mathjs/lib/type/matrix/SparseMatrix.js

"use strict";

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

var _is = require("../../utils/is");

var _number = require("../../utils/number");

var _string = require("../../utils/string");

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

var _array = require("../../utils/array");

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

var _DimensionError = require("../../error/DimensionError");

var name = 'SparseMatrix';
var dependencies = ['typed', 'equalScalar', 'Matrix'];
var createSparseMatrixClass =
/* #__PURE__ */
(0, _factory.factory)(name, dependencies, function (_ref) {
  var typed = _ref.typed,
      equalScalar = _ref.equalScalar,
      Matrix = _ref.Matrix;

  /**
   * Sparse Matrix implementation. This type implements a Compressed Column Storage format
   * for sparse matrices.
   * @class SparseMatrix
   */
  function SparseMatrix(data, datatype) {
    if (!(this instanceof SparseMatrix)) {
      throw new SyntaxError('Constructor must be called with the new operator');
    }

    if (datatype && !(0, _is.isString)(datatype)) {
      throw new Error('Invalid datatype: ' + datatype);
    }

    if ((0, _is.isMatrix)(data)) {
      // create from matrix
      _createFromMatrix(this, data, datatype);
    } else if (data && (0, _is.isArray)(data.index) && (0, _is.isArray)(data.ptr) && (0, _is.isArray)(data.size)) {
      // initialize fields
      this._values = data.values;
      this._index = data.index;
      this._ptr = data.ptr;
      this._size = data.size;
      this._datatype = datatype || data.datatype;
    } else if ((0, _is.isArray)(data)) {
      // create from array
      _createFromArray(this, data, datatype);
    } else if (data) {
      // unsupported type
      throw new TypeError('Unsupported type of data (' + (0, _is.typeOf)(data) + ')');
    } else {
      // nothing provided
      this._values = [];
      this._index = [];
      this._ptr = [0];
      this._size = [0, 0];
      this._datatype = datatype;
    }
  }

  function _createFromMatrix(matrix, source, datatype) {
    // check matrix type
    if (source.type === 'SparseMatrix') {
      // clone arrays
      matrix._values = source._values ? (0, _object.clone)(source._values) : undefined;
      matrix._index = (0, _object.clone)(source._index);
      matrix._ptr = (0, _object.clone)(source._ptr);
      matrix._size = (0, _object.clone)(source._size);
      matrix._datatype = datatype || source._datatype;
    } else {
      // build from matrix data
      _createFromArray(matrix, source.valueOf(), datatype || source._datatype);
    }
  }

  function _createFromArray(matrix, data, datatype) {
    // initialize fields
    matrix._values = [];
    matrix._index = [];
    matrix._ptr = [];
    matrix._datatype = datatype; // discover rows & columns, do not use math.size() to avoid looping array twice

    var rows = data.length;
    var columns = 0; // equal signature to use

    var eq = equalScalar; // zero value

    var zero = 0;

    if ((0, _is.isString)(datatype)) {
      // find signature that matches (datatype, datatype)
      eq = typed.find(equalScalar, [datatype, datatype]) || equalScalar; // convert 0 to the same datatype

      zero = typed.convert(0, datatype);
    } // check we have rows (empty array)


    if (rows > 0) {
      // column index
      var j = 0;

      do {
        // store pointer to values index
        matrix._ptr.push(matrix._index.length); // loop rows


        for (var i = 0; i < rows; i++) {
          // current row
          var row = data[i]; // check row is an array

          if ((0, _is.isArray)(row)) {
            // update columns if needed (only on first column)
            if (j === 0 && columns < row.length) {
              columns = row.length;
            } // check row has column


            if (j < row.length) {
              // value
              var v = row[j]; // check value != 0

              if (!eq(v, zero)) {
                // store value
                matrix._values.push(v); // index


                matrix._index.push(i);
              }
            }
          } else {
            // update columns if needed (only on first column)
            if (j === 0 && columns < 1) {
              columns = 1;
            } // check value != 0 (row is a scalar)


            if (!eq(row, zero)) {
              // store value
              matrix._values.push(row); // index


              matrix._index.push(i);
            }
          }
        } // increment index


        j++;
      } while (j < columns);
    } // store number of values in ptr


    matrix._ptr.push(matrix._index.length); // size


    matrix._size = [rows, columns];
  }

  SparseMatrix.prototype = new Matrix();
  /**
   * Create a new SparseMatrix
   */

  SparseMatrix.prototype.createSparseMatrix = function (data, datatype) {
    return new SparseMatrix(data, datatype);
  };
  /**
   * Attach type information
   */


  SparseMatrix.prototype.type = 'SparseMatrix';
  SparseMatrix.prototype.isSparseMatrix = true;
  /**
   * Get the matrix type
   *
   * Usage:
   *    const matrixType = matrix.getDataType()  // retrieves the matrix type
   *
   * @memberOf SparseMatrix
   * @return {string}   type information; if multiple types are found from the Matrix, it will return "mixed"
   */

  SparseMatrix.prototype.getDataType = function () {
    return (0, _array.getArrayDataType)(this._values, _is.typeOf);
  };
  /**
   * Get the storage format used by the matrix.
   *
   * Usage:
   *     const format = matrix.storage()   // retrieve storage format
   *
   * @memberof SparseMatrix
   * @return {string}           The storage format.
   */


