public void positivityClampedTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5.};
final double[] yValues = new double[] {0., 0.1, 1., 1., 20., 5., 0.};
PiecewisePolynomialInterpolator interp = new CubicSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interpPos =
new NonnegativityPreservingCubicSplineInterpolator(interp);
PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
assertEquals(resultPos.getDimensions(), result.getDimensions());
assertEquals(resultPos.getNumberOfIntervals(), result.getNumberOfIntervals());
assertEquals(resultPos.getOrder(), result.getOrder());
final int nPts = 101;
for (int i = 0; i < 101; ++i) {
final double key = 1. + 4. / (nPts - 1) * i;
assertTrue(function.evaluate(resultPos, key).get(0) >= 0.);
}
final int nData = xValues.length;
for (int i = 1; i < nData - 2; ++i) {
final double tau = Math.signum(resultPos.getCoefMatrix().get(i, 3));
assertTrue(
resultPos.getCoefMatrix().get(i, 2) * tau
>= -3. * yValues[i + 1] * tau / (xValues[i + 1] - xValues[i]));
assertTrue(
resultPos.getCoefMatrix().get(i, 2) * tau
<= 3. * yValues[i + 1] * tau / (xValues[i] - xValues[i - 1]));
}
}
public void flipTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5., 6.};
final double[] yValues = new double[] {3., 0.1, 0.01, 0.01, 0.1, 3.};
final double[] xValuesFlip = new double[] {6., 2., 3., 5., 4., 1.};
final double[] yValuesFlip = new double[] {3., 0.1, 0.01, 0.1, 0.01, 3.};
PiecewisePolynomialInterpolator interp = new NaturalSplineInterpolator();
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interpPos =
new NonnegativityPreservingCubicSplineInterpolator(interp);
PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
PiecewisePolynomialResult resultPosFlip = interpPos.interpolate(xValuesFlip, yValuesFlip);
assertEquals(resultPos.getDimensions(), resultPosFlip.getDimensions());
assertEquals(resultPos.getNumberOfIntervals(), resultPosFlip.getNumberOfIntervals());
assertEquals(resultPos.getOrder(), resultPosFlip.getOrder());
final int nPts = 101;
for (int i = 0; i < 101; ++i) {
final double key = 1. + 5. / (nPts - 1) * i;
assertTrue(function.evaluate(resultPos, key).get(0) >= 0.);
}
final int nData = xValues.length;
for (int i = 0; i < nData - 1; ++i) {
for (int k = 0; k < 4; ++k)
assertEquals(resultPos.getCoefMatrix().get(i, k), resultPosFlip.getCoefMatrix().get(i, k));
}
}
/** PiecewiseCubicHermiteSplineInterpolator is not modified for positive data */
public void noModificationTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5.};
final double[][] yValues = new double[][] {{0.1, 1., 1., 20., 5.}, {1., 2., 3., 0., 0.}};
PiecewisePolynomialInterpolator interp = new PiecewiseCubicHermiteSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
PiecewisePolynomialInterpolator interpPos =
new NonnegativityPreservingCubicSplineInterpolator(interp);
PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
assertEquals(resultPos.getDimensions(), result.getDimensions());
assertEquals(resultPos.getNumberOfIntervals(), result.getNumberOfIntervals());
assertEquals(resultPos.getOrder(), result.getOrder());
for (int i = 1; i < xValues.length - 1; ++i) {
for (int j = 0; j < 4; ++j) {
final double ref =
result.getCoefMatrix().get(i, j) == 0.
? 1.
