Java Code Examples for org.apache.commons.math3.exception.util.LocalizedFormats#NUMBER_OF_POINTS

/**
 * Gets a copy of the quadrature rule with the given number of integration
 * points.
 *
 * @param numberOfPoints Number of integration points.
 * @return a copy of the integration rule.
 * @throws NotStrictlyPositiveException if {@code numberOfPoints < 1}.
 * @throws DimensionMismatchException if the elements of the rule pair do not
 * have the same length.
 */
public Pair<double[], double[]> getRule(int numberOfPoints)
    throws NotStrictlyPositiveException, DimensionMismatchException {

    if (numberOfPoints <= 0) {
        throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_POINTS,
                                               numberOfPoints);
    }

    // Try to obtain the rule from the cache.
    Pair<double[], double[]> cached = pointsAndWeightsDouble.get(numberOfPoints);

    if (cached == null) {
        // Rule not computed yet.

        // Compute the rule.
        final Pair<T[], T[]> rule = getRuleInternal(numberOfPoints);
        cached = convertToDouble(rule);

        // Cache it.
        pointsAndWeightsDouble.put(numberOfPoints, cached);
    }

    // Return a copy.
    return new Pair<double[], double[]>(cached.getFirst().clone(),
                                        cached.getSecond().clone());
}
 

/**
 * Computes a linear interpolating function for the data set.
 *
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws NonMonotonicSequenceException if {@code x} is not sorted in
 * strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 2.
 */
public PolynomialSplineFunction interpolate(double x[], double y[])
    throws DimensionMismatchException,
           NumberIsTooSmallException,
           NonMonotonicSequenceException {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 2) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 2, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Slope of the lines between the datapoints.
    final double m[] = new double[n];
    for (int i = 0; i < n; i++) {
        m[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]);
    }

    final PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[2];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = m[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Gets a copy of the quadrature rule with the given number of integration
 * points.
 *
 * @param numberOfPoints Number of integration points.
 * @return a copy of the integration rule.
 * @throws NotStrictlyPositiveException if {@code numberOfPoints < 1}.
 * @throws DimensionMismatchException if the elements of the rule pair do not
 * have the same length.
 */
public Pair<double[], double[]> getRule(int numberOfPoints)
    throws NotStrictlyPositiveException, DimensionMismatchException {

    if (numberOfPoints <= 0) {
        throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_POINTS,
                                               numberOfPoints);
    }

    // Try to obtain the rule from the cache.
    Pair<double[], double[]> cached = pointsAndWeightsDouble.get(numberOfPoints);

    if (cached == null) {
        // Rule not computed yet.

        // Compute the rule.
        final Pair<T[], T[]> rule = getRuleInternal(numberOfPoints);
        cached = convertToDouble(rule);

        // Cache it.
        pointsAndWeightsDouble.put(numberOfPoints, cached);
    }

    // Return a copy.
    return new Pair<double[], double[]>(cached.getFirst().clone(),
                                        cached.getSecond().clone());
}
 

/**
 * Computes a linear interpolating function for the data set.
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws org.apache.commons.math3.exception.NonMonotonicSequenceException
 * if {@code x} is not sorted in strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 2.
 */
public PolynomialSplineFunction interpolate(double x[], double y[]) {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 2) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 2, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Slope of the lines between the datapoints.
    final double m[] = new double[n];
    for (int i = 0; i < n; i++) {
        m[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]);
    }

    PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[2];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = m[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Computes a linear interpolating function for the data set.
 *
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws NonMonotonicSequenceException if {@code x} is not sorted in
 * strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 2.
 */
public PolynomialSplineFunction interpolate(double x[], double y[])
    throws DimensionMismatchException,
           NumberIsTooSmallException,
           NonMonotonicSequenceException {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 2) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 2, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Slope of the lines between the datapoints.
    final double m[] = new double[n];
    for (int i = 0; i < n; i++) {
        m[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]);
    }

    final PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[2];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = m[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Gets a copy of the quadrature rule with the given number of integration
 * points.
 *
 * @param numberOfPoints Number of integration points.
 * @return a copy of the integration rule.
 * @throws NotStrictlyPositiveException if {@code numberOfPoints < 1}.
 * @throws DimensionMismatchException if the elements of the rule pair do not
 * have the same length.
 */
public Pair<double[], double[]> getRule(int numberOfPoints)
    throws NotStrictlyPositiveException, DimensionMismatchException {

    if (numberOfPoints <= 0) {
        throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_POINTS,
                                               numberOfPoints);
    }

    // Try to obtain the rule from the cache.
    Pair<double[], double[]> cached = pointsAndWeightsDouble.get(numberOfPoints);

    if (cached == null) {
        // Rule not computed yet.

        // Compute the rule.
        final Pair<T[], T[]> rule = getRuleInternal(numberOfPoints);
        cached = convertToDouble(rule);

        // Cache it.
        pointsAndWeightsDouble.put(numberOfPoints, cached);
    }

    // Return a copy.
    return new Pair<double[], double[]>(cached.getFirst().clone(),
                                        cached.getSecond().clone());
}
 

/**
 * Computes a linear interpolating function for the data set.
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws org.apache.commons.math3.exception.NonMonotonicSequenceException
 * if {@code x} is not sorted in strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 2.
 */
public PolynomialSplineFunction interpolate(double x[], double y[]) {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 2) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 2, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Slope of the lines between the datapoints.
    final double m[] = new double[n];
    for (int i = 0; i < n; i++) {
        m[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]);
    }

    PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[2];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = m[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Gets a copy of the quadrature rule with the given number of integration
 * points.
 *
 * @param numberOfPoints Number of integration points.
 * @return a copy of the integration rule.
 * @throws NotStrictlyPositiveException if {@code numberOfPoints < 1}.
 * @throws DimensionMismatchException if the elements of the rule pair do not
 * have the same length.
 */
public Pair<double[], double[]> getRule(int numberOfPoints)
    throws NotStrictlyPositiveException, DimensionMismatchException {

    if (numberOfPoints <= 0) {
        throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_POINTS,
                                               numberOfPoints);
    }

    // Try to obtain the rule from the cache.
    Pair<double[], double[]> cached = pointsAndWeightsDouble.get(numberOfPoints);

    if (cached == null) {
        // Rule not computed yet.

        // Compute the rule.
        final Pair<T[], T[]> rule = getRuleInternal(numberOfPoints);
        cached = convertToDouble(rule);

        // Cache it.
        pointsAndWeightsDouble.put(numberOfPoints, cached);
    }

    // Return a copy.
    return new Pair<double[], double[]>(cached.getFirst().clone(),
                                        cached.getSecond().clone());
}
 

/**
 * Computes a linear interpolating function for the data set.
 *
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws NonMonotonicSequenceException if {@code x} is not sorted in
 * strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 2.
 */
public PolynomialSplineFunction interpolate(double x[], double y[])
    throws DimensionMismatchException,
           NumberIsTooSmallException,
           NonMonotonicSequenceException {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 2) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 2, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Slope of the lines between the datapoints.
    final double m[] = new double[n];
    for (int i = 0; i < n; i++) {
        m[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]);
    }

    final PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[2];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = m[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Gets a copy of the quadrature rule with the given number of integration
 * points.
 *
 * @param numberOfPoints Number of integration points.
 * @return a copy of the integration rule.
 * @throws NotStrictlyPositiveException if {@code numberOfPoints < 1}.
 * @throws DimensionMismatchException if the elements of the rule pair do not
 * have the same length.
 */
public Pair<double[], double[]> getRule(int numberOfPoints)
    throws NotStrictlyPositiveException, DimensionMismatchException {

    if (numberOfPoints <= 0) {
        throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_POINTS,
                                               numberOfPoints);
    }

    // Try to obtain the rule from the cache.
    Pair<double[], double[]> cached = pointsAndWeightsDouble.get(numberOfPoints);

    if (cached == null) {
        // Rule not computed yet.

