cholmod_sparse *MultivariateFNormalSufficientSparse::compute_PWP() const
{
// PWP = PW
IMP_LOG(TERSE, "MVNsparse: computing PWP" << std::endl);
//solve for X in Sigma*X=W
cholmod_sparse *tmp = cholmod_spsolve(CHOLMOD_A, L_, W_, c_);
//and then Y in trans(X)=Sigma*Y
cholmod_sparse *tx = cholmod_transpose(tmp, 1, c_);
cholmod_free_sparse(&tmp, c_);
cholmod_sparse *R = cholmod_spsolve(CHOLMOD_A, L_, tx, c_);
cholmod_free_sparse(&tx, c_);
IMP_LOG(TERSE, "MVNsparse: done" << std::endl);
return R;
}
cholmod_sparse *MultivariateFNormalSufficientSparse::compute_PTP() const
{
IMP_LOG(TERSE, "MVNsparse: computing PTP" << std::endl);
cholmod_sparse *eps = cholmod_dense_to_sparse(epsilon_, true, c_);
cholmod_sparse *tmp = cholmod_spsolve(CHOLMOD_A, L_, eps, c_);
cholmod_sparse *ptp = cholmod_aat(tmp, nullptr, 0, 1, c_);
cholmod_free_sparse(&eps, c_);
cholmod_free_sparse(&tmp, c_);
return ptp;
}
int CholeskyFactorization::solve(Matrix& rhs, Matrix& solution) {
if (m_matrix_type == Matrix::MATRIX_SPARSE) {
cholmod_dense *x;
/* cast the RHS as a cholmod_dense b = rhs */
if (rhs.m_type == Matrix::MATRIX_DENSE) {
cholmod_dense *b;
b = cholmod_allocate_dense(rhs.m_nrows, rhs.m_ncols, rhs.m_nrows, CHOLMOD_REAL, Matrix::cholmod_handle());
b->x = rhs.m_data;
/* Solve - rhs is dense*/
x = cholmod_solve(CHOLMOD_A, m_factor, b, Matrix::cholmod_handle());
solution = Matrix(rhs.m_nrows, rhs.m_ncols);
solution.m_delete_data = false;
memcpy(solution.m_data, static_cast<double*> (x->x), rhs.m_nrows * rhs.m_ncols * sizeof (double));
cholmod_free_dense(&x, Matrix::cholmod_handle());
} else if (rhs.m_type == Matrix::MATRIX_SPARSE) {
// still untested!
cholmod_sparse * rhs_sparse;
if (rhs.m_sparse == NULL) {
const_cast<Matrix&> (rhs)._createSparse();
}
rhs_sparse = rhs.m_sparse;
cholmod_sparse * result = cholmod_spsolve(CHOLMOD_LDLt, m_factor, rhs_sparse, Matrix::cholmod_handle());
solution = Matrix(rhs.m_nrows, rhs.m_ncols, Matrix::MATRIX_SPARSE);
solution.m_sparse = result;
solution._createTriplet();
} else {
throw std::logic_error("Not supported");
}
return ForBESUtils::STATUS_OK;
} else { /* the matrix to be factorized is not sparse */
int info = ForBESUtils::STATUS_UNDEFINED_FUNCTION;
solution = Matrix(rhs);
if (m_matrix_type == Matrix::MATRIX_DENSE) {
info = LAPACKE_dpotrs(LAPACK_COL_MAJOR, 'L', m_matrix_nrows, rhs.m_ncols, m_L, m_matrix_nrows, solution.m_data, m_matrix_nrows);
} else if (m_matrix_type == Matrix::MATRIX_SYMMETRIC) {
info = LAPACKE_dpptrs(LAPACK_COL_MAJOR, 'L', m_matrix_nrows, rhs.m_ncols, m_L, solution.m_data, m_matrix_nrows);
} else {
throw std::invalid_argument("This matrix type is not supported - only DENSE, SPARSE and SYMMETRIC are supported");
}
return info;
}
}
SEXP CHMfactor_spsolve(SEXP a, SEXP b, SEXP system)
{
CHM_FR L = AS_CHM_FR(a);
CHM_SP B = AS_CHM_SP__(b);
int sys = asInteger(system);
R_CheckStack();
if (!(sys--)) /* align with CHOLMOD defs: R's {1:9} --> {0:8},
see ./CHOLMOD/Cholesky/cholmod_solve.c */
error(_("system argument is not valid"));
// dimnames:
SEXP dn = PROTECT(allocVector(VECSXP, 2));
// none from a: our CHMfactor objects have no dimnames
SET_VECTOR_ELT(dn, 1, duplicate(VECTOR_ELT(GET_SLOT(b, Matrix_DimNamesSym), 1)));
UNPROTECT(1);
return chm_sparse_to_SEXP(cholmod_spsolve(sys, L, B, &c),
1/*do_free*/, 0/*uploT*/, 0/*Rkind*/, "", dn);
