public void testUniformGridMesher()
{
int[] dims = new int[] { 5, 7, 8 };
List <int> dim = new List <int>(dims);
FdmLinearOpLayout layout = new FdmLinearOpLayout(dim);
List <Pair <double?, double?> > boundaries = new List <Pair <double?, double?> > ();;
boundaries.Add(new Pair <double?, double?>(-5, 10));
boundaries.Add(new Pair <double?, double?>(5, 100));
boundaries.Add(new Pair <double?, double?>(10, 20));
UniformGridMesher mesher = new UniformGridMesher(layout, boundaries);
double dx1 = 15.0 / (dim[0] - 1);
double dx2 = 95.0 / (dim[1] - 1);
double dx3 = 10.0 / (dim[2] - 1);
double tol = 100 * Const.QL_EPSILON;
if (Math.Abs(dx1 - mesher.dminus(layout.begin(), 0).Value) > tol ||
Math.Abs(dx1 - mesher.dplus(layout.begin(), 0).Value) > tol ||
Math.Abs(dx2 - mesher.dminus(layout.begin(), 1).Value) > tol ||
Math.Abs(dx2 - mesher.dplus(layout.begin(), 1).Value) > tol ||
Math.Abs(dx3 - mesher.dminus(layout.begin(), 2).Value) > tol ||
Math.Abs(dx3 - mesher.dplus(layout.begin(), 2).Value) > tol)
{
QAssert.Fail("inconsistent uniform mesher object");
}
}
public void testFdmMesherIntegral()
{
FdmMesherComposite mesher =
new FdmMesherComposite(
new Concentrating1dMesher(-1, 1.6, 21, new Pair <double?, double?>(0, 0.1)),
new Concentrating1dMesher(-3, 4, 11, new Pair <double?, double?>(1, 0.01)),
new Concentrating1dMesher(-2, 1, 5, new Pair <double?, double?>(0.5, 0.1)));
FdmLinearOpLayout layout = mesher.layout();
Vector f = new Vector(mesher.layout().size());
for (FdmLinearOpIterator iter = layout.begin();
iter != layout.end(); ++iter)
{
double x = mesher.location(iter, 0);
double y = mesher.location(iter, 1);
double z = mesher.location(iter, 2);
f[iter.index()] = x * x + 3 * y * y - 3 * z * z
+ 2 * x * y - x * z - 3 * y * z
+ 4 * x - y - 3 * z + 2;
}
double tol = 1e-12;
// Simpson's rule has to be exact here, Mathematica code gives
// Integrate[x*x+3*y*y-3*z*z+2*x*y-x*z-3*y*z+4*x-y-3*z+2,
// {x, -1, 16/10}, {y, -3, 4}, {z, -2, 1}]
double expectedSimpson = 876.512;
double calculatedSimpson
= new FdmMesherIntegral(mesher, new DiscreteSimpsonIntegral().value).integrate(f);
if (Math.Abs(calculatedSimpson - expectedSimpson) > tol * expectedSimpson)
{
QAssert.Fail("discrete mesher integration using Simpson's rule failed: "
+ "\n calculated: " + calculatedSimpson
+ "\n expected: " + expectedSimpson);
}
double expectedTrapezoid = 917.0148209153263;
double calculatedTrapezoid
= new FdmMesherIntegral(mesher, new DiscreteTrapezoidIntegral().value).integrate(f);
if (Math.Abs(calculatedTrapezoid - expectedTrapezoid)
> tol * expectedTrapezoid)
{
QAssert.Fail("discrete mesher integration using Trapezoid rule failed: "
+ "\n calculated: " + calculatedTrapezoid
+ "\n expected: " + expectedTrapezoid);
}
}
public void testCrankNicolsonWithDamping()
{
SavedSettings backup = new SavedSettings();
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(100.0);
YieldTermStructure qTS = Utilities.flatRate(today, 0.06, dc);
YieldTermStructure rTS = Utilities.flatRate(today, 0.06, dc);
BlackVolTermStructure volTS = Utilities.flatVol(today, 0.35, dc);
StrikedTypePayoff payoff =
new CashOrNothingPayoff(Option.Type.Put, 100, 10.0);
