'

import { arraySize } from '../../utils/array.js'

import { createMatAlgo11xS0s } from '../../type/matrix/utils/matAlgo11xS0s.js'

import { createMatAlgo14xDs } from '../../type/matrix/utils/matAlgo14xDs.js'

const name = 'multiply'

const dependencies = [

'typed',

'matrix',

'addScalar',

'multiplyScalar',

'equalScalar',

'dot'

]

export const createMultiply = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, addScalar, multiplyScalar, equalScalar, dot }) => {

const matAlgo11xS0s = createMatAlgo11xS0s({ typed, equalScalar })

const matAlgo14xDs = createMatAlgo14xDs({ 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

const adata = a._data

const asize = a._size

const adt = a._datatype || a.getDataType()

// b dense

const bdata = b._data

const bsize = b._size

const bdt = b._datatype || b.getDataType()

// rows & columns

const alength = asize[0]

const bcolumns = bsize[1]

// datatype

let dt

// addScalar signature to use

let af = addScalar

// multiplyScalar signature to use

let mf = multiplyScalar

// process data types

if (adt && bdt && adt === bdt && typeof adt === 'string' && adt !== 'mixed') {

// datatype

dt = adt

// find signatures that matches (dt, dt)

af = typed.find(addScalar, [dt, dt])

mf = typed.find(multiplyScalar, [dt, dt])

}

// result

const c = []

// loop matrix columns

for (let j = 0; j < bcolumns; j++) {

// sum (do not initialize it with zero)

let sum = mf(adata[0], bdata[0][j])

// loop vector

for (let 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: adt === a._datatype && bdt === b._datatype ? dt : undefined

})

}

/**

* C = A * B

*

* @param {Matrix} a Matrix (MxN)

* @param {Matrix} b Dense Vector (N)

*

* @return {Matrix} Dense Vector (M)

*/

const _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)

*/

const _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

const adata = a._data

const asize = a._size

const adt = a._datatype || a.getDataType()

// b dense

const bdata = b._data

const bdt = b._datatype || b.getDataType()

// rows & columns

const arows = asize[0]

const acolumns = asize[1]

// datatype

let dt

// addScalar signature to use

let af = addScalar

// multiplyScalar signature to use

let mf = multiplyScalar

// process data types

if (adt && bdt && adt === bdt && typeof adt === 'string' && adt !== 'mixed') {

// datatype

dt = adt

// find signatures that matches (dt, dt)

af = typed.find(addScalar, [dt, dt])

mf = typed.find(multiplyScalar, [dt, dt])

}

// result

const c = []

// loop matrix a rows

for (let i = 0; i < arows; i++) {

// current row

const row = adata[i]

// sum (do not initialize it with zero)

let sum = mf(row[0], bdata[0])

// loop matrix a columns

for (let 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: adt === a._datatype && bdt === b._datatype ? dt : undefined

})

}

/**

* C = A * B

*

* @param {Matrix} a DenseMatrix (MxN)

* @param {Matrix} b DenseMatrix (NxC)

*

* @return {Matrix} DenseMatrix (MxC)

*/

function _multiplyDenseMatrixDenseMatrix (a, b) { // getDataType()

// a dense

const adata = a._data

const asize = a._size

const adt = a._datatype || a.getDataType()

// b dense

const bdata = b._data

const bsize = b._size

const bdt = b._datatype || b.getDataType()

// rows & columns

const arows = asize[0]

const acolumns = asize[1]

const bcolumns = bsize[1]

// datatype

let dt

// addScalar signature to use

let af = addScalar

// multiplyScalar signature to use

let mf = multiplyScalar

// process data types

if (adt && bdt && adt === bdt && typeof adt === 'string' && adt !== 'mixed' && adt !== 'mixed') {

// datatype

dt = adt

// find signatures that matches (dt, dt)

af = typed.find(addScalar, [dt, dt])

mf = typed.find(multiplyScalar, [dt, dt])

}

// result

const c = []

// loop matrix a rows

for (let i = 0; i < arows; i++) {

// current row

const row = adata[i]

// initialize row array

c[i] = []

// loop matrix b columns

for (let j = 0; j < bcolumns; j++) {

// sum (avoid initializing sum to zero)

let sum = mf(row[0], bdata[0][j])

// loop matrix a columns

for (let 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: adt === a._datatype && bdt === b._datatype ? dt : undefined

})

}

/**

* C = A * B

*

* @param {Matrix} a DenseMatrix (MxN)

