| // 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 monotone cubic spline interpolator. |
| * |
| * See http://en.wikipedia.org/wiki/Monotone_cubic_interpolation. |
| * |
| */ |
| |
| goog.provide('goog.math.interpolator.Pchip1'); |
| |
| goog.require('goog.math'); |
| goog.require('goog.math.interpolator.Spline1'); |
| |
| |
| |
| /** |
| * A one dimensional monotone cubic spline interpolator. |
| * @extends {goog.math.interpolator.Spline1} |
| * @constructor |
| * @final |
| */ |
| goog.math.interpolator.Pchip1 = function() { |
| goog.math.interpolator.Pchip1.base(this, 'constructor'); |
| }; |
| goog.inherits(goog.math.interpolator.Pchip1, goog.math.interpolator.Spline1); |
| |
| |
| /** @override */ |
| goog.math.interpolator.Pchip1.prototype.computeDerivatives = function( |
| dx, slope) { |
| var len = dx.length; |
| var deriv = new Array(len + 1); |
| for (var i = 1; i < len; ++i) { |
| if (goog.math.sign(slope[i - 1]) * goog.math.sign(slope[i]) <= 0) { |
| deriv[i] = 0; |
| } else { |
| var w1 = 2 * dx[i] + dx[i - 1]; |
| var w2 = dx[i] + 2 * dx[i - 1]; |
| deriv[i] = (w1 + w2) / (w1 / slope[i - 1] + w2 / slope[i]); |
| } |
| } |
| deriv[0] = this.computeDerivativeAtBoundary_( |
| dx[0], dx[1], slope[0], slope[1]); |
| deriv[len] = this.computeDerivativeAtBoundary_( |
| dx[len - 1], dx[len - 2], slope[len - 1], slope[len - 2]); |
| return deriv; |
| }; |
| |
| |
| /** |
| * Computes the derivative of a data point at a boundary. |
| * @param {number} dx0 The spacing of the 1st data point. |
| * @param {number} dx1 The spacing of the 2nd data point. |
| * @param {number} slope0 The slope of the 1st data point. |
| * @param {number} slope1 The slope of the 2nd data point. |
| * @return {number} The derivative at the 1st data point. |
| * @private |
| */ |
| goog.math.interpolator.Pchip1.prototype.computeDerivativeAtBoundary_ = function( |
| dx0, dx1, slope0, slope1) { |
| var deriv = ((2 * dx0 + dx1) * slope0 - dx0 * slope1) / (dx0 + dx1); |
| if (goog.math.sign(deriv) != goog.math.sign(slope0)) { |
| deriv = 0; |
| } else if (goog.math.sign(slope0) != goog.math.sign(slope1) && |
| Math.abs(deriv) > Math.abs(3 * slope0)) { |
| deriv = 3 * slope0; |
| } |
| return deriv; |
| }; |