Update wmts-hidpi, add nicer-api-docs

nicer-api-docs/closure-library/closure/goog/math/tdma.js

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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;
+};