  SparseMatrix.prototype.storage = function () {
    return 'sparse';
  };
  /**
   * Get the datatype of the data stored in the matrix.
   *
   * Usage:
   *     const format = matrix.datatype()    // retrieve matrix datatype
   *
   * @memberof SparseMatrix
   * @return {string}           The datatype.
   */


  SparseMatrix.prototype.datatype = function () {
    return this._datatype;
  };
  /**
   * Create a new SparseMatrix
   * @memberof SparseMatrix
   * @param {Array} data
   * @param {string} [datatype]
   */


  SparseMatrix.prototype.create = function (data, datatype) {
    return new SparseMatrix(data, datatype);
  };
  /**
   * Get the matrix density.
   *
   * Usage:
   *     const density = matrix.density()                   // retrieve matrix density
   *
   * @memberof SparseMatrix
   * @return {number}           The matrix density.
   */


  SparseMatrix.prototype.density = function () {
    // rows & columns
    var rows = this._size[0];
    var columns = this._size[1]; // calculate density

    return rows !== 0 && columns !== 0 ? this._index.length / (rows * columns) : 0;
  };
  /**
   * Get a subset of the matrix, or replace a subset of the matrix.
   *
   * Usage:
   *     const subset = matrix.subset(index)               // retrieve subset
   *     const value = matrix.subset(index, replacement)   // replace subset
   *
   * @memberof SparseMatrix
   * @param {Index} index
   * @param {Array | Matrix | *} [replacement]
   * @param {*} [defaultValue=0]      Default value, filled in on new entries when
   *                                  the matrix is resized. If not provided,
   *                                  new matrix elements will be filled with zeros.
   */


  SparseMatrix.prototype.subset = function (index, replacement, defaultValue) {
    // check it is a pattern matrix
    if (!this._values) {
      throw new Error('Cannot invoke subset on a Pattern only matrix');
    } // check arguments


    switch (arguments.length) {
      case 1:
        return _getsubset(this, index);
      // intentional fall through

      case 2:
      case 3:
        return _setsubset(this, index, replacement, defaultValue);

      default:
        throw new SyntaxError('Wrong number of arguments');
    }
  };

  function _getsubset(matrix, idx) {
    // check idx
    if (!(0, _is.isIndex)(idx)) {
      throw new TypeError('Invalid index');
    }

    var isScalar = idx.isScalar();

    if (isScalar) {
      // return a scalar
      return matrix.get(idx.min());
    } // validate dimensions


    var size = idx.size();

    if (size.length !== matrix._size.length) {
      throw new _DimensionError.DimensionError(size.length, matrix._size.length);
    } // vars


    var i, ii, k, kk; // validate if any of the ranges in the index is out of range

    var min = idx.min();
    var max = idx.max();

    for (i = 0, ii = matrix._size.length; i < ii; i++) {
      (0, _array.validateIndex)(min[i], matrix._size[i]);
      (0, _array.validateIndex)(max[i], matrix._size[i]);
    } // matrix arrays


    var mvalues = matrix._values;
    var mindex = matrix._index;
    var mptr = matrix._ptr; // rows & columns dimensions for result matrix

    var rows = idx.dimension(0);
    var columns = idx.dimension(1); // workspace & permutation vector

    var w = [];
    var pv = []; // loop rows in resulting matrix

    rows.forEach(function (i, r) {
      // update permutation vector
      pv[i] = r[0]; // mark i in workspace

      w[i] = true;
    }); // result matrix arrays

    var values = mvalues ? [] : undefined;
    var index = [];
    var ptr = []; // loop columns in result matrix

    columns.forEach(function (j) {
      // update ptr
      ptr.push(index.length); // loop values in column j

      for (k = mptr[j], kk = mptr[j + 1]; k < kk; k++) {
        // row
        i = mindex[k]; // check row is in result matrix

        if (w[i] === true) {
          // push index
          index.push(pv[i]); // check we need to process values

          if (values) {
            values.push(mvalues[k]);
          }
        }
      }
    }); // update ptr

    ptr.push(index.length); // return matrix

    return new SparseMatrix({
      values: values,
      index: index,
      ptr: ptr,
      size: size,
      datatype: matrix._datatype
    });
  }

  function _setsubset(matrix, index, submatrix, defaultValue) {
    // check index
    if (!index || index.isIndex !== true) {
      throw new TypeError('Invalid index');
    } // get index size and check whether the index contains a single value


    var iSize = index.size();
    var isScalar = index.isScalar(); // calculate the size of the submatrix, and convert it into an Array if needed

    var sSize;

    if ((0, _is.isMatrix)(submatrix)) {
      // submatrix size
      sSize = submatrix.size(); // use array representation

      submatrix = submatrix.toArray();
    } else {
      // get submatrix size (array, scalar)
      sSize = (0, _array.arraySize)(submatrix);
    } // check index is a scalar


    if (isScalar) {
      // verify submatrix is a scalar
      if (sSize.length !== 0) {
        throw new TypeError('Scalar expected');
      } // set value