: Math.abs(result.getCoefMatrix().get(i, j));
assertEquals(
resultPos.getCoefMatrix().get(i, j), result.getCoefMatrix().get(i, j), ref * EPS);
}
}
}
public void positivityEndIntervalsTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5., 6.};
final double[][] yValues =
new double[][] {{0.01, 0.01, 0.01, 10., 20., 1.}, {0.01, 0.01, 10., 10., 0.01, 0.01}};
PiecewisePolynomialInterpolator interp = new NaturalSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interpPos =
new NonnegativityPreservingCubicSplineInterpolator(interp);
PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
assertEquals(resultPos.getDimensions(), result.getDimensions());
assertEquals(resultPos.getNumberOfIntervals(), result.getNumberOfIntervals());
assertEquals(resultPos.getOrder(), result.getOrder());
final int nPts = 101;
for (int i = 0; i < 101; ++i) {
final double key = 1. + 5. / (nPts - 1) * i;
assertTrue(function.evaluate(resultPos, key).get(0) >= 0.);
}
int dim = yValues.length;
int nData = xValues.length;
for (int j = 0; j < dim; ++j) {
for (int i = 1; i < nData - 2; ++i) {
DoubleMatrix coefMatrix = resultPos.getCoefMatrix();
double tau = Math.signum(coefMatrix.get(dim * i + j, 3));
assertTrue(
coefMatrix.get(dim * i + j, 2) * tau
>= -3. * yValues[j][i] * tau / (xValues[i + 1] - xValues[i]));
assertTrue(
coefMatrix.get(dim * i + j, 2) * tau
<= 3. * yValues[j][i] * tau / (xValues[i] - xValues[i - 1]));
}
}
}
@Override
public PiecewisePolynomialResult interpolate(final double[] xValues, final double[] yValues) {
ArgumentChecker.notNull(xValues, "xValues");
ArgumentChecker.notNull(yValues, "yValues");
ArgumentChecker.isTrue(
xValues.length == yValues.length | xValues.length + 2 == yValues.length,
"(xValues length = yValues length) or (xValues length + 2 = yValues length)");
ArgumentChecker.isTrue(xValues.length > 2, "Data points should be more than 2");
final int nDataPts = xValues.length;
final int yValuesLen = yValues.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) {
ArgumentChecker.isFalse(Double.isNaN(yValues[i]), "yValues containing NaN");
ArgumentChecker.isFalse(Double.isInfinite(yValues[i]), "yValues containing Infinity");
}
for (int i = 0; i < nDataPts - 1; ++i) {
for (int j = i + 1; j < nDataPts; ++j) {
ArgumentChecker.isFalse(xValues[i] == xValues[j], "xValues should be distinct");
}
}
double[] xValuesSrt = Arrays.copyOf(xValues, nDataPts);
double[] yValuesSrt = new double[nDataPts];
if (nDataPts == yValuesLen) {
yValuesSrt = Arrays.copyOf(yValues, nDataPts);
} else {
yValuesSrt = Arrays.copyOfRange(yValues, 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, yValues);
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];
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 i = 0; i < nDataPts - 2; ++i) {
if (first[i + 1] > 0.) {
if (intervalsA[i + 1][1] + Math.abs(intervalsA[i + 1][1]) * ERROR
< intervalsB[i][0] - Math.abs(intervalsB[i][0]) * ERROR
| intervalsA[i + 1][0] - Math.abs(intervalsA[i + 1][0]) * ERROR
> intervalsB[i][1] + Math.abs(intervalsB[i][1]) * ERROR) {
++k;
first[i + 1] = firstDerivativesRecalculator(intervals, slopes, aValues, bValues, i + 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);
final double[][] coefs = _solver.solve(yValuesSrt, intervals, slopes, first, second);
for (int i = 0; i < nDataPts - 1; ++i) {
for (int j = 0; j < 6; ++j) {
ArgumentChecker.isFalse(Double.isNaN(coefs[i][j]), "Too large input");
ArgumentChecker.isFalse(Double.isInfinite(coefs[i][j]), "Too large input");
}
}
