mathjs/src/type/matrix/utils/algorithm04.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

'use strict'

const DimensionError = require('../../../error/DimensionError')

function factory (type, config, load, typed) {
  const equalScalar = load(require('../../../function/relational/equalScalar'))

  const SparseMatrix = type.SparseMatrix

  /**
   * Iterates over SparseMatrix A and SparseMatrix B nonzero items and invokes the callback function f(Aij, Bij).
   * Callback function invoked MAX(NNZA, NNZB) times
   *
   *
   *          ┌  f(Aij, Bij)  ; A(i,j) !== 0 && B(i,j) !== 0
   * C(i,j) = ┤  A(i,j)       ; A(i,j) !== 0
   *          └  B(i,j)       ; B(i,j) !== 0
   *
   *
   * @param {Matrix}   a                 The SparseMatrix instance (A)
   * @param {Matrix}   b                 The SparseMatrix instance (B)
   * @param {Function} callback          The f(Aij,Bij) operation to invoke
   *
   * @return {Matrix}                    SparseMatrix (C)
   *
   * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294
   */
  const algorithm04 = function (a, b, callback) {
    // sparse matrix arrays
    const avalues = a._values
    const aindex = a._index
    const aptr = a._ptr
    const asize = a._size
    const adt = a._datatype
    // sparse matrix arrays
    const bvalues = b._values
    const bindex = b._index
    const bptr = b._ptr
    const bsize = b._size
    const bdt = b._datatype

    // validate dimensions
    if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }

    // check rows & columns
    if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }

    // rows & columns
    const rows = asize[0]
    const columns = asize[1]

    // datatype
    let dt
    // equal signature to use
    let eq = equalScalar
    // zero value
    let zero = 0
    // callback signature to use
    let cf = callback

    // process data types
    if (typeof adt === 'string' && adt === bdt) {
      // datatype
      dt = adt
      // find signature that matches (dt, dt)
      eq = typed.find(equalScalar, [dt, dt])
      // convert 0 to the same datatype
      zero = typed.convert(0, dt)
      // callback
      cf = typed.find(callback, [dt, dt])
    }

    // result arrays
    const cvalues = avalues && bvalues ? [] : undefined
    const cindex = []
    const cptr = []
    // matrix
    const c = new SparseMatrix({
      values: cvalues,
      index: cindex,
      ptr: cptr,
      size: [rows, columns],
      datatype: dt
    })

    // workspace
    const xa = avalues && bvalues ? [] : undefined
    const xb = avalues && bvalues ? [] : undefined
    // marks indicating we have a value in x for a given column
    const wa = []
    const wb = []

    // vars
    let i, j, k, k0, k1

    // loop columns
    for (j = 0; j < columns; j++) {
      // update cptr
      cptr[j] = cindex.length
      // columns mark
      const mark = j + 1
      // loop A(:,j)
      for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {
        // row
        i = aindex[k]
        // update c
        cindex.push(i)
        // update workspace
        wa[i] = mark
        // check we need to process values
        if (xa) { xa[i] = avalues[k] }
      }
      // loop B(:,j)
      for (k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {
        // row
        i = bindex[k]
        // check row exists in A
        if (wa[i] === mark) {
          // update record in xa @ i
          if (xa) {
            // invoke callback
            const v = cf(xa[i], bvalues[k])
            // check for zero
            if (!eq(v, zero)) {
              // update workspace
              xa[i] = v
            } else {
              // remove mark (index will be removed later)
              wa[i] = null
            }
          }
        } else {
          // update c
          cindex.push(i)
          // update workspace
          wb[i] = mark
          // check we need to process values
          if (xb) { xb[i] = bvalues[k] }
        }
      }
      // check we need to process values (non pattern matrix)
      if (xa && xb) {
        // initialize first index in j
        k = cptr[j]
        // loop index in j
        while (k < cindex.length) {
          // row
          i = cindex[k]
          // check workspace has value @ i
          if (wa[i] === mark) {
            // push value (Aij != 0 || (Aij != 0 && Bij != 0))
            cvalues[k] = xa[i]
            // increment pointer
            k++
          } else if (wb[i] === mark) {
            // push value (bij != 0)
            cvalues[k] = xb[i]
            // increment pointer
            k++
          } else {
            // remove index @ k
            cindex.splice(k, 1)
          }
        }
      }
    }
    // update cptr
    cptr[columns] = cindex.length

    // return sparse matrix
    return c
  }

  return algorithm04
}

exports.name = 'algorithm04'
exports.factory = factory