        // Compute the rule.
        final Pair<T[], T[]> rule = getRuleInternal(numberOfPoints);
        cached = convertToDouble(rule);

        // Cache it.
        pointsAndWeightsDouble.put(numberOfPoints, cached);
    }

    // Return a copy.
    return new Pair<double[], double[]>(cached.getFirst().clone(),
                                        cached.getSecond().clone());
}
 

/**
 * Computes an interpolating function for the data set.
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws org.apache.commons.math3.exception.NonMonotonicSequenceException
 * if {@code x} is not sorted in strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 3.
 */
public PolynomialSplineFunction interpolate(double x[], double y[]) {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 3) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 3, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Differences between knot points
    double h[] = new double[n];
    for (int i = 0; i < n; i++) {
        h[i] = x[i + 1] - x[i];
    }

    double mu[] = new double[n];
    double z[] = new double[n + 1];
    mu[0] = 0d;
    z[0] = 0d;
    double g = 0;
    for (int i = 1; i < n; i++) {
        g = 2d * (x[i+1]  - x[i - 1]) - h[i - 1] * mu[i -1];
        mu[i] = h[i] / g;
        z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) /
                (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;
    }

    // cubic spline coefficients --  b is linear, c quadratic, d is cubic (original y's are constants)
    double b[] = new double[n];
    double c[] = new double[n + 1];
    double d[] = new double[n];

    z[n] = 0d;
    c[n] = 0d;

    for (int j = n -1; j >=0; j--) {
        c[j] = z[j] - mu[j] * c[j + 1];
        b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
        d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
    }

    PolynomialFunction polynomials[] = new PolynomialFunction[n];
    double coefficients[] = new double[4];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = b[i];
        coefficients[2] = c[i];
        coefficients[3] = d[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Computes an interpolating function for the data set.
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws NonMonotonicSequenceException if {@code x} is not sorted in
 * strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 3.
 */
public PolynomialSplineFunction interpolate(double x[], double y[])
    throws DimensionMismatchException,
           NumberIsTooSmallException,
           NonMonotonicSequenceException {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 3) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 3, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    final int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Differences between knot points
    final double h[] = new double[n];
    for (int i = 0; i < n; i++) {
        h[i] = x[i + 1] - x[i];
    }

    final double mu[] = new double[n];
    final double z[] = new double[n + 1];
    mu[0] = 0d;
    z[0] = 0d;
    double g = 0;
    for (int i = 1; i < n; i++) {
        g = 2d * (x[i+1]  - x[i - 1]) - h[i - 1] * mu[i -1];
        mu[i] = h[i] / g;
        z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) /
                (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;
    }

    // cubic spline coefficients --  b is linear, c quadratic, d is cubic (original y's are constants)
    final double b[] = new double[n];
    final double c[] = new double[n + 1];
    final double d[] = new double[n];

    z[n] = 0d;
    c[n] = 0d;

    for (int j = n -1; j >=0; j--) {
        c[j] = z[j] - mu[j] * c[j + 1];
        b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
        d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
    }

    final PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[4];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = b[i];
        coefficients[2] = c[i];
        coefficients[3] = d[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Computes an interpolating function for the data set.
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws NonMonotonicSequenceException if {@code x} is not sorted in
 * strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 3.
 */
public PolynomialSplineFunction interpolate(double x[], double y[])
    throws DimensionMismatchException,
           NumberIsTooSmallException,
           NonMonotonicSequenceException {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 3) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 3, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    final int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Differences between knot points
    final double h[] = new double[n];
    for (int i = 0; i < n; i++) {
        h[i] = x[i + 1] - x[i];
    }

    final double mu[] = new double[n];
    final double z[] = new double[n + 1];
    mu[0] = 0d;
    z[0] = 0d;
    double g = 0;
    for (int i = 1; i < n; i++) {
        g = 2d * (x[i+1]  - x[i - 1]) - h[i - 1] * mu[i -1];
        mu[i] = h[i] / g;
        z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) /
                (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;
    }