}
void MultivariateFNormalSufficientSparse::set_Sigma(
const SparseMatrix<double>& Sigma)
{
if (Sigma.cols() != Sigma.rows()) {
IMP_THROW("need a square matrix!", ModelException);
}
//std::cout << "set_sigma" << std::endl;
if (Sigma_) cholmod_free_sparse(&Sigma_, c_);
cholmod_sparse A(Eigen::viewAsCholmod(
Sigma.selfadjointView<Eigen::Upper>()));
Sigma_=cholmod_copy_sparse(&A, c_);
//cholmod_print_sparse(Sigma_,"Sigma",c_);
IMP_LOG(TERSE, "MVNsparse: set Sigma to new matrix" << std::endl);
IMP_LOG(TERSE, "MVNsparse: computing Cholesky decomposition"
<< std::endl);
// compute Cholesky decomposition for determinant and inverse
//c_->final_asis=1; // setup LDLT calculation
//c_->supernodal = CHOLMOD_SIMPLICIAL;
// convert matrix to cholmod format
//symbolic and numeric factorization
L_ = cholmod_analyze(Sigma_, c_);
int success = cholmod_factorize(Sigma_, L_, c_);
//cholmod_print_factor(L_,"L",c_);
if (success == 0 || L_->minor < L_->n)
IMP_THROW("Sigma matrix is not positive semidefinite!",
ModelException);
// determinant and derived constants
cholmod_factor *Lcp(cholmod_copy_factor(L_, c_));
cholmod_sparse *Lsp(cholmod_factor_to_sparse(Lcp,c_));
double logDetSigma=0;
if ((Lsp->itype != CHOLMOD_INT) &&
(Lsp->xtype != CHOLMOD_REAL))
IMP_THROW("types are not int and real, update them here first",
ModelException);
int *p=(int*) Lsp->p;
double *x=(double*) Lsp->x;
for (size_t i=0; i < (size_t) M_; ++i)
logDetSigma += std::log(x[p[i]]);
cholmod_free_sparse(&Lsp,c_);
cholmod_free_factor(&Lcp,c_);
IMP_LOG(TERSE, "MVNsparse: log det(Sigma) = "
<< logDetSigma << std::endl);
IMP_LOG(TERSE, "MVNsparse: det(Sigma) = "
<< exp(logDetSigma) << std::endl);
norm_= std::pow(2*IMP::PI, -double(N_*M_)/2.0)
* exp(-double(N_)/2.0*logDetSigma);
lnorm_=double(N_*M_)/2 * log(2*IMP::PI) + double(N_)/2 * logDetSigma;
IMP_LOG(TERSE, "MVNsparse: norm = " << norm_ << " lnorm = "
<< lnorm_ << std::endl);
//inverse
IMP_LOG(TERSE, "MVNsparse: solving for inverse" << std::endl);
cholmod_sparse* id = cholmod_speye(M_,M_,CHOLMOD_REAL,c_);
if (P_) cholmod_free_sparse(&P_, c_);
P_ = cholmod_spsolve(CHOLMOD_A, L_, id, c_);
cholmod_free_sparse(&id, c_);
if (!P_) IMP_THROW("Unable to solve for inverse!", ModelException);
//WP
IMP_LOG(TERSE, "MVNsparse: solving for PW" << std::endl);
if (PW_) cholmod_free_sparse(&PW_, c_);
PW_ = cholmod_spsolve(CHOLMOD_A, L_, W_, c_);
if (!PW_) IMP_THROW("Unable to solve for PW!", ModelException);
IMP_LOG(TERSE, "MVNsparse: done" << std::endl);
}
int main(int argc, char *argv[])
{
char *name = "main";
char *seperator = "**********************************************************";
// Setup the data structure with parameters of the problem
switch (argc)
{
case 1:
printf("No input file specified. Using dia1P.inp\n");
dia1P_initialize("dia1P.inp",name);
break;
case 2:
dia1P_initialize(argv[1],name);
break;
default:
dia1P_errHandler(errCode_TooManyArguments,name,name,errMesg_TooManyArguments);
}
// Print the problem to make sure
dia1P_printPD(name);
/* The prefix M_ is used for components that can be reused in several
failure simulations. For example, it is not necessary to compute
the first stiffness matrix M_M or its decomposition M_L for each
failure simulation. On the other hand, the matrix of fuse strengths,
S, needs to be repopulated every time.
