void SteadyState::classifyState( const double* T )
{
#ifdef USE_GSL
// unsigned int nConsv = numVarPools_ - rank_;
gsl_matrix* J = gsl_matrix_calloc ( numVarPools_, numVarPools_ );
// double* yprime = new double[ numVarPools_ ];
// vector< double > yprime( numVarPools_, 0.0 );
// Generate an approximation to the Jacobean by generating small
// increments to each of the molecules in the steady state, one
// at a time, and putting the resultant rate vector into a column
// of the J matrix.
// This needs a bit of heuristic to decide what is a 'small' increment.
// Use the CoInits for this. Stoichiometry shouldn't matter too much.
// I used the totals from consv rules earlier, but that can have
// negative values.
double tot = 0.0;
Stoich* s = reinterpret_cast< Stoich* >( stoich_.eref().data() );
vector< double > nVec = LookupField< unsigned int, vector< double > >::get(
s->getKsolve(), "nVec", 0 );
for ( unsigned int i = 0; i < numVarPools_; ++i ) {
tot += nVec[i];
}
tot *= DELTA;
vector< double > yprime( nVec.size(), 0.0 );
// Fill up Jacobian
for ( unsigned int i = 0; i < numVarPools_; ++i ) {
double orig = nVec[i];
if ( isnan( orig ) ) {
cout << "Warning: SteadyState::classifyState: orig=nan\n";
solutionStatus_ = 2; // Steady state OK, eig failed
gsl_matrix_free ( J );
return;
}
if ( isnan( tot ) ) {
cout << "Warning: SteadyState::classifyState: tot=nan\n";
solutionStatus_ = 2; // Steady state OK, eig failed
gsl_matrix_free ( J );
return;
}
nVec[i] = orig + tot;
/// Here we assume we always use voxel zero.
s->updateRates( &nVec[0], &yprime[0], 0 );
nVec[i] = orig;
// Assign the rates for each mol.
for ( unsigned int j = 0; j < numVarPools_; ++j ) {
gsl_matrix_set( J, i, j, yprime[j] );
}
}
// Jacobian is now ready. Find eigenvalues.
gsl_vector_complex* vec = gsl_vector_complex_alloc( numVarPools_ );
gsl_eigen_nonsymm_workspace* workspace =
gsl_eigen_nonsymm_alloc( numVarPools_ );
int status = gsl_eigen_nonsymm( J, vec, workspace );
eigenvalues_.clear();
eigenvalues_.resize( numVarPools_, 0.0 );
if ( status != GSL_SUCCESS ) {
cout << "Warning: SteadyState::classifyState failed to find eigenvalues. Status = " <<
status << endl;
solutionStatus_ = 2; // Steady state OK, eig classification failed
} else { // Eigenvalues are ready. Classify state.
nNegEigenvalues_ = 0;
nPosEigenvalues_ = 0;
for ( unsigned int i = 0; i < numVarPools_; ++i ) {
gsl_complex z = gsl_vector_complex_get( vec, i );
double r = GSL_REAL( z );
nNegEigenvalues_ += ( r < -EPSILON );
nPosEigenvalues_ += ( r > EPSILON );
eigenvalues_[i] = r;
// We have a problem here because numVarPools_ usually > rank
// This means we have several zero eigenvalues.
}
if ( nNegEigenvalues_ == rank_ )
stateType_ = 0; // Stable
else if ( nPosEigenvalues_ == rank_ ) // Never see it.
stateType_ = 1; // Unstable
else if (nPosEigenvalues_ == 1)
stateType_ = 2; // Saddle
else if ( nPosEigenvalues_ >= 2 )
stateType_ = 3; // putative oscillatory
else if ( nNegEigenvalues_ == ( rank_ - 1) && nPosEigenvalues_ == 0 )
stateType_ = 4; // one zero or unclassified eigenvalue. Messy.
