/**
* Copyright (C) 2013 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.math.function;
import java.util.Arrays;
import com.opengamma.analytics.math.FunctionUtils;
import com.opengamma.analytics.math.interpolation.PiecewisePolynomialResult;
import com.opengamma.analytics.math.matrix.DoubleMatrix1D;
import com.opengamma.analytics.math.matrix.DoubleMatrix2D;
import com.opengamma.util.ArgumentChecker;
/**
* Give a struct {@link PiecewisePolynomialResult}, Compute value, first derivative and integral of piecewise polynomial function
*/
public class PiecewisePolynomialFunction1D {
/**
* Default constructor
*/
public PiecewisePolynomialFunction1D() {
}
/**
* @param pp PiecewisePolynomialResult
* @param xKey
* @return Values of piecewise polynomial functions at xKey
* When _dim in PiecewisePolynomialResult is greater than 1, i.e., the struct contains multiple splines, an element in the return values corresponds to each spline
*/
public DoubleMatrix1D evaluate(final PiecewisePolynomialResult pp, final double xKey) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.isFalse(Double.isNaN(xKey), "xKey containing NaN");
ArgumentChecker.isFalse(Double.isInfinite(xKey), "xKey containing Infinity");
final double[] knots = pp.getKnots().getData();
final int nKnots = knots.length;
final DoubleMatrix2D coefMatrix = pp.getCoefMatrix();
final int dim = pp.getDimensions();
double[] res = new double[dim];
int indicator = FunctionUtils.getLowerBoundIndex(knots, xKey);
if (indicator == nKnots - 1) {
indicator--; //there is 1 less interval that knots
}
for (int j = 0; j < dim; ++j) {
final double[] coefs = coefMatrix.getRowVector(dim * indicator + j).getData();
res[j] = getValue(coefs, xKey, knots[indicator]);
ArgumentChecker.isFalse(Double.isInfinite(res[j]), "Too large input");
ArgumentChecker.isFalse(Double.isNaN(res[j]), "Too large input");
}
return new DoubleMatrix1D(res);
}
/**
* @param pp PiecewisePolynomialResult
* @param xKeys
* @return Values of piecewise polynomial functions at xKeys
* When _dim in PiecewisePolynomialResult is greater than 1, i.e., the struct contains multiple piecewise polynomials, a row vector of return value corresponds to each piecewise polynomial
*/
public DoubleMatrix2D evaluate(final PiecewisePolynomialResult pp, final double[] xKeys) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.notNull(xKeys, "xKeys");
final int keyLength = xKeys.length;
for (int i = 0; i < keyLength; ++i) {
ArgumentChecker.isFalse(Double.isNaN(xKeys[i]), "xKeys containing NaN");
ArgumentChecker.isFalse(Double.isInfinite(xKeys[i]), "xKeys containing Infinity");
}
final double[] knots = pp.getKnots().getData();
final int nKnots = knots.length;
final DoubleMatrix2D coefMatrix = pp.getCoefMatrix();
final int dim = pp.getDimensions();
double[][] res = new double[dim][keyLength];
for (int k = 0; k < dim; ++k) {
for (int j = 0; j < keyLength; ++j) {
int indicator = 0;
if (xKeys[j] < knots[1]) {
indicator = 0;
} else {
for (int i = 1; i < nKnots - 1; ++i) {
if (knots[i] <= xKeys[j]) {
indicator = i;
}
}
}
final double[] coefs = coefMatrix.getRowVector(dim * indicator + k).getData();
res[k][j] = getValue(coefs, xKeys[j], knots[indicator]);
ArgumentChecker.isFalse(Double.isInfinite(res[k][j]), "Too large input");
ArgumentChecker.isFalse(Double.isNaN(res[k][j]), "Too large input");
}
}
return new DoubleMatrix2D(res);
}
/**
* @param pp PiecewisePolynomialResult
* @param xKeys
* @return Values of piecewise polynomial functions at xKeys
* When _dim in PiecewisePolynomialResult is greater than 1, i.e., the struct contains multiple piecewise polynomials,