*/
/* START REUSABLE COMPONENTS DECLARATIONS */
// Stiffness matrix M
cholmod_sparse *M_M;
// J = M_V2C*V; where J = current flowing into the bottom nodes,
// and V = vector of voltages of all nodes
cholmod_sparse *M_V2C;
// Voltages at top and bottom nodes
cholmod_sparse *M_vTop, *M_vBot;
// Cholesky factor of the stiffness matrix M
cholmod_factor *M_L;
// Cholmod Common object
cholmod_common Common;
// Basic scalars, one and minus one
double one [2] = {1,0}, m1 [2] = {-1,0} ;
/* END REUSABLE COMPONENTS DECLARATIONS */
/* START REUSABLE COMPONENTS INITIALIZATIONS */
// Start cholmod, and the cholmod_common object
cholmod_start(&Common);
// Populated the top and bottom node voltages
// Bottom row is "grounded", thus has zero
// voltage by convention.
// cholmod_spzeros(NRow,NCol,stype,xtype,*common)
M_vBot = cholmod_spzeros(pD.gridSize/2,1,0,CHOLMOD_REAL,&Common);
// The top row has voltage = 1. Since cholmod has no inbuild
// function to return a sparse vector of all ones (makes sense)
// so we first create a dense vector of ones and then
// convert it to a sparse vector
{ // limit the scope of temporary variables
cholmod_dense *temp;
temp = cholmod_ones(pD.gridSize/2,1,CHOLMOD_REAL,&Common);
M_vTop = cholmod_dense_to_sparse(temp,1,&Common);
cholmod_free_dense(&temp,&Common);
}
// Polulate voltage to current matrix and check it for
// consistency
M_V2C = dia1P_voltageToCurrentMatrix(&Common,name);
cholmod_check_sparse(M_V2C,&Common);
// Populate stiffness matrix
M_M = dia1P_stiffnessMatrix(&Common,name);
// Check it for consistency
cholmod_check_sparse(M_M,&Common);
// Analyze and factorise the stiffness matrix
M_L = cholmod_analyze(M_M,&Common);
cholmod_factorize(M_M,M_L,&Common);
// Check the factor for consistency
cholmod_check_factor(M_L,&Common);
/* END REUSABLE COMPONENTS INITIALIZATIONS */
// Depending on the mode in which the program is run
// various levels of output are given to the user.
// The three modes implemented so far are:
// 0: Silent,
// 1: minimal,
// 2: normal
// 3: verbose
switch (pD.diagMode)
{
case 0:
break;
case 1:
fprintf(pD.diagFile,"NSim\tnF\t\tnAv\t\tV\t\tC\n");
fflush(pD.diagFile);
break;
case 2:
break;
case 3:
fprintf(pD.diagFile,"Initial Stiffness Matrix\n");
cholmod_write_sparse(pD.diagFile,M_M,NULL,NULL,&Common);
fflush(pD.diagFile);
break;
default:
dia1P_errHandler(errCode_UnknownDiagMode,name,name,errMesg_UnknownDiagMode);
}
/* START MAIN SIMULATIONS LOOP */
// Number of simulations performed
int countSims = 0;
while (countSims < pD.NSim)
{
/* START LOOP COMPONENTS DECLARATIONS */
// The sampleFailed flag remains zeros as long as
// the sample is not broken (a spanning crack is
// not encountered; it becomes 1 otherwise.
int sampleFailed = 0;
// nFail counts the number of bonds snapped till
// sample failure
int nFail = 0;
// Cholesky factor L will hold the cholesky factor that will be updated after each bond snapping
cholmod_factor *L;
// Vector of random fuse strengths
double *S;
// Matrix that maps the node voltages to the vector of
// currents flowing into the bottom nodes.