    // cubic spline coefficients --  b is linear, c quadratic, d is cubic (original y's are constants)
    final double b[] = new double[n];
    final double c[] = new double[n + 1];
    final double d[] = new double[n];

    z[n] = 0d;
    c[n] = 0d;

    for (int j = n -1; j >=0; j--) {
        c[j] = z[j] - mu[j] * c[j + 1];
        b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
        d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
    }

    final PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[4];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = b[i];
        coefficients[2] = c[i];
        coefficients[3] = d[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Computes an interpolating function for the data set.
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws NonMonotonicSequenceException if {@code x} is not sorted in
 * strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 3.
 */
public PolynomialSplineFunction interpolate(double x[], double y[])
    throws DimensionMismatchException,
           NumberIsTooSmallException,
           NonMonotonicSequenceException {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 3) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 3, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    final int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Differences between knot points
    final double h[] = new double[n];
    for (int i = 0; i < n; i++) {
        h[i] = x[i + 1] - x[i];
    }

    final double mu[] = new double[n];
    final double z[] = new double[n + 1];
    mu[0] = 0d;
    z[0] = 0d;
    double g = 0;
    for (int i = 1; i < n; i++) {
        g = 2d * (x[i+1]  - x[i - 1]) - h[i - 1] * mu[i -1];
        mu[i] = h[i] / g;
        z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) /
                (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;
    }

    // cubic spline coefficients --  b is linear, c quadratic, d is cubic (original y's are constants)
    final double b[] = new double[n];
    final double c[] = new double[n + 1];
    final double d[] = new double[n];

    z[n] = 0d;
    c[n] = 0d;

    for (int j = n -1; j >=0; j--) {
        c[j] = z[j] - mu[j] * c[j + 1];
        b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
        d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
    }

    final PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[4];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = b[i];
        coefficients[2] = c[i];
        coefficients[3] = d[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Computes an interpolating function for the data set.
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws org.apache.commons.math3.exception.NonMonotonicSequenceException
 * if {@code x} is not sorted in strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 3.
 */
public PolynomialSplineFunction interpolate(double x[], double y[]) {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 3) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 3, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Differences between knot points
    double h[] = new double[n];
    for (int i = 0; i < n; i++) {
        h[i] = x[i + 1] - x[i];
    }

    double mu[] = new double[n];
    double z[] = new double[n + 1];
    mu[0] = 0d;
    z[0] = 0d;
    double g = 0;
    for (int i = 1; i < n; i++) {
        g = 2d * (x[i+1]  - x[i - 1]) - h[i - 1] * mu[i -1];
        mu[i] = h[i] / g;
        z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) /
                (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;
    }

    // cubic spline coefficients --  b is linear, c quadratic, d is cubic (original y's are constants)
    double b[] = new double[n];
    double c[] = new double[n + 1];
    double d[] = new double[n];

    z[n] = 0d;
    c[n] = 0d;

    for (int j = n -1; j >=0; j--) {
        c[j] = z[j] - mu[j] * c[j + 1];
        b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
        d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
    }

    PolynomialFunction polynomials[] = new PolynomialFunction[n];
    double coefficients[] = new double[4];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = b[i];
        coefficients[2] = c[i];
        coefficients[3] = d[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Creates a Hermite cubic spline interpolation from the set of (x,y) value
 * pairs and their derivatives. This is modeled off of the
 * InterpolateHermiteSorted method in the Math.NET CubicSpline class.
 *
 * @param xvals x values for interpolation
 * @param yvals y values for interpolation
 * @param firstDerivatives first derivative values of the function
 * @return polynomial that fits the function
 */
private PolynomialSplineFunction interpolateHermiteSorted(double[] xvals,
                                                          double[] yvals,
                                                          double[] firstDerivatives) {
    if (xvals.length != yvals.length) {
        throw new DimensionMismatchException(xvals.length, yvals.length);
    }