double maturity = 0.75;
Date exDate = today + Convert.ToInt32(maturity * 360 + 0.5);
Exercise exercise = new EuropeanExercise(exDate);
BlackScholesMertonProcess process = new
BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine =
new AnalyticEuropeanEngine(process);
VanillaOption opt = new VanillaOption(payoff, exercise);
opt.setPricingEngine(engine);
double expectedPV = opt.NPV();
double expectedGamma = opt.gamma();
// fd pricing using implicit damping steps and Crank Nicolson
int csSteps = 25, dampingSteps = 3, xGrid = 400;
List <int> dim = new InitializedList <int>(1, xGrid);
FdmLinearOpLayout layout = new FdmLinearOpLayout(dim);
Fdm1dMesher equityMesher =
new FdmBlackScholesMesher(
dim[0], process, maturity, payoff.strike(),
null, null, 0.0001, 1.5,
new Pair <double?, double?>(payoff.strike(), 0.01));
FdmMesher mesher =
new FdmMesherComposite(equityMesher);
FdmBlackScholesOp map =
new FdmBlackScholesOp(mesher, process, payoff.strike());
FdmInnerValueCalculator calculator =
new FdmLogInnerValue(payoff, mesher, 0);
object rhs = new Vector(layout.size());
Vector x = new Vector(layout.size());
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter;
++iter)
{
(rhs as Vector)[iter.index()] = calculator.avgInnerValue(iter, maturity);
x[iter.index()] = mesher.location(iter, 0);
}
FdmBackwardSolver solver = new FdmBackwardSolver(map, new FdmBoundaryConditionSet(),
new FdmStepConditionComposite(),
new FdmSchemeDesc().Douglas());
solver.rollback(ref rhs, maturity, 0.0, csSteps, dampingSteps);
MonotonicCubicNaturalSpline spline = new MonotonicCubicNaturalSpline(x, x.Count, rhs as Vector);
double s = spot.value();
double calculatedPV = spline.value(Math.Log(s));
double calculatedGamma = (spline.secondDerivative(Math.Log(s))
- spline.derivative(Math.Log(s))) / (s * s);
double relTol = 2e-3;
if (Math.Abs(calculatedPV - expectedPV) > relTol * expectedPV)
{
QAssert.Fail("Error calculating the PV of the digital option" +
"\n rel. tolerance: " + relTol +
"\n expected: " + expectedPV +
"\n calculated: " + calculatedPV);
}
if (Math.Abs(calculatedGamma - expectedGamma) > relTol * expectedGamma)
{
QAssert.Fail("Error calculating the Gamma of the digital option" +
"\n rel. tolerance: " + relTol +
"\n expected: " + expectedGamma +
"\n calculated: " + calculatedGamma);
}
}
public void testTripleBandMapSolve()
{
int[] dims = new int[] { 100, 400 };
List <int> dim = new List <int>(dims);
FdmLinearOpLayout layout = new FdmLinearOpLayout(dim);
List <Pair <double?, double?> > boundaries = new List <Pair <double?, double?> > ();
boundaries.Add(new Pair <double?, double?>(0, 1.0));
boundaries.Add(new Pair <double?, double?>(0, 1.0));
FdmMesher mesher = new UniformGridMesher(layout, boundaries);
FirstDerivativeOp dy = new FirstDerivativeOp(1, mesher);
dy.axpyb(new Vector(1, 2.0), dy, dy, new Vector(1, 1.0));
// check copy constructor
FirstDerivativeOp copyOfDy = new FirstDerivativeOp(dy);
Vector u = new Vector(layout.size());
for (int i = 0; i < layout.size(); ++i)
{
u[i] = Math.Sin(0.1 * i) + Math.Cos(0.35 * i);
}
Vector t = new Vector(dy.solve_splitting(copyOfDy.apply(u), 1.0, 0.0));
for (int i = 0; i < u.size(); ++i)
{
