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Commit b9e712ac authored by Oliver Sander's avatar Oliver Sander
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Rip out the complete test for eigenValuesNonSym and replace it by the Rosser... 

Rip out the complete test for eigenValuesNonSym and replace it by the Rosser matrix test from fieldmatrixtest.cc

The old test was complete nonsense: an implementation of some sort of strange
undocumented shape function set that happened to need eigenvalues for something.
Lots of undocumented code, and no checks at all whether the values obtained
by eigenValuesNonSym actually make sense.

Only, for the particular choice of parameters used, eigenValuesNonSym was never
called.  Yes, you read this correctly: these hundreds of lines of code didn't
actually test anything.

The new test is copied form fieldmatrixtest.cc and adapted for DynamicMatrix
types.  It computes eigenvalues of a given 8x8 matrix and compares with the known
results.  Unfortunately, the test matrix is only symmetric.  Tests with more
general matrices are left for another day.
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dune/common/test/eigenvaluestest.cc
+ 76
− 234
View file @ b9e712ac
...@@ -4,257 +4,99 @@ ...@@ -4,257 +4,99 @@
#include "config.h" #include "config.h"
#endif #endif
//==============================================================================
//!
//! \date Nov 9 2011
//!
//! \author Arne Morten Kvarving / SINTEF
//!
//==============================================================================
#include <dune/common/fvector.hh> #include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
#include <dune/common/dynmatrixev.hh> #include <dune/common/dynmatrixev.hh>
#include <algorithm> #include <algorithm>
#include <complex> #include <complex>
using namespace Dune;
//! \brief Represents a cardinal function on a line /** \brief Test the eigenvalue code with the Rosser test matrix
template<class ctype, class rtype>
class LagrangeCardinalFunction
{
public:
//! \brief Empty default constructor
LagrangeCardinalFunction() {}
//! \brief Construct a cardinal function with the given nodes
//! \param[in] nodes_ The nodes
//! \param[in] i The node this function is associated with
LagrangeCardinalFunction(const std::vector<rtype>& nodes_,
size_t i)
: nodes(nodes_), node(i) {}
//! \brief Evaluate the shape function
//! \param[in] local The local coordinates
rtype evaluateFunction(const ctype& local) const
{
rtype result = 1;
for (size_t i=0; i < nodes.size(); ++i) {
if (i != node)
result *= (local-nodes[i])/(nodes[node]-nodes[i]);
}
return result;
}
//! \brief Evaluate the derivative of the cardinal function
//! \param[in] local The local coordinates
rtype evaluateGradient(const ctype& local) const
{
rtype result = 0;
for (size_t i=0; i < nodes.size(); ++i) {
rtype f = 1;
for (int j=0; j < nodes.size(); ++j) {
if (i != j && j != node)
f *= (local-nodes[j])/(nodes[node]-nodes[j]);
}
result += f/(nodes[node]-nodes[i]);
}
return result;
}
private: This matrix was a challenge for many matrix eigenvalue
//! \brief The nodes algorithms. But the Francis QR algorithm, as perfected by
std::vector<rtype> nodes; Wilkinson and implemented in EISPACK, has no trouble with it. The
matrix is 8-by-8 with integer elements. It has:
size_t node; * A double eigenvalue
}; * Three nearly equal eigenvalues
* Dominant eigenvalues of opposite sign
* A zero eigenvalue
* A small, nonzero eigenvalue
//! \brief Represents a tensor-product of 1D functions */
template<class rtype, class ctype, class ftype, int dim> template<typename ft>
class TensorProductFunction void testRosserMatrix()
{ {
public: // Hack: I want this matrix to be a DynamicMatrix, but currently I cannot
//! \brief The dimension of the function // initialize such a matrix from initializer lists. Therefore I take the
enum { dimension = dim }; // detour over a FieldMatrix.
FieldMatrix<ft,8,8> AField = {
//! \brief Empty default constructor { 611, 196, -192, 407, -8, -52, -49, 29 },
TensorProductFunction() {} { 196, 899, 113, -192, -71, -43, -8, -44 },
{ -192, 113, 899, 196, 61, 49, 8, 52 },
//! \brief Construct a tensor-product function { 407, -192, 196, 611, 8, 44, 59, -23 },
//! \param[in] funcs_ The functions { -8, -71, 61, 8, 411, -599, 208, 208 },
TensorProductFunction(const Dune::FieldVector<ftype, dim>& funcs_) { -52, -43, 49, 44, -599, 411, 208, 208 },
: funcs(funcs_) {} { -49, -8, 8, 59, 208, 208, 99, -911 },
{ 29, -44, 52, -23, 208, 208, -911, 99}
//! \brief Evaluate the function };
//! \param[in] local The local coordinates
