/**
* @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), DoubleMatrix2D.noCopy(res), nCoefs - 1, pp.getDimensions());
return evaluate(ppDiff, xKeys);
}
/**
* @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), DoubleMatrix2D.noCopy(res), nCoefs + 1, 1);
return new DoubleMatrix1D(evaluate(ppInt, xKeys).getData()[0]);
}
/**
* @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, false).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] = DoubleMatrix2D.noCopy(res[i]);
}
return resMat;
}
@Override
public PiecewisePolynomialResult interpolate(
final double[] xValues, final double[][] yValuesMatrix) {
ArgumentChecker.notNull(xValues, "xValues");
ArgumentChecker.notNull(yValuesMatrix, "yValuesMatrix");
ArgumentChecker.isTrue(
xValues.length == yValuesMatrix[0].length | xValues.length + 2 == yValuesMatrix[0].length,
"(xValues length = yValuesMatrix's row vector length) or (xValues length + 2 = yValuesMatrix's row vector length)");
ArgumentChecker.isTrue(xValues.length > 2, "Data points should be more than 2");
final int nDataPts = xValues.length;
final int yValuesLen = yValuesMatrix[0].length;
final int dim = yValuesMatrix.length;
for (int i = 0; i < nDataPts; ++i) {
ArgumentChecker.isFalse(Double.isNaN(xValues[i]), "xValues containing NaN");
ArgumentChecker.isFalse(Double.isInfinite(xValues[i]), "xValues containing Infinity");
}
for (int i = 0; i < yValuesLen; ++i) {
for (int j = 0; j < dim; ++j) {
ArgumentChecker.isFalse(Double.isNaN(yValuesMatrix[j][i]), "yValuesMatrix containing NaN");
ArgumentChecker.isFalse(
Double.isInfinite(yValuesMatrix[j][i]), "yValuesMatrix containing Infinity");
}
}
for (int i = 0; i < nDataPts; ++i) {
for (int j = i + 1; j < nDataPts; ++j) {
ArgumentChecker.isFalse(xValues[i] == xValues[j], "xValues should be distinct");
}
}
double[] xValuesSrt = new double[nDataPts];
DoubleMatrix2D[] coefMatrix = new DoubleMatrix2D[dim];
for (int i = 0; i < dim; ++i) {
xValuesSrt = Arrays.copyOf(xValues, nDataPts);
double[] yValuesSrt = new double[nDataPts];
if (nDataPts == yValuesLen) {
yValuesSrt = Arrays.copyOf(yValuesMatrix[i], nDataPts);
} else {
yValuesSrt = Arrays.copyOfRange(yValuesMatrix[i], 1, nDataPts + 1);
}
ParallelArrayBinarySort.parallelBinarySort(xValuesSrt, yValuesSrt);
final double[] intervals = _solver.intervalsCalculator(xValuesSrt);
final double[] slopes = _solver.slopesCalculator(yValuesSrt, intervals);
final PiecewisePolynomialResult result = _method.interpolate(xValues, yValuesMatrix[i]);
ArgumentChecker.isTrue(result.getOrder() >= 3, "Primary interpolant should be degree >= 2");
final double[] initialFirst = _function.differentiate(result, xValuesSrt).getData()[0];
final double[] initialSecond = _function.differentiateTwice(result, xValuesSrt).getData()[0];
final double[] first = firstDerivativeCalculator(yValuesSrt, intervals, slopes, initialFirst);
boolean modFirst = false;
int k;
double[] aValues = aValuesCalculator(slopes, first);
double[] bValues = bValuesCalculator(slopes, first);
double[][] intervalsA = getIntervalsA(intervals, slopes, first, bValues);
double[][] intervalsB = getIntervalsB(intervals, slopes, first, aValues);
while (modFirst == false) {
k = 0;
for (int j = 0; j < nDataPts - 2; ++j) {
if (first[j + 1] > 0.) {
if (intervalsA[j + 1][1] + Math.abs(intervalsA[j + 1][1]) * ERROR
< intervalsB[j][0] - Math.abs(intervalsB[j][0]) * ERROR
| intervalsA[j + 1][0] - Math.abs(intervalsA[j + 1][0]) * ERROR
> intervalsB[j][1] + Math.abs(intervalsB[j][1]) * ERROR) {
++k;
first[j + 1] =
firstDerivativesRecalculator(intervals, slopes, aValues, bValues, j + 1);
}
}
}
if (k == 0) {
modFirst = true;
}
aValues = aValuesCalculator(slopes, first);
bValues = bValuesCalculator(slopes, first);
intervalsA = getIntervalsA(intervals, slopes, first, bValues);
intervalsB = getIntervalsB(intervals, slopes, first, aValues);
}
final double[] second = secondDerivativeCalculator(initialSecond, intervalsA, intervalsB);
coefMatrix[i] =
new DoubleMatrix2D(_solver.solve(yValuesSrt, intervals, slopes, first, second));
}
final int nIntervals = coefMatrix[0].getNumberOfRows();
final int nCoefs = coefMatrix[0].getNumberOfColumns();
double[][] resMatrix = new double[dim * nIntervals][nCoefs];
for (int i = 0; i < nIntervals; ++i) {
for (int j = 0; j < dim; ++j) {
resMatrix[dim * i + j] = coefMatrix[j].getRowVector(i, false).getData();
}
}
for (int i = 0; i < (nIntervals * dim); ++i) {
for (int j = 0; j < nCoefs; ++j) {
ArgumentChecker.isFalse(Double.isNaN(resMatrix[i][j]), "Too large input");
ArgumentChecker.isFalse(Double.isInfinite(resMatrix[i][j]), "Too large input");
}
}
return new PiecewisePolynomialResult(
new DoubleMatrix1D(xValuesSrt, false), DoubleMatrix2D.noCopy(resMatrix), nCoefs, dim);
}
