void FunctionTests::checkFunctionsAgree(FunctionPtr f1, FunctionPtr f2, BasisCachePtr basisCache) {
ASSERT_EQ(f1->rank(), f2->rank())
<< "f1->rank() " << f1->rank() << " != f2->rank() " << f2->rank() << endl;
int rank = f1->rank();
int numCells = basisCache->getPhysicalCubaturePoints().dimension(0);
int numPoints = basisCache->getPhysicalCubaturePoints().dimension(1);
int spaceDim = basisCache->getPhysicalCubaturePoints().dimension(2);
Teuchos::Array<int> dim;
dim.append(numCells);
dim.append(numPoints);
for (int i=0; i<rank; i++) {
dim.append(spaceDim);
}
FieldContainer<double> f1Values(dim);
FieldContainer<double> f2Values(dim);
f1->values(f1Values,basisCache);
f2->values(f2Values,basisCache);
double tol = 1e-14;
double maxDiff;
EXPECT_TRUE(fcsAgree(f1Values,f2Values,tol,maxDiff))
<< "Test failed: f1 and f2 disagree; maxDiff " << maxDiff << ".\n"
<< "f1Values: \n" << f1Values
<< "f2Values: \n" << f2Values;
}
bool ElementTests::testNeighborPointMapping()
{
bool success = true;
double tol = 1e-15;
double maxDiff;
int SOUTH = 0, EAST = 1, NORTH = 2, WEST = 3;
// determine expected values
int numPoints = _testPoints1D.dimension(0);
FieldContainer<double> neighborPointsForSW_east_side = FieldContainer<double>(numPoints,1);
// universal rule is just flip along (-1,1): x --> -x
for (int i=0; i<numPoints; i++)
{
neighborPointsForSW_east_side(i, 0) = - _testPoints1D(i,0);
}
// determine actual values, and compare
FieldContainer<double> neighborRefPoints = FieldContainer<double>(numPoints,1);
_sw->getSidePointsInNeighborRefCoords(neighborRefPoints, EAST, _testPoints1D);
if ( !fcsAgree(neighborRefPoints,neighborPointsForSW_east_side,tol,maxDiff) )
{
cout << "Failure in mapping to neighbor ref coords; maxDiff = " << maxDiff << endl;
success = false;
}
return success;
}
bool ScratchPadTests::testConstantFunctionProduct()
{
bool success = true;
// set up basisCache (even though it won't really be used here)
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache( _elemType, _spectralConfusionMesh ) );
vector<GlobalIndexType> cellIDs;
int cellID = 0;
cellIDs.push_back(cellID);
basisCache->setPhysicalCellNodes( _spectralConfusionMesh->physicalCellNodesForCell(cellID),
cellIDs, true );
int numCells = _basisCache->getPhysicalCubaturePoints().dimension(0);
int numPoints = _testPoints.dimension(0);
FunctionPtr three = Function::constant(3.0);
FunctionPtr two = Function::constant(2.0);
FieldContainer<double> values(numCells,numPoints);
two->values(values,basisCache);
three->scalarMultiplyBasisValues( values, basisCache );
FieldContainer<double> expectedValues(numCells,numPoints);
expectedValues.initialize( 3.0 * 2.0 );
double tol = 1e-15;
double maxDiff = 0.0;
if ( ! fcsAgree(expectedValues, values, tol, maxDiff) )
{
success = false;
cout << "Expected product differs from actual; maxDiff: " << maxDiff << endl;
}
return success;
}
bool ElementTests::testParentPointMapping()
{
bool success = true;
double tol = 1e-15;
double maxDiff;
int SOUTH = 0, EAST = 1, NORTH = 2, WEST = 3;
// determine expected values
int numPoints = _testPoints1D.dimension(0);
FieldContainer<double> sw_east_points_for_ne_child = FieldContainer<double>(numPoints,1);
// along the east side, ne child is the second: so rule is add 1 and divide by 2
for (int i=0; i<numPoints; i++)
{
sw_east_points_for_ne_child(i, 0) = (_testPoints1D(i,0)+1.0)/2.0;
}
FieldContainer<double> sw_east_points_for_se_child = FieldContainer<double>(numPoints,1);
// along the east side, se child is the first: so rule is subtract 1 and divide by 2