    if (xvals.length != firstDerivatives.length) {
        throw new DimensionMismatchException(xvals.length,
                                             firstDerivatives.length);
    }

    final int minimumLength = 2;
    if (xvals.length < minimumLength) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            xvals.length, minimumLength,
                                            true);
    }

    final int size = xvals.length - 1;
    final PolynomialFunction[] polynomials = new PolynomialFunction[size];
    final double[] coefficients = new double[4];

    for (int i = 0; i < polynomials.length; i++) {
        final double w = xvals[i + 1] - xvals[i];
        final double w2 = w * w;

        final double yv = yvals[i];
        final double yvP = yvals[i + 1];

        final double fd = firstDerivatives[i];
        final double fdP = firstDerivatives[i + 1];

        coefficients[0] = yv;
        coefficients[1] = firstDerivatives[i];
        coefficients[2] = (3 * (yvP - yv) / w - 2 * fd - fdP) / w;
        coefficients[3] = (2 * (yv - yvP) / w + fd + fdP) / w2;
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(xvals, polynomials);

}
 

/**
 * Computes an interpolating function for the data set.
 * @param x the arguments for the interpolation points
 * @param y the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code x} and {@code y}
 * have different sizes.
 * @throws NonMonotonicSequenceException if {@code x} is not sorted in
 * strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code x} is smaller
 * than 3.
 */
public PolynomialSplineFunction interpolate(double x[], double y[])
    throws DimensionMismatchException,
           NumberIsTooSmallException,
           NonMonotonicSequenceException {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 3) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            x.length, 3, true);
    }

    // Number of intervals.  The number of data points is n + 1.
    final int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Differences between knot points
    final double h[] = new double[n];
    for (int i = 0; i < n; i++) {
        h[i] = x[i + 1] - x[i];
    }

    final double mu[] = new double[n];
    final double z[] = new double[n + 1];
    mu[0] = 0d;
    z[0] = 0d;
    double g = 0;
    for (int i = 1; i < n; i++) {
        g = 2d * (x[i+1]  - x[i - 1]) - h[i - 1] * mu[i -1];
        mu[i] = h[i] / g;
        z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) /
                (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;
    }

    // cubic spline coefficients --  b is linear, c quadratic, d is cubic (original y's are constants)
    final double b[] = new double[n];
    final double c[] = new double[n + 1];
    final double d[] = new double[n];

    z[n] = 0d;
    c[n] = 0d;

    for (int j = n -1; j >=0; j--) {
        c[j] = z[j] - mu[j] * c[j + 1];
        b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
        d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
    }

    final PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[4];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = b[i];
        coefficients[2] = c[i];
        coefficients[3] = d[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}
 

/**
 * Computes an interpolating function for the data set.
 *
 * @param xvals the arguments for the interpolation points
 * @param yvals the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException if {@code xvals} and {@code yvals} have
 *         different sizes.
 * @throws NonMonotonicSequenceException if {@code xvals} is not sorted in
 *         strict increasing order.
 * @throws NumberIsTooSmallException if the size of {@code xvals} is smaller
 *         than 5.
 */
public PolynomialSplineFunction interpolate(double[] xvals,
                                            double[] yvals)
    throws DimensionMismatchException,
           NumberIsTooSmallException,
           NonMonotonicSequenceException {
    if (xvals == null ||
        yvals == null) {
        throw new NullArgumentException();
    }

    if (xvals.length != yvals.length) {
        throw new DimensionMismatchException(xvals.length, yvals.length);
    }

    if (xvals.length < MINIMUM_NUMBER_POINTS) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                            xvals.length,
                                            MINIMUM_NUMBER_POINTS, true);
    }