      matrix.set(index.min(), submatrix, defaultValue);
    } else {
      // validate dimensions, index size must be one or two dimensions
      if (iSize.length !== 1 && iSize.length !== 2) {
        throw new _DimensionError.DimensionError(iSize.length, matrix._size.length, '<');
      } // check submatrix and index have the same dimensions


      if (sSize.length < iSize.length) {
        // calculate number of missing outer dimensions
        var i = 0;
        var outer = 0;

        while (iSize[i] === 1 && sSize[i] === 1) {
          i++;
        }

        while (iSize[i] === 1) {
          outer++;
          i++;
        } // unsqueeze both outer and inner dimensions


        submatrix = (0, _array.unsqueeze)(submatrix, iSize.length, outer, sSize);
      } // check whether the size of the submatrix matches the index size


      if (!(0, _object.deepStrictEqual)(iSize, sSize)) {
        throw new _DimensionError.DimensionError(iSize, sSize, '>');
      } // offsets


      var x0 = index.min()[0];
      var y0 = index.min()[1]; // submatrix rows and columns

      var m = sSize[0];
      var n = sSize[1]; // loop submatrix

      for (var x = 0; x < m; x++) {
        // loop columns
        for (var y = 0; y < n; y++) {
          // value at i, j
          var v = submatrix[x][y]; // invoke set (zero value will remove entry from matrix)

          matrix.set([x + x0, y + y0], v, defaultValue);
        }
      }
    }

    return matrix;
  }
  /**
   * Get a single element from the matrix.
   * @memberof SparseMatrix
   * @param {number[]} index   Zero-based index
   * @return {*} value
   */


  SparseMatrix.prototype.get = function (index) {
    if (!(0, _is.isArray)(index)) {
      throw new TypeError('Array expected');
    }

    if (index.length !== this._size.length) {
      throw new _DimensionError.DimensionError(index.length, this._size.length);
    } // check it is a pattern matrix


    if (!this._values) {
      throw new Error('Cannot invoke get on a Pattern only matrix');
    } // row and column


    var i = index[0];
    var j = index[1]; // check i, j are valid

    (0, _array.validateIndex)(i, this._size[0]);
    (0, _array.validateIndex)(j, this._size[1]); // find value index

    var k = _getValueIndex(i, this._ptr[j], this._ptr[j + 1], this._index); // check k is prior to next column k and it is in the correct row


    if (k < this._ptr[j + 1] && this._index[k] === i) {
      return this._values[k];
    }

    return 0;
  };
  /**
   * Replace a single element in the matrix.
   * @memberof SparseMatrix
   * @param {number[]} index   Zero-based index
   * @param {*} v
   * @param {*} [defaultValue]        Default value, filled in on new entries when
   *                                  the matrix is resized. If not provided,
   *                                  new matrix elements will be set to zero.
   * @return {SparseMatrix} self
   */


  SparseMatrix.prototype.set = function (index, v, defaultValue) {
    if (!(0, _is.isArray)(index)) {
      throw new TypeError('Array expected');
    }

    if (index.length !== this._size.length) {
      throw new _DimensionError.DimensionError(index.length, this._size.length);
    } // check it is a pattern matrix


    if (!this._values) {
      throw new Error('Cannot invoke set on a Pattern only matrix');
    } // row and column


    var i = index[0];
    var j = index[1]; // rows & columns

    var rows = this._size[0];
    var columns = this._size[1]; // equal signature to use

    var eq = equalScalar; // zero value

    var zero = 0;

    if ((0, _is.isString)(this._datatype)) {
      // find signature that matches (datatype, datatype)
      eq = typed.find(equalScalar, [this._datatype, this._datatype]) || equalScalar; // convert 0 to the same datatype

      zero = typed.convert(0, this._datatype);
    } // check we need to resize matrix


    if (i > rows - 1 || j > columns - 1) {
      // resize matrix
      _resize(this, Math.max(i + 1, rows), Math.max(j + 1, columns), defaultValue); // update rows & columns


      rows = this._size[0];
      columns = this._size[1];
    } // check i, j are valid


    (0, _array.validateIndex)(i, rows);
    (0, _array.validateIndex)(j, columns); // find value index

    var k = _getValueIndex(i, this._ptr[j], this._ptr[j + 1], this._index); // check k is prior to next column k and it is in the correct row


    if (k < this._ptr[j + 1] && this._index[k] === i) {
      // check value != 0
      if (!eq(v, zero)) {
        // update value
        this._values[k] = v;
      } else {
        // remove value from matrix
        _remove(k, j, this._values, this._index, this._ptr);
      }
    } else {
      // insert value @ (i, j)
      _insert(k, i, j, v, this._values, this._index, this._ptr);
    }

    return this;
  };

  function _getValueIndex(i, top, bottom, index) {
    // check row is on the bottom side
    if (bottom - top === 0) {
      return bottom;
    } // loop rows [top, bottom[


    for (var r = top; r < bottom; r++) {
      // check we found value index
      if (index[r] === i) {
        return r;
      }
    } // we did not find row


    return top;
  }

  function _remove(k, j, values, index, ptr) {
    // remove value @ k
    values.splice(k, 1);
    index.splice(k, 1); // update pointers

