public virtual void test_lastNode()
{
BoundCurveInterpolator bci = NATURAL_CUBLIC_SPLINE_INTERPOLATOR.bind(X_DATA, Y_DATA, FLAT_EXTRAPOLATOR, FLAT_EXTRAPOLATOR);
assertEquals(bci.interpolate(5.0), 2.0, TOL);
assertEquals(bci.parameterSensitivity(5.0).get(X_DATA.size() - 2), 0d, TOL);
assertEquals(bci.parameterSensitivity(5.0).get(X_DATA.size() - 1), 1d, TOL);
}
//-------------------------------------------------------------------------
public virtual void test_firstNode()
{
BoundCurveInterpolator bci = INTERPOLATOR.bind(X_DATA, Y_DATA, FLAT_EXTRAPOLATOR, FLAT_EXTRAPOLATOR);
assertEquals(bci.interpolate(0.0), 3.0, TOL);
assertEquals(bci.parameterSensitivity(0.0).get(0), 1d, TOL);
assertEquals(bci.parameterSensitivity(0.0).get(1), 0d, TOL);
}
public virtual void test_lastNode()
{
BoundCurveInterpolator bci = LINEAR_INTERPOLATOR.bind(X_DATA, Y_DATA, FLAT_EXTRAPOLATOR, FLAT_EXTRAPOLATOR);
assertEquals(bci.interpolate(5.0), 2.0, TOL);
assertEquals(bci.firstDerivative(5.0), bci.firstDerivative(4.99), TOL);
assertEquals(bci.parameterSensitivity(5.0).get(X_DATA.size() - 2), 0d, TOL);
assertEquals(bci.parameterSensitivity(5.0).get(X_DATA.size() - 1), 1d, TOL);
}
public virtual void test_exceptionThrown()
{
BoundCurveInterpolator bci = CurveInterpolators.LINEAR.bind(X_DATA, Y_DATA, EXCEPTION_EXTRAPOLATOR, EXCEPTION_EXTRAPOLATOR);
assertThrows(() => bci.interpolate(-1d), typeof(System.NotSupportedException));
assertThrows(() => bci.firstDerivative(-1d), typeof(System.NotSupportedException));
assertThrows(() => bci.parameterSensitivity(-1d), typeof(System.NotSupportedException));
assertThrows(() => bci.interpolate(10d), typeof(System.NotSupportedException));
assertThrows(() => bci.firstDerivative(10d), typeof(System.NotSupportedException));
assertThrows(() => bci.parameterSensitivity(10d), typeof(System.NotSupportedException));
}
public virtual void test_parameterSensitivity()
{
BoundCurveInterpolator bci = STEP_UPPER_INTERPOLATOR.bind(X_DATA, Y_DATA, FLAT_EXTRAPOLATOR, FLAT_EXTRAPOLATOR);
for (int i = 0; i < X_DATA.size(); i++)
{
assertTrue(DoubleArrayMath.fuzzyEquals(bci.parameterSensitivity(X_DATA.get(i)).toArray(), DoubleArray.filled(SIZE).with(i, 1d).toArray(), TOL));
}
for (int i = 0; i < X_TEST.size(); i++)
{
assertTrue(DoubleArrayMath.fuzzyEquals(bci.parameterSensitivity(X_TEST.get(i)).toArray(), DoubleArray.filled(SIZE).with(INDEX_TEST.get(i), 1d).toArray(), TOL));
}
}
public virtual void limitingTest()
{
BoundCurveInterpolator bci = LINEAR.bind(X_DATA, Y_DATA, DISCOUNT_FACTOR_QUADRATIC_LEFT_ZERO_RATE, PRODUCT_LINEAR);
double small = 1.0e-8;
assertEquals(bci.interpolate(small), bci.interpolate(10d * small), Y_DATA.get(0) * 10d * small);
double derivative = bci.firstDerivative(small);
double derivativeExp = (bci.interpolate(small + 0.5 * small) - bci.interpolate(small - 0.5 * small)) / small;
assertEquals(derivative, derivativeExp, Y_DATA.get(0) * small);
DoubleArray sensi = bci.parameterSensitivity(small);
DoubleArray sensiS = bci.parameterSensitivity(small * 5d);
assertTrue(DoubleArrayMath.fuzzyEquals(sensi.toArray(), sensiS.toArray(), Y_DATA.get(0) * 10d * small));
}
internal Bound(DoubleArray xValues, DoubleArray yValues, BoundCurveInterpolator interpolator)
{
this.nodeCount = xValues.size();
this.firstXValue = xValues.get(0);
this.firstYValue = yValues.get(0);
this.lastXValue = xValues.get(nodeCount - 1);
this.lastYValue = yValues.get(nodeCount - 1);
this.eps = EPS * (lastXValue - firstXValue);
// left
this.leftGradient = (interpolator.interpolate(firstXValue + eps) - firstYValue) / eps;
this.leftSens = interpolator.parameterSensitivity(firstXValue + eps);
