| // Copyright 2011 The Closure Library Authors. All Rights Reserved. |
| // |
| // Licensed under the Apache License, Version 2.0 (the "License"); |
| // you may not use this file except in compliance with the License. |
| // You may obtain a copy of the License at |
| // |
| // http://www.apache.org/licenses/LICENSE-2.0 |
| // |
| // Unless required by applicable law or agreed to in writing, software |
| // distributed under the License is distributed on an "AS-IS" BASIS, |
| // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| // See the License for the specific language governing permissions and |
| // limitations under the License. |
| |
| /** |
| * @fileoverview The Tridiagonal matrix algorithm solver solves a special |
| * version of a sparse linear system Ax = b where A is tridiagonal. |
| * |
| * See http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm |
| * |
| */ |
| |
| goog.provide('goog.math.tdma'); |
| |
| |
| /** |
| * Solves a linear system where the matrix is square tri-diagonal. That is, |
| * given a system of equations: |
| * |
| * A * result = vecRight, |
| * |
| * this class computes result = inv(A) * vecRight, where A has the special form |
| * of a tri-diagonal matrix: |
| * |
| * |dia(0) sup(0) 0 0 ... 0| |
| * |sub(0) dia(1) sup(1) 0 ... 0| |
| * A =| ... | |
| * |0 ... 0 sub(n-2) dia(n-1) sup(n-1)| |
| * |0 ... 0 0 sub(n-1) dia(n)| |
| * |
| * @param {!Array<number>} subDiag The sub diagonal of the matrix. |
| * @param {!Array<number>} mainDiag The main diagonal of the matrix. |
| * @param {!Array<number>} supDiag The super diagonal of the matrix. |
| * @param {!Array<number>} vecRight The right vector of the system |
| * of equations. |
| * @param {Array<number>=} opt_result The optional array to store the result. |
| * @return {!Array<number>} The vector that is the solution to the system. |
| */ |
| goog.math.tdma.solve = function( |
| subDiag, mainDiag, supDiag, vecRight, opt_result) { |
| // Make a local copy of the main diagonal and the right vector. |
| mainDiag = mainDiag.slice(); |
| vecRight = vecRight.slice(); |
| |
| // The dimension of the matrix. |
| var nDim = mainDiag.length; |
| |
| // Construct a modified linear system of equations with the same solution |
| // as the input one. |
| for (var i = 1; i < nDim; ++i) { |
| var m = subDiag[i - 1] / mainDiag[i - 1]; |
| mainDiag[i] = mainDiag[i] - m * supDiag[i - 1]; |
| vecRight[i] = vecRight[i] - m * vecRight[i - 1]; |
| } |
| |
| // Solve the new system of equations by simple back-substitution. |
| var result = opt_result || new Array(vecRight.length); |
| result[nDim - 1] = vecRight[nDim - 1] / mainDiag[nDim - 1]; |
| for (i = nDim - 2; i >= 0; --i) { |
| result[i] = (vecRight[i] - supDiag[i] * result[i + 1]) / mainDiag[i]; |
| } |
| return result; |
| }; |