    for (var x = j + 1; x < ptr.length; x++) {
      ptr[x]--;
    }
  }

  function _insert(k, i, j, v, values, index, ptr) {
    // insert value
    values.splice(k, 0, v); // update row for k

    index.splice(k, 0, i); // update column pointers

    for (var x = j + 1; x < ptr.length; x++) {
      ptr[x]++;
    }
  }
  /**
   * Resize the matrix to the given size. Returns a copy of the matrix when
   * `copy=true`, otherwise return the matrix itself (resize in place).
   *
   * @memberof SparseMatrix
   * @param {number[]} size           The new size the matrix should have.
   * @param {*} [defaultValue=0]      Default value, filled in on new entries.
   *                                  If not provided, the matrix elements will
   *                                  be filled with zeros.
   * @param {boolean} [copy]          Return a resized copy of the matrix
   *
   * @return {Matrix}                 The resized matrix
   */


  SparseMatrix.prototype.resize = function (size, defaultValue, copy) {
    // validate arguments
    if (!(0, _is.isArray)(size)) {
      throw new TypeError('Array expected');
    }

    if (size.length !== 2) {
      throw new Error('Only two dimensions matrix are supported');
    } // check sizes


    size.forEach(function (value) {
      if (!(0, _is.isNumber)(value) || !(0, _number.isInteger)(value) || value < 0) {
        throw new TypeError('Invalid size, must contain positive integers ' + '(size: ' + (0, _string.format)(size) + ')');
      }
    }); // matrix to resize

    var m = copy ? this.clone() : this; // resize matrix

    return _resize(m, size[0], size[1], defaultValue);
  };

  function _resize(matrix, rows, columns, defaultValue) {
    // value to insert at the time of growing matrix
    var value = defaultValue || 0; // equal signature to use

    var eq = equalScalar; // zero value

    var zero = 0;

    if ((0, _is.isString)(matrix._datatype)) {
      // find signature that matches (datatype, datatype)
      eq = typed.find(equalScalar, [matrix._datatype, matrix._datatype]) || equalScalar; // convert 0 to the same datatype

      zero = typed.convert(0, matrix._datatype); // convert value to the same datatype

      value = typed.convert(value, matrix._datatype);
    } // should we insert the value?


    var ins = !eq(value, zero); // old columns and rows

    var r = matrix._size[0];
    var c = matrix._size[1];
    var i, j, k; // check we need to increase columns

    if (columns > c) {
      // loop new columns
      for (j = c; j < columns; j++) {
        // update matrix._ptr for current column
        matrix._ptr[j] = matrix._values.length; // check we need to insert matrix._values

        if (ins) {
          // loop rows
          for (i = 0; i < r; i++) {
            // add new matrix._values
            matrix._values.push(value); // update matrix._index


            matrix._index.push(i);
          }
        }
      } // store number of matrix._values in matrix._ptr


      matrix._ptr[columns] = matrix._values.length;
    } else if (columns < c) {
      // truncate matrix._ptr
      matrix._ptr.splice(columns + 1, c - columns); // truncate matrix._values and matrix._index


      matrix._values.splice(matrix._ptr[columns], matrix._values.length);

      matrix._index.splice(matrix._ptr[columns], matrix._index.length);
    } // update columns


    c = columns; // check we need to increase rows

    if (rows > r) {
      // check we have to insert values
      if (ins) {
        // inserts
        var n = 0; // loop columns

        for (j = 0; j < c; j++) {
          // update matrix._ptr for current column
          matrix._ptr[j] = matrix._ptr[j] + n; // where to insert matrix._values

          k = matrix._ptr[j + 1] + n; // pointer

          var p = 0; // loop new rows, initialize pointer

          for (i = r; i < rows; i++, p++) {
            // add value
            matrix._values.splice(k + p, 0, value); // update matrix._index


            matrix._index.splice(k + p, 0, i); // increment inserts


            n++;
          }
        } // store number of matrix._values in matrix._ptr


        matrix._ptr[c] = matrix._values.length;
      }
    } else if (rows < r) {
      // deletes
      var d = 0; // loop columns

      for (j = 0; j < c; j++) {
        // update matrix._ptr for current column
        matrix._ptr[j] = matrix._ptr[j] - d; // where matrix._values start for next column

        var k0 = matrix._ptr[j];
        var k1 = matrix._ptr[j + 1] - d; // loop matrix._index

        for (k = k0; k < k1; k++) {
          // row
          i = matrix._index[k]; // check we need to delete value and matrix._index

          if (i > rows - 1) {
            // remove value
            matrix._values.splice(k, 1); // remove item from matrix._index


            matrix._index.splice(k, 1); // increase deletes


            d++;
          }
        }
      } // update matrix._ptr for current column


      matrix._ptr[j] = matrix._values.length;
    } // update matrix._size


    matrix._size[0] = rows;
    matrix._size[1] = columns; // return matrix

    return matrix;
  }
  /**
   * Reshape the matrix to the given size. Returns a copy of the matrix when
   * `copy=true`, otherwise return the matrix itself (reshape in place).
   *
   * NOTE: This might be better suited to copy by default, instead of modifying
   *       in place. For now, it operates in place to remain consistent with
   *       resize().
   *
   * @memberof SparseMatrix
   * @param {number[]} size           The new size the matrix should have.
   * @param {boolean} [copy]          Return a reshaped copy of the matrix
   *
   * @return {Matrix}                 The reshaped matrix
   */


