mathjs/src/function/algebra/sparse/csSymperm.js

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

const name = 'csSymperm'
const dependencies = ['conj', 'SparseMatrix']

export const createCsSymperm = /* #__PURE__ */ factory(name, dependencies, ({ conj, SparseMatrix }) => {
  /**
   * Computes the symmetric permutation of matrix A accessing only
   * the upper triangular part of A.
   *
   * C = P * A * P'
   *
   * @param {Matrix}  a               The A matrix
   * @param {Array}   pinv            The inverse of permutation vector
   * @param {boolean} values          Process matrix values (true)
   *
   * @return {Matrix}                 The C matrix, C = P * A * P'
   *
   * Reference: http://faculty.cse.tamu.edu/davis/publications.html
   */
  return function csSymperm (a, pinv, values) {
    // A matrix arrays
    const avalues = a._values
    const aindex = a._index
    const aptr = a._ptr
    const asize = a._size
    // columns
    const n = asize[1]
    // C matrix arrays
    const cvalues = values && avalues ? [] : null
    const cindex = [] // (nz)
    const cptr = [] // (n + 1)
    // variables
    let i, i2, j, j2, p, p0, p1
    // create workspace vector
    const w = [] // (n)
    // count entries in each column of C
    for (j = 0; j < n; j++) {
      // column j of A is column j2 of C
      j2 = pinv ? pinv[j] : j
      // loop values in column j
      for (p0 = aptr[j], p1 = aptr[j + 1], p = p0; p < p1; p++) {
        // row
        i = aindex[p]
        // skip lower triangular part of A
        if (i > j) { continue }
        // row i of A is row i2 of C
        i2 = pinv ? pinv[i] : i
        // column count of C
        w[Math.max(i2, j2)]++
      }
    }
    // compute column pointers of C
    csCumsum(cptr, w, n)
    // loop columns
    for (j = 0; j < n; j++) {
      // column j of A is column j2 of C
      j2 = pinv ? pinv[j] : j
      // loop values in column j
      for (p0 = aptr[j], p1 = aptr[j + 1], p = p0; p < p1; p++) {
        // row
        i = aindex[p]
        // skip lower triangular part of A
        if (i > j) { continue }
        // row i of A is row i2 of C
        i2 = pinv ? pinv[i] : i
        // C index for column j2
        const q = w[Math.max(i2, j2)]++
        // update C index for entry q
        cindex[q] = Math.min(i2, j2)
        // check we need to process values
        if (cvalues) { cvalues[q] = (i2 <= j2) ? avalues[p] : conj(avalues[p]) }
      }
    }
    // return C matrix
    return new SparseMatrix({
      values: cvalues,
      index: cindex,
      ptr: cptr,
      size: [n, n]
    })
  }
})