if (Math.Abs(u[i] - t[i]) > 1e-6)
{
QAssert.Fail("solve and apply are not consistent "
+ "\n expected : " + u[i]
+ "\n calculated : " + t[i]);
}
}
FirstDerivativeOp dx = new FirstDerivativeOp(0, mesher);
dx.axpyb(new Vector(), dx, dx, new Vector(1, 1.0));
FirstDerivativeOp copyOfDx = new FirstDerivativeOp(0, mesher);
// check assignment
copyOfDx = dx;
t = dx.solve_splitting(copyOfDx.apply(u), 1.0, 0.0);
for (int i = 0; i < u.size(); ++i)
{
if (Math.Abs(u[i] - t[i]) > 1e-6)
{
QAssert.Fail("solve and apply are not consistent "
+ "\n expected : " + u[i]
+ "\n calculated : " + t[i]);
}
}
SecondDerivativeOp dxx = new SecondDerivativeOp(0, mesher);
dxx.axpyb(new Vector(1, 0.5), dxx, dx, new Vector(1, 1.0));
// check of copy constructor
SecondDerivativeOp copyOfDxx = new SecondDerivativeOp(dxx);
t = dxx.solve_splitting(copyOfDxx.apply(u), 1.0, 0.0);
for (int i = 0; i < u.size(); ++i)
{
if (Math.Abs(u[i] - t[i]) > 1e-6)
{
QAssert.Fail("solve and apply are not consistent "
+ "\n expected : " + u[i]
+ "\n calculated : " + t[i]);
}
}
//check assignment operator
copyOfDxx.add(new SecondDerivativeOp(1, mesher));
copyOfDxx = dxx;
t = dxx.solve_splitting(copyOfDxx.apply(u), 1.0, 0.0);
for (int i = 0; i < u.size(); ++i)
{
if (Math.Abs(u[i] - t[i]) > 1e-6)
{
QAssert.Fail("solve and apply are not consistent "
+ "\n expected : " + u[i]
+ "\n calculated : " + t[i]);
}
}
}
public void testSecondOrderMixedDerivativesMapApply()
{
int[] dims = new int[] { 50, 50, 50 };
List <int> dim = new List <int>(dims);
FdmLinearOpLayout index = new FdmLinearOpLayout(dim);
List <Pair <double?, double?> > boundaries = new List <Pair <double?, double?> > ();
boundaries.Add(new Pair <double?, double?>(0, 0.5));
boundaries.Add(new Pair <double?, double?>(0, 0.5));
boundaries.Add(new Pair <double?, double?>(0, 0.5));
FdmMesher mesher = new UniformGridMesher(index, boundaries);
Vector r = new Vector(mesher.layout().size());
FdmLinearOpIterator endIter = index.end();
for (FdmLinearOpIterator iter = index.begin(); iter != endIter; ++iter)
{
double x = mesher.location(iter, 0);
double y = mesher.location(iter, 1);
double z = mesher.location(iter, 2);
r[iter.index()] = Math.Sin(x) * Math.Cos(y) * Math.Exp(z);
}
Vector t = new SecondOrderMixedDerivativeOp(0, 1, mesher).apply(r);
Vector u = new SecondOrderMixedDerivativeOp(1, 0, mesher).apply(r);
double tol = 5e-2;
for (FdmLinearOpIterator iter = index.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double x = mesher.location(iter, 0);
double y = mesher.location(iter, 1);
double z = mesher.location(iter, 2);
double d = -Math.Cos(x) * Math.Sin(y) * Math.Exp(z);
if (Math.Abs(d - t[i]) > tol)
{
QAssert.Fail("numerical derivative in dxdy deviation is too big"
+ "\n found at " + x + " " + y + " " + z);
}
if (Math.Abs(t[i] - u[i]) > 1e5 * Const.QL_EPSILON)
{
QAssert.Fail("numerical derivative in dxdy not equal to dydx"
+ "\n found at " + x + " " + y + " " + z
+ "\n value " + Math.Abs(t[i] - u[i]));
}
}
t = new SecondOrderMixedDerivativeOp(0, 2, mesher).apply(r);
u = new SecondOrderMixedDerivativeOp(2, 0, mesher).apply(r);
for (FdmLinearOpIterator iter = index.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double x = mesher.location(iter, 0);