for (int i=0; i<numPoints; i++)
{
sw_east_points_for_se_child(i, 0) = (_testPoints1D(i,0)-1.0)/2.0;
}
// determine actual values, and compare
FieldContainer<double> parentRefPoints = FieldContainer<double>(numPoints,1);
_sw_ne->getSidePointsInParentRefCoords(parentRefPoints, EAST, _testPoints1D);
if ( !fcsAgree(parentRefPoints,sw_east_points_for_ne_child,tol,maxDiff) )
{
cout << "Failure in mapping to parent ref coords for NE child; maxDiff = " << maxDiff << endl;
success = false;
}
_sw_se->getSidePointsInParentRefCoords(parentRefPoints, EAST, _testPoints1D);
if ( !fcsAgree(parentRefPoints,sw_east_points_for_se_child,tol,maxDiff) )
{
cout << "Failure in mapping to parent ref coords for SE child; maxDiff = " << maxDiff << endl;
success = false;
}
return success;
}
bool ScratchPadTests::testSpatiallyFilteredFunction()
{
bool success = true;
FunctionPtr one = Function::constant(1.0);
SpatialFilterPtr positiveX = Teuchos::rcp( new PositiveX );
FunctionPtr heaviside = Teuchos::rcp( new SpatiallyFilteredFunction<double>(one, positiveX) );
int numCells = _basisCache->getPhysicalCubaturePoints().dimension(0);
int numPoints = _testPoints.dimension(0);
FieldContainer<double> values(numCells,numPoints);
FieldContainer<double> expectedValues(numCells,numPoints);
for (int cellIndex=0; cellIndex<numCells; cellIndex++)
{
for (int ptIndex=0; ptIndex<numPoints; ptIndex++)
{
double x = _basisCache->getPhysicalCubaturePoints()(cellIndex,ptIndex,0);
if (x > 0)
{
expectedValues(cellIndex,ptIndex) = 1.0;
}
else
{
expectedValues(cellIndex,ptIndex) = 0.0;
}
}
}
heaviside->values(values,_basisCache);
double tol = 1e-15;
double maxDiff = 0.0;
if ( ! fcsAgree(expectedValues, values, tol, maxDiff) )
{
success = false;
cout << "testSpatiallyFilteredFunction: Expected values differ from actual; maxDiff: " << maxDiff << endl;
}
return success;
}
TEST_F(MPIWrapperTests, TestEntryWiseSum)
{
int numProcs = Teuchos::GlobalMPISession::getNProc();
int rank = Teuchos::GlobalMPISession::getRank();
FieldContainer<double> expectedValues(2);
for (int i=0; i<numProcs; i++) {
expectedValues[0] += i*i;
expectedValues[1] += 1;
}
FieldContainer<double> values(2);
values[0] = rank*rank;
values[1] = 1;
MPIWrapper::entryWiseSum(values);
double tol = 1e-16;
double maxDiff = 0;
EXPECT_TRUE(fcsAgree(values, expectedValues, tol, maxDiff))
<< "MPIWrapperTests::testentryWiseSum() failed with maxDiff " << maxDiff << endl;
// EXPECT_EQ(rank, 2) << "rank " << rank << endl;
}
bool MPIWrapperTests::testentryWiseSum() {
bool success = true;
int numProcs = Teuchos::GlobalMPISession::getNProc();
int rank = Teuchos::GlobalMPISession::getRank();
FieldContainer<double> expectedValues(2);
for (int i=0; i<numProcs; i++) {
expectedValues[0] += i*i;
expectedValues[1] += 1;
}
FieldContainer<double> values(2);
values[0] = rank*rank;
values[1] = 1;
MPIWrapper::entryWiseSum(values);
double tol = 1e-16;
double maxDiff = 0;
if (! fcsAgree(values, expectedValues, tol, maxDiff) ) {
success = false;
cout << "MPIWrapperTests::testentryWiseSum() failed with maxDiff " << maxDiff << endl;
}
return success;
}
bool LinearTermTests::testBoundaryPlusVolumeTerms()
{
bool success = true;
// notion is integration by parts:
// (div f, v) = < f * n, v > - (f, grad v)
// We perform two subtests for each test: first we try with a particular
// function substituted for the variable. Second, we integrate over the
// basis for the mesh (i.e. we test a whole bunch of functions, whose
// precise definition is a bit complicated).
// A third test is against the two-term LinearTerm::integrate() method.
