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// Copyright 2012 The Closure Library Authors. All Rights Reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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//      http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS-IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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/**
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 * @fileoverview A one dimensional monotone cubic spline interpolator.
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 *
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 * See http://en.wikipedia.org/wiki/Monotone_cubic_interpolation.
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 *
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 */
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goog.provide('goog.math.interpolator.Pchip1');
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goog.require('goog.math');
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goog.require('goog.math.interpolator.Spline1');
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/**
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 * A one dimensional monotone cubic spline interpolator.
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 * @extends {goog.math.interpolator.Spline1}
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 * @constructor
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 * @final
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 */
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goog.math.interpolator.Pchip1 = function() {
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  goog.math.interpolator.Pchip1.base(this, 'constructor');
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};
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goog.inherits(goog.math.interpolator.Pchip1, goog.math.interpolator.Spline1);
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/** @override */
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goog.math.interpolator.Pchip1.prototype.computeDerivatives = function(
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    dx, slope) {
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  var len = dx.length;
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  var deriv = new Array(len + 1);
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  for (var i = 1; i < len; ++i) {
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    if (goog.math.sign(slope[i - 1]) * goog.math.sign(slope[i]) <= 0) {
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      deriv[i] = 0;
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    } else {
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      var w1 = 2 * dx[i] + dx[i - 1];
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      var w2 = dx[i] + 2 * dx[i - 1];
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      deriv[i] = (w1 + w2) / (w1 / slope[i - 1] + w2 / slope[i]);
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    }
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  }
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  deriv[0] =
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      this.computeDerivativeAtBoundary_(dx[0], dx[1], slope[0], slope[1]);
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  deriv[len] = this.computeDerivativeAtBoundary_(
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      dx[len - 1], dx[len - 2], slope[len - 1], slope[len - 2]);
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  return deriv;
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};
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/**
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 * Computes the derivative of a data point at a boundary.
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 * @param {number} dx0 The spacing of the 1st data point.
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 * @param {number} dx1 The spacing of the 2nd data point.
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 * @param {number} slope0 The slope of the 1st data point.
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 * @param {number} slope1 The slope of the 2nd data point.
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 * @return {number} The derivative at the 1st data point.
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 * @private
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 */
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goog.math.interpolator.Pchip1.prototype.computeDerivativeAtBoundary_ = function(
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    dx0, dx1, slope0, slope1) {
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  var deriv = ((2 * dx0 + dx1) * slope0 - dx0 * slope1) / (dx0 + dx1);
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  if (goog.math.sign(deriv) != goog.math.sign(slope0)) {
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    deriv = 0;
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  } else if (
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      goog.math.sign(slope0) != goog.math.sign(slope1) &&
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      Math.abs(deriv) > Math.abs(3 * slope0)) {
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    deriv = 3 * slope0;
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  }
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  return deriv;
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};
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