'use strict';

Object.defineProperty(exports, "__esModule", {
  value: true
});
exports.createLup = void 0;

var _object = require("../../../utils/object");

var _factory = require("../../../utils/factory");

var name = 'lup';
var dependencies = ['typed', 'matrix', 'abs', 'addScalar', 'divideScalar', 'multiplyScalar', 'subtract', 'larger', 'equalScalar', 'unaryMinus', 'DenseMatrix', 'SparseMatrix', 'Spa'];
var createLup =
/* #__PURE__ */
(0, _factory.factory)(name, dependencies, function (_ref) {
  var typed = _ref.typed,
      matrix = _ref.matrix,
      abs = _ref.abs,
      addScalar = _ref.addScalar,
      divideScalar = _ref.divideScalar,
      multiplyScalar = _ref.multiplyScalar,
      subtract = _ref.subtract,
      larger = _ref.larger,
      equalScalar = _ref.equalScalar,
      unaryMinus = _ref.unaryMinus,
      DenseMatrix = _ref.DenseMatrix,
      SparseMatrix = _ref.SparseMatrix,
      Spa = _ref.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 DenseMatrix(m) {
      return _denseLUP(m);
    },
    'SparseMatrix': function SparseMatrix(m) {
      return _sparseLUP(m);
    },
    'Array': function Array(a) {
      // create dense matrix from array
      var m = matrix(a); // lup, use matrix implementation

      var r = _denseLUP(m); // result


      return {
        L: r.L.valueOf(),
        U: r.U.valueOf(),
        p: r.p
      };
    }
  });

  function _denseLUP(m) {
    // rows & columns
    var rows = m._size[0];
    var columns = m._size[1]; // minimum rows and columns

    var n = Math.min(rows, columns); // matrix array, clone original data

    var data = (0, _object.clone)(m._data); // l matrix arrays

    var ldata = [];
    var lsize = [rows, n]; // u matrix arrays

    var udata = [];
    var usize = [n, columns]; // vars

    var i, j, k; // permutation vector

    var 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
          var min = Math.min(i, j); // v[i, j]

          var 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


      var pi = j;
      var pabsv = 0;
      var vjj = 0; // loop rows

      for (i = j; i < rows; i++) {
        // data @ i, j
        var v = data[i][j]; // absolute value

        var 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
          var 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


    var l = new DenseMatrix({
      data: ldata,
      size: lsize
    }); // u matrix

    var u = new DenseMatrix({
      data: udata,
      size: usize
    }); // p vector

    var 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 toString() {
        return 'L: ' + this.L.toString() + '\nU: ' + this.U.toString() + '\nP: ' + this.p;
      }
    };
  }

  function _sparseLUP(m) {
    // rows & columns
    var rows = m._size[0];
    var columns = m._size[1]; // minimum rows and columns

    var n = Math.min(rows, columns); // matrix arrays (will not be modified, thanks to permutation vector)

    var values = m._values;
    var index = m._index;
    var ptr = m._ptr; // l matrix arrays

    var lvalues = [];
    var lindex = [];
    var lptr = [];
    var lsize = [rows, n]; // u matrix arrays

    var uvalues = [];
    var uindex = [];
    var uptr = [];
    var usize = [n, columns]; // vars

    var i, j, k; // permutation vectors, (current index -> original index) and (original index -> current index)

    var pvCo = [];
    var pvOc = [];

    for (i = 0; i < rows; i++) {
      pvCo[i] = i;
      pvOc[i] = i;
    } // swap indices in permutation vectors (condition x < y)!


    var swapIndeces = function swapIndeces(x, y) {
      // find pv indeces getting data from x and y
      var kx = pvOc[x];
      var 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


    var _loop = function _loop() {
      // sparse accumulator
      var 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]

      var k0 = ptr[j];
      var 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


      var pi = j;
      var vjj = spa.get(j);
      var pabsv = abs(vjj); // loop values in spa (order by row, below diagonal)

      spa.forEach(j + 1, rows - 1, function (x, v) {
        // absolute value
        var 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);
          }
        }
      });
    };

    for (j = 0; j < columns; j++) {
      _loop();
    } // 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 toString() {
        return 'L: ' + this.L.toString() + '\nU: ' + this.U.toString() + '\nP: ' + this.p;
      }
    };
  }
});
exports.createLup = createLup;