// This doesn't do integration by parts, but rather tests that
// (u + u->dot_normal(), v) = (u,v) + (u->dot_normal(), v)
///////////// FIRST TEST ////////////////
// start simply: define f to be (x, 0)
// (div f, v) = (1, v)
// < f * n, v > - (f, grad v) = < x n1, v > - ( x, v->dx() )
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
FunctionPtr x2 = Function::xn(2);
FunctionPtr y2 = Function::yn(2);
FunctionPtr x3 = Function::xn(3);
FunctionPtr y3 = Function::yn(3);
vector< FunctionPtr > f_fxns;
f_fxns.push_back( Function::vectorize( x, Function::zero() ) ); // div of this = 1
f_fxns.push_back( Function::vectorize( x2 / 6.0, x2 * y / 2.0 ) ); // div of this = x / 3 + x^2 / 2
for ( vector< FunctionPtr >::iterator fIt = f_fxns.begin(); fIt != f_fxns.end(); fIt++)
{
FunctionPtr vector_fxn = *fIt;
LinearTermPtr lt_v = vector_fxn->div()*v1;
// part a: substitute v1 = x*y^2
FunctionPtr v1_value = x*y2;
map< int, FunctionPtr > var_values;
var_values[v1->ID()] = v1_value;
double expectedValue = lt_v->evaluate(var_values, false)->integrate(mesh);
FunctionPtr n = Function::normal();
LinearTermPtr ibp = vector_fxn * n * v1 - vector_fxn * v1->grad();
int numCells = basisCache->getPhysicalCubaturePoints().dimension(0);
int numPoints = basisCache->getPhysicalCubaturePoints().dimension(1);
int spaceDim = basisCache->getSpaceDim();
FieldContainer<double> vector_fxn_values(numCells,numPoints,spaceDim);
vector_fxn->values(vector_fxn_values,basisCache);
// cout << "vector_fxn values: \n" << vector_fxn_values;
double boundaryIntegralSum = ibp->evaluate(var_values,true)->integrate(mesh);
double volumeIntegralSum = ibp->evaluate(var_values,false)->integrate(mesh);
double actualValue = boundaryIntegralSum + volumeIntegralSum;
double tol = 1e-14;
if (abs(expectedValue - actualValue)>tol)
{
success = false;
}
// part b: integrate the bases over each of the cells:
int num_dofs = testOrder->totalDofs();
FieldContainer<double> integrals_expected( mesh->numActiveElements(), num_dofs );
FieldContainer<double> integrals_actual( mesh->numActiveElements(), num_dofs );
lt_v->integrate(integrals_expected,testOrder,basisCache);
ibp->integrate(integrals_actual,testOrder,basisCache);
double maxDiff = 0;
if (! fcsAgree(integrals_actual, integrals_expected, tol, maxDiff) )
{
cout << "LT integrated by parts does not agree with the original; maxDiff: " << maxDiff << endl;
success = false;
}
// just on the odd chance that ordering makes a difference, repeat this test with the opposite order in ibp:
ibp = - vector_fxn * v1->grad() + vector_fxn * n * v1;
ibp->integrate(integrals_actual,testOrder,basisCache, false, false);
maxDiff = 0;
if (! fcsAgree(integrals_actual, integrals_expected, tol, maxDiff) )
{
cout << "LT integrated by parts does not agree with the original; maxDiff: " << maxDiff << endl;
success = false;
}
// part c: two-term integrals
FieldContainer<double> integrals_expected_two_term( mesh->numActiveElements(), num_dofs, num_dofs);
FieldContainer<double> integrals_actual_two_term( mesh->numActiveElements(), num_dofs, num_dofs );
LinearTermPtr ibp1 = vector_fxn * n * v1;
LinearTermPtr ibp2 = - vector_fxn * v1->grad();
lt_v->integrate(integrals_expected_two_term, testOrder, ibp1 + ibp2, testOrder, basisCache, false, false);
lt_v->integrate(integrals_actual_two_term, testOrder, ibp1, testOrder, basisCache, false, false); // don't forceBoundary, don't sumInto
lt_v->integrate(integrals_actual_two_term, testOrder, ibp2, testOrder, basisCache, false, true); // DO sumInto
maxDiff = 0;
if (! fcsAgree(integrals_actual_two_term, integrals_expected_two_term, tol, maxDiff) )
{
cout << "two-term integration is not bilinear; maxDiff: " << maxDiff << endl;
success = false;
}
// now, same thing but with the roles of ibp{1|2} and lt_v reversed:
(ibp1 + ibp2)->integrate(integrals_expected_two_term, testOrder, lt_v, testOrder, basisCache, false, false);