// right
this.rightGradient = (lastYValue - interpolator.interpolate(lastXValue - eps)) / eps;
this.rightSens = interpolator.parameterSensitivity(lastXValue - eps);
}
public virtual void sampleDataTest()
{
DoubleArray xValues = DoubleArray.of(0.5, 1.0, 2.5, 4.2, 10.0, 15.0, 30.0);
DoubleArray yValues = DoubleArray.of(4.0, 2.0, 1.0, 5.0, 10.0, 3.5, -2.0);
int nData = yValues.size();
DoubleArray pValues = DoubleArray.of(nData, i => xValues.get(i) * yValues.get(i));
System.Func <double, bool> domain = (double?x) =>
{
return(x.Value >= xValues.get(0) && x.Value <= xValues.get(nData - 1));
};
DoubleArray keys = DoubleArray.of(xValues.get(0), 0.7, 1.2, 7.8, 10.0, 17.52, 25.0, xValues.get(nData - 1));
int nKeys = keys.size();
BoundCurveInterpolator bound = INTERP.bind(xValues, yValues);
PiecewisePolynomialResultsWithSensitivity ppRes = BASE_INTERP.interpolateWithSensitivity(xValues.toArray(), pValues.toArray());
System.Func <double, double> funcDeriv = x => bound.interpolate(x.Value);
for (int i = 0; i < nKeys; ++i)
{
// interpolate
assertEquals(bound.interpolate(keys.get(i)), FUNCTION.evaluate(ppRes, keys.get(i)).get(0) / keys.get(i), TOL);
// first derivative
double firstExp = DIFF_CALC.differentiate(funcDeriv, domain).apply(keys.get(i));
assertEquals(bound.firstDerivative(keys.get(i)), firstExp, EPS);
// parameter sensitivity
int index = i;
System.Func <DoubleArray, double> funcSensi = x => INTERP.bind(xValues, x).interpolate(keys.get(index));
DoubleArray sensExp = SENS_CALC.differentiate(funcSensi).apply(yValues);
assertTrue(DoubleArrayMath.fuzzyEquals(bound.parameterSensitivity(keys.get(i)).toArray(), sensExp.toArray(), EPS));
}
}
public virtual void sameIntervalsTest()
{
DoubleArray xValues = DoubleArray.of(-1.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0);
DoubleArray[] yValues = new DoubleArray[] { DoubleArray.of(1.001, 1.001, 1.001, 1.001, 1.001, 1.001, 1.001, 1.001, 1.001, 1.001), DoubleArray.of(11.0, 11.0, 8.0, 5.0, 1.001, 1.001, 5.0, 8.0, 11.0, 11.0), DoubleArray.of(1.001, 1.001, 5.0, 8.0, 9.0, 9.0, 11.0, 12.0, 18.0, 18.0) };
int nKeys = 100;
double[] keys = new double[nKeys];
double interval = 0.061;
for (int i = 0; i < nKeys; ++i)
{
keys[i] = xValues.get(0) + interval * i;
}
CurveExtrapolator extrap = InterpolatorCurveExtrapolator.INSTANCE;
int yDim = yValues.Length;
for (int k = 0; k < yDim; ++k)
{
BoundCurveInterpolator boundInterp = CurveInterpolators.SQUARE_LINEAR.bind(xValues, yValues[k], extrap, extrap);
AbstractBoundCurveInterpolator baseInterp = (AbstractBoundCurveInterpolator)boundInterp;
for (int j = 0; j < nKeys; ++j)
{
// value
assertEquals(boundInterp.interpolate(keys[j]), baseInterp.doInterpolate(keys[j]), TOL);
// derivative
assertEquals(boundInterp.firstDerivative(keys[j]), baseInterp.doFirstDerivative(keys[j]), TOL);
// sensitivity
assertTrue(boundInterp.parameterSensitivity(keys[j]).equalWithTolerance(baseInterp.doParameterSensitivity(keys[j]), TOL));
}
}
}
public virtual void negativeDataTest()
{
DoubleArray xValues = DoubleArray.of(-34.5, -27.0, -22.5, -14.2, -10.0, -5.0, -0.3);
DoubleArray yValues = DoubleArray.of(4.0, 2.0, 1.0, 5.0, 10.0, 3.5, -2.0);
int nData = yValues.size();
DoubleArray pValues = DoubleArray.of(nData, i => xValues.get(i) * yValues.get(i));
System.Func <double, bool> domain = (double?x) =>
{
return(x.Value >= xValues.get(0) && x.Value <= xValues.get(nData - 1));
};
DoubleArray keys = DoubleArray.of(xValues.get(0), -27.7, -21.2, -17.8, -9.99, -1.52, -0.35, xValues.get(nData - 1));
int nKeys = keys.size();
BoundCurveInterpolator bound = INTERP.bind(xValues, yValues);
