/**
* @brief Solves a sparse matrix factorization.
*
* This solves Ax = b.
*
* @param[in,out] b Input right side vector that gets set to the output solution.
* @param[in] fact Factorization of the sparse matrix.
*/
void cs_fact_solve( double *b, cs_fact_t *fact )
{
#ifdef USE_UMFPACK
int ret;
double info[ UMFPACK_INFO ];
int fnan, finf;
#endif /* USE_UMFPACK */
int k;
switch (fact->type) {
case CS_FACT_CHOLESKY:
cs_ipvec( fact->S->pinv, b, fact->x, fact->n );
cs_lsolve( fact->N->L, fact->x );
cs_ltsolve( fact->N->L, fact->x );
cs_pvec( fact->S->pinv, fact->x, b, fact->n );
break;
case CS_FACT_LU:
cs_ipvec( fact->N->pinv, b, fact->x, fact->n );
cs_lsolve( fact->N->L, fact->x );
cs_usolve( fact->N->U, fact->x );
cs_ipvec( fact->S->q, fact->x, b, fact->n );
break;
case CS_FACT_QR:
cs_ipvec( fact->S->pinv, b, fact->x, fact->n );
for (k=0; k<fact->n; k++)
cs_happly( fact->N->L, k, fact->N->B[k], fact->x );
cs_usolve( fact->N->U, fact->x );
cs_ipvec( fact->S->q, fact->x, b, fact->n );
break;
case CS_FACT_UMFPACK:
#ifdef USE_UMFPACK
ret = umfpack_di_wsolve( UMFPACK_A, /* Solving Ax=b problem. */
fact->A->p, fact->A->i, fact->A->x,
fact->x, b, fact->numeric, NULL, info, fact->wi, fact->w );
if (ret == UMFPACK_WARNING_singular_matrix) {
fprintf( stderr, "UMFPACK: wsolver Matrix singular!\n" );
fnan = 0;
finf = 0;
for (k=0; k<fact->n; k++) {
if (isnan(fact->x[k])) {
fact->x[k] = 0.;
fnan = 1;
}
else if (isinf(fact->x[k])) {
fact->x[k] = 0.;
finf = 1;
}
}
if (fnan)
fprintf( stderr, "UMFPACK: NaN values detected!\n" );
if (finf)
fprintf( stderr, "UMFPACK: Infinity values detected!\n" );
}
memcpy( b, fact->x, fact->n*sizeof(double) );
#endif /* USE_UMFPACK */
default:
break;
}
}
SEXP sparseQR_coef(SEXP qr, SEXP y)
{
SEXP ans = PROTECT(dup_mMatrix_as_dgeMatrix(y)),
qslot = GET_SLOT(qr, install("q"));
CSP V = AS_CSP(GET_SLOT(qr, install("V"))),
R = AS_CSP(GET_SLOT(qr, install("R")));
int *ydims = INTEGER(GET_SLOT(ans, Matrix_DimSym)),
*q = INTEGER(qslot),
j, lq = LENGTH(qslot), m = R->m, n = R->n;
double *ax = REAL(GET_SLOT(ans, Matrix_xSym)),
*x = Alloca(m, double);
R_CheckStack();
R_CheckStack();
/* apply row permutation and multiply by Q' */
sparseQR_Qmult(V, REAL(GET_SLOT(qr, install("beta"))),
INTEGER(GET_SLOT(qr, Matrix_pSym)), 1,
REAL(GET_SLOT(ans, Matrix_xSym)), ydims);
for (j = 0; j < ydims[1]; j++) {
double *aj = ax + j * m;
cs_usolve(R, aj);
if (lq) {
cs_ipvec(q, aj, x, n);
Memcpy(aj, x, n);
}
}
UNPROTECT(1);
return ans;
}
SEXP dgCMatrix_matrix_solve(SEXP Ap, SEXP b, SEXP give_sparse)
// FIXME: add 'keep_dimnames' as argument
{
Rboolean sparse = asLogical(give_sparse);
if(sparse) {
// FIXME: implement this
error(_("dgCMatrix_matrix_solve(.., sparse=TRUE) not yet implemented"));
/* Idea: in the for(j = 0; j < nrhs ..) loop below, build the *sparse* result matrix
* ----- *column* wise -- which is perfect for dgCMatrix
* --> build (i,p,x) slots "increasingly" [well, allocate in batches ..]
