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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 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;
};
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