ibp1->integrate(integrals_actual_two_term, testOrder, lt_v, testOrder, basisCache, false, false); // don't forceBoundary, don't sumInto
ibp2->integrate(integrals_actual_two_term, testOrder, lt_v, testOrder, basisCache, false, true); // DO sumInto
maxDiff = 0;
if (! fcsAgree(integrals_actual_two_term, integrals_expected_two_term, tol, maxDiff) )
{
cout << "two-term integration is not bilinear; maxDiff: " << maxDiff << endl;
success = false;
}
// now, test that two-term integration commutes in the two terms:
ibp1->integrate(integrals_expected_two_term, testOrder, lt_v, testOrder, basisCache, false, false);
lt_v->integrate(integrals_actual_two_term, testOrder, ibp1, testOrder, basisCache, false, false);
// we expect the integrals to commute up to a transpose, so let's transpose one of the containers:
transposeFieldContainer(integrals_expected_two_term);
maxDiff = 0;
if (! fcsAgree(integrals_actual_two_term, integrals_expected_two_term, tol, maxDiff) )
{
cout << "two-term integration does not commute for boundary value (ibp1); maxDiff: " << maxDiff << endl;
success = false;
}
ibp2->integrate(integrals_expected_two_term, testOrder, lt_v, testOrder, basisCache, false, false);
lt_v->integrate(integrals_actual_two_term, testOrder, ibp2, testOrder, basisCache, false, false);
// we expect the integrals to commute up to a transpose, so let's transpose one of the containers:
transposeFieldContainer(integrals_expected_two_term);
maxDiff = 0;
if (! fcsAgree(integrals_actual_two_term, integrals_expected_two_term, tol, maxDiff) )
{
cout << "two-term integration does not commute for volume value (ibp2); maxDiff: " << maxDiff << endl;
success = false;
}
// part d: to suss out where the integration failure happens in the non-commuting case:
// 1. Substitute v1 = 1 in ibp2; get a function ibp2_at_v1_equals_one back.
// 2. Substitute v1 = 1 in lt_v; get a function lt_v_at_v1_equals_one back.
// 3. Integrate ibp2_at_v1_equals_one * lt_v_at_v1_equals_one over the mesh. Get a double result.
// 4. Because basis is nodal, the representation for v1 = 1 is just all 1s for coefficients.
// Therefore, the sum of the entries in the integrals_*_two_term matrices will should match
// the function integral. Whichever doesn't match is wrong.
// first, let's confirm that the v1 basis *is* nodal:
BasisPtr v1Basis = testOrder->getBasis(v1->ID());
if (! v1Basis->isNodal())
{
cout << "testBoundaryPlusVolumeTerms: final part of test relies on a nodal basis, but the basis is not nodal.";
cout << " Exiting test early (with whatever success value we have thus far).\n";
return success;
}
map< int, FunctionPtr > v1_equals_one;
v1_equals_one[v1->ID()] = Function::constant(1.0);
FunctionPtr ibp1_at_v1_equals_one = ibp1->evaluate(v1_equals_one,true); // ibp1 has only a boundary term, so we just ask for this
FunctionPtr ibp2_at_v1_equals_one = ibp2->evaluate(v1_equals_one,false); // ibp2 has no boundary terms, so we don't ask for these
FunctionPtr lt_v_at_v1_equals_one = lt_v->evaluate(v1_equals_one,false); // lt_v also has no boundary terms
if (ibp1_at_v1_equals_one->isZero())
{
cout << "ibp1_at_v1_equals_one->isZero() = true.\n";
}
if (lt_v_at_v1_equals_one->isZero())
{
cout << "lt_v_at_v1_equals_one->isZero() = true.\n";
}
FieldContainer<double> integrals_lt_v_first( mesh->numActiveElements(), num_dofs, num_dofs );
FieldContainer<double> integrals_ibp1_first( mesh->numActiveElements(), num_dofs, num_dofs );
FieldContainer<double> integrals_ibp2_first( mesh->numActiveElements(), num_dofs, num_dofs );
double lt_v_first_integral = 0.0, ibp1_first_integral = 0.0, ibp2_first_integral = 0.0;
double integral = (ibp1_at_v1_equals_one * lt_v_at_v1_equals_one)->integrate(mesh);
ibp1->integrate(integrals_ibp1_first, testOrder, lt_v, testOrder, basisCache, false, false);
lt_v->integrate(integrals_lt_v_first, testOrder, ibp1, testOrder, basisCache, false, false);