*
* --> maybe first a protoype in R
*/
}
SEXP ans = PROTECT(dup_mMatrix_as_dgeMatrix(b)),
lu, qslot;
CSP L, U;
int *bdims = INTEGER(GET_SLOT(ans, Matrix_DimSym)), *p, *q;
int j, n = bdims[0], nrhs = bdims[1];
double *x, *ax = REAL(GET_SLOT(ans, Matrix_xSym));
C_or_Alloca_TO(x, n, double);
if (isNull(lu = get_factors(Ap, "LU"))) {
install_lu(Ap, /* order = */ 1, /* tol = */ 1.0, /* err_sing = */ TRUE,
/* keep_dimnames = */ TRUE);
lu = get_factors(Ap, "LU");
}
qslot = GET_SLOT(lu, install("q"));
L = AS_CSP__(GET_SLOT(lu, install("L")));
U = AS_CSP__(GET_SLOT(lu, install("U")));
R_CheckStack();
if (U->n != n)
error(_("Dimensions of system to be solved are inconsistent"));
if(nrhs >= 1 && n >= 1) {
p = INTEGER(GET_SLOT(lu, Matrix_pSym));
q = LENGTH(qslot) ? INTEGER(qslot) : (int *) NULL;
for (j = 0; j < nrhs; j++) {
cs_pvec(p, ax + j * n, x, n); /* x = b(p) */
cs_lsolve(L, x); /* x = L\x */
cs_usolve(U, x); /* x = U\x */
if (q) /* r(q) = x , hence
r = Q' U{^-1} L{^-1} P b = A^{-1} b */
cs_ipvec(q, x, ax + j * n, n);
else
Memcpy(ax + j * n, x, n);
}
}
if(n >= SMALL_4_Alloca) Free(x);
UNPROTECT(1);
return ans;
}
/* x=A\b where A can be rectangular; b overwritten with solution */
int cs_qrsol (int order, const cs *A, double *b)
{
double *x ;
css *S ;
csn *N ;
cs *AT = NULL ;
int k, m, n, ok ;
if (!CS_CSC (A) || !b) return (0) ; /* check inputs */
n = A->n ;
m = A->m ;
if (m >= n)
{
S = cs_sqr (order, A, 1) ; /* ordering and symbolic analysis */
N = cs_qr (A, S) ; /* numeric QR factorization */
x = cs_calloc (S ? S->m2 : 1, sizeof (double)) ; /* get workspace */
ok = (S && N && x) ;
if (ok)
{
cs_ipvec (S->pinv, b, x, m) ; /* x(0:m-1) = b(p(0:m-1) */
for (k = 0 ; k < n ; k++) /* apply Householder refl. to x */
{
cs_happly (N->L, k, N->B [k], x) ;
}
cs_usolve (N->U, x) ; /* x = R\x */
cs_ipvec (S->q, x, b, n) ; /* b(q(0:n-1)) = x(0:n-1) */
}
}
else
{
AT = cs_transpose (A, 1) ; /* Ax=b is underdetermined */
S = cs_sqr (order, AT, 1) ; /* ordering and symbolic analysis */
N = cs_qr (AT, S) ; /* numeric QR factorization of A' */
x = cs_calloc (S ? S->m2 : 1, sizeof (double)) ; /* get workspace */
ok = (AT && S && N && x) ;
if (ok)
{
cs_pvec (S->q, b, x, m) ; /* x(q(0:m-1)) = b(0:m-1) */
cs_utsolve (N->U, x) ; /* x = R'\x */
for (k = m-1 ; k >= 0 ; k--) /* apply Householder refl. to x */
{
cs_happly (N->L, k, N->B [k], x) ;
}
cs_pvec (S->pinv, x, b, n) ; /* b(0:n-1) = x(p(0:n-1)) */
}
}
cs_free (x) ;
cs_sfree (S) ;
cs_nfree (N) ;
cs_spfree (AT) ;
return (ok) ;
}
/* x=A\b where A is unsymmetric; b overwritten with solution */
csi cs_lusol_inverse (const cs *A, double *b,double *d, csn *N, double *x)
{
csi n;
n = A->n ;
/* get workspace */
cs_ipvec (N->pinv, b, x, n) ; /* x = b(p) */
cs_lsolve (N->L, x) ; /* x = L\x */
cs_usolve (N->U, x) ; /* x = U\x */
cs_ipvec (N->q, x, d, n) ; /* b(q) = x */
return (1) ;
}
/* Solve Ax = b with the factorization of A stored in the cs_lu_A
* This is extracted from cs_lusol, you need to synchronize any changes! */
csi cs_solve (cs_lu_factors* cs_lu_A, double* x, double *b)
{
assert(cs_lu_A);
csi ok;
csi n = cs_lu_A->n;
css* S = cs_lu_A->S;
csn* N = cs_lu_A->N;
ok = (S && N && x) ;
if (ok)
{
cs_ipvec (N->pinv, b, x, n) ; /* x = b(p) */
cs_lsolve (N->L, x) ; /* x = L\x */
cs_usolve (N->U, x) ; /* x = U\x */
cs_ipvec (S->q, x, b, n) ; /* b(q) = x */
}
return (ok);
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Umatrix, Bmatrix, *U, *B, *X ;
double *x, *b ;
int top, nz, p, *xi ;
if (nargout > 1 || nargin != 2)
{
mexErrMsgTxt ("Usage: x = cs_usolve(U,b)") ;
}
U = cs_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */
if (mxIsSparse (pargin [1]))
{
