@rayyamhk/matrix
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A professional, comprehensive and high-performance library for you to manipulate matrices.
151 lines (113 loc) • 4.79 kB
JavaScript
function _slicedToArray(arr, i) { return _arrayWithHoles(arr) || _iterableToArrayLimit(arr, i) || _unsupportedIterableToArray(arr, i) || _nonIterableRest(); }
function _nonIterableRest() { throw new TypeError("Invalid attempt to destructure non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method."); }
function _unsupportedIterableToArray(o, minLen) { if (!o) return; if (typeof o === "string") return _arrayLikeToArray(o, minLen); var n = Object.prototype.toString.call(o).slice(8, -1); if (n === "Object" && o.constructor) n = o.constructor.name; if (n === "Map" || n === "Set") return Array.from(o); if (n === "Arguments" || /^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(n)) return _arrayLikeToArray(o, minLen); }
function _arrayLikeToArray(arr, len) { if (len == null || len > arr.length) len = arr.length; for (var i = 0, arr2 = new Array(len); i < len; i++) { arr2[i] = arr[i]; } return arr2; }
function _iterableToArrayLimit(arr, i) { var _i = arr == null ? null : typeof Symbol !== "undefined" && arr[Symbol.iterator] || arr["@@iterator"]; if (_i == null) return; var _arr = []; var _n = true; var _d = false; var _s, _e; try { for (_i = _i.call(arr); !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"] != null) _i["return"](); } finally { if (_d) throw _e; } } return _arr; }
function _arrayWithHoles(arr) { if (Array.isArray(arr)) return arr; }
var _require = require('../../Error'),
INVALID_MATRIX = _require.INVALID_MATRIX;
/**
* Calculates the LUP decomposition of the Matrix,
* where L is lower triangular matrix which diagonal entries are always 1,
* U is upper triangular matrix, and P is permutation matrix.<br><br>
*
* It is implemented using Gaussian Elimination with Partial Pivoting in order to
* reduce the error caused by floating-point arithmetic.<br><br>
*
* Note that if optimized is true, P is a Permutation Array and both L and U are merged
* into one matrix in order to improve performance.
* @memberof Matrix
* @static
* @param {Matrix} A - Any matrix
* @param {boolean} [optimized=false] - Returns [P, LU] if it is true, [P, L, U] if it is false
* @returns {Matrix[]} The LUP decomposition of Matrix
*/
function LU(A) {
var optimized = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : false;
if (!(A instanceof this)) {
throw new Error(INVALID_MATRIX);
}
var _A$size = A.size(),
_A$size2 = _slicedToArray(_A$size, 2),
row = _A$size2[0],
col = _A$size2[1];
var size = Math.min(row, col);
var EPSILON = 1 / (Math.pow(10, A._digit) * 2);
var permutation = initPermutation(row);
var copy = this.clone(A)._matrix;
for (var i = 0; i < row - 1; i++) {
var currentCol = Math.min(i, col); // apply Partial Pivoting
PartialPivoting(copy, permutation, currentCol, row, col);
var ith = permutation[i];
var pivot = copy[ith][currentCol];
if (Math.abs(pivot) < EPSILON) {
continue;
}
for (var j = i + 1; j < row; j++) {
var jth = permutation[j];
var entry = copy[jth][currentCol];
if (Math.abs(entry) >= EPSILON) {
var factor = entry / pivot;
for (var k = currentCol; k < col; k++) {
copy[jth][k] -= factor * copy[ith][k];
}
copy[jth][currentCol] = factor;
}
}
}
var result = new Array(row);
for (var _i2 = 0; _i2 < row; _i2++) {
result[_i2] = copy[permutation[_i2]];
}
if (optimized) {
return [permutation, new this(result)];
}
var P = this.generate(row, row, function (i, j) {
var idx = permutation[i];
if (j === idx) {
return 1;
}
return 0;
});
var L = this.generate(row, size, function (i, j) {
if (i === j) {
return 1;
}
if (i < j) {
return 0;
}
return result[i][j];
});
var U = this.generate(size, col, function (i, j) {
if (i > j) {
return 0;
}
return result[i][j];
});
return [P, L, U];
}
;
function initPermutation(size) {
var permutation = new Array(size);
for (var i = 0; i < size; i++) {
permutation[i] = i;
}
return permutation;
}
function PartialPivoting(matrix, permutation, pos, row, col) {
var currentCol = Math.min(pos, col);
var maxIdx = pos;
var max = Math.abs(matrix[permutation[pos]][currentCol]);
for (var i = pos + 1; i < row; i++) {
var value = Math.abs(matrix[permutation[i]][currentCol]);
if (value > max) {
maxIdx = i;
max = value;
}
}
var t = permutation[pos];
permutation[pos] = permutation[maxIdx];
permutation[maxIdx] = t;
}
module.exports = LU;
;