else
stateType_ = 5; // Other
}
gsl_vector_complex_free( vec );
gsl_matrix_free ( J );
gsl_eigen_nonsymm_free( workspace );
#endif
}
void SteadyState::classifyState( const double* T )
{
/* column_major trait is needed for fortran */
ublas::matrix<double, ublas::column_major> J(numVarPools_, numVarPools_);
double tot = 0.0;
Stoich* s = reinterpret_cast< Stoich* >( stoich_.eref().data() );
vector< double > nVec = LookupField< unsigned int, vector< double > >::get(
s->getKsolve(), "nVec", 0 );
for ( unsigned int i = 0; i < numVarPools_; ++i )
tot += nVec[i];
tot *= DELTA;
vector< double > yprime( nVec.size(), 0.0 );
// Fill up Jacobian
for ( unsigned int i = 0; i < numVarPools_; ++i )
{
double orig = nVec[i];
if ( std::isnan( orig ) or std::isinf( orig ) )
{
cout << "Warning: SteadyState::classifyState: orig=nan\n";
solutionStatus_ = 2; // Steady state OK, eig failed
J.clear();
return;
}
if ( std::isnan( tot ) or std::isinf( tot ))
{
cout << "Warning: SteadyState::classifyState: tot=nan\n";
solutionStatus_ = 2; // Steady state OK, eig failed
J.clear();
return;
}
nVec[i] = orig + tot;
pool_.updateRates( &nVec[0], &yprime[0] );
nVec[i] = orig;
// Assign the rates for each mol.
for ( unsigned int j = 0; j < numVarPools_; ++j )
{
if( std::isnan( yprime[j] ) or std::isinf( yprime[j] ) )
{
cout << "Warning: Overflow/underflow. Can't continue " << endl;
solutionStatus_ = 2;
return;
}
J(i, j) = yprime[j];
}
}
// Jacobian is now ready. Find eigenvalues.
ublas::vector< std::complex< double > > eigenVec ( J.size1() );
ublas::matrix< std::complex<double>, ublas::column_major >* vl, *vr;
vl = NULL; vr = NULL;
/*-----------------------------------------------------------------------------
* INFO: Calling lapack routine geev to compute eigen vector of matrix J.
*
* Argument 3 and 4 are left- and right-eigenvectors. Since we do not need
* them, they are set to NULL. Argument 2 holds eigen-vector and result is
* copied to it (output ).
*-----------------------------------------------------------------------------*/
int status = lapack::geev( J, eigenVec, vl, vr, lapack::optimal_workspace() );
eigenvalues_.clear();
eigenvalues_.resize( numVarPools_, 0.0 );
if ( status != 0 )
{
cout << "Warning: SteadyState::classifyState failed to find eigenvalues. Status = " <<
status << endl;
solutionStatus_ = 2; // Steady state OK, eig classification failed
}
else // Eigenvalues are ready. Classify state.
{
nNegEigenvalues_ = 0;
nPosEigenvalues_ = 0;
for ( unsigned int i = 0; i < numVarPools_; ++i )
{
std::complex<value_type> z = eigenVec[ i ];
double r = z.real();
nNegEigenvalues_ += ( r < -EPSILON );
nPosEigenvalues_ += ( r > EPSILON );
eigenvalues_[i] = r;
// We have a problem here because numVarPools_ usually > rank
// This means we have several zero eigenvalues.
}
if ( nNegEigenvalues_ == rank_ )
stateType_ = 0; // Stable
else if ( nPosEigenvalues_ == rank_ ) // Never see it.
stateType_ = 1; // Unstable
else if (nPosEigenvalues_ == 1)
stateType_ = 2; // Saddle
else if ( nPosEigenvalues_ >= 2 )
stateType_ = 3; // putative oscillatory
else if ( nNegEigenvalues_ == ( rank_ - 1) && nPosEigenvalues_ == 0 )
stateType_ = 4; // one zero or unclassified eigenvalue. Messy.
else
stateType_ = 5; // Other
}
}