Example usage for org.apache.commons.math3.analysis.interpolation BicubicSplineInterpolatingFunction partialDerivativeX

Introduction

In this page you can find the example usage for org.apache.commons.math3.analysis.interpolation BicubicSplineInterpolatingFunction partialDerivativeX.

Prototype

BivariateFunction partialDerivativeX

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Document

First partial derivative along x.

Usage

From source file:au.gov.ga.conn4d.utils.TricubicSplineInterpolator.java

/**
 * {@inheritDoc}/*w ww.  j  ava 2s.c  om*/
 */
public TricubicSplineInterpolatingFunction interpolate(final double[] zval, final double[] yval,
        final double[] xval, final double[][][] fval)
        throws NoDataException, DimensionMismatchException, NonMonotonicSequenceException {
    if (zval.length == 0 || yval.length == 0 || xval.length == 0 || fval.length == 0) {
        throw new NoDataException();
    }
    if (zval.length != fval.length) {
        throw new DimensionMismatchException(zval.length, fval.length);
    }

    MathArrays.checkOrder(zval);
    MathArrays.checkOrder(yval);

    final int zLen = zval.length;
    final int yLen = yval.length;
    final int xLen = xval.length;

    final double[] zzval;
    final double[][][] ffval = new double[zLen][][];

    if (zval[0] > zval[zLen - 1]) {
        zzval = VectorMath.selectionSort(zval);
        for (int i = 0; i < zLen; i++) {
            ffval[i] = fval[zLen - 1 - i];
        }
    } else {
        zzval = zval;
    }

    // Samples, re-ordered as (z, x, y) and (y, z, x) tuplets
    // fvalXY[k][i][j] = f(xval[i], yval[j], zval[k])
    // fvalZX[j][k][i] = f(xval[i], yval[j], zval[k])
    final double[][][] fvalXY = new double[xLen][zLen][yLen];
    final double[][][] fvalZX = new double[yLen][xLen][zLen];
    for (int i = 0; i < zLen; i++) {
        if (ffval[i].length != yLen) {
            throw new DimensionMismatchException(ffval[i].length, yLen);
        }

        for (int j = 0; j < yLen; j++) {
            if (ffval[i][j].length != xLen) {
                throw new DimensionMismatchException(ffval[i][j].length, xLen);
            }

            for (int k = 0; k < xLen; k++) {
                final double v = ffval[i][j][k];
                fvalXY[k][i][j] = v;
                fvalZX[j][k][i] = v;
            }
        }
    }

    final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator();

    // For each line x[i] (0 <= i < xLen), construct a 2D spline in y and z
    final BicubicSplineInterpolatingFunction[] xSplineYZ = new BicubicSplineInterpolatingFunction[zLen];
    for (int i = 0; i < zLen; i++) {
        xSplineYZ[i] = bsi.interpolate(yval, xval, ffval[i]);
    }

    // For each line y[j] (0 <= j < yLen), construct a 2D spline in z and x
    final BicubicSplineInterpolatingFunction[] ySplineZX = new BicubicSplineInterpolatingFunction[yLen];
    for (int j = 0; j < yLen; j++) {
        ySplineZX[j] = bsi.interpolate(xval, zzval, fvalZX[j]);
    }

    // For each line z[k] (0 <= k < zLen), construct a 2D spline in x and y
    final BicubicSplineInterpolatingFunction[] zSplineXY = new BicubicSplineInterpolatingFunction[xLen];
    for (int k = 0; k < xLen; k++) {
        zSplineXY[k] = bsi.interpolate(zzval, yval, fvalXY[k]);
    }

    // Partial derivatives wrt x and wrt y
    final double[][][] dFdX = new double[zLen][yLen][xLen];
    final double[][][] dFdY = new double[zLen][yLen][xLen];
    final double[][][] d2FdXdY = new double[zLen][yLen][xLen];
    for (int k = 0; k < xLen; k++) {
        final BicubicSplineInterpolatingFunction f = zSplineXY[k];
        for (int i = 0; i < zLen; i++) {
            final double z = zzval[i];
            for (int j = 0; j < yLen; j++) {
                final double y = yval[j];
                dFdX[i][j][k] = f.partialDerivativeX(z, y);
                dFdY[i][j][k] = f.partialDerivativeY(z, y);
                d2FdXdY[i][j][k] = f.partialDerivativeXY(z, y);
            }
        }
    }

