Update wmts-hidpi, add nicer-api-docs

nicer-api-docs/closure-library/closure/goog/math/interpolator/spline1.js

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+// Copyright 2012 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 A one dimensional cubic spline interpolator with not-a-knot
+ * boundary conditions.
+ *
+ * See http://en.wikipedia.org/wiki/Spline_interpolation.
+ *
+ */
+
+goog.provide('goog.math.interpolator.Spline1');
+
+goog.require('goog.array');
+goog.require('goog.math');
+goog.require('goog.math.interpolator.Interpolator1');
+goog.require('goog.math.tdma');
+
+
+
+/**
+ * A one dimensional cubic spline interpolator with natural boundary conditions.
+ * @implements {goog.math.interpolator.Interpolator1}
+ * @constructor
+ */
+goog.math.interpolator.Spline1 = function() {
+  /**
+   * The abscissa of the data points.
+   * @type {!Array.<number>}
+   * @private
+   */
+  this.x_ = [];
+
+  /**
+   * The spline interval coefficients.
+   * Note that, in general, the length of coeffs and x is not the same.
+   * @type {!Array.<!Array.<number>>}
+   * @private
+   */
+  this.coeffs_ = [[0, 0, 0, Number.NaN]];
+};
+
+
+/** @override */
+goog.math.interpolator.Spline1.prototype.setData = function(x, y) {
+  goog.asserts.assert(x.length == y.length,
+      'input arrays to setData should have the same length');
+  if (x.length > 0) {
+    this.coeffs_ = this.computeSplineCoeffs_(x, y);
+    this.x_ = x.slice();
+  } else {
+    this.coeffs_ = [[0, 0, 0, Number.NaN]];
+    this.x_ = [];
+  }
+};
+
+
+/** @override */
+goog.math.interpolator.Spline1.prototype.interpolate = function(x) {
+  var pos = goog.array.binarySearch(this.x_, x);
+  if (pos < 0) {
+    pos = -pos - 2;
+  }
+  pos = goog.math.clamp(pos, 0, this.coeffs_.length - 1);
+
+  var d = x - this.x_[pos];
+  var d2 = d * d;
+  var d3 = d2 * d;
+  var coeffs = this.coeffs_[pos];
+  return coeffs[0] * d3 + coeffs[1] * d2 + coeffs[2] * d + coeffs[3];
+};
+
+
+/**
+ * Solve for the spline coefficients such that the spline precisely interpolates
+ * the data points.
+ * @param {Array.<number>} x The abscissa of the spline data points.
+ * @param {Array.<number>} y The ordinate of the spline data points.
+ * @return {!Array.<!Array.<number>>} The spline interval coefficients.
+ * @private
+ */
+goog.math.interpolator.Spline1.prototype.computeSplineCoeffs_ = function(x, y) {
+  var nIntervals = x.length - 1;
+  var dx = new Array(nIntervals);
+  var delta = new Array(nIntervals);
+  for (var i = 0; i < nIntervals; ++i) {
+    dx[i] = x[i + 1] - x[i];
+    delta[i] = (y[i + 1] - y[i]) / dx[i];
+  }
+
+  // Compute the spline coefficients from the 1st order derivatives.
+  var coeffs = [];
+  if (nIntervals == 0) {
+    // Nearest neighbor interpolation.
+    coeffs[0] = [0, 0, 0, y[0]];
+  } else if (nIntervals == 1) {
+    // Straight line interpolation.
+    coeffs[0] = [0, 0, delta[0], y[0]];
+  } else if (nIntervals == 2) {
+    // Parabola interpolation.
+    var c3 = 0;
+    var c2 = (delta[1] - delta[0]) / (dx[0] + dx[1]);
+    var c1 = delta[0] - c2 * dx[0];
+    var c0 = y[0];
+    coeffs[0] = [c3, c2, c1, c0];
+  } else {
+    // General Spline interpolation. Compute the 1st order derivatives from
+    // the Spline equations.
+    var deriv = this.computeDerivatives(dx, delta);
+    for (var i = 0; i < nIntervals; ++i) {
+      var c3 = (deriv[i] - 2 * delta[i] + deriv[i + 1]) / (dx[i] * dx[i]);
+      var c2 = (3 * delta[i] - 2 * deriv[i] - deriv[i + 1]) / dx[i];
+      var c1 = deriv[i];
+      var c0 = y[i];
+      coeffs[i] = [c3, c2, c1, c0];
+    }
+  }
+  return coeffs;
+};
+
+
+/**
+ * Computes the derivative at each point of the spline such that
+ * the curve is C2. It uses not-a-knot boundary conditions.
+ * @param {Array.<number>} dx The spacing between consecutive data points.
+ * @param {Array.<number>} slope The slopes between consecutive data points.
+ * @return {Array.<number>} The Spline derivative at each data point.
+ * @protected
+ */
+goog.math.interpolator.Spline1.prototype.computeDerivatives = function(
+    dx, slope) {
+  var nIntervals = dx.length;
+
+  // Compute the main diagonal of the system of equations.
+  var mainDiag = new Array(nIntervals + 1);
+  mainDiag[0] = dx[1];
+  for (var i = 1; i < nIntervals; ++i) {
+    mainDiag[i] = 2 * (dx[i] + dx[i - 1]);
+  }
+  mainDiag[nIntervals] = dx[nIntervals - 2];
+
+  // Compute the sub diagonal of the system of equations.
+  var subDiag = new Array(nIntervals);
+  for (var i = 0; i < nIntervals; ++i) {
+    subDiag[i] = dx[i + 1];
+  }
+  subDiag[nIntervals - 1] = dx[nIntervals - 2] + dx[nIntervals - 1];
+
+  // Compute the super diagonal of the system of equations.
+  var supDiag = new Array(nIntervals);
+  supDiag[0] = dx[0] + dx[1];
+  for (var i = 1; i < nIntervals; ++i) {
+    supDiag[i] = dx[i - 1];
+  }
+
+  // Compute the right vector of the system of equations.
+  var vecRight = new Array(nIntervals + 1);
+  vecRight[0] = ((dx[0] + 2 * supDiag[0]) * dx[1] * slope[0] +
+      dx[0] * dx[0] * slope[1]) / supDiag[0];
+  for (var i = 1; i < nIntervals; ++i) {
+    vecRight[i] = 3 * (dx[i] * slope[i - 1] + dx[i - 1] * slope[i]);
+  }
+  vecRight[nIntervals] = (dx[nIntervals - 1] * dx[nIntervals - 1] *
+      slope[nIntervals - 2] + (2 * subDiag[nIntervals - 1] +
+      dx[nIntervals - 1]) * dx[nIntervals - 2] * slope[nIntervals - 1]) /
+      subDiag[nIntervals - 1];
+
+  // Solve the system of equations.
+  var deriv = goog.math.tdma.solve(
+      subDiag, mainDiag, supDiag, vecRight);
+
+  return deriv;
+};
+
+
+/**
+ * Note that the inverse of a cubic spline is not a cubic spline in general.
+ * As a result the inverse implementation is only approximate. In
+ * particular, it only guarantees the exact inverse at the original input data
+ * points passed to setData.
+ * @override
+ */
+goog.math.interpolator.Spline1.prototype.getInverse = function() {
+  var interpolator = new goog.math.interpolator.Spline1();
+  var y = [];
+  for (var i = 0; i < this.x_.length; i++) {
+    y[i] = this.interpolate(this.x_[i]);
+  }
+  interpolator.setData(y, this.x_);
+  return interpolator;
+};