    MathArrays.checkOrder(xvals);

    final int numberOfDiffAndWeightElements = xvals.length - 1;

    final double[] differences = new double[numberOfDiffAndWeightElements];
    final double[] weights = new double[numberOfDiffAndWeightElements];

    for (int i = 0; i < differences.length; i++) {
        differences[i] = (yvals[i + 1] - yvals[i]) / (xvals[i + 1] - xvals[i]);
    }

    for (int i = 1; i < weights.length; i++) {
        weights[i] = FastMath.abs(differences[i] - differences[i - 1]);
    }

    // Prepare Hermite interpolation scheme.
    final double[] firstDerivatives = new double[xvals.length];

    for (int i = 2; i < firstDerivatives.length - 2; i++) {
        final double wP = weights[i + 1];
        final double wM = weights[i - 1];
        if (Precision.equals(wP, 0.0) &&
            Precision.equals(wM, 0.0)) {
            final double xv = xvals[i];
            final double xvP = xvals[i + 1];
            final double xvM = xvals[i - 1];
            firstDerivatives[i] = (((xvP - xv) * differences[i - 1]) + ((xv - xvM) * differences[i])) / (xvP - xvM);
        } else {
            firstDerivatives[i] = ((wP * differences[i - 1]) + (wM * differences[i])) / (wP + wM);
        }
    }

    firstDerivatives[0] = differentiateThreePoint(xvals, yvals, 0, 0, 1, 2);
    firstDerivatives[1] = differentiateThreePoint(xvals, yvals, 1, 0, 1, 2);
    firstDerivatives[xvals.length - 2] = differentiateThreePoint(xvals, yvals, xvals.length - 2,
                                                                 xvals.length - 3, xvals.length - 2,
                                                                 xvals.length - 1);
    firstDerivatives[xvals.length - 1] = differentiateThreePoint(xvals, yvals, xvals.length - 1,
                                                                 xvals.length - 3, xvals.length - 2,
                                                                 xvals.length - 1);

    return interpolateHermiteSorted(xvals, yvals, firstDerivatives);
}
 

/**
 * Builds an integrator with given accuracies and iterations counts.
 *
 * @param n Number of integration points.
 * @param relativeAccuracy Relative accuracy of the result.
 * @param absoluteAccuracy Absolute accuracy of the result.
 * @param minimalIterationCount Minimum number of iterations.
 * @param maximalIterationCount Maximum number of iterations.
 * @throws NotStrictlyPositiveException if minimal number of iterations
 * or number of points are not strictly positive.
 * @throws NumberIsTooSmallException if maximal number of iterations
 * is smaller than or equal to the minimal number of iterations.
 */
public IterativeLegendreGaussIntegrator(final int n,
                                        final double relativeAccuracy,
                                        final double absoluteAccuracy,
                                        final int minimalIterationCount,
                                        final int maximalIterationCount)
    throws NotStrictlyPositiveException, NumberIsTooSmallException {
    super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
    if (n <= 0) {
        throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_POINTS, n);
    }
   numberOfPoints = n;
}
 

/**
 * Builds an integrator with given accuracies and iterations counts.
 *
 * @param n Number of integration points.
 * @param relativeAccuracy Relative accuracy of the result.
 * @param absoluteAccuracy Absolute accuracy of the result.
 * @param minimalIterationCount Minimum number of iterations.
 * @param maximalIterationCount Maximum number of iterations.
 * @throws NotStrictlyPositiveException if minimal number of iterations
 * or number of points are not strictly positive.
 * @throws NumberIsTooSmallException if maximal number of iterations
 * is smaller than or equal to the minimal number of iterations.
 */
public IterativeLegendreGaussIntegrator(final int n,
                                        final double relativeAccuracy,
                                        final double absoluteAccuracy,
                                        final int minimalIterationCount,
                                        final int maximalIterationCount)
    throws NotStrictlyPositiveException, NumberIsTooSmallException {
    super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
    if (n <= 0) {
        throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_POINTS, n);
    }
   numberOfPoints = n;
}