* @param {Matrix} b SparseMatrix (NxC)

*

* @return {Matrix} SparseMatrix (MxC)

*/

function _multiplyDenseMatrixSparseMatrix (a, b) {

// a dense

const adata = a._data

const asize = a._size

const adt = a._datatype || a.getDataType()

// b sparse

const bvalues = b._values

const bindex = b._index

const bptr = b._ptr

const bsize = b._size

const bdt = b._datatype || b._data === undefined ? b._datatype : b.getDataType()

// validate b matrix

if (!bvalues) { throw new Error('Cannot multiply Dense Matrix times Pattern only Matrix') }

// rows & columns

const arows = asize[0]

const bcolumns = bsize[1]

// datatype

let dt

// addScalar signature to use

let af = addScalar

// multiplyScalar signature to use

let mf = multiplyScalar

// equalScalar signature to use

let eq = equalScalar

// zero value

let zero = 0

// process data types

if (adt && bdt && adt === bdt && typeof adt === 'string' && adt !== 'mixed') {

// 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

const cvalues = []

const cindex = []

const cptr = []

// c matrix

const c = b.createSparseMatrix({

values: cvalues,

index: cindex,

ptr: cptr,

size: [arows, bcolumns],

datatype: adt === a._datatype && bdt === b._datatype ? dt : undefined

})

// loop b columns

for (let jb = 0; jb < bcolumns; jb++) {

// update ptr

cptr[jb] = cindex.length

// indeces in column jb

const kb0 = bptr[jb]

const kb1 = bptr[jb + 1]

// do not process column jb if no data exists

if (kb1 > kb0) {

// last row mark processed

let last = 0

// loop a rows

for (let i = 0; i < arows; i++) {

// column mark

const mark = i + 1

// C[i, jb]

let cij

// values in b column j

for (let kb = kb0; kb < kb1; kb++) {

// row

const 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

const avalues = a._values

const aindex = a._index

const aptr = a._ptr

const adt = a._datatype || a._data === undefined ? a._datatype : a.getDataType()

// validate a matrix

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

// b dense

const bdata = b._data

const bdt = b._datatype || b.getDataType()

// rows & columns

const arows = a._size[0]

const brows = b._size[0]

// result

const cvalues = []

const cindex = []

const cptr = []

// datatype

let dt

// addScalar signature to use

let af = addScalar

// multiplyScalar signature to use

let mf = multiplyScalar

// equalScalar signature to use

let eq = equalScalar

// zero value

let zero = 0

// process data types

if (adt && bdt && adt === bdt && typeof adt === 'string' && adt !== 'mixed') {

// 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

const x = []

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

const w = []

// update ptr

cptr[0] = 0

// rows in b

for (let ib = 0; ib < brows; ib++) {

// b[ib]

const vbi = bdata[ib]

// check b[ib] != 0, avoid loops

if (!eq(vbi, zero)) {

// A values & index in ib column

for (let ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {

// a row

const 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 (let p1 = cindex.length, p = 0; p < p1; p++) {

// row

const ic = cindex[p]

// copy value

cvalues[p] = x[ic]

}

// update ptr

cptr[1] = cindex.length

// matrix to return

return a.createSparseMatrix({

values: cvalues,

index: cindex,

ptr: cptr,

size: [arows, 1],

datatype: adt === a._datatype && bdt === b._datatype ? dt : undefined

})

}

/**

* C = A * B

*

* @param {Matrix} a SparseMatrix (MxN)

* @param {Matrix} b DenseMatrix (NxC)

*

* @return {Matrix} SparseMatrix (MxC)

*/

function _multiplySparseMatrixDenseMatrix (a, b) {

// a sparse

const avalues = a._values

const aindex = a._index

const aptr = a._ptr

const adt = a._datatype || a._data === undefined ? a._datatype : a.getDataType()

// validate a matrix

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

// b dense

const bdata = b._data

const bdt = b._datatype || b.getDataType()

// rows & columns

const arows = a._size[0]

const brows = b._size[0]

const bcolumns = b._size[1]

// datatype

let dt

// addScalar signature to use

let af = addScalar

// multiplyScalar signature to use

let mf = multiplyScalar

// equalScalar signature to use

let eq = equalScalar

// zero value

let zero = 0

// process data types

if (adt && bdt && adt === bdt && typeof adt === 'string' && adt !== 'mixed') {

// 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

const cvalues = []

const cindex = []

const cptr = []