return new PiecewisePolynomialResult(
new DoubleMatrix1D(xValuesSrt), new DoubleMatrix2D(coefs), 6, 1);
}
@Override
public PiecewisePolynomialResultsWithSensitivity interpolateWithSensitivity(
final double[] xValues, final double[] yValues) {
ArgumentChecker.notNull(xValues, "xValues");
ArgumentChecker.notNull(yValues, "yValues");
ArgumentChecker.isTrue(
xValues.length == yValues.length | xValues.length + 2 == yValues.length,
"(xValues length = yValues length) or (xValues length + 2 = yValues length)");
ArgumentChecker.isTrue(xValues.length > 2, "Data points should be more than 2");
final int nDataPts = xValues.length;
final int yValuesLen = yValues.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) {
ArgumentChecker.isFalse(Double.isNaN(yValues[i]), "yValues containing NaN");
ArgumentChecker.isFalse(Double.isInfinite(yValues[i]), "yValues containing Infinity");
}
for (int i = 0; i < nDataPts - 1; ++i) {
for (int j = i + 1; j < nDataPts; ++j) {
ArgumentChecker.isFalse(xValues[i] == xValues[j], "xValues should be distinct");
}
}
double[] yValuesSrt = new double[nDataPts];
if (nDataPts == yValuesLen) {
yValuesSrt = Arrays.copyOf(yValues, nDataPts);
} else {
yValuesSrt = Arrays.copyOfRange(yValues, 1, nDataPts + 1);
}
final double[] intervals = _solver.intervalsCalculator(xValues);
final double[] slopes = _solver.slopesCalculator(yValuesSrt, intervals);
double[][] slopesSensitivity = _solver.slopeSensitivityCalculator(intervals);
final DoubleMatrix1D[] firstWithSensitivity = new DoubleMatrix1D[nDataPts + 1];
final DoubleMatrix1D[] secondWithSensitivity = new DoubleMatrix1D[nDataPts + 1];
final PiecewisePolynomialResult result = _method.interpolate(xValues, yValues);
ArgumentChecker.isTrue(result.getOrder() >= 3, "Primary interpolant should be degree >= 2");
final double[] initialFirst = _function.differentiate(result, xValues).getData()[0];
final double[] initialSecond = _function.differentiateTwice(result, xValues).getData()[0];
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 i = 0; i < nDataPts - 2; ++i) {
if (first[i + 1] > 0.) {
if (intervalsA[i + 1][1] + Math.abs(intervalsA[i + 1][1]) * ERROR
< intervalsB[i][0] - Math.abs(intervalsB[i][0]) * ERROR
| intervalsA[i + 1][0] - Math.abs(intervalsA[i + 1][0]) * ERROR
> intervalsB[i][1] + Math.abs(intervalsB[i][1]) * ERROR) {
++k;
first[i + 1] = firstDerivativesRecalculator(intervals, slopes, aValues, bValues, i + 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);
firstWithSensitivity[0] = new DoubleMatrix1D(first);
secondWithSensitivity[0] = new DoubleMatrix1D(second);
/*
* Centered finite difference method is used for computing node sensitivity
*/
int nExtra = (nDataPts == yValuesLen) ? 0 : 1;
final double[] yValuesUp = Arrays.copyOf(yValues, nDataPts + 2 * nExtra);
final double[] yValuesDw = Arrays.copyOf(yValues, nDataPts + 2 * nExtra);
final double[][] tmpFirst = new double[nDataPts][nDataPts];
final double[][] tmpSecond = new double[nDataPts][nDataPts];
for (int l = nExtra; l < nDataPts + nExtra; ++l) {
final double den = Math.abs(yValues[l]) < SMALL ? EPS : yValues[l] * EPS;
yValuesUp[l] = Math.abs(yValues[l]) < SMALL ? EPS : yValues[l] * (1. + EPS);
yValuesDw[l] = Math.abs(yValues[l]) < SMALL ? -EPS : yValues[l] * (1. - EPS);
final double[] yValuesSrtUp = Arrays.copyOfRange(yValuesUp, nExtra, nDataPts + nExtra);
final double[] yValuesSrtDw = Arrays.copyOfRange(yValuesDw, nExtra, nDataPts + nExtra);
final DoubleMatrix1D[] yValuesUpDw =
