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-// 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;
-};