    // Partial derivatives wrt y and wrt z
    final double[][][] dFdZ = new double[zLen][yLen][xLen];
    final double[][][] d2FdYdZ = new double[zLen][yLen][xLen];
    for (int i = 0; i < zLen; i++) {
        final BicubicSplineInterpolatingFunction f = xSplineYZ[i];
        for (int j = 0; j < yLen; j++) {
            final double y = yval[j];
            for (int k = 0; k < xLen; k++) {
                final double x = xval[k];
                dFdZ[i][j][k] = f.partialDerivativeY(y, x);
                d2FdYdZ[i][j][k] = f.partialDerivativeXY(y, x);
            }
        }
    }

    // Partial derivatives wrt x and wrt z
    final double[][][] d2FdZdX = new double[zLen][yLen][xLen];
    for (int j = 0; j < yLen; j++) {
        final BicubicSplineInterpolatingFunction f = ySplineZX[j];
        for (int k = 0; k < xLen; k++) {
            final double x = xval[k];
            for (int i = 0; i < zLen; i++) {
                final double z = zzval[i];
                d2FdZdX[i][j][k] = f.partialDerivativeXY(x, z);
            }
        }
    }

    // Third partial cross-derivatives
    final double[][][] d3FdXdYdZ = new double[zLen][yLen][xLen];
    for (int i = 0; i < zLen; i++) {
        final int nI = nextIndex(i, zLen);
        final int pI = previousIndex(i);
        for (int j = 0; j < yLen; j++) {
            final int nJ = nextIndex(j, yLen);
            final int pJ = previousIndex(j);
            for (int k = 0; k < xLen; k++) {
                final int nK = nextIndex(k, xLen);
                final int pK = previousIndex(k);

                // XXX Not sure about this formula
                d3FdXdYdZ[i][j][k] = (ffval[nI][nJ][nK] - ffval[nI][pJ][nK] - ffval[pI][nJ][nK]
                        + ffval[pI][pJ][nK] - ffval[nI][nJ][pK] + ffval[nI][pJ][pK] + ffval[pI][nJ][pK]
                        - ffval[pI][pJ][pK])
                        / ((zzval[nI] - zzval[pI]) * (yval[nJ] - yval[pJ]) * (xval[nK] - xval[pK]));
            }
        }
    }

    // Create the interpolating splines
    return new TricubicSplineInterpolatingFunction(zzval, yval, xval, ffval, dFdX, dFdY, dFdZ, d2FdXdY, d2FdZdX,
            d2FdYdZ, d3FdXdYdZ);
}

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From source file:au.gov.ga.conn4d.utils.TricubicSplineInterpolator.java

public TricubicSplineInterpolatingFunction interpolate(final double[] zval, final double[] yval,
        final double[] xval, final float[][][] fval)
        throws NoDataException, DimensionMismatchException, NonMonotonicSequenceException {
    if (zval.length == 0 || yval.length == 0 || xval.length == 0 || fval.length == 0) {
        throw new NoDataException();
    }//from  w ww  . j  av  a2  s  . c  o m
    if (zval.length != fval.length) {
        throw new DimensionMismatchException(zval.length, fval.length);
    }

    MathArrays.checkOrder(yval);
    MathArrays.checkOrder(xval);

    final int zLen = zval.length;
    final int yLen = yval.length;
    final int xLen = xval.length;

    final double[] zzval;
    float[][][] ffval = new float[zLen][][];

    if (zval[0] > zval[zLen - 1]) {
        zzval = VectorMath.selectionSort(zval);
        for (int i = 0; i < zLen; i++) {
            ffval[i] = fval[zLen - 1 - i];
        }
    } else {
        zzval = zval;
        ffval = fval;
    }

    // Samples, re-ordered as (z, x, y) and (y, z, x) tuplets
    // fvalXY[k][i][j] = f(xval[i], yval[j], zval[k])
    // fvalZX[j][k][i] = f(xval[i], yval[j], zval[k])
    final double[][][] fvalXY = new double[xLen][zLen][yLen];
    final double[][][] fvalZX = new double[yLen][xLen][zLen];
    for (int i = 0; i < zLen; i++) {
        if (ffval[i].length != yLen) {
            throw new DimensionMismatchException(ffval[i].length, yLen);
        }

        for (int j = 0; j < yLen; j++) {
            if (ffval[i][j].length != xLen) {
                throw new DimensionMismatchException(ffval[i][j].length, xLen);
            }

            for (int k = 0; k < xLen; k++) {
                final double v = ffval[i][j][k];
                fvalXY[k][i][j] = v;
                fvalZX[j][k][i] = v;
            }
        }
    }

    final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator();