  SparseMatrix.prototype.reshape = function (size, copy) {
    // validate arguments
    if (!(0, _is.isArray)(size)) {
      throw new TypeError('Array expected');
    }

    if (size.length !== 2) {
      throw new Error('Sparse matrices can only be reshaped in two dimensions');
    } // check sizes


    size.forEach(function (value) {
      if (!(0, _is.isNumber)(value) || !(0, _number.isInteger)(value) || value < 0) {
        throw new TypeError('Invalid size, must contain positive integers ' + '(size: ' + (0, _string.format)(size) + ')');
      }
    }); // m * n must not change

    if (this._size[0] * this._size[1] !== size[0] * size[1]) {
      throw new Error('Reshaping sparse matrix will result in the wrong number of elements');
    } // matrix to reshape


    var m = copy ? this.clone() : this; // return unchanged if the same shape

    if (this._size[0] === size[0] && this._size[1] === size[1]) {
      return m;
    } // Convert to COO format (generate a column index)


    var colIndex = [];

    for (var i = 0; i < m._ptr.length; i++) {
      for (var j = 0; j < m._ptr[i + 1] - m._ptr[i]; j++) {
        colIndex.push(i);
      }
    } // Clone the values array


    var values = m._values.slice(); // Clone the row index array


    var rowIndex = m._index.slice(); // Transform the (row, column) indices


    for (var _i = 0; _i < m._index.length; _i++) {
      var r1 = rowIndex[_i];
      var c1 = colIndex[_i];
      var flat = r1 * m._size[1] + c1;
      colIndex[_i] = flat % size[1];
      rowIndex[_i] = Math.floor(flat / size[1]);
    } // Now reshaping is supposed to preserve the row-major order, BUT these sparse matrices are stored
    // in column-major order, so we have to reorder the value array now. One option is to use a multisort,
    // sorting several arrays based on some other array.
    // OR, we could easily just:
    // 1. Remove all values from the matrix


    m._values.length = 0;
    m._index.length = 0;
    m._ptr.length = size[1] + 1;
    m._size = size.slice();

    for (var _i2 = 0; _i2 < m._ptr.length; _i2++) {
      m._ptr[_i2] = 0;
    } // 2. Re-insert all elements in the proper order (simplified code from SparseMatrix.prototype.set)
    // This step is probably the most time-consuming


    for (var h = 0; h < values.length; h++) {
      var _i3 = rowIndex[h];
      var _j = colIndex[h];
      var v = values[h];

      var k = _getValueIndex(_i3, m._ptr[_j], m._ptr[_j + 1], m._index);

      _insert(k, _i3, _j, v, m._values, m._index, m._ptr);
    } // The value indices are inserted out of order, but apparently that's... still OK?


    return m;
  };
  /**
   * Create a clone of the matrix
   * @memberof SparseMatrix
   * @return {SparseMatrix} clone
   */


  SparseMatrix.prototype.clone = function () {
    var m = new SparseMatrix({
      values: this._values ? (0, _object.clone)(this._values) : undefined,
      index: (0, _object.clone)(this._index),
      ptr: (0, _object.clone)(this._ptr),
      size: (0, _object.clone)(this._size),
      datatype: this._datatype
    });
    return m;
  };
  /**
   * Retrieve the size of the matrix.
   * @memberof SparseMatrix
   * @returns {number[]} size
   */


  SparseMatrix.prototype.size = function () {
    return this._size.slice(0); // copy the Array
  };
  /**
   * Create a new matrix with the results of the callback function executed on
   * each entry of the matrix.
   * @memberof SparseMatrix
   * @param {Function} callback   The callback function is invoked with three
   *                              parameters: the value of the element, the index
   *                              of the element, and the Matrix being traversed.
   * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.
   *
   * @return {SparseMatrix} matrix
   */


  SparseMatrix.prototype.map = function (callback, skipZeros) {
    // check it is a pattern matrix
    if (!this._values) {
      throw new Error('Cannot invoke map on a Pattern only matrix');
    } // matrix instance


    var me = this; // rows and columns

    var rows = this._size[0];
    var columns = this._size[1]; // invoke callback

    var invoke = function invoke(v, i, j) {
      // invoke callback
      return callback(v, [i, j], me);
    }; // invoke _map


    return _map(this, 0, rows - 1, 0, columns - 1, invoke, skipZeros);
  };
  /**
   * Create a new matrix with the results of the callback function executed on the interval
   * [minRow..maxRow, minColumn..maxColumn].
   */


  function _map(matrix, minRow, maxRow, minColumn, maxColumn, callback, skipZeros) {
    // result arrays
    var values = [];
    var index = [];
    var ptr = []; // equal signature to use

    var eq = equalScalar; // zero value

    var zero = 0;

    if ((0, _is.isString)(matrix._datatype)) {
      // find signature that matches (datatype, datatype)
      eq = typed.find(equalScalar, [matrix._datatype, matrix._datatype]) || equalScalar; // convert 0 to the same datatype

      zero = typed.convert(0, matrix._datatype);
    } // invoke callback


    var invoke = function invoke(v, x, y) {
      // invoke callback
      v = callback(v, x, y); // check value != 0