// c matrix

const c = a.createSparseMatrix({

values: cvalues,

index: cindex,

ptr: cptr,

size: [arows, bcolumns],

datatype: adt === a._datatype && bdt === b._datatype ? dt : undefined

})

// workspace

const x = []

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

const w = []

// loop b columns

for (let jb = 0; jb < bcolumns; jb++) {

// update ptr

cptr[jb] = cindex.length

// mark in workspace for current column

const mark = jb + 1

// rows in jb

for (let ib = 0; ib < brows; ib++) {

// b[ib, jb]

const vbij = bdata[ib][jb]

// check b[ib, jb] != 0, avoid loops

if (!eq(vbij, zero)) {

// A values & index in ib column

for (let ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {

// a row

const 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 (let p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {

// row

const 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

const avalues = a._values

const aindex = a._index

const aptr = a._ptr

const adt = a._datatype || a._data === undefined ? a._datatype : a.getDataType()

// b sparse

const bvalues = b._values

const bindex = b._index

const bptr = b._ptr

const bdt = b._datatype || b._data === undefined ? b._datatype : b.getDataType()

// rows & columns

const arows = a._size[0]

const bcolumns = b._size[1]

// flag indicating both matrices (a & b) contain data

const values = avalues && bvalues

// datatype

let dt

// addScalar signature to use

let af = addScalar

// multiplyScalar signature to use

let mf = multiplyScalar

// process data types

if (adt && bdt && adt === bdt && typeof adt === 'string' && adt !== 'mixed') {

// datatype

dt = adt

// find signatures that matches (dt, dt)

af = typed.find(addScalar, [dt, dt])

mf = typed.find(multiplyScalar, [dt, dt])

}

// result

const cvalues = values ? [] : undefined

const cindex = []

const cptr = []

// c matrix

const c = a.createSparseMatrix({

values: cvalues,

index: cindex,

ptr: cptr,

size: [arows, bcolumns],

datatype: adt === a._datatype && bdt === b._datatype ? dt : undefined

})

// workspace

const x = values ? [] : undefined

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

const w = []

// variables

let ka, ka0, ka1, kb, kb0, kb1, ia, ib

// loop b columns

for (let jb = 0; jb < bcolumns; jb++) {

// update ptr

cptr[jb] = cindex.length

// mark in workspace for current column

const 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 (let p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {

// row

const 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 | bigint | Fraction | Complex | Unit | Array | Matrix} x First value to multiply

* @param {number | BigNumber | bigint | Fraction | Complex | Unit | Array | Matrix} y Second value to multiply

* @return {number | BigNumber | bigint | Fraction | Complex | Unit | Array | Matrix} Multiplication of `x` and `y`

*/

return typed(name, multiplyScalar, {

// we extend the signatures of multiplyScalar with signatures dealing with matrices

'Array, Array': typed.referTo('Matrix, Matrix', selfMM => (x, y) => {

// check dimensions

_validateMatrixDimensions(arraySize(x), arraySize(y))

// use dense matrix implementation

const m = selfMM(matrix(x), matrix(y))

// return array or scalar

return isMatrix(m) ? m.valueOf() : m

}),

'Matrix, Matrix': function (x, y) {

// dimensions

const xsize = x.size()

const 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': typed.referTo('Matrix,Matrix', selfMM =>

(x, y) => selfMM(x, matrix(y))),

'Array, Matrix': typed.referToSelf(self => (x, y) => {

// use Matrix * Matrix implementation

return self(matrix(x, y.storage()), y)

}),

'SparseMatrix, any': function (x, y) {

return matAlgo11xS0s(x, y, multiplyScalar, false)

},

'DenseMatrix, any': function (x, y) {

return matAlgo14xDs(x, y, multiplyScalar, false)

},

'any, SparseMatrix': function (x, y) {

return matAlgo11xS0s(y, x, multiplyScalar, true)

},

'any, DenseMatrix': function (x, y) {

return matAlgo14xDs(y, x, multiplyScalar, true)

},

'Array, any': function (x, y) {

// use matrix implementation

return matAlgo14xDs(matrix(x), y, multiplyScalar, false).valueOf()

},

'any, Array': function (x, y) {

// use matrix implementation

return matAlgo14xDs(matrix(y), x, multiplyScalar, true).valueOf()

},

'any, any': multiplyScalar,

'any, any, ...any': typed.referToSelf(self => (x, y, rest) => {

let result = self(x, y)

for (let i = 0; i < rest.length; i++) {

result = self(result, rest[i])

}

return result

})

})

})