double y = mesher.location(iter, 1);
double z = mesher.location(iter, 2);
double d = Math.Cos(x) * Math.Cos(y) * Math.Exp(z);
if (Math.Abs(d - t[i]) > tol)
{
QAssert.Fail("numerical derivative in dxdy deviation is too big"
+ "\n found at " + x + " " + y + " " + z);
}
if (Math.Abs(t[i] - u[i]) > 1e5 * Const.QL_EPSILON)
{
QAssert.Fail("numerical derivative in dxdz not equal to dzdx"
+ "\n found at " + x + " " + y + " " + z
+ "\n value " + Math.Abs(t[i] - u[i]));
}
}
t = new SecondOrderMixedDerivativeOp(1, 2, mesher).apply(r);
u = new SecondOrderMixedDerivativeOp(2, 1, mesher).apply(r);
for (FdmLinearOpIterator iter = index.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double x = mesher.location(iter, 0);
double y = mesher.location(iter, 1);
double z = mesher.location(iter, 2);
double d = -Math.Sin(x) * Math.Sin(y) * Math.Exp(z);
if (Math.Abs(d - t[i]) > tol)
{
QAssert.Fail("numerical derivative in dydz deviation is too big"
+ "\n found at " + x + " " + y + " " + z);
}
if (Math.Abs(t[i] - u[i]) > 1e5 * Const.QL_EPSILON)
{
QAssert.Fail("numerical derivative in dydz not equal to dzdy"
+ "\n found at " + x + " " + y + " " + z
+ "\n value " + Math.Abs(t[i] - u[i]));
}
}
}
public void testFdmLinearOpLayout()
{
int[] dims = new int[] { 5, 7, 8 };
List <int> dim = new List <int>(dims);
FdmLinearOpLayout layout = new FdmLinearOpLayout(dim);
int calculatedDim = layout.dim().Count;
int expectedDim = dim.Count;
if (calculatedDim != expectedDim)
{
QAssert.Fail("index.dimensions() should be " + expectedDim
+ ", but is " + calculatedDim);
}
int calculatedSize = layout.size();
int expectedSize = dim.accumulate(0, 3, 1, (x, y) => (x * y));
if (calculatedSize != expectedSize)
{
QAssert.Fail("index.size() should be "
+ expectedSize + ", but is " + calculatedSize);
}
for (int k = 0; k < dim[0]; ++k)
{
for (int l = 0; l < dim[1]; ++l)
{
for (int m = 0; m < dim[2]; ++m)
{
List <int> tmp = new InitializedList <int>(3);
tmp[0] = k; tmp[1] = l; tmp[2] = m;
int calculatedIndex = layout.index(tmp);
int expectedIndex = k + l * dim[0] + m * dim[0] * dim[1];
if (expectedIndex != layout.index(tmp))
{
QAssert.Fail("index.size() should be " + expectedIndex
+ ", but is " + calculatedIndex);
}
}
}
}
FdmLinearOpIterator iter = layout.begin();
for (int m = 0; m < dim[2]; ++m)
{
for (int l = 0; l < dim[1]; ++l)
{
for (int k = 0; k < dim[0]; ++k, ++iter)
{
for (int n = 1; n < 4; ++n)
{
int nn = layout.neighbourhood(iter, 1, n);
int calculatedIndex = k + m * dim[0] * dim[1]
+ ((l < dim[1] - n)? l + n
: dim[1] - 1 - (l + n - (dim[1] - 1))) * dim[0];
if (nn != calculatedIndex)
{
QAssert.Fail("next neighbourhood index is " + nn
+ " but should be " + calculatedIndex);
}
}
for (int n = 1; n < 7; ++n)
{
int nn = layout.neighbourhood(iter, 2, -n);
int calculatedIndex = k + l * dim[0]
+ ((m < n) ? n - m : m - n) * dim[0] * dim[1];
if (nn != calculatedIndex)
{
QAssert.Fail("next neighbourhood index is " + nn
+ " but should be " + calculatedIndex);
}
}
}
}
}
}
public void testDerivativeWeightsOnNonUniformGrids()
{
Fdm1dMesher mesherX =
new Concentrating1dMesher(-2.0, 3.0, 50, new Pair <double?, double?>(0.5, 0.01));
