text: import { clone } from '../../../utils/object'
  import { factory } from '../../../utils/factory'
  
  const name = 'lup'
  const dependencies = [
    'typed',
    'matrix',
    'abs',
    'addScalar',
    'divideScalar',
    'multiplyScalar',
    'subtract',
    'larger',
    'equalScalar',
    'unaryMinus',
    'DenseMatrix',
    'SparseMatrix',
    'Spa'
  ]
  
  export const createLup = /* #__PURE__ */ factory(name, dependencies, (
    {
      typed,
      matrix,
      abs,
      addScalar,
      divideScalar,
      multiplyScalar,
      subtract,
      larger,
      equalScalar,
      unaryMinus,
      DenseMatrix,
      SparseMatrix,
      Spa
    }
  ) => {
    /**
     * Calculate the Matrix LU decomposition with partial pivoting. Matrix `A` is decomposed in two matrices (`L`, `U`) and a
     * row permutation vector `p` where `A[p,:] = L * U`
     *
     * Syntax:
     *
     *    math.lup(A)
     *
     * Example:
     *
     *    const m = [[2, 1], [1, 4]]
     *    const r = math.lup(m)
     *    // r = {
     *    //   L: [[1, 0], [0.5, 1]],
     *    //   U: [[2, 1], [0, 3.5]],
     *    //   P: [0, 1]
     *    // }
     *
     * See also:
     *
     *    slu, lsolve, lusolve, usolve
     *
     * @param {Matrix | Array} A    A two dimensional matrix or array for which to get the LUP decomposition.
     *
     * @return {{L: Array | Matrix, U: Array | Matrix, P: Array.<number>}} The lower triangular matrix, the upper triangular matrix and the permutation matrix.
     */
    return typed(name, {
  
      'DenseMatrix': function (m) {
        return _denseLUP(m)
      },
  
      'SparseMatrix': function (m) {
        return _sparseLUP(m)
      },
  
      'Array': function (a) {
        // create dense matrix from array
        const m = matrix(a)
        // lup, use matrix implementation
        const r = _denseLUP(m)
        // result
        return {
          L: r.L.valueOf(),
          U: r.U.valueOf(),
          p: r.p
        }
      }
    })
  
    function _denseLUP (m) {
      // rows & columns
      const rows = m._size[0]
      const columns = m._size[1]
      // minimum rows and columns
      let n = Math.min(rows, columns)
      // matrix array, clone original data
      const data = clone(m._data)
      // l matrix arrays
      const ldata = []
      const lsize = [rows, n]
      // u matrix arrays
      const udata = []
      const usize = [n, columns]
      // vars
      let i, j, k
      // permutation vector
      const p = []
      for (i = 0; i < rows; i++) { p[i] = i }
      // loop columns
      for (j = 0; j < columns; j++) {
        // skip first column in upper triangular matrix
        if (j > 0) {
          // loop rows
          for (i = 0; i < rows; i++) {
            // min i,j
            const min = Math.min(i, j)
            // v[i, j]
            let s = 0
            // loop up to min
            for (k = 0; k < min; k++) {
              // s = l[i, k] - data[k, j]
              s = addScalar(s, multiplyScalar(data[i][k], data[k][j]))
            }
            data[i][j] = subtract(data[i][j], s)
          }
        }
        // row with larger value in cvector, row >= j
        let pi = j
        let pabsv = 0
        let vjj = 0
        // loop rows
        for (i = j; i < rows; i++) {
          // data @ i, j
          const v = data[i][j]
          // absolute value
          const absv = abs(v)
          // value is greater than pivote value
          if (larger(absv, pabsv)) {
            // store row
            pi = i
            // update max value
            pabsv = absv
            // value @ [j, j]
            vjj = v
          }
        }
        // swap rows (j <-> pi)
        if (j !== pi) {
          // swap values j <-> pi in p
          p[j] = [p[pi], p[pi] = p[j]][0]
          // swap j <-> pi in data
          DenseMatrix._swapRows(j, pi, data)
        }
        // check column is in lower triangular matrix
        if (j < rows) {
          // loop rows (lower triangular matrix)
          for (i = j + 1; i < rows; i++) {
            // value @ i, j
            const vij = data[i][j]
            if (!equalScalar(vij, 0)) {
              // update data
              data[i][j] = divideScalar(data[i][j], vjj)
            }
          }
        }
      }
      // loop columns
      for (j = 0; j < columns; j++) {
        // loop rows
        for (i = 0; i < rows; i++) {
          // initialize row in arrays
          if (j === 0) {
            // check row exists in upper triangular matrix
            if (i < columns) {
              // U
              udata[i] = []
            }
            // L
            ldata[i] = []
          }
          // check we are in the upper triangular matrix
          if (i < j) {
            // check row exists in upper triangular matrix
            if (i < columns) {
              // U
              udata[i][j] = data[i][j]
            }
            // check column exists in lower triangular matrix
            if (j < rows) {
              // L
              ldata[i][j] = 0
            }
            continue
          }
          // diagonal value
          if (i === j) {
            // check row exists in upper triangular matrix
            if (i < columns) {
              // U
              udata[i][j] = data[i][j]
            }
            // check column exists in lower triangular matrix
            if (j < rows) {
              // L
              ldata[i][j] = 1
            }
            continue
          }
          // check row exists in upper triangular matrix
          if (i < columns) {
            // U
            udata[i][j] = 0
          }
          // check column exists in lower triangular matrix
          if (j < rows) {
            // L
            ldata[i][j] = data[i][j]
          }
        }
      }
      // l matrix
      const l = new DenseMatrix({
        data: ldata,
        size: lsize
      })
      // u matrix
      const u = new DenseMatrix({
        data: udata,
        size: usize
      })
      // p vector
      const pv = []
      for (i = 0, n = p.length; i < n; i++) { pv[p[i]] = i }
      // return matrices
      return {
        L: l,
        U: u,
        p: pv,
        toString: function () {
          return 'L: ' + this.L.toString() + '\nU: ' + this.U.toString() + '\nP: ' + this.p
        }
      }
    }
  