for (int i=0; i<integrals_lt_v_first.size(); i++)
{
lt_v_first_integral += integrals_lt_v_first[i];
ibp1_first_integral += integrals_ibp1_first[i];
}
if (abs(lt_v_first_integral - integral) > tol)
{
double diff = abs(lt_v_first_integral - integral);
success = false;
cout << "Integral with v1=1 substituted does not match two-term integration of (lt_v,ibp1) with lt_v as this. diff = " << diff << "\n";
cout << "lt_v_first_integral = " << lt_v_first_integral << endl;
cout << " (true) integral = " << integral << endl;
}
if (abs(ibp1_first_integral - integral) > tol)
{
double diff = abs(ibp1_first_integral - integral);
success = false;
cout << "Integral with v1=1 substituted does not match two-term integration of (lt_v,ibp1) with ibp1 as this. diff = " << diff << "\n";
cout << "ibp1_first_integral = " << ibp1_first_integral << endl;
cout << " (true) integral = " << integral << endl;
}
// now, do the same but for ibp2
integral = (ibp2_at_v1_equals_one * lt_v_at_v1_equals_one)->integrate(mesh);
ibp2->integrate(integrals_ibp2_first, testOrder, lt_v, testOrder, basisCache, false, false);
lt_v->integrate(integrals_lt_v_first, testOrder, ibp2, testOrder, basisCache, false, false);
// reset the sums:
lt_v_first_integral = 0.0;
ibp1_first_integral = 0.0;
ibp2_first_integral = 0.0;
for (int i=0; i<integrals_lt_v_first.size(); i++)
{
lt_v_first_integral += integrals_lt_v_first[i];
ibp2_first_integral += integrals_ibp2_first[i];
}
if (abs(lt_v_first_integral - integral) > tol)
{
double diff = abs(lt_v_first_integral - integral);
success = false;
cout << "Integral with v1=1 substituted does not match two-term integration of (lt_v,ibp2) with lt_v as this. diff = " << diff << "\n";
cout << "lt_v_first_integral = " << lt_v_first_integral << endl;
cout << " (true) integral = " << integral << endl;
}
if (abs(ibp2_first_integral - integral) > tol)
{
double diff = abs(ibp2_first_integral - integral);
success = false;
cout << "Integral with v1=1 substituted does not match two-term integration of (lt_v,ibp2) with ibp2 as this. diff = " << diff << "\n";
cout << "ibp1_first_integral = " << ibp1_first_integral << endl;
cout << " (true) integral = " << integral << endl;
}
}
return success;
}
bool ParametricCurveTests::testGradientWrapper()
{
bool success = true;
// create an artificial function whose gradient is "interesting" and known
FunctionPtr t1 = Function::xn(1);
FunctionPtr t2 = Function::yn(1);
FunctionPtr xt = t1 + t1 * t2;
FunctionPtr yt = t2 + 2 * t1 * t2;
FunctionPtr xt_dt1 = 1 + t2;
FunctionPtr xt_dt2 = t1;
FunctionPtr yt_dt1 = 2 * t2;
FunctionPtr yt_dt2 = 1 + 2 * t1;
FunctionPtr ft = Function::vectorize(xt, yt);
FunctionPtr ft_dt1 = Function::vectorize(xt_dt1, yt_dt1);
FunctionPtr ft_dt2 = Function::vectorize(xt_dt2, yt_dt2);
FunctionPtr ft_gradt = Function::vectorize(ft_dt1, ft_dt2);
// first test: confirm that on a parametric quad, the wrapped function agrees with the naked one
int cubatureDegree = 5;
BasisCachePtr parametricQuadCache = BasisCache::parametricQuadCache(cubatureDegree);
FunctionPtr fx_gradx = ParametricCurve::parametricGradientWrapper(ft_gradt, true);
double tol = 1e-14;
if (! ft_gradt->equals(fx_gradx, parametricQuadCache))
{
success = false;
cout << "on a parametric quad, the wrapped gradient doesn't agree with the naked one";
reportFunctionValueDifferences(ft_gradt, fx_gradx, parametricQuadCache, tol);
}
if (! ft_gradt->equals(ft->grad(), parametricQuadCache))
{
success = false;
cout << "on a parametric quad, manual gradient disagrees with automatic one (error in test construction, likely).";
reportFunctionValueDifferences(ft_gradt, ft->grad(), parametricQuadCache, tol);
}
// on the quad domain defined by (0,0), (1,0), (2,3), (0,1),
// some algebra shows that for x and y as functions of the parametric
// coordinates, we have
// x = t1 + t1 * t2
// y = t2 + 2 * t1 * t2