* one element of return vector of DoubleMatrix2D corresponds to each piecewise polynomial
*/
public DoubleMatrix2D[] evaluate(final PiecewisePolynomialResult pp, final double[][] xKeys) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.notNull(xKeys, "xKeys");
final int keyLength = xKeys[0].length;
final int keyDim = xKeys.length;
for (int j = 0; j < keyDim; ++j) {
for (int i = 0; i < keyLength; ++i) {
ArgumentChecker.isFalse(Double.isNaN(xKeys[j][i]), "xKeys containing NaN");
ArgumentChecker.isFalse(Double.isInfinite(xKeys[j][i]), "xKeys containing Infinity");
}
}
final double[] knots = pp.getKnots().getData();
final int nKnots = knots.length;
final DoubleMatrix2D coefMatrix = pp.getCoefMatrix();
final int dim = pp.getDimensions();
double[][][] res = new double[dim][keyDim][keyLength];
for (int k = 0; k < dim; ++k) {
for (int l = 0; l < keyDim; ++l) {
for (int j = 0; j < keyLength; ++j) {
int indicator = 0;
if (xKeys[l][j] < knots[1]) {
indicator = 0;
} else {
for (int i = 1; i < nKnots - 1; ++i) {
if (knots[i] <= xKeys[l][j]) {
indicator = i;
}
}
}
final double[] coefs = coefMatrix.getRowVector(dim * indicator + k).getData();
res[k][l][j] = getValue(coefs, xKeys[l][j], knots[indicator]);
ArgumentChecker.isFalse(Double.isInfinite(res[k][l][j]), "Too large input");
ArgumentChecker.isFalse(Double.isNaN(res[k][l][j]), "Too large input");
}
}
}
DoubleMatrix2D[] resMat = new DoubleMatrix2D[dim];
for (int i = 0; i < dim; ++i) {
resMat[i] = new DoubleMatrix2D(res[i]);
}
return resMat;
}
/**
* @param pp PiecewisePolynomialResult
* @param xKey
* @return First derivatives of piecewise polynomial functions at xKey
* When _dim in PiecewisePolynomialResult is greater than 1, i.e., the struct contains multiple piecewise polynomials, an element in the return values corresponds to each piecewise polynomial
*/
public DoubleMatrix1D differentiate(final PiecewisePolynomialResult pp, final double xKey) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.isFalse(pp.getOrder() < 2, "polynomial degree < 1");
final double[][] coefs = pp.getCoefMatrix().getData();
final double[] knots = pp.getKnots().getData();
final int nKnots = pp.getNumberOfIntervals() + 1;
final int nCoefs = pp.getOrder();
final int dim = pp.getDimensions();
double[][] res = new double[dim * (nKnots - 1)][nCoefs - 1];
for (int i = 0; i < dim * (nKnots - 1); ++i) {
Arrays.fill(res[i], 0.);
}
for (int i = 0; i < dim * (nKnots - 1); ++i) {
for (int j = 0; j < nCoefs - 1; ++j) {
res[i][j] = coefs[i][j] * (nCoefs - j - 1);
}
}
PiecewisePolynomialResult ppDiff = new PiecewisePolynomialResult(new DoubleMatrix1D(knots), new DoubleMatrix2D(res), nCoefs - 1, pp.getDimensions());
return evaluate(ppDiff, xKey);
}
/**
* @param pp
* @param xKeys
* @return First derivatives of piecewise polynomial functions at xKeys
* When _dim in PiecewisePolynomialResult is greater than 1, i.e., the struct contains multiple piecewise polynomials, a row vector of return value corresponds to each piecewise polynomial
*/
public DoubleMatrix2D differentiate(final PiecewisePolynomialResult pp, final double[] xKeys) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.isFalse(pp.getOrder() < 2, "polynomial degree < 1");
final double[][] coefs = pp.getCoefMatrix().getData();
final double[] knots = pp.getKnots().getData();
final int nKnots = pp.getNumberOfIntervals() + 1;
final int nCoefs = pp.getOrder();
final int dim = pp.getDimensions();
double[][] res = new double[dim * (nKnots - 1)][nCoefs - 1];
for (int i = 0; i < dim * (nKnots - 1); ++i) {