Fdm1dMesher mesherY =
new Concentrating1dMesher(0.5, 5.0, 25, new Pair <double?, double?>(0.5, 0.1));
Fdm1dMesher mesherZ =
new Concentrating1dMesher(-1.0, 2.0, 31, new Pair <double?, double?>(1.5, 0.01));
FdmMesher meshers =
new FdmMesherComposite(mesherX, mesherY, mesherZ);
FdmLinearOpLayout layout = meshers.layout();
FdmLinearOpIterator endIter = layout.end();
double tol = 1e-13;
for (int direction = 0; direction < 3; ++direction)
{
SparseMatrix dfdx
= new FirstDerivativeOp(direction, meshers).toMatrix();
SparseMatrix d2fdx2
= new SecondDerivativeOp(direction, meshers).toMatrix();
Vector gridPoints = meshers.locations(direction);
for (FdmLinearOpIterator iter = layout.begin();
iter != endIter; ++iter)
{
int c = iter.coordinates()[direction];
int index = iter.index();
int indexM1 = layout.neighbourhood(iter, direction, -1);
int indexP1 = layout.neighbourhood(iter, direction, +1);
// test only if not on the boundary
if (c == 0)
{
Vector twoPoints = new Vector(2);
twoPoints[0] = 0.0;
twoPoints[1] = gridPoints[indexP1] - gridPoints[index];
Vector ndWeights1st = new NumericalDifferentiation(x => x, 1, twoPoints).weights();
double beta1 = dfdx[index, index];
double gamma1 = dfdx[index, indexP1];
if (Math.Abs((beta1 - ndWeights1st[0]) / beta1) > tol ||
Math.Abs((gamma1 - ndWeights1st[1]) / gamma1) > tol)
{
QAssert.Fail("can not reproduce the weights of the "
+ "first order derivative operator "
+ "on the lower boundary"
+ "\n expected beta: " + ndWeights1st[0]
+ "\n calculated beta: " + beta1
+ "\n difference beta: "
+ (beta1 - ndWeights1st[0])
+ "\n expected gamma: " + ndWeights1st[1]
+ "\n calculated gamma: " + gamma1
+ "\n difference gamma: "
+ (gamma1 - ndWeights1st[1]));
}
// free boundary condition by default
double beta2 = d2fdx2[index, index];
double gamma2 = d2fdx2[index, indexP1];
if (Math.Abs(beta2) > Const.QL_EPSILON ||
Math.Abs(gamma2) > Const.QL_EPSILON)
{
QAssert.Fail("can not reproduce the weights of the "
+ "second order derivative operator "
+ "on the lower boundary"
+ "\n expected beta: " + 0.0
+ "\n calculated beta: " + beta2
+ "\n expected gamma: " + 0.0
+ "\n calculated gamma: " + gamma2);
}
}
else if (c == layout.dim()[direction] - 1)
{
Vector twoPoints = new Vector(2);
twoPoints[0] = gridPoints[indexM1] - gridPoints[index];
twoPoints[1] = 0.0;
Vector ndWeights1st = new NumericalDifferentiation(x => x, 1, twoPoints).weights();
double alpha1 = dfdx[index, indexM1];
double beta1 = dfdx[index, index];
if (Math.Abs((alpha1 - ndWeights1st[0]) / alpha1) > tol ||
Math.Abs((beta1 - ndWeights1st[1]) / beta1) > tol)
{
QAssert.Fail("can not reproduce the weights of the "
+ "first order derivative operator "
+ "on the upper boundary"
+ "\n expected alpha: " + ndWeights1st[0]
+ "\n calculated alpha: " + alpha1
+ "\n difference alpha: "
+ (alpha1 - ndWeights1st[0])
+ "\n expected beta: " + ndWeights1st[1]
+ "\n calculated beta: " + beta1
+ "\n difference beta: "
+ (beta1 - ndWeights1st[1]));
}
// free boundary condition by default
double alpha2 = d2fdx2[index, indexM1];
double beta2 = d2fdx2[index, index];
if (Math.Abs(alpha2) > Const.QL_EPSILON ||
Math.Abs(beta2) > Const.QL_EPSILON)
