mathjs
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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
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JavaScript
import { isArray, isBigNumber, isCollection, isIndex, isMatrix, isNumber, isString, typeOf } from '../../utils/is.js';
import { isInteger } from '../../utils/number.js';
import { format } from '../../utils/string.js';
import { clone, deepStrictEqual } from '../../utils/object.js';
import { arraySize, getArrayDataType, processSizesWildcard, unsqueeze, validateIndex } from '../../utils/array.js';
import { factory } from '../../utils/factory.js';
import { DimensionError } from '../../error/DimensionError.js';
import { optimizeCallback } from '../../utils/optimizeCallback.js';
var name = 'SparseMatrix';
var dependencies = ['typed', 'equalScalar', 'Matrix'];
export var createSparseMatrixClass = /* #__PURE__ */factory(name, dependencies, _ref => {
var {
typed,
equalScalar,
Matrix
} = _ref;
/**
* Sparse Matrix implementation. This type implements
* a [Compressed Column Storage](https://en.wikipedia.org/wiki/Sparse_matrix#Compressed_sparse_column_(CSC_or_CCS))
* format for two-dimensional 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 && !isString(datatype)) {
throw new Error('Invalid datatype: ' + datatype);
}
if (isMatrix(data)) {
// create from matrix
_createFromMatrix(this, data, datatype);
} else if (data && isArray(data.index) && isArray(data.ptr) && 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 (isArray(data)) {
// create from array
_createFromArray(this, data, datatype);
} else if (data) {
// unsupported type
throw new TypeError('Unsupported type of data (' + 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 ? clone(source._values) : undefined;
matrix._index = clone(source._index);
matrix._ptr = clone(source._ptr);
matrix._size = 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 (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 (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
*/
Object.defineProperty(SparseMatrix, 'name', {
value: 'SparseMatrix'
});
SparseMatrix.prototype.constructor = SparseMatrix;
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 getArrayDataType(this._values, 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 (!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(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++) {
validateIndex(min[i], matrix._size[i]);
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,
index,
ptr,
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 (isMatrix(submatrix)) {
// submatrix size
sSize = submatrix.size();
// use array representation
submatrix = submatrix.toArray();
} else {
// get submatrix size (array, scalar)
sSize = 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(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 = unsqueeze(submatrix, iSize.length, outer, sSize);
}
// check whether the size of the submatrix matches the index size
if (!deepStrictEqual(iSize, sSize)) {
throw new DimensionError(iSize, sSize, '>');
}
// insert the sub matrix
if (iSize.length === 1) {
// if the replacement index only has 1 dimension, go trough each one and set its value
var range = index.dimension(0);
range.forEach(function (dataIndex, subIndex) {
validateIndex(dataIndex);
matrix.set([dataIndex, 0], submatrix[subIndex[0]], defaultValue);
});
} else {
// if the replacement index has 2 dimensions, go through each one and set the value in the correct index
var firstDimensionRange = index.dimension(0);
var secondDimensionRange = index.dimension(1);
firstDimensionRange.forEach(function (firstDataIndex, firstSubIndex) {
validateIndex(firstDataIndex);
secondDimensionRange.forEach(function (secondDataIndex, secondSubIndex) {
validateIndex(secondDataIndex);
matrix.set([firstDataIndex, secondDataIndex], submatrix[firstSubIndex[0]][secondSubIndex[0]], 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 (!isArray(index)) {
throw new TypeError('Array expected');
}
if (index.length !== this._size.length) {
throw new 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
validateIndex(i, this._size[0]);
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 (!isArray(index)) {
throw new TypeError('Array expected');
}
if (index.length !== this._size.length) {
throw new 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 (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
validateIndex(i, rows);
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 {
if (!eq(v, zero)) {
// 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[] | Matrix} size The new size the matrix should have.