new DoubleMatrix1D[] {new DoubleMatrix1D(yValuesUp), new DoubleMatrix1D(yValuesDw)};
final DoubleMatrix1D[] yValuesSrtUpDw =
new DoubleMatrix1D[] {new DoubleMatrix1D(yValuesSrtUp), new DoubleMatrix1D(yValuesSrtDw)};
final DoubleMatrix1D[] firstSecondUpDw = new DoubleMatrix1D[4];
for (int ii = 0; ii < 2; ++ii) {
final double[] slopesUpDw =
_solver.slopesCalculator(yValuesSrtUpDw[ii].getData(), intervals);
final PiecewisePolynomialResult resultUpDw =
_method.interpolate(xValues, yValuesUpDw[ii].getData());
final double[] initialFirstUpDw = _function.differentiate(resultUpDw, xValues).getData()[0];
final double[] initialSecondUpDw =
_function.differentiateTwice(resultUpDw, xValues).getData()[0];
double[] firstUpDw =
firstDerivativeCalculator(
yValuesSrtUpDw[ii].getData(), intervals, slopesUpDw, initialFirstUpDw);
boolean modFirstUpDw = false;
double[] aValuesUpDw = aValuesCalculator(slopesUpDw, firstUpDw);
double[] bValuesUpDw = bValuesCalculator(slopesUpDw, firstUpDw);
double[][] intervalsAUpDw = getIntervalsA(intervals, slopesUpDw, firstUpDw, bValuesUpDw);
double[][] intervalsBUpDw = getIntervalsB(intervals, slopesUpDw, firstUpDw, aValuesUpDw);
while (modFirstUpDw == false) {
k = 0;
for (int i = 0; i < nDataPts - 2; ++i) {
if (firstUpDw[i + 1] > 0.) {
if (intervalsAUpDw[i + 1][1] + Math.abs(intervalsAUpDw[i + 1][1]) * ERROR
< intervalsBUpDw[i][0] - Math.abs(intervalsBUpDw[i][0]) * ERROR
| intervalsAUpDw[i + 1][0] - Math.abs(intervalsAUpDw[i + 1][0]) * ERROR
> intervalsBUpDw[i][1] + Math.abs(intervalsBUpDw[i][1]) * ERROR) {
++k;
firstUpDw[i + 1] =
firstDerivativesRecalculator(
intervals, slopesUpDw, aValuesUpDw, bValuesUpDw, i + 1);
}
}
}
if (k == 0) {
modFirstUpDw = true;
}
aValuesUpDw = aValuesCalculator(slopesUpDw, firstUpDw);
bValuesUpDw = bValuesCalculator(slopesUpDw, firstUpDw);
intervalsAUpDw = getIntervalsA(intervals, slopesUpDw, firstUpDw, bValuesUpDw);
intervalsBUpDw = getIntervalsB(intervals, slopesUpDw, firstUpDw, aValuesUpDw);
}
final double[] secondUpDw =
secondDerivativeCalculator(initialSecondUpDw, intervalsAUpDw, intervalsBUpDw);
firstSecondUpDw[ii] = new DoubleMatrix1D(firstUpDw);
firstSecondUpDw[2 + ii] = new DoubleMatrix1D(secondUpDw);
}
for (int j = 0; j < nDataPts; ++j) {
tmpFirst[j][l - nExtra] =
0.5 * (firstSecondUpDw[0].getData()[j] - firstSecondUpDw[1].getData()[j]) / den;
tmpSecond[j][l - nExtra] =
0.5 * (firstSecondUpDw[2].getData()[j] - firstSecondUpDw[3].getData()[j]) / den;
}
yValuesUp[l] = yValues[l];
yValuesDw[l] = yValues[l];
}
for (int i = 0; i < nDataPts; ++i) {
firstWithSensitivity[i + 1] = new DoubleMatrix1D(tmpFirst[i]);
secondWithSensitivity[i + 1] = new DoubleMatrix1D(tmpSecond[i]);
}
final DoubleMatrix2D[] resMatrix =
_solver.solveWithSensitivity(
yValuesSrt,
intervals,
slopes,
slopesSensitivity,
firstWithSensitivity,
secondWithSensitivity);
for (int l = 0; l < nDataPts; ++l) {
DoubleMatrix2D m = resMatrix[l];
final int rows = m.getNumberOfRows();
final int cols = m.getNumberOfColumns();
for (int i = 0; i < rows; ++i) {
for (int j = 0; j < cols; ++j) {
ArgumentChecker.isTrue(
Doubles.isFinite(m.getEntry(i, j)), "Matrix contains a NaN or infinite");
}
}
}
final DoubleMatrix2D coefMatrix = resMatrix[0];
final DoubleMatrix2D[] coefSenseMatrix = new DoubleMatrix2D[nDataPts - 1];
System.arraycopy(resMatrix, 1, coefSenseMatrix, 0, nDataPts - 1);
final int nCoefs = coefMatrix.getNumberOfColumns();
return new PiecewisePolynomialResultsWithSensitivity(
new DoubleMatrix1D(xValues), coefMatrix, nCoefs, 1, coefSenseMatrix);
}