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package org.apache.commons.math3.analysis.polynomials;

import java.util.Arrays;

import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.MathArrays;

Represents a polynomial spline function.

A polynomial spline function consists of a set of
interpolating polynomials and an ascending array of domain
knot points, determining the intervals over which the spline function
is defined by the constituent polynomials.  The polynomials are assumed to
have been computed to match the values of another function at the knot
points.  The value consistency constraints are not currently enforced by
PolynomialSplineFunction itself, but are assumed to hold among
the polynomials and knot points passed to the constructor.

N.B.:  The polynomials in the polynomials property must be
centered on the knot points to compute the spline function values.
See below.

The domain of the polynomial spline function is
[smallest knot, largest knot].  Attempts to evaluate the
function at values outside of this range generate IllegalArgumentExceptions.


The value of the polynomial spline function for an argument x
is computed as follows:

The knot array is searched to find the segment to which x
belongs.  If x is less than the smallest knot point or greater
than the largest one, an IllegalArgumentException
is thrown.
 Let j be the index of the largest knot point that is less
than or equal to x. The value returned is polynomials[j](x - knot[j])
/**
 * Represents a polynomial spline function.
 * <p>
 * A <strong>polynomial spline function</strong> consists of a set of
 * <i>interpolating polynomials</i> and an ascending array of domain
 * <i>knot points</i>, determining the intervals over which the spline function
 * is defined by the constituent polynomials.  The polynomials are assumed to
 * have been computed to match the values of another function at the knot
 * points.  The value consistency constraints are not currently enforced by
 * <code>PolynomialSplineFunction</code> itself, but are assumed to hold among
 * the polynomials and knot points passed to the constructor.</p>
 * <p>
 * N.B.:  The polynomials in the <code>polynomials</code> property must be
 * centered on the knot points to compute the spline function values.
 * See below.</p>
 * <p>
 * The domain of the polynomial spline function is
 * <code>[smallest knot, largest knot]</code>.  Attempts to evaluate the
 * function at values outside of this range generate IllegalArgumentExceptions.
 * </p>
 * <p>
 * The value of the polynomial spline function for an argument <code>x</code>
 * is computed as follows:
 * <ol>
 * <li>The knot array is searched to find the segment to which <code>x</code>
 * belongs.  If <code>x</code> is less than the smallest knot point or greater
 * than the largest one, an <code>IllegalArgumentException</code>
 * is thrown.</li>
 * <li> Let <code>j</code> be the index of the largest knot point that is less
 * than or equal to <code>x</code>.  The value returned is
 * {@code polynomials[j](x - knot[j])}</li></ol>
 *
 */
public class PolynomialSplineFunction implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
    
Spline segment interval delimiters (knots).
Size is n + 1 for n segments.
/**
     * Spline segment interval delimiters (knots).
     * Size is n + 1 for n segments.
     */
    private final double knots[];
    
The polynomial functions that make up the spline. The first element determines the value of the spline over the first subinterval, the second over the second, etc. Spline function values are determined by evaluating these functions at (x - knot[i]) where i is the knot segment to which x belongs. /**
     * The polynomial functions that make up the spline.  The first element
     * determines the value of the spline over the first subinterval, the
     * second over the second, etc.   Spline function values are determined by
     * evaluating these functions at {@code (x - knot[i])} where i is the
     * knot segment to which x belongs.
     */
    private final PolynomialFunction polynomials[];
    
Number of spline segments. It is equal to the number of polynomials and
to the number of partition points - 1.
/**
     * Number of spline segments. It is equal to the number of polynomials and
     * to the number of partition points - 1.
     */
    private final int n;


    
Construct a polynomial spline function with the given segment delimiters
and interpolating polynomials.
The constructor copies both arrays and assigns the copies to the knots
and polynomials properties, respectively.
Params:
knots – Spline segment interval delimiters.
polynomials – Polynomial functions that make up the spline.
Throws:
NullArgumentException – if either of the input arrays is null.
NumberIsTooSmallException – if knots has length less than 2.
DimensionMismatchException – if polynomials.length != knots.length - 1.
NonMonotonicSequenceException – if the knots array is not strictly increasing./**
     * Construct a polynomial spline function with the given segment delimiters
     * and interpolating polynomials.
     * The constructor copies both arrays and assigns the copies to the knots
     * and polynomials properties, respectively.
     *
     * @param knots Spline segment interval delimiters.
     * @param polynomials Polynomial functions that make up the spline.
     * @throws NullArgumentException if either of the input arrays is {@code null}.
     * @throws NumberIsTooSmallException if knots has length less than 2.
     * @throws DimensionMismatchException if {@code polynomials.length != knots.length - 1}.
     * @throws NonMonotonicSequenceException if the {@code knots} array is not strictly increasing.
     *
     */
    public PolynomialSplineFunction(double knots[], PolynomialFunction polynomials[])
        throws NullArgumentException, NumberIsTooSmallException,
               DimensionMismatchException, NonMonotonicSequenceException{
        if (knots == null ||
            polynomials == null) {
            throw new NullArgumentException();
        }
        if (knots.length < 2) {
            throw new NumberIsTooSmallException(LocalizedFormats.NOT_ENOUGH_POINTS_IN_SPLINE_PARTITION,
                                                2, knots.length, false);
        }
        if (knots.length - 1 != polynomials.length) {
            throw new DimensionMismatchException(polynomials.length, knots.length);
        }
        MathArrays.checkOrder(knots);

        this.n = knots.length -1;
        this.knots = new double[n + 1];
        System.arraycopy(knots, 0, this.knots, 0, n + 1);
        this.polynomials = new PolynomialFunction[n];
        System.arraycopy(polynomials, 0, this.polynomials, 0, n);
    }