// This matrix is update after every bond breaking
cholmod_sparse *V2C;
// Load vector b. This vector is to be updated after
// every bond breaking
cholmod_sparse *b;
// A data structure that will store information about the
// most recently failed bond
dia1P_failureSite FD;
// A data structure that will store information about the
// sequence of failures in a particular simulation
dia1P_brokenBonds *BB;
/* END LOOP COMPONENTS DECLARATIONS */
/* START LOOP COMPONENTS INITIALIZATIONS */
// Copy the pre-calculated cholesky factor into the local
// cholesky factor
L = cholmod_copy_factor(M_L,&Common);
// Populate fuse strength vector
S = dia1P_strengthVector(name);
//FILE *pf = fopen("16.S","r"); S = cholmod_read_sparse(pf,&Common); fclose(pf);
// Copy the initial voltage to current matrix
V2C = cholmod_copy_sparse(M_V2C,&Common);
// Initialize the structure for keeping records of broken bonds
BB = dia1P_initializeBrokenBonds(name);
// Polulate the load vector b
b = dia1P_loadVector(&Common,name);
// Check to ensure consistency...
cholmod_check_sparse(b,&Common);
/* END LOOP COMPONENTS INITIALIZATIONS */
// Write diagonistic output as requested
switch (pD.diagMode)
{
case 0: break;
case 1: break;
case 2:
fprintf(pD.diagFile,"%s\n",seperator);
fprintf(pD.diagFile,"Starting Simulation Number %d\n",countSims+1);
fprintf(pD.diagFile,"I\t\tJ\t\tV\t\tC\n");
fflush(pD.diagFile);
break;
case 3:
fprintf(pD.diagFile,"%s\n",seperator);
fprintf(pD.diagFile,"Starting Simulation Number %d\n",countSims+1);
fprintf(pD.diagFile,"Matrix of Random Fuse Strengths:\n");
{
int count = 0;
for(count = 0; count < (pD.gridSize)*(pD.gridSize); count++)
{
int n1, n2;
dia1P_getNodeNumbers(&n1,&n2,count,name);
fprintf(pD.diagFile,"%d\t%d\t%G\n",n1,n2,S[count]);
}
fprintf(pD.diagFile,"\n");
}
//cholmod_write_sparse(pD.diagFile,S,NULL,NULL,&Common);
fflush(pD.diagFile);
break;
default: dia1P_errHandler(errCode_UnknownDiagMode,name,name,errMesg_UnknownDiagMode);
}
while(sampleFailed == 0)
{
/* START INNER LOOP COMPONENTS INITIALIZATIONS */
// Vector x will hold the unknown voltages
cholmod_sparse *x;
// Vectors VNode_s and VNode_d hold the full set
// of node voltages (knowns appended to the calculated unknowns)
cholmod_sparse *VNode_s;
cholmod_dense *VNode_d;
// This vector will be used to update the stiffness matrix M
// as M_new = M_old - stiffUpdate*transpose(stiffUpdate)
// Ofcouse, M is not update, rather its cholesky factor L is
cholmod_sparse *stiffUpdate;
// This vector updates the load vector as
// b_new = b_old + loadUpdate
cholmod_sparse *loadUpdate;
// This vector is needed for internal cholmod use.
// We L = PMP^T, where P is the permuation matrix.
// Thus, if U updates M, then PU will update L.
// uper = PU.
cholmod_sparse *uper;
/* END INNER LOOP COMPONENTS INITIALIZATIONS */
// Solve for the unknown voltages
x = cholmod_spsolve(CHOLMOD_A,L,b,&Common);
// Append the known vectors top and the bottom
// row voltages to x to construct the complete
// vector of voltages.
{ // Limit the score of temporary variables
cholmod_sparse *temp1;
temp1 = cholmod_vertcat(M_vBot,x,1,&Common);
VNode_s = cholmod_vertcat(temp1,M_vTop,1,&Common);
cholmod_free_sparse(&temp1,&Common);
}
// Check if the sample is broken, if it is then
// we are done
if(dia1P_isBroken(VNode_s,V2C,&Common,name))
{
sampleFailed = 1;
{
int count = 0;
for(count = 0; count < BB->nFail; count++)
{
fprintf(pD.outFile,"%d\t%d\t%G\t%G\t%G\n",BB->i[count]+1,BB->j[count]+1,BB->v[count],BB->c[count],BB->bondStrength[count]);
}
fprintf(pD.outFile,"%d\t%d\t%G\t%G\t%G\n",0,0,0.f,0.f,0.f);
}
}
else
{ // If the sample is not broken yet, then we need to
// to find which bond will be snapped next.