BoundCurveInterpolator boundBase = BASE_INTERP.bind(xValues, pValues);
System.Func <double, double> funcDeriv = x => bound.interpolate(x.Value);
for (int i = 0; i < nKeys; ++i)
{
// interpolate
assertEquals(bound.interpolate(keys.get(i)), boundBase.interpolate(keys.get(i)) / keys.get(i), TOL);
// first derivative
double firstExp = DIFF_CALC.differentiate(funcDeriv, domain).apply(keys.get(i));
assertEquals(bound.firstDerivative(keys.get(i)), firstExp, EPS);
// parameter sensitivity
int index = i;
System.Func <DoubleArray, double> funcSensi = x => INTERP.bind(xValues, x).interpolate(keys.get(index));
DoubleArray sensExp = SENS_CALC.differentiate(funcSensi).apply(yValues);
assertTrue(DoubleArrayMath.fuzzyEquals(bound.parameterSensitivity(keys.get(i)).toArray(), sensExp.toArray(), EPS));
}
}
public virtual void differentIntervalsTest()
{
DoubleArray xValues = DoubleArray.of(1.0328724558967068, 1.2692381049172323, 2.8611430465380905, 4.296118458251132, 7.011992052151352, 7.293354144919639, 8.557971037612713, 8.77306861567384, 10.572470371584489, 12.96945799507056);
DoubleArray[] yValues = new DoubleArray[] { DoubleArray.of(1.1593075755231343, 2.794957672828094, 4.674733634811079, 5.517689918508841, 6.138447304104604, 6.264375977142906, 6.581666492568779, 8.378685055774037, 10.005246918325483, 10.468304334744241), DoubleArray.of(9.95780079114617, 8.733013195721913, 8.192165283188197, 6.539369493529048, 6.3868683960757515, 4.700471352238411, 4.555354921077598, 3.780781869340659, 2.299369456202763, 0.9182441378327986) };
int nKeys = 100;
double[] keys = new double[nKeys];
double interval = 0.061;
for (int i = 0; i < nKeys; ++i)
{
keys[i] = xValues.get(0) + interval * i;
}
CurveExtrapolator extrap = InterpolatorCurveExtrapolator.INSTANCE;
int yDim = yValues.Length;
for (int k = 0; k < yDim; ++k)
{
BoundCurveInterpolator boundInterp = CurveInterpolators.SQUARE_LINEAR.bind(xValues, yValues[k], extrap, extrap);
AbstractBoundCurveInterpolator baseInterp = (AbstractBoundCurveInterpolator)boundInterp;
for (int j = 0; j < nKeys; ++j)
{
// value
assertEquals(boundInterp.interpolate(keys[j]), baseInterp.doInterpolate(keys[j]), TOL);
// derivative
assertEquals(boundInterp.firstDerivative(keys[j]), baseInterp.doFirstDerivative(keys[j]), TOL);
// sensitivity
assertTrue(boundInterp.parameterSensitivity(keys[j]).equalWithTolerance(baseInterp.doParameterSensitivity(keys[j]), TOL));
}
}
}
public virtual void noRightTest()
{
BoundCurveInterpolator bci = LINEAR.bind(X_DATA, Y_DATA, DISCOUNT_FACTOR_QUADRATIC_LEFT_ZERO_RATE, DISCOUNT_FACTOR_QUADRATIC_LEFT_ZERO_RATE);
assertThrowsIllegalArg(() => bci.interpolate(10d));
assertThrowsIllegalArg(() => bci.firstDerivative(10d));
assertThrowsIllegalArg(() => bci.parameterSensitivity(10d));
}
internal Bound(DoubleArray xValues, DoubleArray yValues, BoundCurveInterpolator interpolator)
{
this.nodeCount = xValues.size();
this.firstXValue = xValues.get(0);
this.firstYValue = yValues.get(0);
this.lastXValue = xValues.get(nodeCount - 1);
this.lastYValue = yValues.get(nodeCount - 1);
this.eps = EPS * (lastXValue - firstXValue);
// left
this.firstGradient = interpolator.firstDerivative(firstXValue);
this.firstSens = Suppliers.memoize(() => interpolator.parameterSensitivity(firstXValue));
this.firstGradSens = Suppliers.memoize(() => interpolator.parameterSensitivity(firstXValue + eps).minus(firstSens.get()).dividedBy(eps));
// right
this.lastGradient = interpolator.firstDerivative(lastXValue);
this.lastSens = Suppliers.memoize(() => interpolator.parameterSensitivity(lastXValue));