{
QAssert.Fail("can not reproduce the weights of the "
+ "second order derivative operator "
+ "on the upper boundary"
+ "\n expected alpha: " + 0.0
+ "\n calculated alpha: " + alpha2
+ "\n expected beta: " + 0.0
+ "\n calculated beta: " + beta2);
}
}
else
{
Vector threePoints = new Vector(3);
threePoints[0] = gridPoints[indexM1] - gridPoints[index];
threePoints[1] = 0.0;
threePoints[2] = gridPoints[indexP1] - gridPoints[index];
Vector ndWeights1st = new NumericalDifferentiation(x => x, 1, threePoints).weights();
double alpha1 = dfdx[index, indexM1];
double beta1 = dfdx[index, index];
double gamma1 = dfdx[index, indexP1];
if (Math.Abs((alpha1 - ndWeights1st[0]) / alpha1) > tol ||
Math.Abs((beta1 - ndWeights1st[1]) / beta1) > tol ||
Math.Abs((gamma1 - ndWeights1st[2]) / gamma1) > tol)
{
QAssert.Fail("can not reproduce the weights of the "
+ "first order derivative operator"
+ "\n expected alpha: " + ndWeights1st[0]
+ "\n calculated alpha: " + alpha1
+ "\n difference alpha: "
+ (alpha1 - ndWeights1st[0])
+ "\n expected beta: " + ndWeights1st[1]
+ "\n calculated beta: " + beta1
+ "\n difference beta: "
+ (beta1 - ndWeights1st[1])
+ "\n expected gamma: " + ndWeights1st[2]
+ "\n calculated gamma: " + gamma1
+ "\n difference gamma: "
+ (gamma1 - ndWeights1st[2]));
}
Vector ndWeights2nd = new NumericalDifferentiation(x => x, 2, threePoints).weights();
double alpha2 = d2fdx2[index, indexM1];
double beta2 = d2fdx2[index, index];
double gamma2 = d2fdx2[index, indexP1];
if (Math.Abs((alpha2 - ndWeights2nd[0]) / alpha2) > tol ||
Math.Abs((beta2 - ndWeights2nd[1]) / beta2) > tol ||
Math.Abs((gamma2 - ndWeights2nd[2]) / gamma2) > tol)
{
QAssert.Fail("can not reproduce the weights of the "
+ "second order derivative operator"
+ "\n expected alpha: " + ndWeights2nd[0]
+ "\n calculated alpha: " + alpha2
+ "\n difference alpha: "
+ (alpha2 - ndWeights2nd[0])
+ "\n expected beta: " + ndWeights2nd[1]
+ "\n calculated beta: " + beta2
+ "\n difference beta: "
+ (beta2 - ndWeights2nd[1])
+ "\n expected gamma: " + ndWeights2nd[2]
+ "\n calculated gamma: " + gamma2
+ "\n difference gamma: "
+ (gamma2 - ndWeights2nd[2]));
}
}
}
}
}
public void testSecondDerivativesMapApply()
{
int[] dims = new int[] { 50, 50, 50 };
List <int> dim = new List <int>(dims);
FdmLinearOpLayout index = new FdmLinearOpLayout(dim);
List <Pair <double?, double?> > boundaries = new List <Pair <double?, double?> > ();
boundaries.Add(new Pair <double?, double?>(0, 0.5));
boundaries.Add(new Pair <double?, double?>(0, 0.5));
boundaries.Add(new Pair <double?, double?>(0, 0.5));
FdmMesher mesher = new UniformGridMesher(index, boundaries);
Vector r = new Vector(mesher.layout().size());
FdmLinearOpIterator endIter = index.end();
for (FdmLinearOpIterator iter = index.begin(); iter != endIter; ++iter)
{
double x = mesher.location(iter, 0);
double y = mesher.location(iter, 1);
double z = mesher.location(iter, 2);
r[iter.index()] = Math.Sin(x) * Math.Cos(y) * Math.Exp(z);
}
Vector t = new SecondDerivativeOp(0, mesher).apply(r);
double tol = 5e-2;
for (FdmLinearOpIterator iter = index.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double x = mesher.location(iter, 0);