    // For each line x[i] (0 <= i < xLen), construct a 2D spline in y and z
    final BicubicSplineInterpolatingFunction[] xSplineYZ = new BicubicSplineInterpolatingFunction[zLen];
    for (int i = 0; i < zLen; i++) {
        xSplineYZ[i] = bsi.interpolate(yval, xval, ffval[i]);
    }

    // For each line y[j] (0 <= j < yLen), construct a 2D spline in z and x
    final BicubicSplineInterpolatingFunction[] ySplineZX = new BicubicSplineInterpolatingFunction[yLen];
    for (int j = 0; j < yLen; j++) {
        ySplineZX[j] = bsi.interpolate(xval, zzval, fvalZX[j]);
    }

    // For each line z[k] (0 <= k < zLen), construct a 2D spline in x and y
    final BicubicSplineInterpolatingFunction[] zSplineXY = new BicubicSplineInterpolatingFunction[xLen];
    for (int k = 0; k < xLen; k++) {
        zSplineXY[k] = bsi.interpolate(zzval, yval, fvalXY[k]);
    }

    // Partial derivatives wrt x and wrt y
    final double[][][] dFdX = new double[zLen][yLen][xLen];
    final double[][][] dFdY = new double[zLen][yLen][xLen];
    final double[][][] d2FdXdY = new double[zLen][yLen][xLen];
    for (int k = 0; k < xLen; k++) {
        final BicubicSplineInterpolatingFunction f = zSplineXY[k];
        for (int i = 0; i < zLen; i++) {
            final double x = zzval[i];
            for (int j = 0; j < yLen; j++) {
                final double y = yval[j];
                dFdX[i][j][k] = f.partialDerivativeX(x, y);
                dFdY[i][j][k] = f.partialDerivativeY(x, y);
                d2FdXdY[i][j][k] = f.partialDerivativeXY(x, y);
            }
        }
    }

    // Partial derivatives wrt y and wrt z
    final double[][][] dFdZ = new double[zLen][yLen][xLen];
    final double[][][] d2FdYdZ = new double[zLen][yLen][xLen];
    for (int i = 0; i < zLen; i++) {
        final BicubicSplineInterpolatingFunction f = xSplineYZ[i];
        for (int j = 0; j < yLen; j++) {
            final double y = yval[j];
            for (int k = 0; k < xLen; k++) {
                final double z = xval[k];
                dFdZ[i][j][k] = f.partialDerivativeY(y, z);
                d2FdYdZ[i][j][k] = f.partialDerivativeXY(y, z);
            }
        }
    }

    // Partial derivatives wrt x and wrt z
    final double[][][] d2FdZdX = new double[zLen][yLen][xLen];
    for (int j = 0; j < yLen; j++) {
        final BicubicSplineInterpolatingFunction f = ySplineZX[j];
        for (int k = 0; k < xLen; k++) {
            final double z = xval[k];
            for (int i = 0; i < zLen; i++) {
                final double x = zzval[i];
                d2FdZdX[i][j][k] = f.partialDerivativeXY(z, x);
            }
        }
    }

    // Third partial cross-derivatives
    final double[][][] d3FdXdYdZ = new double[zLen][yLen][xLen];
    for (int i = 0; i < zLen; i++) {
        final int nI = nextIndex(i, zLen);
        final int pI = previousIndex(i);
        for (int j = 0; j < yLen; j++) {
            final int nJ = nextIndex(j, yLen);
            final int pJ = previousIndex(j);
            for (int k = 0; k < xLen; k++) {
                final int nK = nextIndex(k, xLen);
                final int pK = previousIndex(k);

                // XXX Not sure about this formula
                d3FdXdYdZ[i][j][k] = (ffval[nI][nJ][nK] - ffval[nI][pJ][nK] - ffval[pI][nJ][nK]
                        + ffval[pI][pJ][nK] - ffval[nI][nJ][pK] + ffval[nI][pJ][pK] + ffval[pI][nJ][pK]
                        - ffval[pI][pJ][pK])
                        / ((zzval[nI] - zzval[pI]) * (yval[nJ] - yval[pJ]) * (xval[nK] - xval[pK]));
            }
        }
    }

    // Create the interpolating splines
    return new TricubicSplineInterpolatingFunction(zzval, yval, xval, ffval, dFdX, dFdY, dFdZ, d2FdXdY, d2FdZdX,
            d2FdYdZ, d3FdXdYdZ);
}

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