this.lastGradSens = Suppliers.memoize(() => lastSens.get().minus(interpolator.parameterSensitivity(lastXValue - eps)).dividedBy(eps));
}
public virtual void test_noRight()
{
BoundCurveInterpolator bci = CurveInterpolators.LINEAR.bind(X_DATA, Y_DATA, QL_EXTRAPOLATOR, QL_EXTRAPOLATOR);
assertThrowsIllegalArg(() => bci.interpolate(10d));
assertThrowsIllegalArg(() => bci.firstDerivative(10d));
assertThrowsIllegalArg(() => bci.parameterSensitivity(10d));
}
//-------------------------------------------------------------------------
public virtual void noLeftTest()
{
BoundCurveInterpolator bci = PRODUCT_LINEAR.bind(X_VALUES, Y_VALUES, DISCOUNT_FACTOR_LINEAR_RIGHT_ZERO_RATE, DISCOUNT_FACTOR_LINEAR_RIGHT_ZERO_RATE);
assertThrowsIllegalArg(() => bci.interpolate(0.2d));
assertThrowsIllegalArg(() => bci.firstDerivative(0.3d));
assertThrowsIllegalArg(() => bci.parameterSensitivity(0.6d));
}
internal Bound(DoubleArray xValues, DoubleArray yValues, BoundCurveInterpolator interpolator)
{
this.nodeCount = xValues.size();
this.firstXValue = xValues.get(0);
this.firstYValue = yValues.get(0);
this.firstYValueLog = Math.Log(firstYValue);
this.lastXValue = xValues.get(nodeCount - 1);
this.lastYValue = yValues.get(nodeCount - 1);
this.lastYValueLog = Math.Log(lastYValue);
this.eps = EPS * (lastXValue - firstXValue);
// left
this.leftGradient = interpolator.firstDerivative(firstXValue) / interpolator.interpolate(firstXValue);
this.leftResValueInterpolator = interpolator.interpolate(firstXValue + eps);
this.leftSens = interpolator.parameterSensitivity(firstXValue + eps);
// right
this.rightGradient = interpolator.firstDerivative(lastXValue) / interpolator.interpolate(lastXValue);
this.rightResValueInterpolator = interpolator.interpolate(lastXValue - eps);
this.rightSens = interpolator.parameterSensitivity(lastXValue - eps);
}
public virtual void smallKeyTest()
{
DoubleArray xValues = DoubleArray.of(1e-13, 3e-8, 2e-5);
DoubleArray yValues = DoubleArray.of(1.0, 13.2, 1.5);
double keyDw = 1.0e-12;
BoundCurveInterpolator bound = INTERP.bind(xValues, yValues);
assertThrowsIllegalArg(() => bound.interpolate(keyDw));
assertThrowsIllegalArg(() => bound.firstDerivative(keyDw));
assertThrowsIllegalArg(() => bound.parameterSensitivity(keyDw));
}
//-------------------------------------------------------------------------
public virtual void test_sensitivities()
{
BoundCurveInterpolator bci = DQ_INTERPOLATOR.bind(X_SENS, Y_SENS, FLAT_EXTRAPOLATOR, FLAT_EXTRAPOLATOR);
double lastXValue = X_SENS.get(X_SENS.size() - 1);
for (int i = 0; i < 100; i++)
{
double t = lastXValue * RANDOM.NextDouble();
DoubleArray sensitivity = bci.parameterSensitivity(t);
assertEquals(sensitivity.sum(), 1d, TOL);
}
}
public virtual void test_derivative_sensitivity()
{
BoundCurveInterpolator bind = CurveInterpolators.DOUBLE_QUADRATIC.bind(X_DATA, Y_DATA, EXTRAP, EXTRAP);
System.Func <double, double> derivFunc = x => bind.interpolate(x);
for (int i = 0; i < X_LEFT_TEST.size(); ++i)
{
assertEquals(bind.firstDerivative(X_LEFT_TEST.get(i)), DIFF_CALC.differentiate(derivFunc).apply(X_LEFT_TEST.get(i)), EPS);
int index = i;
System.Func <DoubleArray, double> sensFunc = y => CurveInterpolators.DOUBLE_QUADRATIC.bind(X_DATA, y, EXTRAP, EXTRAP).interpolate(X_LEFT_TEST.get(index));
assertTrue(DoubleArrayMath.fuzzyEquals(bind.parameterSensitivity(X_LEFT_TEST.get(index)).toArray(), SENS_CALC.differentiate(sensFunc).apply(Y_DATA).toArray(), EPS));
}
for (int i = 0; i < X_RIGHT_TEST.size(); ++i)
{
assertEquals(bind.firstDerivative(X_RIGHT_TEST.get(i)), DIFF_CALC.differentiate(derivFunc).apply(X_RIGHT_TEST.get(i)), EPS);