// which gives the result that our original function f(t1,t2) = (t1 + t1 * t2, t2 + 2 * t1 * t2) = (x, y)
FunctionPtr x = Function::xn(1); // understood in physical space
FunctionPtr y = Function::yn(1);
FunctionPtr f1_xy = x;
FunctionPtr f2_xy = y;
FunctionPtr f_xy = Function::vectorize(f1_xy, f2_xy);
// set up the quad domain
FieldContainer<double> physicalCellNodes(1,4,2); // (C,P,D)
physicalCellNodes(0,0,0) = 0;
physicalCellNodes(0,0,1) = 0;
physicalCellNodes(0,1,0) = 1;
physicalCellNodes(0,1,1) = 0;
physicalCellNodes(0,2,0) = 2;
physicalCellNodes(0,2,1) = 3;
physicalCellNodes(0,3,0) = 0;
physicalCellNodes(0,3,1) = 1;
// physical space BasisCache:
shards::CellTopology quad_4(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(physicalCellNodes, quad_4, cubatureDegree));
// as a preliminary test, check that the Jacobian values and inverse values agree with our expectations
// we expect the Jacobian to be:
// [ 1 + t2 t1 ]
// 1/2 * [ ]
// [ 2 * t2 1 + t2 ]
// where (t1,t2) are parametric coordinates and the 1/2 comes from the transformation from reference
// to parametric space
int numCells = 1;
int numPoints = basisCache->getRefCellPoints().dimension(0);
int spaceDim = 2;
FieldContainer<double> jacobianExpected(numCells,numPoints,spaceDim,spaceDim);
FieldContainer<double> jacobianInvExpected(numCells,numPoints,spaceDim,spaceDim);
// also check that the function we've chosen has the expected values
// by first computing its gradient in parametric space and then dividing by 2 to account
// for the transformation from reference to parametric space
FieldContainer<double> fgrad_based_jacobian(numCells,numPoints,spaceDim,spaceDim);
ft_gradt->values(fgrad_based_jacobian, parametricQuadCache);
FieldContainer<double> parametricPoints = basisCache->computeParametricPoints();
for (int ptIndex=0; ptIndex<numPoints; ptIndex++)
{
double t1 = parametricPoints(0,ptIndex,0);
double t2 = parametricPoints(0,ptIndex,1);
jacobianExpected(0,ptIndex,0,0) = 0.5 * (1 + t2);
jacobianExpected(0,ptIndex,0,1) = 0.5 * (t1);
jacobianExpected(0,ptIndex,1,0) = 0.5 * (2 * t2);
jacobianExpected(0,ptIndex,1,1) = 0.5 * (1 + 2 * t1);
jacobianInvExpected(0,ptIndex,0,0) = (2.0 / (1 + 2 * t1 + t2) ) * (1 + 2 * t1);
jacobianInvExpected(0,ptIndex,0,1) = (2.0 / (1 + 2 * t1 + t2) ) * (- t1);
jacobianInvExpected(0,ptIndex,1,0) = (2.0 / (1 + 2 * t1 + t2) ) * (- 2 * t2);
jacobianInvExpected(0,ptIndex,1,1) = (2.0 / (1 + 2 * t1 + t2) ) * (1 + t2);
fgrad_based_jacobian(0,ptIndex,0,0) /= 2.0;
fgrad_based_jacobian(0,ptIndex,0,1) /= 2.0;
fgrad_based_jacobian(0,ptIndex,1,0) /= 2.0;
fgrad_based_jacobian(0,ptIndex,1,1) /= 2.0;
}
FieldContainer<double> jacobian = basisCache->getJacobian();
FieldContainer<double> jacobianInv = basisCache->getJacobianInv();
double maxDiff = 0;
if (! fcsAgree(jacobianExpected, jacobian, tol, maxDiff))
{
success = false;
cout << "Jacobian expected does not match actual.\n";
reportFunctionValueDifferences(parametricPoints, jacobian, jacobianExpected, tol);
}
if (! fcsAgree(jacobianInvExpected, jacobianInv, tol, maxDiff))
{
success = false;
cout << "Jacobian inverse expected does not match actual.\n";
reportFunctionValueDifferences(parametricPoints, jacobianInv, jacobianInvExpected, tol);
}
if (! fcsAgree(fgrad_based_jacobian, jacobianExpected, tol, maxDiff))
{
success = false;
cout << "Jacobian from fgrad does not agree with the transformation jacobian (problem with test?).\n";
reportFunctionValueDifferences(parametricPoints, fgrad_based_jacobian, jacobianExpected, tol);
}
// test that the gradient values agree
if (! fx_gradx->equals(f_xy->grad(), basisCache))
{
success = false;
cout << "wrapped gradient does not agree with analytically transformed function.\n";
reportFunctionValueDifferences(fx_gradx, f_xy->grad(), basisCache, tol);
}
// finally, although this isn't really the right place for this, it is convenient here
// to test the TFI for the "mesh" we were concerned with above.