double y = mesher.location(iter, 1);
double z = mesher.location(iter, 2);
double d = -Math.Sin(x) * Math.Cos(y) * Math.Exp(z);
if (iter.coordinates()[0] == 0 || iter.coordinates()[0] == dims[0] - 1)
{
d = 0;
}
if (Math.Abs(d - t[i]) > tol)
{
QAssert.Fail("numerical derivative in dx^2 deviation is too big"
+ "\n found at " + x + " " + y + " " + z);
}
}
t = new SecondDerivativeOp(1, mesher).apply(r);
for (FdmLinearOpIterator iter = index.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double x = mesher.location(iter, 0);
double y = mesher.location(iter, 1);
double z = mesher.location(iter, 2);
double d = -Math.Sin(x) * Math.Cos(y) * Math.Exp(z);
if (iter.coordinates()[1] == 0 || iter.coordinates()[1] == dims[1] - 1)
{
d = 0;
}
if (Math.Abs(d - t[i]) > tol)
{
QAssert.Fail("numerical derivative in dy^2 deviation is too big"
+ "\n found at " + x + " " + y + " " + z);
}
}
t = new SecondDerivativeOp(2, mesher).apply(r);
for (FdmLinearOpIterator iter = index.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double x = mesher.location(iter, 0);
double y = mesher.location(iter, 1);
double z = mesher.location(iter, 2);
double d = Math.Sin(x) * Math.Cos(y) * Math.Exp(z);
if (iter.coordinates()[2] == 0 || iter.coordinates()[2] == dims[2] - 1)
{
d = 0;
}
if (Math.Abs(d - t[i]) > tol)
{
QAssert.Fail("numerical derivative in dz^2 deviation is too big"
+ "\n found at " + x + " " + y + " " + z);
}
}
}
public void testFirstDerivativesMapApply()
{
int[] dims = new int[] { 400, 100, 50 };
List <int> dim = new List <int>(dims);
FdmLinearOpLayout index = new FdmLinearOpLayout(dim);
List <Pair <double?, double?> > boundaries = new List <Pair <double?, double?> > ();
boundaries.Add(new Pair <double?, double?>(-5, 5));
boundaries.Add(new Pair <double?, double?>(0, 10));
boundaries.Add(new Pair <double?, double?>(5, 15));
FdmMesher mesher = new UniformGridMesher(index, boundaries);
FirstDerivativeOp map = new FirstDerivativeOp(2, mesher);
Vector r = new Vector(mesher.layout().size());
FdmLinearOpIterator endIter = index.end();
for (FdmLinearOpIterator iter = index.begin(); iter != endIter; ++iter)
{
r[iter.index()] = Math.Sin(mesher.location(iter, 0))
+ Math.Cos(mesher.location(iter, 2));
}
Vector t = map.apply(r);
double dz = (boundaries[2].second.Value - boundaries[2].first.Value) / (dims[2] - 1);
for (FdmLinearOpIterator iter = index.begin(); iter != endIter; ++iter)
{
int z = iter.coordinates()[2];
int z0 = (z > 0) ? z - 1 : 1;
int z2 = (z < dims[2] - 1) ? z + 1 : dims[2] - 2;
double lz0 = boundaries[2].first.Value + z0 * dz;
double lz2 = boundaries[2].first.Value + z2 * dz;
double expected;
if (z == 0)
{
expected = (Math.Cos(boundaries[2].first.Value + dz)
- Math.Cos(boundaries[2].first.Value)) / dz;
}
else if (z == dim[2] - 1)
{
expected = (Math.Cos(boundaries[2].second.Value)
- Math.Cos(boundaries[2].second.Value - dz)) / dz;
}
else
{
expected = (Math.Cos(lz2) - Math.Cos(lz0)) / (2 * dz);
}
double calculated = t[iter.index()];
if (Math.Abs(calculated - expected) > 1e-10)
{
QAssert.Fail("first derivative calculation failed."
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
}
}