int index = i;
System.Func <DoubleArray, double> sensFunc = y => CurveInterpolators.DOUBLE_QUADRATIC.bind(X_DATA, y, EXTRAP, EXTRAP).interpolate(X_RIGHT_TEST.get(index));
assertTrue(DoubleArrayMath.fuzzyEquals(bind.parameterSensitivity(X_RIGHT_TEST.get(index)).toArray(), SENS_CALC.differentiate(sensFunc).apply(Y_DATA).toArray(), EPS));
}
}
public virtual void test_sensitivityEdgeCase()
{
BoundCurveInterpolator bci = DQ_INTERPOLATOR.bind(X_SENS, Y_SENS, FLAT_EXTRAPOLATOR, FLAT_EXTRAPOLATOR);
double lastXValue = X_SENS.get(X_SENS.size() - 1);
DoubleArray sensitivity = bci.parameterSensitivity(lastXValue);
for (int i = 0; i < sensitivity.size() - 1; i++)
{
assertEquals(0, sensitivity.get(i), EPS);
}
assertEquals(1.0, sensitivity.get(sensitivity.size() - 1), EPS);
}
internal Bound(DoubleArray xValues, DoubleArray yValues, BoundCurveInterpolator interpolator)
{
this.nodeCount = xValues.size();
this.lastXValue = xValues.get(nodeCount - 1);
this.lastYValue = yValues.get(nodeCount - 1);
this.lastDf = Math.Exp(-lastXValue * lastYValue);
this.eps = EPS * (lastXValue - xValues.get(0));
this.rightYGradient = (lastYValue - interpolator.interpolate(lastXValue - eps)) / eps;
this.rightYSens = interpolator.parameterSensitivity(lastXValue - eps).multipliedBy(-1d);
this.coef1 = -lastYValue * lastDf - lastXValue * lastDf * rightYGradient;
this.coef0 = lastDf - coef1 * lastXValue;
}
public virtual void sensitivity3()
{
BoundCurveInterpolator bci = CurveInterpolators.LINEAR.bind(X_DATA, Y_DATA, EXP_EXTRAPOLATOR, EXP_EXTRAPOLATOR);
double shift = 1e-8;
double value = 6d;
double[] yDataShifted = Y_DATA.toArray();
yDataShifted[Y_DATA.size() - 1] += shift;
BoundCurveInterpolator bciShifted = CurveInterpolators.LINEAR.bind(X_DATA, DoubleArray.ofUnsafe(yDataShifted), EXP_EXTRAPOLATOR, EXP_EXTRAPOLATOR);
assertEquals(bci.parameterSensitivity(value).get(Y_DATA.size() - 1), (bciShifted.interpolate(value) - bci.interpolate(value)) / shift, TOLERANCE_SENSI);
}
//-------------------------------------------------------------------------
public virtual void test_bind()
{
DoubleArray xValues = DoubleArray.of(1, 2, 3);
DoubleArray yValues = DoubleArray.of(2, 4, 5);
BoundCurveInterpolator bound = LINEAR.bind(xValues, yValues, CurveExtrapolators.FLAT, CurveExtrapolators.FLAT);
assertEquals(bound.interpolate(0.5), 2d, 0d);
assertEquals(bound.interpolate(1), 2d, 0d);
assertEquals(bound.interpolate(1.5), 3d, 0d);
assertEquals(bound.interpolate(2), 4d, 0d);
assertEquals(bound.interpolate(2.5), 4.5d, 0d);
assertEquals(bound.interpolate(3), 5d, 0d);
assertEquals(bound.interpolate(3.5), 5d, 0d);
// coverage
assertEquals(bound.parameterSensitivity(0.5).size(), 3);
assertEquals(bound.parameterSensitivity(2).size(), 3);
assertEquals(bound.parameterSensitivity(3.5).size(), 3);
assertEquals(bound.firstDerivative(0.5), 0d, 0d);
assertTrue(bound.firstDerivative(2) != 0d);
assertEquals(bound.firstDerivative(3.5), 0d, 0d);
assertNotNull(bound.ToString());
}
internal Bound(DoubleArray xValues, DoubleArray yValues, BoundCurveInterpolator interpolator)
{
this.nodeCount = xValues.size();
this.firstXValue = xValues.get(0);
this.firstYValue = yValues.get(0);
this.lastXValue = xValues.get(nodeCount - 1);
double gradient = interpolator.firstDerivative(firstXValue);
this.eps = EPS * (lastXValue - firstXValue);
this.leftQuadCoef = gradient / firstXValue - (firstYValue - 1d) / firstXValue / firstXValue;
this.leftLinCoef = -gradient + 2d * (firstYValue - 1d) / firstXValue;
this.leftSens = Suppliers.memoize(() => interpolator.parameterSensitivity(firstXValue + eps));
}