      if (!eq(v, zero)) {
        // store value
        values.push(v); // index

        index.push(x);
      }
    }; // loop columns


    for (var j = minColumn; j <= maxColumn; j++) {
      // store pointer to values index
      ptr.push(values.length); // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]

      var k0 = matrix._ptr[j];
      var k1 = matrix._ptr[j + 1];

      if (skipZeros) {
        // loop k within [k0, k1[
        for (var k = k0; k < k1; k++) {
          // row index
          var i = matrix._index[k]; // check i is in range

          if (i >= minRow && i <= maxRow) {
            // value @ k
            invoke(matrix._values[k], i - minRow, j - minColumn);
          }
        }
      } else {
        // create a cache holding all defined values
        var _values = {};

        for (var _k = k0; _k < k1; _k++) {
          var _i4 = matrix._index[_k];
          _values[_i4] = matrix._values[_k];
        } // loop over all rows (indexes can be unordered so we can't use that),
        // and either read the value or zero


        for (var _i5 = minRow; _i5 <= maxRow; _i5++) {
          var value = _i5 in _values ? _values[_i5] : 0;
          invoke(value, _i5 - minRow, j - minColumn);
        }
      }
    } // store number of values in ptr


    ptr.push(values.length); // return sparse matrix

    return new SparseMatrix({
      values: values,
      index: index,
      ptr: ptr,
      size: [maxRow - minRow + 1, maxColumn - minColumn + 1]
    });
  }
  /**
   * Execute a callback function on each entry of the matrix.
   * @memberof SparseMatrix
   * @param {Function} callback   The callback function is invoked with three
   *                              parameters: the value of the element, the index
   *                              of the element, and the Matrix being traversed.
   * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.
   */


  SparseMatrix.prototype.forEach = function (callback, skipZeros) {
    // check it is a pattern matrix
    if (!this._values) {
      throw new Error('Cannot invoke forEach on a Pattern only matrix');
    } // matrix instance


    var me = this; // rows and columns

    var rows = this._size[0];
    var columns = this._size[1]; // loop columns

    for (var j = 0; j < columns; j++) {
      // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
      var k0 = this._ptr[j];
      var k1 = this._ptr[j + 1];

      if (skipZeros) {
        // loop k within [k0, k1[
        for (var k = k0; k < k1; k++) {
          // row index
          var i = this._index[k]; // value @ k

          callback(this._values[k], [i, j], me);
        }
      } else {
        // create a cache holding all defined values
        var values = {};

        for (var _k2 = k0; _k2 < k1; _k2++) {
          var _i6 = this._index[_k2];
          values[_i6] = this._values[_k2];
        } // loop over all rows (indexes can be unordered so we can't use that),
        // and either read the value or zero


        for (var _i7 = 0; _i7 < rows; _i7++) {
          var value = _i7 in values ? values[_i7] : 0;
          callback(value, [_i7, j], me);
        }
      }
    }
  };
  /**
   * Create an Array with a copy of the data of the SparseMatrix
   * @memberof SparseMatrix
   * @returns {Array} array
   */


  SparseMatrix.prototype.toArray = function () {
    return _toArray(this._values, this._index, this._ptr, this._size, true);
  };
  /**
   * Get the primitive value of the SparseMatrix: a two dimensions array
   * @memberof SparseMatrix
   * @returns {Array} array
   */


  SparseMatrix.prototype.valueOf = function () {
    return _toArray(this._values, this._index, this._ptr, this._size, false);
  };

  function _toArray(values, index, ptr, size, copy) {
    // rows and columns
    var rows = size[0];
    var columns = size[1]; // result

    var a = []; // vars

    var i, j; // initialize array

    for (i = 0; i < rows; i++) {
      a[i] = [];

      for (j = 0; j < columns; j++) {
        a[i][j] = 0;
      }
    } // loop columns


    for (j = 0; j < columns; j++) {
      // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
      var k0 = ptr[j];
      var k1 = ptr[j + 1]; // loop k within [k0, k1[

      for (var k = k0; k < k1; k++) {
        // row index
        i = index[k]; // set value (use one for pattern matrix)

        a[i][j] = values ? copy ? (0, _object.clone)(values[k]) : values[k] : 1;
      }
    }

    return a;
  }
  /**
   * Get a string representation of the matrix, with optional formatting options.
   * @memberof SparseMatrix
   * @param {Object | number | Function} [options]  Formatting options. See
   *                                                lib/utils/number:format for a
   *                                                description of the available
   *                                                options.
   * @returns {string} str
   */


  SparseMatrix.prototype.format = function (options) {
    // rows and columns
    var rows = this._size[0];
    var columns = this._size[1]; // density

    var density = this.density(); // rows & columns

    var str = 'Sparse Matrix [' + (0, _string.format)(rows, options) + ' x ' + (0, _string.format)(columns, options) + '] density: ' + (0, _string.format)(density, options) + '\n'; // loop columns

    for (var j = 0; j < columns; j++) {
      // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
      var k0 = this._ptr[j];
      var k1 = this._ptr[j + 1]; // loop k within [k0, k1[

      for (var k = k0; k < k1; k++) {
        // row index
        var i = this._index[k]; // append value

        str += '\n    (' + (0, _string.format)(i, options) + ', ' + (0, _string.format)(j, options) + ') ==> ' + (this._values ? (0, _string.format)(this._values[k], options) : 'X');
      }
    }

    return str;
  };
  /**
   * Get a string representation of the matrix
   * @memberof SparseMatrix
   * @returns {string} str
   */