int H1Order = 5;
BFPtr bf = VGPStokesFormulation(1.0).bf();
physicalCellNodes.resize(4,2);
int horizontalElements = 1, verticalElements = 1;
MeshPtr mesh = MeshFactory::quadMesh(bf, H1Order, physicalCellNodes);
int cellID = 0;
vector< ParametricCurvePtr > edges = mesh->parametricEdgesForCell(cellID);
ParametricSurfacePtr tfi = ParametricSurface::transfiniteInterpolant(edges);
double v2[2];
edges[2]->value(0, v2[0], v2[1]);
// cout << "v2 = (" << v2[0] << ", " << v2[1] << ")\n";
if ( ! tfi->equals(f_xy, basisCache) )
{
success = false;
cout << "TFI does not agree with analytically constructed transformation function.\n";
reportFunctionValueDifferences(tfi, f_xy, basisCache, tol);
}
if ( ! tfi->grad()->equals(f_xy->grad(), basisCache) )
{
success = false;
cout << "TFI does not agree with analytically constructed transformation function.\n";
reportFunctionValueDifferences(tfi->grad(), f_xy->grad(), basisCache, tol);
}
return success;
}
bool FunctionTests::testValuesDottedWithTensor()
{
bool success = true;
vector< FunctionPtr > vectorFxns;
double xValue = 3, yValue = 4;
FunctionPtr simpleVector = Function::vectorize(Function::constant(xValue), Function::constant(yValue));
vectorFxns.push_back(simpleVector);
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
vectorFxns.push_back( Function::vectorize(x*x, x*y) );
VGPStokesFormulation vgpStokes = VGPStokesFormulation(1.0);
BFPtr bf = vgpStokes.bf();
int h1Order = 1;
MeshPtr mesh = MeshFactory::quadMesh(bf, h1Order);
int cellID=0; // the only cell
BasisCachePtr basisCache = BasisCache::basisCacheForCell(mesh, cellID);
for (int i=0; i<vectorFxns.size(); i++)
{
FunctionPtr vectorFxn_i = vectorFxns[i];
for (int j=0; j<vectorFxns.size(); j++)
{
FunctionPtr vectorFxn_j = vectorFxns[j];
FunctionPtr dotProduct = vectorFxn_i * vectorFxn_j;
FunctionPtr expectedDotProduct = vectorFxn_i->x() * vectorFxn_j->x() + vectorFxn_i->y() * vectorFxn_j->y();
if (! expectedDotProduct->equals(dotProduct, basisCache))
{
cout << "testValuesDottedWithTensor() failed: expected dot product does not match dotProduct.\n";
success = false;
double tol = 1e-14;
reportFunctionValueDifferences(dotProduct, expectedDotProduct, basisCache, tol);
}
}
}
// now, let's try the same thing, but for a LinearTerm dot product
VarFactoryPtr vf = VarFactory::varFactory();
VarPtr v = vf->testVar("v", HGRAD);
DofOrderingPtr dofOrdering = Teuchos::rcp( new DofOrdering(CellTopology::quad()) );
shards::CellTopology quad_4(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
BasisPtr basis = BasisFactory::basisFactory()->getBasis(h1Order, quad_4.getKey(), Camellia::FUNCTION_SPACE_HGRAD);
dofOrdering->addEntry(v->ID(), basis, v->rank());
int numCells = 1;
int numFields = basis->getCardinality();
for (int i=0; i<vectorFxns.size(); i++)
{
FunctionPtr f_i = vectorFxns[i];
LinearTermPtr lt_i = f_i * v;
LinearTermPtr lt_i_x = f_i->x() * v;
LinearTermPtr lt_i_y = f_i->y() * v;
for (int j=0; j<vectorFxns.size(); j++)
{
FunctionPtr f_j = vectorFxns[j];
LinearTermPtr lt_j = f_j * v;
LinearTermPtr lt_j_x = f_j->x() * v;
LinearTermPtr lt_j_y = f_j->y() * v;
FieldContainer<double> values(numCells,numFields,numFields);
lt_i->integrate(values, dofOrdering, lt_j, dofOrdering, basisCache);
FieldContainer<double> values_expected(numCells,numFields,numFields);
lt_i_x->integrate(values_expected,dofOrdering,lt_j_x,dofOrdering,basisCache);
lt_i_y->integrate(values_expected,dofOrdering,lt_j_y,dofOrdering,basisCache);
double tol = 1e-14;
double maxDiff = 0;
if (!fcsAgree(values, values_expected, tol, maxDiff))
{
cout << "FunctionTests::testValuesDottedWithTensor: ";