Arrays.fill(res[i], 0.);
}
for (int i = 0; i < dim * (nKnots - 1); ++i) {
for (int j = 0; j < nCoefs - 1; ++j) {
res[i][j] = coefs[i][j] * (nCoefs - j - 1);
}
}
PiecewisePolynomialResult ppDiff = new PiecewisePolynomialResult(new DoubleMatrix1D(knots), new DoubleMatrix2D(res), nCoefs - 1, pp.getDimensions());
return evaluate(ppDiff, xKeys);
}
/**
* @param pp PiecewisePolynomialResult
* @param xKey
* @return Second derivatives of piecewise polynomial functions at xKey
* When _dim in PiecewisePolynomialResult is greater than 1, i.e., the struct contains multiple piecewise polynomials, an element in the return values corresponds to each piecewise polynomial
*/
public DoubleMatrix1D differentiateTwice(final PiecewisePolynomialResult pp, final double xKey) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.isFalse(pp.getOrder() < 3, "polynomial degree < 2");
final double[][] coefs = pp.getCoefMatrix().getData();
final double[] knots = pp.getKnots().getData();
final int nKnots = pp.getNumberOfIntervals() + 1;
final int nCoefs = pp.getOrder();
final int dim = pp.getDimensions();
double[][] res = new double[dim * (nKnots - 1)][nCoefs - 2];
for (int i = 0; i < dim * (nKnots - 1); ++i) {
Arrays.fill(res[i], 0.);
}
for (int i = 0; i < dim * (nKnots - 1); ++i) {
for (int j = 0; j < nCoefs - 2; ++j) {
res[i][j] = coefs[i][j] * (nCoefs - j - 1) * (nCoefs - j - 2);
}
}
PiecewisePolynomialResult ppDiff = new PiecewisePolynomialResult(new DoubleMatrix1D(knots), new DoubleMatrix2D(res), nCoefs - 1, pp.getDimensions());
return evaluate(ppDiff, xKey);
}
/**
* @param pp
* @param xKeys
* @return Second derivatives of piecewise polynomial functions at xKeys
* When _dim in PiecewisePolynomialResult is greater than 1, i.e., the struct contains multiple piecewise polynomials, a row vector of return value corresponds to each piecewise polynomial
*/
public DoubleMatrix2D differentiateTwice(final PiecewisePolynomialResult pp, final double[] xKeys) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.isFalse(pp.getOrder() < 3, "polynomial degree < 2");
final double[][] coefs = pp.getCoefMatrix().getData();
final double[] knots = pp.getKnots().getData();
final int nKnots = pp.getNumberOfIntervals() + 1;
final int nCoefs = pp.getOrder();
final int dim = pp.getDimensions();
double[][] res = new double[dim * (nKnots - 1)][nCoefs - 2];
for (int i = 0; i < dim * (nKnots - 1); ++i) {
Arrays.fill(res[i], 0.);
}
for (int i = 0; i < dim * (nKnots - 1); ++i) {
for (int j = 0; j < nCoefs - 2; ++j) {
res[i][j] = coefs[i][j] * (nCoefs - j - 1) * (nCoefs - j - 2);
}
}
PiecewisePolynomialResult ppDiff = new PiecewisePolynomialResult(new DoubleMatrix1D(knots), new DoubleMatrix2D(res), nCoefs - 1, pp.getDimensions());
return evaluate(ppDiff, xKeys);
}
/**
* @param pp PiecewisePolynomialResult
* @param initialKey
* @param xKey
* @return Integral of piecewise polynomial between initialKey and xKey
*/
public double integrate(final PiecewisePolynomialResult pp, final double initialKey, final double xKey) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.isFalse(Double.isNaN(initialKey), "initialKey containing NaN");
ArgumentChecker.isFalse(Double.isInfinite(initialKey), "initialKey containing Infinity");
ArgumentChecker.isTrue(pp.getDimensions() == 1, "Dimension should be 1");
final double[] knots = pp.getKnots().getData();
final int nCoefs = pp.getOrder();
final int nKnots = pp.getNumberOfIntervals() + 1;
final double[][] coefMatrix = pp.getCoefMatrix().getData();
double[][] res = new double[nKnots - 1][nCoefs + 1];