  SparseMatrix.prototype.toString = function () {
    return (0, _string.format)(this.toArray());
  };
  /**
   * Get a JSON representation of the matrix
   * @memberof SparseMatrix
   * @returns {Object}
   */


  SparseMatrix.prototype.toJSON = function () {
    return {
      mathjs: 'SparseMatrix',
      values: this._values,
      index: this._index,
      ptr: this._ptr,
      size: this._size,
      datatype: this._datatype
    };
  };
  /**
   * Get the kth Matrix diagonal.
   *
   * @memberof SparseMatrix
   * @param {number | BigNumber} [k=0]     The kth diagonal where the vector will retrieved.
   *
   * @returns {Matrix}                     The matrix vector with the diagonal values.
   */


  SparseMatrix.prototype.diagonal = function (k) {
    // validate k if any
    if (k) {
      // convert BigNumber to a number
      if ((0, _is.isBigNumber)(k)) {
        k = k.toNumber();
      } // is must be an integer


      if (!(0, _is.isNumber)(k) || !(0, _number.isInteger)(k)) {
        throw new TypeError('The parameter k must be an integer number');
      }
    } else {
      // default value
      k = 0;
    }

    var kSuper = k > 0 ? k : 0;
    var kSub = k < 0 ? -k : 0; // rows & columns

    var rows = this._size[0];
    var columns = this._size[1]; // number diagonal values

    var n = Math.min(rows - kSub, columns - kSuper); // diagonal arrays

    var values = [];
    var index = [];
    var ptr = []; // initial ptr value

    ptr[0] = 0; // loop columns

    for (var j = kSuper; j < columns && values.length < n; j++) {
      // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
      var k0 = this._ptr[j];
      var k1 = this._ptr[j + 1]; // loop x within [k0, k1[

      for (var x = k0; x < k1; x++) {
        // row index
        var i = this._index[x]; // check row

        if (i === j - kSuper + kSub) {
          // value on this column
          values.push(this._values[x]); // store row

          index[values.length - 1] = i - kSub; // exit loop

          break;
        }
      }
    } // close ptr


    ptr.push(values.length); // return matrix

    return new SparseMatrix({
      values: values,
      index: index,
      ptr: ptr,
      size: [n, 1]
    });
  };
  /**
   * Generate a matrix from a JSON object
   * @memberof SparseMatrix
   * @param {Object} json  An object structured like
   *                       `{"mathjs": "SparseMatrix", "values": [], "index": [], "ptr": [], "size": []}`,
   *                       where mathjs is optional
   * @returns {SparseMatrix}
   */


  SparseMatrix.fromJSON = function (json) {
    return new SparseMatrix(json);
  };
  /**
   * Create a diagonal matrix.
   *
   * @memberof SparseMatrix
   * @param {Array} size                       The matrix size.
   * @param {number | Array | Matrix } value   The values for the diagonal.
   * @param {number | BigNumber} [k=0]         The kth diagonal where the vector will be filled in.
   * @param {number} [defaultValue]            The default value for non-diagonal
   * @param {string} [datatype]                The Matrix datatype, values must be of this datatype.
   *
   * @returns {SparseMatrix}
   */


  SparseMatrix.diagonal = function (size, value, k, defaultValue, datatype) {
    if (!(0, _is.isArray)(size)) {
      throw new TypeError('Array expected, size parameter');
    }

    if (size.length !== 2) {
      throw new Error('Only two dimensions matrix are supported');
    } // map size & validate


    size = size.map(function (s) {
      // check it is a big number
      if ((0, _is.isBigNumber)(s)) {
        // convert it
        s = s.toNumber();
      } // validate arguments


      if (!(0, _is.isNumber)(s) || !(0, _number.isInteger)(s) || s < 1) {
        throw new Error('Size values must be positive integers');
      }

      return s;
    }); // validate k if any

    if (k) {
      // convert BigNumber to a number
      if ((0, _is.isBigNumber)(k)) {
        k = k.toNumber();
      } // is must be an integer


      if (!(0, _is.isNumber)(k) || !(0, _number.isInteger)(k)) {
        throw new TypeError('The parameter k must be an integer number');
      }
    } else {
      // default value
      k = 0;
    } // equal signature to use


    var eq = equalScalar; // zero value

    var zero = 0;

    if ((0, _is.isString)(datatype)) {
      // find signature that matches (datatype, datatype)
      eq = typed.find(equalScalar, [datatype, datatype]) || equalScalar; // convert 0 to the same datatype

      zero = typed.convert(0, datatype);
    }

    var kSuper = k > 0 ? k : 0;
    var kSub = k < 0 ? -k : 0; // rows and columns

    var rows = size[0];
    var columns = size[1]; // number of non-zero items

    var n = Math.min(rows - kSub, columns - kSuper); // value extraction function

    var _value; // check value


    if ((0, _is.isArray)(value)) {
      // validate array
      if (value.length !== n) {
        // number of values in array must be n
        throw new Error('Invalid value array length');
      } // define function


