"use strict"; Object.defineProperty(exports, "__esModule", { value: true }); exports.createPinv = void 0; var _is = require("../../utils/is.js"); var _array = require("../../utils/array.js"); var _factory = require("../../utils/factory.js"); var _string = require("../../utils/string.js"); var _object = require("../../utils/object.js"); const name = 'pinv'; const dependencies = ['typed', 'matrix', 'inv', 'deepEqual', 'equal', 'dotDivide', 'dot', 'ctranspose', 'divideScalar', 'multiply', 'add', 'Complex']; const createPinv = exports.createPinv = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => { let { typed, matrix, inv, deepEqual, equal, dotDivide, dot, ctranspose, divideScalar, multiply, add, Complex } = _ref; /** * Calculate the Moore–Penrose inverse of a matrix. * * Syntax: * * math.pinv(x) * * Examples: * * math.pinv([[1, 2], [3, 4]]) // returns [[-2, 1], [1.5, -0.5]] * math.pinv([[1, 0], [0, 1], [0, 1]]) // returns [[1, 0, 0], [0, 0.5, 0.5]] * math.pinv(4) // returns 0.25 * * See also: * * inv * * @param {number | Complex | Array | Matrix} x Matrix to be inversed * @return {number | Complex | Array | Matrix} The inverse of `x`. */ return typed(name, { 'Array | Matrix': function (x) { const size = (0, _is.isMatrix)(x) ? x.size() : (0, _array.arraySize)(x); switch (size.length) { case 1: // vector if (_isZeros(x)) return ctranspose(x); // null vector if (size[0] === 1) { return inv(x); // invertible matrix } else { return dotDivide(ctranspose(x), dot(x, x)); } case 2: // two dimensional array { if (_isZeros(x)) return ctranspose(x); // zero matrixx const rows = size[0]; const cols = size[1]; if (rows === cols) { try { return inv(x); // invertible matrix } catch (err) { if (err instanceof Error && err.message.match(/Cannot calculate inverse, determinant is zero/)) { // Expected } else { throw err; } } } if ((0, _is.isMatrix)(x)) { return matrix(_pinv(x.valueOf(), rows, cols), x.storage()); } else { // return an Array return _pinv(x, rows, cols); } } default: // multi dimensional array throw new RangeError('Matrix must be two dimensional ' + '(size: ' + (0, _string.format)(size) + ')'); } }, any: function (x) { // scalar if (equal(x, 0)) return (0, _object.clone)(x); // zero return divideScalar(1, x); } }); /** * Calculate the Moore–Penrose inverse of a matrix * @param {Array[]} mat A matrix * @param {number} rows Number of rows * @param {number} cols Number of columns * @return {Array[]} pinv Pseudoinverse matrix * @private */ function _pinv(mat, rows, cols) { const { C, F } = _rankFact(mat, rows, cols); // TODO: Use SVD instead (may improve precision) const Cpinv = multiply(inv(multiply(ctranspose(C), C)), ctranspose(C)); const Fpinv = multiply(ctranspose(F), inv(multiply(F, ctranspose(F)))); return multiply(Fpinv, Cpinv); } /** * Calculate the reduced row echelon form of a matrix * * Modified from https://rosettacode.org/wiki/Reduced_row_echelon_form * * @param {Array[]} mat A matrix * @param {number} rows Number of rows * @param {number} cols Number of columns * @return {Array[]} Reduced row echelon form * @private */ function _rref(mat, rows, cols) { const M = (0, _object.clone)(mat); let lead = 0; for (let r = 0; r < rows; r++) { if (cols <= lead) { return M; } let i = r; while (_isZero(M[i][lead])) { i++; if (rows === i) { i = r; lead++; if (cols === lead) { return M; } } } [M[i], M[r]] = [M[r], M[i]]; let val = M[r][lead]; for (let j = 0; j < cols; j++) { M[r][j] = dotDivide(M[r][j], val); } for (let i = 0; i < rows; i++) { if (i === r) continue; val = M[i][lead]; for (let j = 0; j < cols; j++) { M[i][j] = add(M[i][j], multiply(-1, multiply(val, M[r][j]))); } } lead++; } return M; } /** * Calculate the rank factorization of a matrix * * @param {Array[]} mat A matrix (M) * @param {number} rows Number of rows * @param {number} cols Number of columns * @return {{C: Array, F: Array}} rank factorization where M = C F * @private */ function _rankFact(mat, rows, cols) { const rref = _rref(mat, rows, cols); const C = mat.map((_, i) => _.filter((_, j) => j < rows && !_isZero(dot(rref[j], rref[j])))); const F = rref.filter((_, i) => !_isZero(dot(rref[i], rref[i]))); return { C, F }; } function _isZero(x) { return equal(add(x, Complex(1, 1)), add(0, Complex(1, 1))); } function _isZeros(arr) { return deepEqual(add(arr, Complex(1, 1)), add(multiply(arr, 0), Complex(1, 1))); } });