    function _sparseLUP (m) {
      // rows & columns
      const rows = m._size[0]
      const columns = m._size[1]
      // minimum rows and columns
      const n = Math.min(rows, columns)
      // matrix arrays (will not be modified, thanks to permutation vector)
      const values = m._values
      const index = m._index
      const ptr = m._ptr
      // l matrix arrays
      const lvalues = []
      const lindex = []
      const lptr = []
      const lsize = [rows, n]
      // u matrix arrays
      const uvalues = []
      const uindex = []
      const uptr = []
      const usize = [n, columns]
      // vars
      let i, j, k
      // permutation vectors, (current index -> original index) and (original index -> current index)
      const pvCo = []
      const pvOc = []
      for (i = 0; i < rows; i++) {
        pvCo[i] = i
        pvOc[i] = i
      }
      // swap indices in permutation vectors (condition x < y)!
      const swapIndeces = function (x, y) {
        // find pv indeces getting data from x and y
        const kx = pvOc[x]
        const ky = pvOc[y]
        // update permutation vector current -> original
        pvCo[kx] = y
        pvCo[ky] = x
        // update permutation vector original -> current
        pvOc[x] = ky
        pvOc[y] = kx
      }
      // loop columns
      for (j = 0; j < columns; j++) {
        // sparse accumulator
        const spa = new Spa()
        // check lower triangular matrix has a value @ column j
        if (j < rows) {
          // update ptr
          lptr.push(lvalues.length)
          // first value in j column for lower triangular matrix
          lvalues.push(1)
          lindex.push(j)
        }
        // update ptr
        uptr.push(uvalues.length)
        // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
        const k0 = ptr[j]
        const k1 = ptr[j + 1]
        // copy column j into sparse accumulator
        for (k = k0; k < k1; k++) {
          // row
          i = index[k]
          // copy column values into sparse accumulator (use permutation vector)
          spa.set(pvCo[i], values[k])
        }
        // skip first column in upper triangular matrix
        if (j > 0) {
          // loop rows in column j (above diagonal)
          spa.forEach(0, j - 1, function (k, vkj) {
            // loop rows in column k (L)
            SparseMatrix._forEachRow(k, lvalues, lindex, lptr, function (i, vik) {
              // check row is below k
              if (i > k) {
                // update spa value
                spa.accumulate(i, unaryMinus(multiplyScalar(vik, vkj)))
              }
            })
          })
        }
        // row with larger value in spa, row >= j
        let pi = j
        let vjj = spa.get(j)
        let pabsv = abs(vjj)
        // loop values in spa (order by row, below diagonal)
        spa.forEach(j + 1, rows - 1, function (x, v) {
          // absolute value
          const absv = abs(v)
          // value is greater than pivote value
          if (larger(absv, pabsv)) {
            // store row
            pi = x
            // update max value
            pabsv = absv
            // value @ [j, j]
            vjj = v
          }
        })
        // swap rows (j <-> pi)
        if (j !== pi) {
          // swap values j <-> pi in L
          SparseMatrix._swapRows(j, pi, lsize[1], lvalues, lindex, lptr)
          // swap values j <-> pi in U
          SparseMatrix._swapRows(j, pi, usize[1], uvalues, uindex, uptr)
          // swap values in spa
          spa.swap(j, pi)
          // update permutation vector (swap values @ j, pi)
          swapIndeces(j, pi)
        }
        // loop values in spa (order by row)
        spa.forEach(0, rows - 1, function (x, v) {
          // check we are above diagonal
          if (x <= j) {
            // update upper triangular matrix
            uvalues.push(v)
            uindex.push(x)
          } else {
            // update value
            v = divideScalar(v, vjj)
            // check value is non zero
            if (!equalScalar(v, 0)) {
              // update lower triangular matrix
              lvalues.push(v)
              lindex.push(x)
            }
          }
        })
      }
      // update ptrs
      uptr.push(uvalues.length)
      lptr.push(lvalues.length)
  
      // return matrices
      return {
        L: new SparseMatrix({
          values: lvalues,
          index: lindex,
          ptr: lptr,
          size: lsize
        }),
        U: new SparseMatrix({
          values: uvalues,
          index: uindex,
          ptr: uptr,
          size: usize
        }),
        p: pvCo,
        toString: function () {
          return 'L: ' + this.L.toString() + '\nU: ' + this.U.toString() + '\nP: ' + this.p
        }
      }
    }
  })
  