68 lines
2.4 KiB
JavaScript
68 lines
2.4 KiB
JavaScript
"use strict";
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Object.defineProperty(exports, "__esModule", { value: true });
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exports.assoc_legendre = exports.legendre = void 0;
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//================================================================
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/**
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* @packageDocumentation
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* @module std
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*/
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//================================================================
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var InvalidArgument_1 = require("../../exception/InvalidArgument");
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/**
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* Legendre polynomials.
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*
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* @reference http://en.cppreference.com/w/cpp/numeric/special_math/legendre
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*/
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function legendre(n, x) {
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return assoc_legendre(n, 0, x);
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}
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exports.legendre = legendre;
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/**
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* Associated Legendre polynomials.
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*
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* @reference https://en.wikipedia.org/wiki/Associated_Legendre_polynomials
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*/
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function assoc_legendre(n, m, x) {
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// VALIDATE PARAMETERS
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if ((n = Math.floor(n)) < 0 || (m = Math.floor(m)) < 0)
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throw new InvalidArgument_1.InvalidArgument("Error on std.assoc_legendre(): both n and m must be unsigned integer -> (n = ".concat(n, ", m = ").concat(m, ")."));
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else if (Math.abs(x) > 1)
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throw new InvalidArgument_1.InvalidArgument("Error on std.assoc_legendre(): must be |x| <= 1 -> (x = ".concat(x, ")."));
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// MEMORIZATION
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var matrix = [[1, x]];
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matrix.length = m + 1;
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for (var i = 1; i < matrix.length; ++i)
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matrix[i] = [];
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// COMPUTE RETURN VALUE
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return _Compute_assoc_legendre(n, m, x, matrix);
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}
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exports.assoc_legendre = assoc_legendre;
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function _Compute_legendre(n, x, memory) {
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if (memory.length > n)
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return memory[n];
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var pn_1 = _Compute_legendre(n - 1, x, memory);
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var pn_2 = _Compute_legendre(n - 2, x, memory);
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var ret = (2 * n - 1) * x * pn_1 - (n - 1) * pn_2;
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ret /= n;
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memory[n] = ret;
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return ret;
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}
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function _Compute_assoc_legendre(n, m, x, matrix) {
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if (n < 0)
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n = -n - 1;
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if (m === 0)
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return _Compute_legendre(n, x, matrix[0]);
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else if (matrix[m].length > n && matrix[m][n] !== undefined)
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return matrix[m][n];
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var left = (n - m + 1) *
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(n - m + 2) *
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_Compute_assoc_legendre(n + 1, m - 1, x, matrix);
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var right = (n + m - 1) *
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(n + m) *
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_Compute_assoc_legendre(n - 1, m - 1, x, matrix);
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var ret = (left - right) / (2 * n + 1);
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ret /= Math.sqrt(1 - x * x);
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matrix[m][n] = ret;
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return ret;
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}
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//# sourceMappingURL=legendres.js.map
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