public virtual void differentIntervalsTest()
{
DoubleArray xValues = DoubleArray.of(1.0328724558967068, 1.2692381049172323, 2.8611430465380905, 4.296118458251132, 7.011992052151352, 7.293354144919639, 8.557971037612713, 8.77306861567384, 10.572470371584489, 12.96945799507056);
DoubleArray[] yValues = new DoubleArray[] { DoubleArray.of(1.1593075755231343, 2.794957672828094, 4.674733634811079, 5.517689918508841, 6.138447304104604, 6.264375977142906, 6.581666492568779, 8.378685055774037, 10.005246918325483, 10.468304334744241), DoubleArray.of(9.95780079114617, 8.733013195721913, 8.192165283188197, 6.539369493529048, 6.3868683960757515, 4.700471352238411, 4.555354921077598, 3.780781869340659, 2.299369456202763, 0.9182441378327986) };
int nData = xValues.size();
int nKeys = 100 * nData;
double[] xKeys = new double[nKeys];
double xMin = 0.0;
double xMax = xValues.get(nData - 1) + 2.0;
double step = (xMax - xMin) / nKeys;
for (int i = 0; i < nKeys; ++i)
{
xKeys[i] = xMin + step * i;
}
CurveExtrapolator extrap = QuadraticLeftCurveExtrapolator.INSTANCE;
int yDim = yValues.Length;
for (int k = 0; k < yDim; ++k)
{
BoundCurveInterpolator bci = CurveInterpolators.LOG_NATURAL_SPLINE_MONOTONE_CUBIC.bind(xValues, yValues[k], extrap, CurveExtrapolators.LOG_LINEAR);
// Check C0 continuity
assertEquals(bci.interpolate(xValues.get(0) - 1.e-14), bci.interpolate(xValues.get(0)), TOL);
// Check C1 continuity
assertEquals(bci.firstDerivative(xValues.get(0) - TOL), bci.firstDerivative(xValues.get(0)), TOL * 1.e2);
// Test sensitivity
double[] yValues1Up = yValues[k].toArray();
double[] yValues1Dw = yValues[k].toArray();
for (int j = 0; j < nData; ++j)
{
yValues1Up[j] = yValues[k].get(j) * (1.0 + EPS);
yValues1Dw[j] = yValues[k].get(j) * (1.0 - EPS);
BoundCurveInterpolator bciUp = CurveInterpolators.LOG_NATURAL_SPLINE_MONOTONE_CUBIC.bind(xValues, DoubleArray.ofUnsafe(yValues1Up), extrap, CurveExtrapolators.LOG_LINEAR);
BoundCurveInterpolator bciDw = CurveInterpolators.LOG_NATURAL_SPLINE_MONOTONE_CUBIC.bind(xValues, DoubleArray.ofUnsafe(yValues1Dw), extrap, CurveExtrapolators.LOG_LINEAR);
for (int i = 0; i < nKeys; ++i)
{
double res1 = 0.5 * (bciUp.interpolate(xKeys[i]) - bciDw.interpolate(xKeys[i])) / EPS / yValues[k].get(j);
assertEquals(res1, bci.parameterSensitivity(xKeys[i]).get(j), Math.Max(Math.Abs(yValues[k].get(j)) * EPS, EPS) * 1.e2); //because gradient is NOT exact
}
yValues1Up[j] = yValues[k].get(j);
yValues1Dw[j] = yValues[k].get(j);
}
}
}
public virtual void sameIntervalsTest()
{
DoubleArray xValues = DoubleArray.of(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0);
DoubleArray[] yValues = new DoubleArray[] { DoubleArray.of(1.001, 1.001, 1.001, 1.001, 1.001, 1.001, 1.001, 1.001), DoubleArray.of(11.0, 8.0, 5.0, 1.001, 1.001, 5.0, 8.0, 11.0), DoubleArray.of(1.001, 1.001, 5.0, 9.0, 9.0, 12.0, 18.0, 18.0) };
int nData = xValues.size();
int nKeys = 100 * nData;
double[] xKeys = new double[nKeys];
double xMin = 0.0;
double xMax = xValues.get(nData - 1) + 2.0;
double step = (xMax - xMin) / nKeys;
for (int i = 0; i < nKeys; ++i)
{
xKeys[i] = xMin + step * i;
}
CurveExtrapolator extrap = QuadraticLeftCurveExtrapolator.INSTANCE;
int yDim = yValues.Length;
for (int k = 0; k < yDim; ++k)
{
BoundCurveInterpolator bci = CurveInterpolators.LOG_NATURAL_SPLINE_MONOTONE_CUBIC.bind(xValues, yValues[k], extrap, CurveExtrapolators.LOG_LINEAR);
// Check C0 continuity
assertEquals(bci.interpolate(xValues.get(0) - 1.e-14), bci.interpolate(xValues.get(0)), TOL);
// Check C1 continuity
assertEquals(bci.firstDerivative(xValues.get(0) - TOL), bci.firstDerivative(xValues.get(0)), TOL * 1.e2);
