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 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 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);
}
}
}