cout << "dot product and sum of the products of scalar components differ by maxDiff " << maxDiff;
cout << " in LinearTerm::integrate().\n";
success = false;
}
}
}
// // finally, let's try the same sort of thing, but now with a vector-valued basis
// BasisPtr vectorBasisTemp = BasisFactory::basisFactory()->getBasis(h1Order, quad_4.getKey(), Camellia::FUNCTION_SPACE_VECTOR_HGRAD);
// VectorBasisPtr vectorBasis = Teuchos::rcp( (VectorizedBasis<double, FieldContainer<double> > *)vectorBasisTemp.get(),false);
//
// BasisPtr compBasis = vectorBasis->getComponentBasis();
//
// // create a new v, and a new dofOrdering
// VarPtr v_vector = vf->testVar("v_vector", VECTOR_HGRAD);
// dofOrdering = Teuchos::rcp( new DofOrdering );
// dofOrdering->addEntry(v_vector->ID(), vectorBasis, v_vector->rank());
//
// DofOrderingPtr dofOrderingComp = Teuchos::rcp( new DofOrdering );
// dofOrderingComp->addEntry(v->ID(), compBasis, v->rank());
//
return success;
}
bool FunctionTests::testJacobianOrdering()
{
bool success = true;
FunctionPtr y = Function::yn(1);
FunctionPtr f = Function::vectorize(y, Function::zero());
// test 1: Jacobian ordering is f_i,j
int spaceDim = 2;
int cellID = 0;
BasisCachePtr basisCache = BasisCache::basisCacheForCell(_spectralConfusionMesh, cellID);
FieldContainer<double> physicalPoints = basisCache->getPhysicalCubaturePoints();
int numCells = physicalPoints.dimension(0);
int numPoints = physicalPoints.dimension(1);
FieldContainer<double> expectedValues(numCells, numPoints, spaceDim, spaceDim);
for (int cellIndex=0; cellIndex<numCells; cellIndex++)
{
for (int ptIndex=0; ptIndex<numPoints; ptIndex++)
{
expectedValues(cellIndex,ptIndex,0,0) = 0;
expectedValues(cellIndex,ptIndex,0,1) = 1;
expectedValues(cellIndex,ptIndex,1,0) = 0;
expectedValues(cellIndex,ptIndex,1,1) = 0;
}
}
FieldContainer<double> values(numCells, numPoints, spaceDim, spaceDim);
f->grad(spaceDim)->values(values, basisCache);
double maxDiff = 0;
double tol = 1e-14;
if (! fcsAgree(expectedValues, values, tol, maxDiff))
{
cout << "expectedValues does not match values in testJacobianOrdering().\n";
reportFunctionValueDifferences(physicalPoints, expectedValues, values, tol);
success = false;
}
// test 2: ordering of VectorizedBasis agrees
// (actually implemented where it belongs, in Vectorized_BasisTestSuite)
// test 3: ordering of CellTools::getJacobian
FieldContainer<double> nodes(1,4,2);
nodes(0,0,0) = 1;
nodes(0,0,1) = -2;
nodes(0,1,0) = 1;
nodes(0,1,1) = 2;
nodes(0,2,0) = -1;
nodes(0,2,1) = 2;
nodes(0,3,0) = -1;
nodes(0,3,1) = -2;
shards::CellTopology quad_4(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
int cubDegree = 4;
BasisCachePtr rotatedCache = Teuchos::rcp( new BasisCache(nodes, quad_4, cubDegree) );
physicalPoints = rotatedCache->getPhysicalCubaturePoints();
numCells = physicalPoints.dimension(0);
numPoints = physicalPoints.dimension(1);
FieldContainer<double> expectedJacobian(numCells,numPoints,spaceDim,spaceDim);
for (int cellIndex=0; cellIndex<numCells; cellIndex++)
{
for (int ptIndex=0; ptIndex<numPoints; ptIndex++)
{
expectedJacobian(cellIndex,ptIndex,0,0) = 0;
expectedJacobian(cellIndex,ptIndex,0,1) = -1;
expectedJacobian(cellIndex,ptIndex,1,0) = 2;
expectedJacobian(cellIndex,ptIndex,1,1) = 0;
}
}
FieldContainer<double> jacobianValues = rotatedCache->getJacobian();
maxDiff = 0;
if (! fcsAgree(expectedJacobian, jacobianValues, tol, maxDiff))
{
cout << "expectedJacobian does not match jacobianValues in testJacobianOrdering().\n";
reportFunctionValueDifferences(physicalPoints, expectedJacobian, jacobianValues, tol);
success = false;
}
return success;
}