void TestSimpleUniformSourceParabolicPdeMethods() throw(Exception)
{
// Create a PDE object
SimpleUniformSourceParabolicPde<2> pde(0.1);
// Test that the member variables have been initialised correctly
TS_ASSERT_EQUALS(pde.GetCoefficient(),0.1);
// Test methods
ChastePoint<2> point;
TS_ASSERT_DELTA(pde.ComputeSourceTerm(point,DBL_MAX), 0.1, 1e-6);
TS_ASSERT_DELTA(pde.ComputeDuDtCoefficientFunction(point), 1.0, 1e-6);
c_matrix<double,2,2> diffusion_matrix = pde.ComputeDiffusionTerm(point);
for (unsigned i=0; i<2; i++)
{
for (unsigned j=0; j<2; j++)
{
double value = 0.0;
if (i == j)
{
value = 1.0;
}
TS_ASSERT_DELTA(diffusion_matrix(i,j), value, 1e-6);
}
}
}
void TestSimpleUniformSourcePdeMethods() throw(Exception)
{
EXIT_IF_PARALLEL;
// Create a PDE object
SimpleUniformSourcePde<2> pde(0.05);
// Test that the member variables have been initialised correctly
TS_ASSERT_DELTA(pde.GetCoefficient(), 0.05, 1e-6);
ChastePoint<2> point;
TS_ASSERT_DELTA(pde.ComputeConstantInUSourceTerm(point, NULL), 0.0, 1e-6);
TS_ASSERT_DELTA(pde.ComputeLinearInUCoeffInSourceTerm(point, NULL), 0.05, 1e-6);
c_matrix<double,2,2> diffusion_matrix = pde.ComputeDiffusionTerm(point);
for (unsigned i=0; i<2; i++)
{
for (unsigned j=0; j<2; j++)
{
double value = 0.0;
if (i == j)
{
value = 1.0;
}
TS_ASSERT_DELTA(diffusion_matrix(i,j), value, 1e-6);
}
}
}
DenseSymmetricMatrix compute_diffusion_matrix(RandomAccessIterator begin, RandomAccessIterator end, DistanceCallback callback,
const ScalarType width)
{
timed_context context("Diffusion map matrix computation");
const IndexType n_vectors = end-begin;
DenseSymmetricMatrix diffusion_matrix(n_vectors,n_vectors);
DenseVector p = DenseVector::Zero(n_vectors);
RESTRICT_ALLOC;
// compute gaussian kernel matrix
#pragma omp parallel shared(diffusion_matrix,begin,callback) default(none)
{
IndexType i_index_iter, j_index_iter;
#pragma omp for nowait
for (i_index_iter=0; i_index_iter<n_vectors; ++i_index_iter)
{
for (j_index_iter=i_index_iter; j_index_iter<n_vectors; ++j_index_iter)
{
ScalarType k = callback.distance(begin[i_index_iter],begin[j_index_iter]);
ScalarType gk = exp(-(k*k)/width);
diffusion_matrix(i_index_iter,j_index_iter) = gk;
diffusion_matrix(j_index_iter,i_index_iter) = gk;
}
}
}
// compute column sum vector
p = diffusion_matrix.colwise().sum();
// compute full matrix as we need to compute sum later
// TODO add weighting alpha, use linear algebra to compute D^-alpha K D^-alpha
for (IndexType i=0; i<n_vectors; i++)
for (IndexType j=0; j<n_vectors; j++)
diffusion_matrix(i,j) /= p(i)*p(j);
// compute sqrt of column sum vector
p = diffusion_matrix.colwise().sum().cwiseSqrt();
for (IndexType i=0; i<n_vectors; i++)
for (IndexType j=0; j<n_vectors; j++)
diffusion_matrix(i,j) /= p(i)*p(j);
UNRESTRICT_ALLOC;
return diffusion_matrix;
}
void TestCellwiseSourcePdeMethods() throw(Exception)
{
EXIT_IF_PARALLEL;
// Set up cell population
HoneycombMeshGenerator generator(5, 5, 0);
MutableMesh<2,2>* p_mesh = generator.GetMesh();
std::vector<CellPtr> cells;
CellsGenerator<FixedDurationGenerationBasedCellCycleModel, 2> cells_generator;
cells_generator.GenerateBasic(cells, p_mesh->GetNumNodes());
MeshBasedCellPopulation<2> cell_population(*p_mesh, cells);
// Create a PDE object