    
Compute the value for the function. See PolynomialSplineFunction for details on the algorithm for computing the value of the function. 
Params:
v – Point for which the function value should be computed.
Throws:
OutOfRangeException – if v is outside of the domain of the spline function (smaller than the smallest knot point or larger than the largest knot point).
Returns:
the value./**
     * Compute the value for the function.
     * See {@link PolynomialSplineFunction} for details on the algorithm for
     * computing the value of the function.
     *
     * @param v Point for which the function value should be computed.
     * @return the value.
     * @throws OutOfRangeException if {@code v} is outside of the domain of the
     * spline function (smaller than the smallest knot point or larger than the
     * largest knot point).
     */
    public double value(double v) {
        if (v < knots[0] || v > knots[n]) {
            throw new OutOfRangeException(v, knots[0], knots[n]);
        }
        int i = Arrays.binarySearch(knots, v);
        if (i < 0) {
            i = -i - 2;
        }
        // This will handle the case where v is the last knot value
        // There are only n-1 polynomials, so if v is the last knot
        // then we will use the last polynomial to calculate the value.
        if ( i >= polynomials.length ) {
            i--;
        }
        return polynomials[i].value(v - knots[i]);
    }

    
Get the derivative of the polynomial spline function.
Returns:
the derivative function./**
     * Get the derivative of the polynomial spline function.
     *
     * @return the derivative function.
     */
    public UnivariateFunction derivative() {
        return polynomialSplineDerivative();
    }

    
Get the derivative of the polynomial spline function.
Returns:
the derivative function./**
     * Get the derivative of the polynomial spline function.
     *
     * @return the derivative function.
     */
    public PolynomialSplineFunction polynomialSplineDerivative() {
        PolynomialFunction derivativePolynomials[] = new PolynomialFunction[n];
        for (int i = 0; i < n; i++) {
            derivativePolynomials[i] = polynomials[i].polynomialDerivative();
        }
        return new PolynomialSplineFunction(knots, derivativePolynomials);
    }


    
{@inheritDoc}
Since:
3.1/** {@inheritDoc}
     * @since 3.1
     */
    public DerivativeStructure value(final DerivativeStructure t) {
        final double t0 = t.getValue();
        if (t0 < knots[0] || t0 > knots[n]) {
            throw new OutOfRangeException(t0, knots[0], knots[n]);
        }
        int i = Arrays.binarySearch(knots, t0);
        if (i < 0) {
            i = -i - 2;
        }
        // This will handle the case where t is the last knot value
        // There are only n-1 polynomials, so if t is the last knot
        // then we will use the last polynomial to calculate the value.
        if ( i >= polynomials.length ) {
            i--;
        }
        return polynomials[i].value(t.subtract(knots[i]));
    }

    
Get the number of spline segments.
It is also the number of polynomials and the number of knot points - 1.
Returns:
the number of spline segments./**
     * Get the number of spline segments.
     * It is also the number of polynomials and the number of knot points - 1.
     *
     * @return the number of spline segments.
     */
    public int getN() {
        return n;
    }

    
Get a copy of the interpolating polynomials array.
It returns a fresh copy of the array. Changes made to the copy will
not affect the polynomials property.
Returns:
the interpolating polynomials./**
     * Get a copy of the interpolating polynomials array.
     * It returns a fresh copy of the array. Changes made to the copy will
     * not affect the polynomials property.
     *
     * @return the interpolating polynomials.
     */
    public PolynomialFunction[] getPolynomials() {
        PolynomialFunction p[] = new PolynomialFunction[n];
        System.arraycopy(polynomials, 0, p, 0, n);
        return p;
    }

    
Get an array copy of the knot points.
It returns a fresh copy of the array. Changes made to the copy
will not affect the knots property.
Returns:
the knot points./**
     * Get an array copy of the knot points.
     * It returns a fresh copy of the array. Changes made to the copy
     * will not affect the knots property.
     *
     * @return the knot points.
     */
    public double[] getKnots() {
        double out[] = new double[n + 1];
        System.arraycopy(knots, 0, out, 0, n + 1);
        return out;
    }

    
Indicates whether a point is within the interpolation range.
Params:
x – Point.
Returns:
true if x is a valid point./**
     * Indicates whether a point is within the interpolation range.
     *
     * @param x Point.
     * @return {@code true} if {@code x} is a valid point.
     */
    public boolean isValidPoint(double x) {
        if (x < knots[0] ||
            x > knots[n]) {
            return false;
        } else {
            return true;
        }
    }
}