for (int i = 0; i < nKnots - 1; ++i) {
Arrays.fill(res[i], 0.);
}
for (int i = 0; i < nKnots - 1; ++i) {
for (int j = 0; j < nCoefs; ++j) {
res[i][j] = coefMatrix[i][j] / (nCoefs - j);
}
}
double[] constTerms = new double[nKnots - 1];
Arrays.fill(constTerms, 0.);
int indicator = 0;
if (initialKey <= knots[1]) {
indicator = 0;
} else {
for (int i = 1; i < nKnots - 1; ++i) {
if (knots[i] < initialKey) {
indicator = i;
}
}
}
double sum = getValue(res[indicator], initialKey, knots[indicator]);
for (int i = indicator; i < nKnots - 2; ++i) {
constTerms[i + 1] = constTerms[i] + getValue(res[i], knots[i + 1], knots[i]) - sum;
sum = 0.;
}
constTerms[indicator] = -getValue(res[indicator], initialKey, knots[indicator]);
for (int i = indicator - 1; i > -1; --i) {
constTerms[i] = constTerms[i + 1] - getValue(res[i], knots[i + 1], knots[i]);
}
for (int i = 0; i < nKnots - 1; ++i) {
res[i][nCoefs] = constTerms[i];
}
final PiecewisePolynomialResult ppInt = new PiecewisePolynomialResult(new DoubleMatrix1D(knots), new DoubleMatrix2D(res), nCoefs + 1, 1);
return evaluate(ppInt, xKey).getData()[0];
}
/**
* @param pp PiecewisePolynomialResult
* @param initialKey
* @param xKeys
* @return Integral of piecewise polynomial between initialKey and xKeys
*/
public DoubleMatrix1D integrate(final PiecewisePolynomialResult pp, final double initialKey, final double[] xKeys) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.notNull(xKeys, "xKeys");
ArgumentChecker.isFalse(Double.isNaN(initialKey), "initialKey containing NaN");
ArgumentChecker.isFalse(Double.isInfinite(initialKey), "initialKey containing Infinity");
ArgumentChecker.isTrue(pp.getDimensions() == 1, "Dimension should be 1");
final double[] knots = pp.getKnots().getData();
final int nCoefs = pp.getOrder();
final int nKnots = pp.getNumberOfIntervals() + 1;
final double[][] coefMatrix = pp.getCoefMatrix().getData();
double[][] res = new double[nKnots - 1][nCoefs + 1];
for (int i = 0; i < nKnots - 1; ++i) {
Arrays.fill(res[i], 0.);
}
for (int i = 0; i < nKnots - 1; ++i) {
for (int j = 0; j < nCoefs; ++j) {
res[i][j] = coefMatrix[i][j] / (nCoefs - j);
}
}
double[] constTerms = new double[nKnots - 1];
Arrays.fill(constTerms, 0.);
int indicator = 0;
if (initialKey <= knots[1]) {
indicator = 0;
} else {
for (int i = 1; i < nKnots - 1; ++i) {
if (knots[i] < initialKey) {
indicator = i;
}
}
}
double sum = getValue(res[indicator], initialKey, knots[indicator]);
for (int i = indicator; i < nKnots - 2; ++i) {
constTerms[i + 1] = constTerms[i] + getValue(res[i], knots[i + 1], knots[i]) - sum;
sum = 0.;
}
constTerms[indicator] = -getValue(res[indicator], initialKey, knots[indicator]);
for (int i = indicator - 1; i > -1; --i) {
constTerms[i] = constTerms[i + 1] - getValue(res[i], knots[i + 1], knots[i]);
}
for (int i = 0; i < nKnots - 1; ++i) {
res[i][nCoefs] = constTerms[i];
}
final PiecewisePolynomialResult ppInt = new PiecewisePolynomialResult(new DoubleMatrix1D(knots), new DoubleMatrix2D(res), nCoefs + 1, 1);
return new DoubleMatrix1D(evaluate(ppInt, xKeys).getData()[0]);
}
/**
* @param coefs {a_n,a_{n-1},...} of f(x) = a_n x^{n} + a_{n-1} x^{n-1} + ....
* @param x
* @param leftknot Knot specifying underlying interpolation function
* @return Value of the underlying interpolation function at the value of x
*/
private double getValue(final double[] coefs, final double x, final double leftknot) {
final int nCoefs = coefs.length;
final double s = x - leftknot;
double res = coefs[0];
for (int i = 1; i < nCoefs; i++) {
res *= s;
res += coefs[i];
}
return res;
}
}