// Test sensitivity
double[] yValues1Up = yValues[k].toArray();
double[] yValues1Dw = yValues[k].toArray();
for (int j = 0; j < nData; ++j)
{
yValues1Up[j] = yValues[k].get(j) * (1.0 + EPS);
yValues1Dw[j] = yValues[k].get(j) * (1.0 - EPS);
BoundCurveInterpolator bciUp = CurveInterpolators.LOG_NATURAL_SPLINE_MONOTONE_CUBIC.bind(xValues, DoubleArray.ofUnsafe(yValues1Up), extrap, CurveExtrapolators.LOG_LINEAR);
BoundCurveInterpolator bciDw = CurveInterpolators.LOG_NATURAL_SPLINE_MONOTONE_CUBIC.bind(xValues, DoubleArray.ofUnsafe(yValues1Dw), extrap, CurveExtrapolators.LOG_LINEAR);
for (int i = 0; i < nKeys; ++i)
{
double res1 = 0.5 * (bciUp.interpolate(xKeys[i]) - bciDw.interpolate(xKeys[i])) / EPS / yValues[k].get(j);
assertEquals(res1, bci.parameterSensitivity(xKeys[i]).get(j), Math.Max(Math.Abs(yValues[k].get(j)) * EPS, EPS) * 1.e2); //because gradient is NOT exact
}
yValues1Up[j] = yValues[k].get(j);
yValues1Dw[j] = yValues[k].get(j);
}
}
}
//-------------------------------------------------------------------------
public virtual void test_lookup()
{
InterpolatedNodalCurve test = InterpolatedNodalCurve.of(METADATA, XVALUES, YVALUES, INTERPOLATOR);
BoundCurveInterpolator interp = INTERPOLATOR.bind(XVALUES, YVALUES, FLAT_EXTRAPOLATOR, FLAT_EXTRAPOLATOR);
assertThat(test.yValue(XVALUES.get(0))).isEqualTo(YVALUES.get(0));
assertThat(test.yValue(XVALUES.get(1))).isEqualTo(YVALUES.get(1));
assertThat(test.yValue(XVALUES.get(2))).isEqualTo(YVALUES.get(2));
assertThat(test.yValue(10d)).isEqualTo(interp.interpolate(10d));
assertThat(test.yValueParameterSensitivity(10d).MarketDataName).isEqualTo(CURVE_NAME);
assertThat(test.yValueParameterSensitivity(10d).Sensitivity).isEqualTo(interp.parameterSensitivity(10d));
assertThat(test.firstDerivative(10d)).isEqualTo(interp.firstDerivative(10d));
}
public virtual void test_extrapolation()
{
BoundCurveInterpolator bci = CurveInterpolators.LINEAR.bind(X_DATA, Y_DATA, FLAT_EXTRAPOLATOR, FLAT_EXTRAPOLATOR);
for (int i = 0; i < 100; i++)
{
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final double x = RANDOM.nextDouble() * 20.0 - 10;
double x = RANDOM.NextDouble() * 20.0 - 10;
if (x < 0)
{
assertEquals(bci.interpolate(x), 3.0, 1e-12);
assertEquals(bci.firstDerivative(x), 0.0, 1e-12);
assertEquals(bci.parameterSensitivity(x).get(0), 1.0, 1e-12);
}
else if (x > 5.0)
{
assertEquals(bci.interpolate(x), 2.0, 1e-12);
assertEquals(bci.firstDerivative(x), 0.0, 1e-12);
assertEquals(bci.parameterSensitivity(x).get(X_DATA.size() - 1), 1.0, 1e-12);
}
}
}
public virtual void errorTest()
{
DoubleArray xValues1 = DoubleArray.of(1, 2, 3);
DoubleArray xValues2 = DoubleArray.of(-3, -2, -1);
DoubleArray yValues = DoubleArray.of(1, 2, 3);
BoundCurveInterpolator bind1 = CurveInterpolators.DOUBLE_QUADRATIC.bind(xValues1, yValues, EXTRAP, EXTRAP);
BoundCurveInterpolator bind2 = CurveInterpolators.DOUBLE_QUADRATIC.bind(xValues2, yValues, EXTRAP, EXTRAP);
assertThrowsIllegalArg(() => bind1.interpolate(-1));
assertThrowsIllegalArg(() => bind1.firstDerivative(-1));
assertThrowsIllegalArg(() => bind1.parameterSensitivity(-1));
assertThrowsIllegalArg(() => bind2.interpolate(1));
assertThrowsIllegalArg(() => bind2.firstDerivative(1));
assertThrowsIllegalArg(() => bind2.parameterSensitivity(1));
}
// regression to ISDA curve
public virtual void curveNegativeRateRegressionTest()
{
double[] xValues = new double[] { 0.09589041095890412, 0.1726027397260274, 0.2547945205479452, 0.5041095890410959, 0.7561643835616438, 1.0082191780821919, 2.0136986301369864, 3.0109589041095894, 4.008219178082192, 5.010958904109589, 6.010958904109589, 7.010958904109589, 8.016438356164384, 9.013698630136986, 10.013698630136986, 12.013698630136986, 15.016438356164384, 20.021917808219175, 30.032876712328765 };