* Since sparse matrices are always two-dimensional,
* size must be two numbers in either an array or a matrix
* @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 (!isCollection(size)) {
throw new TypeError('Array or Matrix expected');
}
// SparseMatrix input is always 2d, flatten this into 1d if it's indeed a vector
var sizeArray = size.valueOf().map(value => {
return Array.isArray(value) && value.length === 1 ? value[0] : value;
});
if (sizeArray.length !== 2) {
throw new Error('Only two dimensions matrix are supported');
}
// check sizes
sizeArray.forEach(function (value) {
if (!isNumber(value) || !isInteger(value) || value < 0) {
throw new TypeError('Invalid size, must contain positive integers ' + '(size: ' + format(sizeArray) + ')');
}
});
// matrix to resize
var m = copy ? this.clone() : this;
// resize matrix
return _resize(m, sizeArray[0], sizeArray[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 (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[]} sizes The new size the matrix should have.
* Since sparse matrices are always two-dimensional,
* size must be two numbers in either an array or a matrix
* @param {boolean} [copy] Return a reshaped copy of the matrix
*
* @return {Matrix} The reshaped matrix
*/
SparseMatrix.prototype.reshape = function (sizes, copy) {
// validate arguments
if (!isArray(sizes)) {
throw new TypeError('Array expected');
}
if (sizes.length !== 2) {
throw new Error('Sparse matrices can only be reshaped in two dimensions');
}
// check sizes
sizes.forEach(function (value) {
if (!isNumber(value) || !isInteger(value) || value <= -2 || value === 0) {
throw new TypeError('Invalid size, must contain positive integers or -1 ' + '(size: ' + format(sizes) + ')');
}
});
var currentLength = this._size[0] * this._size[1];
sizes = processSizesWildcard(sizes, currentLength);
var newLength = sizes[0] * sizes[1];
// m * n must not change
if (currentLength !== newLength) {
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] === sizes[0] && this._size[1] === sizes[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 % sizes[1];
rowIndex[_i] = Math.floor(flat / sizes[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 = sizes[1] + 1;
m._size = sizes.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 ? clone(this._values) : undefined,
index: clone(this._index),
ptr: clone(this._ptr),
size: 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];
var fastCallback = optimizeCallback(callback, me, 'map');
// invoke callback
var invoke = function invoke(v, i, j) {
// invoke callback
return fastCallback.fn(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 (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
var value = callback(v, x, y);
// check value != 0
if (!eq(value, zero)) {
// store value
values.push(value);
// 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,
index,
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.
* If false, the indices are guaranteed to be in order,
* if true, the indices can be unordered.
*/
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];
var fastCallback = optimizeCallback(callback, me, 'forEach');
// 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
// TODO apply a non indexed version of algorithm in case fastCallback is not optimized
fastCallback.fn(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;
fastCallback.fn(value, [_i7, j], me);
}
}
}
};
/**
* Iterate over the matrix elements, skipping zeros
* @return {Iterable<{ value, index: number[] }>}
*/
SparseMatrix.prototype[Symbol.iterator] = function* () {
if (!this._values) {
throw new Error('Cannot iterate a Pattern only matrix');
}
var columns = this._size[1];
for (var j = 0; j < columns; j++) {
var k0 = this._ptr[j];
var k1 = this._ptr[j + 1];
for (var k = k0; k < k1; k++) {
// row index
var i = this._index[k];
yield {
value: this._values[k],
index: [i, j]
};
}
}
};
/**
* 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 ? 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 [' + format(rows, options) + ' x ' + format(columns, options) + '] density: ' + 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 (' + format(i, options) + ', ' + format(j, options) + ') ==> ' + (this._values ? 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 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 (isBigNumber(k)) {
k = k.toNumber();
}
// is must be an integer
if (!isNumber(k) || !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,
index,
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 (!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 (isBigNumber(s)) {
// convert it
s = s.toNumber();
}
// validate arguments
if (!isNumber(s) || !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 (isBigNumber(k)) {
k = k.toNumber();
}
// is must be an integer
if (!isNumber(k) || !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 (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 (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 (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,
index,
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 (!isNumber(i) || !isInteger(i) || !isNumber(j) || !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
validateIndex(i, this._size[0]);
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
});