rtype evaluateFunction(const Dune::FieldVector<ctype,dim>& local) const DynamicMatrix<ft> A(8,8);
for (int i=0; i<8; i++)
for (int j=0; j<8; j++)
A[i][j] = AField[i][j];
// compute eigenvalues
DynamicVector<std::complex<ft> > eigenComplex;
DynamicMatrixHelp::eigenValuesNonSym(A, eigenComplex);
// test results
/*
reference solution computed with octave 3.2
> format long e
> eig(rosser())
*/
std::vector<ft> reference = {
-1.02004901843000e+03,
-4.14362871168386e-14,
9.80486407214362e-02,
1.00000000000000e+03,
1.00000000000000e+03,
1.01990195135928e+03,
1.02000000000000e+03,
1.02004901843000e+03
};
std::vector<ft> eigenRealParts(8);
for (int i=0; i<8; i++)
eigenRealParts[i] = std::real(eigenComplex[i]);
std::sort(eigenRealParts.begin(), eigenRealParts.end());
for (int i=0; i<8; i++)
{ {
rtype result = 1; if (std::fabs(std::imag(eigenComplex[i])) > 1e-10)
for (int i=0; i < dim; ++i) DUNE_THROW(MathError, "Symmetric matrix has complex eigenvalue");
result *= funcs[i].evaluateFunction(local[i]);
return result; if( std::fabs(reference[i] - eigenRealParts[i]) > 1e-10 )
DUNE_THROW(MathError,"error computing eigenvalues");
} }
Dune::FieldVector<rtype, dim> std::cout << "Eigenvalues of Rosser matrix: " << eigenComplex << std::endl;
evaluateGradient(const Dune::FieldVector<ctype,dim>& local) const }
{
Dune::FieldVector<rtype, dim> result;
for (int i=0; i < dim; ++i)
result[i] = funcs[i].evaluateGradient(local[i]);
}
private:
Dune::FieldVector<ftype, dim> funcs;
};
template<int dim>
class PNShapeFunctionSet
{
public:
typedef LagrangeCardinalFunction<double, double> CardinalFunction;
typedef TensorProductFunction<double, double, CardinalFunction, dim>
ShapeFunction;
PNShapeFunctionSet(int n1, int n2, int n3=0)
{
int dims[3] = {n1, n2, n3};
cfuncs.resize(dim);
for (int i=0; i < dim; ++i) {
std::vector<double> grid;
grid = gaussLobattoLegendreGrid(dims[i]);
for (int j=0; j<dims[i]; ++j)
cfuncs[i].push_back(CardinalFunction(grid,j));
}
int l=0;
Dune::FieldVector<CardinalFunction,dim> fs;
if (dim == 3) {
f.resize(n1*n2*n3);
for (int k=0; k < n3; ++k) {
for (int j=0; j < n2; ++j)
for (int i=0; i< n1; ++i) {
fs[0] = cfuncs[0][i];
fs[1] = cfuncs[1][j];
fs[2] = cfuncs[2][k];
f[l++] = ShapeFunction(fs);
}
}
} else {
f.resize(n1*n2);
for (int j=0; j < n2; ++j) {
for (int i=0; i< n1; ++i) {
fs[0] = cfuncs[0][i];
fs[1] = cfuncs[1][j];
f[l++] = ShapeFunction(fs);
}
}
}
}
//! \brief Obtain a given shape function
//! \param[in] i The requested shape function
const ShapeFunction& operator[](int i) const
{
return f[i];
}
int size()
{
return f.size();
}
protected:
std::vector< std::vector<CardinalFunction> > cfuncs;
std::vector<ShapeFunction> f;
double legendre(double x, int n)
{
std::vector<double> Ln;
Ln.resize(n+1);
Ln[0] = 1.f;
Ln[1] = x;
if( n > 1 ) {
for( int i=1; i<n; i++ )
Ln[i+1] = (2*i+1.0)/(i+1.0)*x*Ln[i]-i/(i+1.0)*Ln[i-1];
}
return Ln[n];
}
double legendreDerivative(double x, int n)
{
std::vector<double> Ln;
Ln.resize(n+1);
Ln[0] = 1.0; Ln[1] = x;
if( (x == 1.0) || (x == -1.0) )
return( pow(x,n-1)*n*(n+1.0)/2.0 );
else {
for( int i=1; i<n; i++ )
Ln[i+1] = (2.0*i+1.0)/(i+1.0)*x*Ln[i]-(double)i/(i+1.0)*Ln[i-1];
return( (double)n/(1.0-x*x)*Ln[n-1]-n*x/(1-x*x)*Ln[n] );
}
}
std::vector<double> gaussLegendreGrid(int n)
{
Dune::DynamicMatrix<double> A(n,n,0.0);
A[0][1] = 1.f;
for (int i=1; i<n-1; ++i) {
A[i][i-1] = (double)i/(2.0*(i+1.0)-1.0);
A[i][i+1] = (double)(i+1.0)/(2*(i+1.0)-1.0);
}
A[n-1][n-2] = (n-1.0)/(2.0*n-1.0);
Dune::DynamicVector<std::complex<double> > eigenValues(n);
Dune::DynamicMatrixHelp::eigenValuesNonSym(A, eigenValues);
std::vector<double> result(n);
for (int i=0; i < n; ++i)
result[i] = std::real(eigenValues[i]);
std::sort(result.begin(),result.begin()+n);
return result;
}
std::vector<double> gaussLobattoLegendreGrid(int n)
{
assert(n > 1);
const double tolerance = 1.e-15;
std::vector<double> result(n);
result[0] = 0.0;
result[n-1] = 1.0;
if (n == 3)
result[1] = 0.5;
if (n < 4)
return result;
std::vector<double> glgrid = gaussLegendreGrid(n-1);
for (int i=1; i<n-1; ++i) {
result[i] = (glgrid[i-1]+glgrid[i])/2.0;
double old = 0.0;
while (std::abs(old-result[i]) > tolerance) {
old = result[i];
double L = legendre(old, n-1);
double Ld = legendreDerivative(old, n-1);
result[i] += (1.0-old*old)*Ld/((n-1.0)*n*L);
}
result[i] = (result[i]+1.0)/2.0;
}
return result;
}
};
int main() int main() try
{ {
// Not really a test but better than nothing. testRosserMatrix<double>();
PNShapeFunctionSet<2> lbasis(2, 3);
return 0; return 0;
} catch (Exception exception)
{
std::cerr << exception << std::endl;
return 1;
} }
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