// Increment the number of failed bonds, since we know
// that one is going to snap
nFail++;
// Make a dense vector of voltages
VNode_d = cholmod_sparse_to_dense(VNode_s,&Common);
// Find which bond to break and store the information
// in the data structure FD.
dia1P_bondToSnap(S,VNode_d,VNode_s,V2C,BB,&FD,&Common,name);
// Update the data structure BB, which stores the entire
// sequence of broken bonds
dia1P_updateBrokenBonds(BB,&FD,name);
// Update the voltage to current matrix.
// This matrix will change only if a fuse connected to the
// bottom edge is blown.
dia1P_updateVoltageToCurrentMatrix(V2C,&FD,&Common,name);
// Find the vector to update the stiffness matrix.
// This vector is never empty, it has either 1 or 2 nonzero components
// depending on weather a boundary node is involved in the snapping or not
stiffUpdate = dia1P_stiffnessUpdateVector(&FD,&Common,name);
// Find the vector to update the load vector.
// This vector is non-zero only if a fuse connected to the
// top edge is blown.
loadUpdate = dia1P_loadUpdateVector(&FD,&Common,name);
// Update the load vector
{ // Limit the score of temporary variables
cholmod_sparse *temp;
temp = cholmod_copy_sparse(b,&Common);
// Free the current memory occupied by b before reallocating
cholmod_free_sparse(&b,&Common);
// Reallocate b
b = cholmod_add(temp,loadUpdate,one,one,1,0,&Common);
// Free temp
cholmod_free_sparse(&temp,&Common);
}
// Calculate the permuted update vector for updating the cholesky factor
uper = cholmod_submatrix(stiffUpdate,L->Perm,L->n,NULL,-1,1,1,&Common);
// update (downdate) the cholesky factor
cholmod_updown(0,uper,L,&Common);
// Write appropriate diagnostic output
switch (pD.diagMode)
{
case 0: break;
case 1: break;
case 2:
fprintf(pD.diagFile,"%d\t\t%d\t\t%.3f\t%.3f\n",FD.node1+1,FD.node2+1,FD.fVol,FD.fCur);
break;
case 3:
fprintf(pD.diagFile,"\nPass No. %d\nUnknown Node Voltages:\n",nFail);
cholmod_write_sparse(pD.diagFile,x,NULL,NULL,&Common);
fprintf(pD.diagFile,"\nSnapped Bond: \nI\t\tJ\t\tV\t\tC\n");
fprintf(pD.diagFile,"%d\t\t%d\t\t%.3f\t%.3f\n\n",FD.node1+1,FD.node2+1,FD.fVol,FD.fCur);
fprintf(pD.diagFile,"\nStiffNess Update Vector\n");
cholmod_write_sparse(pD.diagFile,stiffUpdate,NULL,NULL,&Common);
fprintf(pD.diagFile,"\nLoad Update Vector\n");
cholmod_write_sparse(pD.diagFile,loadUpdate,NULL,NULL,&Common);
break;
default: dia1P_errHandler(errCode_UnknownDiagMode,name,name,errMesg_UnknownDiagMode);
}
//Free memory
cholmod_free_dense(&VNode_d,&Common);
cholmod_free_sparse(&stiffUpdate,&Common);
cholmod_free_sparse(&loadUpdate,&Common);
cholmod_free_sparse(&uper,&Common);
}//ESLE
cholmod_free_sparse(&x,&Common);
cholmod_free_sparse(&VNode_s,&Common);
}//ELIHW, loop for nth simulation
// Free memory
free(S);
cholmod_free_sparse(&b,&Common);
cholmod_free_sparse(&V2C,&Common);
cholmod_free_factor(&L,&Common);
dia1P_freeBrokenBonds(&BB,name);
countSims++;
}//ELIHW, main loop for NSim simulations
// This completes the requested set of NSim simulations.
// Free memory
cholmod_free_sparse(&M_M,&Common);
cholmod_free_sparse(&M_V2C,&Common);
cholmod_free_sparse(&M_vBot,&Common);
cholmod_free_sparse(&M_vTop,&Common);
cholmod_free_factor(&M_L,&Common);
// Close dia1P and cholmod
dia1P_finish(name);
// cholmod_print_common("FuseNet Statistics",&Common);
cholmod_finish(&Common);
return(0);
}