double[] yValues = new double[] { -0.0020786675364765166, -0.0016860241245632032, -0.0013445488774423426, -4.237821212705129E-4, 2.5198253623336676E-5, 5.935456094577134E-4, -3.2426565772714425E-4, 6.147334333200949E-4, 0.0019060366773708986, 0.0033107384678633615, 0.004774430364382846, 0.006237401212672876, 0.007639615209817064, 0.00896830709117619, 0.010164859928720184, 0.012196812821300893, 0.014410766977011871, 0.01623618497051232, 0.016522578536714926 };
CurveExtrapolator left = CurveExtrapolators.FLAT;
CurveExtrapolator right = CurveExtrapolators.PRODUCT_LINEAR;
BoundCurveInterpolator interp = INTERP.bind(DoubleArray.ofUnsafe(xValues), DoubleArray.ofUnsafe(yValues), left, right);
double[] keys = new double[] { 1d / 365d, 17d / 365d, 30d / 365d, 98d / 365d, 1d, 2.35, 6d, 10d, 12.6, 28d, 32d, 39d };
// interpolate
double[] expected = new double[] { -0.0020786675364765166, -0.0020786675364765166, -0.0020786675364765166, -0.0012495606047715551, 5.795315650672766E-4, 8.145045403416393E-5, 0.004761034017457297, 0.010150085453826136, 0.01271200378309255, 0.016480992621622493, 0.016557789252559695, 0.016654277327326956 };
for (int i = 0; i < keys.Length; ++i)
{
double computed = interp.interpolate(keys[i]);
assertEquals(computed, expected[i], EPS);
}
// sensitivity
double[][] sensiExp = new double[][]
{
new double[] { 1d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.0 },
new double[] { 1d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.0 },
new double[] { 1d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.0 },
new double[] { 0d, 0d, 0.8968378560215295, 0.1031621439784705, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.0 },
new double[] { 0d, 0d, 0d, 0d, 0.024657534246575567, 0.9753424657534244, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.0 },
new double[] { 0d, 0d, 0d, 0d, 0d, 0d, 0.5679270452660136, 0.43207295473398644, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.0 },
new double[] { 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.009152436354538397, 0.9908475636454616, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.0 },
new double[] { 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.012347532370050315, 0.9876524676299496, 0d, 0d, 0d, 0.0 },
new double[] { 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.7672982701729827, 0.23270172982701726, 0d, 0.0 },
new double[] { 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0.1452054794520546, 0.8547945205479454 },
new double[] { 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, -0.12294520547945219, 1.1229452054794522 },
new double[] { 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, -0.4598524762908325, 1.4598524762908325 }
};
for (int i = 0; i < keys.Length; ++i)
{
DoubleArray computed = interp.parameterSensitivity(keys[i]);
assertTrue(DoubleArrayMath.fuzzyEquals(computed.toArray(), sensiExp[i], EPS));
}
// fwd rate
double[] fwdExp = new double[] { -0.0020786675364765166, -0.0020786675364765166, -0.0020786675364765166, 5.172212669050933E-4, 0.0022985876769608432, 0.0025107892902424037, 0.012108930306120206, 0.02095022660137702, 0.023268603631019753, 0.017095365669120136, 0.017095365669120136, 0.017095365669120136 };
for (int i = 0; i < keys.Length; ++i)
{
double value = interp.interpolate(keys[i]);
double deriv = interp.firstDerivative(keys[i]);
double computed = deriv * keys[i] + value;
assertEquals(computed, fwdExp[i], EPS);
}
}