      _value = function _value(i) {
        // return value @ i
        return value[i];
      };
    } else if ((0, _is.isMatrix)(value)) {
      // matrix size
      var ms = value.size(); // validate matrix

      if (ms.length !== 1 || ms[0] !== n) {
        // number of values in array must be n
        throw new Error('Invalid matrix length');
      } // define function


      _value = function _value(i) {
        // return value @ i
        return value.get([i]);
      };
    } else {
      // define function
      _value = function _value() {
        // return value
        return value;
      };
    } // create arrays


    var values = [];
    var index = [];
    var ptr = []; // loop items

    for (var j = 0; j < columns; j++) {
      // number of rows with value
      ptr.push(values.length); // diagonal index

      var i = j - kSuper; // check we need to set diagonal value

      if (i >= 0 && i < n) {
        // get value @ i
        var v = _value(i); // check for zero


        if (!eq(v, zero)) {
          // column
          index.push(i + kSub); // add value

          values.push(v);
        }
      }
    } // last value should be number of values


    ptr.push(values.length); // create SparseMatrix

    return new SparseMatrix({
      values: values,
      index: index,
      ptr: ptr,
      size: [rows, columns]
    });
  };
  /**
   * Swap rows i and j in Matrix.
   *
   * @memberof SparseMatrix
   * @param {number} i       Matrix row index 1
   * @param {number} j       Matrix row index 2
   *
   * @return {Matrix}        The matrix reference
   */


  SparseMatrix.prototype.swapRows = function (i, j) {
    // check index
    if (!(0, _is.isNumber)(i) || !(0, _number.isInteger)(i) || !(0, _is.isNumber)(j) || !(0, _number.isInteger)(j)) {
      throw new Error('Row index must be positive integers');
    } // check dimensions


    if (this._size.length !== 2) {
      throw new Error('Only two dimensional matrix is supported');
    } // validate index


    (0, _array.validateIndex)(i, this._size[0]);
    (0, _array.validateIndex)(j, this._size[0]); // swap rows

    SparseMatrix._swapRows(i, j, this._size[1], this._values, this._index, this._ptr); // return current instance


    return this;
  };
  /**
   * Loop rows with data in column j.
   *
   * @param {number} j            Column
   * @param {Array} values        Matrix values
   * @param {Array} index         Matrix row indeces
   * @param {Array} ptr           Matrix column pointers
   * @param {Function} callback   Callback function invoked for every row in column j
   */


  SparseMatrix._forEachRow = function (j, values, index, ptr, callback) {
    // indeces for column j
    var k0 = ptr[j];
    var k1 = ptr[j + 1]; // loop

    for (var k = k0; k < k1; k++) {
      // invoke callback
      callback(index[k], values[k]);
    }
  };
  /**
   * Swap rows x and y in Sparse Matrix data structures.
   *
   * @param {number} x         Matrix row index 1
   * @param {number} y         Matrix row index 2
   * @param {number} columns   Number of columns in matrix
   * @param {Array} values     Matrix values
   * @param {Array} index      Matrix row indeces
   * @param {Array} ptr        Matrix column pointers
   */


  SparseMatrix._swapRows = function (x, y, columns, values, index, ptr) {
    // loop columns
    for (var j = 0; j < columns; j++) {
      // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
      var k0 = ptr[j];
      var k1 = ptr[j + 1]; // find value index @ x

      var kx = _getValueIndex(x, k0, k1, index); // find value index @ x


      var ky = _getValueIndex(y, k0, k1, index); // check both rows exist in matrix


      if (kx < k1 && ky < k1 && index[kx] === x && index[ky] === y) {
        // swap values (check for pattern matrix)
        if (values) {
          var v = values[kx];
          values[kx] = values[ky];
          values[ky] = v;
        } // next column


        continue;
      } // check x row exist & no y row


      if (kx < k1 && index[kx] === x && (ky >= k1 || index[ky] !== y)) {
        // value @ x (check for pattern matrix)
        var vx = values ? values[kx] : undefined; // insert value @ y

        index.splice(ky, 0, y);

        if (values) {
          values.splice(ky, 0, vx);
        } // remove value @ x (adjust array index if needed)


        index.splice(ky <= kx ? kx + 1 : kx, 1);

        if (values) {
          values.splice(ky <= kx ? kx + 1 : kx, 1);
        } // next column


        continue;
      } // check y row exist & no x row


      if (ky < k1 && index[ky] === y && (kx >= k1 || index[kx] !== x)) {
        // value @ y (check for pattern matrix)
        var vy = values ? values[ky] : undefined; // insert value @ x

        index.splice(kx, 0, x);

        if (values) {
          values.splice(kx, 0, vy);
        } // remove value @ y (adjust array index if needed)


        index.splice(kx <= ky ? ky + 1 : ky, 1);

        if (values) {
          values.splice(kx <= ky ? ky + 1 : ky, 1);
        }
      }
    }
  };

  return SparseMatrix;
}, {
  isClass: true
});
exports.createSparseMatrixClass = createSparseMatrixClass;