CellwiseSourcePde<2> pde(cell_population, 0.05);
// Test that the member variables have been initialised correctly
TS_ASSERT_EQUALS(&(pde.rGetCellPopulation()), &cell_population);
TS_ASSERT_DELTA(pde.GetCoefficient(), 0.05, 1e-6);
// Test methods
Node<2>* p_node = cell_population.GetNodeCorrespondingToCell(*(cell_population.Begin()));
TS_ASSERT_DELTA(pde.ComputeLinearInUCoeffInSourceTermAtNode(*p_node), 0.05, 1e-6);
ChastePoint<2> point;
c_matrix<double,2,2> diffusion_matrix = pde.ComputeDiffusionTerm(point);
for (unsigned i=0; i<2; i++)
{
for (unsigned j=0; j<2; j++)
{
double value = 0.0;
if (i == j)
{
value = 1.0;
}
TS_ASSERT_DELTA(diffusion_matrix(i,j), value, 1e-6);
}
}
}
void TestAveragedSourcePdeMethods() throw(Exception)
{
EXIT_IF_PARALLEL;
// Set up cell population
HoneycombMeshGenerator generator(5, 5, 0);
MutableMesh<2,2>* p_mesh = generator.GetMesh();
std::vector<CellPtr> cells;
CellsGenerator<FixedDurationGenerationBasedCellCycleModel, 2> cells_generator;
cells_generator.GenerateBasic(cells, p_mesh->GetNumNodes());
MeshBasedCellPopulation<2> cell_population(*p_mesh, cells);
// Create a PDE object
AveragedSourcePde<2> pde(cell_population, 0.05);
// Test that the member variables have been initialised correctly
TS_ASSERT_EQUALS(&(pde.rGetCellPopulation()), &cell_population);
TS_ASSERT_DELTA(pde.GetCoefficient(), 0.05, 1e-6);
// For simplicity we create a very large coarse mesh, so we know that all cells are contained in one element
TrianglesMeshReader<2,2> mesh_reader("mesh/test/data/square_2_elements");
TetrahedralMesh<2,2> coarse_mesh;
coarse_mesh.ConstructFromMeshReader(mesh_reader);
coarse_mesh.Scale(10.0, 10.0);
// Test SetupSourceTerms() when no map between cells and coarse mesh elements is supplied
pde.SetupSourceTerms(coarse_mesh);
TS_ASSERT_EQUALS(pde.mCellDensityOnCoarseElements.size(), 2u);
// The first element has area 0.5*10*10 = 50 and there are 5*5 = 25 cells, so the cell density is 25/50 = 0.5
TS_ASSERT_DELTA(pde.mCellDensityOnCoarseElements[0], 0.5, 1e-6);
// The first element doesn't contain any cells, so the cell density is zero
TS_ASSERT_DELTA(pde.mCellDensityOnCoarseElements[1], 0.0, 1e-6);
// Now test SetupSourceTerms() when a map between cells and coarse mesh elements is supplied
std::map<CellPtr, unsigned> cell_pde_element_map;
for (AbstractCellPopulation<2>::Iterator cell_iter = cell_population.Begin();
cell_iter != cell_population.End();
++cell_iter)
{
cell_pde_element_map[*cell_iter] = 0;
}
pde.SetupSourceTerms(coarse_mesh, &cell_pde_element_map);
TS_ASSERT_DELTA(pde.mCellDensityOnCoarseElements[0], 0.5, 1e-6);
TS_ASSERT_DELTA(pde.mCellDensityOnCoarseElements[1], 0.0, 1e-6);
// Test GetUptakeRateForElement()
TS_ASSERT_DELTA(pde.GetUptakeRateForElement(0), 0.5, 1e-6);
TS_ASSERT_DELTA(pde.GetUptakeRateForElement(1), 0.0, 1e-6);
// Test other methods
ChastePoint<2> point;
TS_ASSERT_DELTA(pde.ComputeLinearInUCoeffInSourceTerm(point, coarse_mesh.GetElement(0)), 0.05*0.5, 1e-6);
TS_ASSERT_DELTA(pde.ComputeConstantInUSourceTerm(point, NULL), 0.0, 1e-6);
c_matrix<double,2,2> diffusion_matrix = pde.ComputeDiffusionTerm(point);
for (unsigned i=0; i<2; i++)
{
for (unsigned j=0; j<2; j++)
{
double value = 0.0;
if (i == j)
{
value = 1.0;
}
TS_ASSERT_DELTA(diffusion_matrix(i,j), value, 1e-6);
}
}
}