com.opengamma.analytics.math.interpolation.TimeSquareInterpolator1D.java Source code

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Here is the source code for com.opengamma.analytics.math.interpolation.TimeSquareInterpolator1D.java

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/**
 * Copyright (C) 2012 - present by OpenGamma Inc. and the OpenGamma group of companies
 * 
 * Please see distribution for license.
 */
package com.opengamma.analytics.math.interpolation;

import org.apache.commons.lang.Validate;

import com.opengamma.analytics.math.interpolation.data.ArrayInterpolator1DDataBundle;
import com.opengamma.analytics.math.interpolation.data.InterpolationBoundedValues;
import com.opengamma.analytics.math.interpolation.data.Interpolator1DDataBundle;
import com.opengamma.util.ArgumentChecker;

/**
 * A one-dimensional interpolator.
 * The interpolation is linear on x y^2. The interpolator is used for interpolation on integrated variance for options.
 */
public class TimeSquareInterpolator1D extends Interpolator1D {
    private static final long serialVersionUID = 1L;

    @Override
    public Double interpolate(final Interpolator1DDataBundle data, final Double value) {
        Validate.notNull(value, "Value to be interpolated must not be null");
        ArgumentChecker.isTrue(value > 0, "Value should be stricly positive");
        Validate.notNull(data, "Data bundle must not be null");
        final InterpolationBoundedValues boundedValues = data.getBoundedValues(value);
        final double x1 = boundedValues.getLowerBoundKey();
        final double y1 = boundedValues.getLowerBoundValue();
        if (data.getLowerBoundIndex(value) == data.size() - 1) {
            return y1;
        }
        final double x2 = boundedValues.getHigherBoundKey();
        final double y2 = boundedValues.getHigherBoundValue();
        final double w = (x2 - value) / (x2 - x1);
        final double xy21 = x1 * y1 * y1;
        final double xy22 = x2 * y2 * y2;
        final double xy2 = w * xy21 + (1 - w) * xy22;
        return Math.sqrt(xy2 / value);
    }

    @Override
    public double firstDerivative(final Interpolator1DDataBundle data, final Double value) {
        Validate.notNull(value, "Value to be interpolated must not be null");
        ArgumentChecker.isTrue(value > 0, "Value should be stricly positive");
        Validate.notNull(data, "Data bundle must not be null");
        final InterpolationBoundedValues boundedValues = data.getBoundedValues(value);
        final double x1 = boundedValues.getLowerBoundKey();
        final double y1 = boundedValues.getLowerBoundValue();
        if (data.getLowerBoundIndex(value) == data.size() - 1) {
            return 0.;
        }
        final double x2 = boundedValues.getHigherBoundKey();
        final double y2 = boundedValues.getHigherBoundValue();
        final double w = (x2 - value) / (x2 - x1);
        final double xy21 = x1 * y1 * y1;
        final double xy22 = x2 * y2 * y2;
        final double xy2 = w * xy21 + (1 - w) * xy22;
        return 0.5 * (-Math.sqrt(xy2 / value) + (-xy21 + xy22) / (x2 - x1) / Math.sqrt(xy2 / value)) / value;
    }

    @Override
    public double[] getNodeSensitivitiesForValue(final Interpolator1DDataBundle data, final Double value) {
        Validate.notNull(value, "Value to be interpolated must not be null");
        Validate.notNull(data, "Data bundle must not be null");
        final int n = data.size();
        final double[] resultSensitivity = new double[n];
        final InterpolationBoundedValues boundedValues = data.getBoundedValues(value);
        final double x1 = boundedValues.getLowerBoundKey();
        final double y1 = boundedValues.getLowerBoundValue();
        final int index = data.getLowerBoundIndex(value);
        if (index == n - 1) {
            resultSensitivity[n - 1] = 1.0;
            return resultSensitivity;
        }
        final double x2 = boundedValues.getHigherBoundKey();
        final double y2 = boundedValues.getHigherBoundValue();
        final double w = (x2 - value) / (x2 - x1);
        final double xy21 = x1 * y1 * y1;
        final double xy22 = x2 * y2 * y2;
        final double xy2 = w * xy21 + (1 - w) * xy22;
        final double resultValue = Math.sqrt(xy2 / value);
        final double resultValueBar = 1.0;
        final double xy2Bar = 0.5 / resultValue / value * resultValueBar;
        final double xy21Bar = w * xy2Bar;
        final double xy22Bar = (1 - w) * xy2Bar;
        final double y2Bar = 2 * x2 * y2 * xy22Bar;
        final double y1Bar = 2 * x1 * y1 * xy21Bar;
        resultSensitivity[index] = y1Bar;
        resultSensitivity[index + 1] = y2Bar;
        return resultSensitivity;
    }

    @Override
    public Interpolator1DDataBundle getDataBundle(final double[] x, final double[] y) {
        return new ArrayInterpolator1DDataBundle(x, y);
    }

    @Override
    public Interpolator1DDataBundle getDataBundleFromSortedArrays(final double[] x, final double[] y) {
        return new ArrayInterpolator1DDataBundle(x, y, true);
    }

}