B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b */
cs_mex_check (0, U->n, 1, 0, 1, 1, pargin [1]) ;
xi = cs_malloc (2*U->n, sizeof (int)) ; /* get workspace */
x = cs_malloc (U->n, sizeof (double)) ;
top = cs_spsolve (U, B, 0, xi, x, NULL, 0) ; /* x = U\b */
X = cs_spalloc (U->n, 1, U->n-top, 1, 0) ; /* create sparse x*/
X->p [0] = 0 ;
nz = 0 ;
for (p = top ; p < U->n ; p++)
{
X->i [nz] = xi [p] ;
X->x [nz++] = x [xi [p]] ;
}
X->p [1] = nz ;
pargout [0] = cs_mex_put_sparse (&X) ;
cs_free (x) ;
cs_free (xi) ;
}
else
{
b = cs_mex_get_double (U->n, pargin [1]) ; /* get full b */
x = cs_mex_put_double (U->n, b, &(pargout [0])) ; /* x = b */
cs_usolve (U, x) ; /* x = U\x */
}
}
int lusoln(ode_workspace *odews, double *b)
{
// Can only be called if newton_matrix has been called already
double *x;
int n = odews->W->J->n;
x = cs_malloc (n, sizeof (*x));
int ok = odews->S && odews->N && x;
if (ok)
{
cs_ipvec(odews->N->pinv, b, x, n);
cs_lsolve(odews->N->L, x);
cs_usolve(odews->N->U, x);
cs_ipvec(odews->S->q, x, b, n);
}
cs_free (x);
return ok;
}
returnValue ACADOcsparse::solve(double *b)
{
// CONSISTENCY CHECKS:
// -------------------
if (dim <= 0)
return ACADOERROR(RET_MEMBER_NOT_INITIALISED);
if (nDense <= 0)
return ACADOERROR(RET_MEMBER_NOT_INITIALISED);
if (S == 0)
return ACADOERROR(RET_MEMBER_NOT_INITIALISED);
// CASE: LU
cs_ipvec(N->pinv, b, x, dim); /* x = b(p) */
cs_lsolve(N->L, x); /* x = L\x */
cs_usolve(N->U, x); /* x = U\x */
cs_ipvec(S->q, x, b, dim); /* b(q) = x */
return SUCCESSFUL_RETURN;
}
void CSparseInternal::solve(double* x, int nrhs, bool transpose){
casadi_assert(prepared_);
casadi_assert(N_!=0);
double *t = &temp_.front();
for(int k=0; k<nrhs; ++k){
if(transpose){
cs_ipvec (N_->pinv, x, t, AT_.n) ; // t = P1\b
cs_lsolve (N_->L, t) ; // t = L\t
cs_usolve (N_->U, t) ; // t = U\t
cs_ipvec (S_->q, t, x, AT_.n) ; // x = P2\t
} else {
cs_pvec (S_->q, x, t, AT_.n) ; // t = P2*b
casadi_assert(N_->U!=0);
cs_utsolve (N_->U, t) ; // t = U'\t
cs_ltsolve (N_->L, t) ; // t = L'\t
cs_pvec (N_->pinv, t, x, AT_.n) ; // x = P1*t
}
x += nrow();
}
}
SEXP dtCMatrix_matrix_solve(SEXP a, SEXP b, SEXP classed)
{
int cl = asLogical(classed);
SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("dgeMatrix")));
CSP A = AS_CSP(a);
int *adims = INTEGER(GET_SLOT(a, Matrix_DimSym)),
*bdims = INTEGER(cl ? GET_SLOT(b, Matrix_DimSym) :
getAttrib(b, R_DimSymbol));
int j, n = bdims[0], nrhs = bdims[1], lo = (*uplo_P(a) == 'L');
double *bx;
R_CheckStack();
if (*adims != n || nrhs < 1 || *adims < 1 || *adims != adims[1])
error(_("Dimensions of system to be solved are inconsistent"));
Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2)), bdims, 2);
/* FIXME: copy dimnames or Dimnames as well */
bx = Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, n * nrhs)),
REAL(cl ? GET_SLOT(b, Matrix_xSym):b), n * nrhs);
for (j = 0; j < nrhs; j++)
lo ? cs_lsolve(A, bx + n * j) : cs_usolve(A, bx + n * j);
UNPROTECT(1);
return ans;
}
void CsparseInterface::solve(double* x, int nrhs, bool transpose) {
double time_start=0;
if (CasadiOptions::profiling&& CasadiOptions::profilingBinary) {
time_start = getRealTime(); // Start timer
profileWriteEntry(CasadiOptions::profilingLog, this);
}
casadi_assert(prepared_);
casadi_assert(N_!=0);
double *t = &temp_.front();
for (int k=0; k<nrhs; ++k) {
if (transpose) {
cs_pvec(S_->q, x, t, A_.n) ; // t = P2*b
casadi_assert(N_->U!=0);
cs_utsolve(N_->U, t) ; // t = U'\t
cs_ltsolve(N_->L, t) ; // t = L'\t
cs_pvec(N_->pinv, t, x, A_.n) ; // x = P1*t
} else {
cs_ipvec(N_->pinv, x, t, A_.n) ; // t = P1\b
cs_lsolve(N_->L, t) ; // t = L\t
cs_usolve(N_->U, t) ; // t = U\t
cs_ipvec(S_->q, t, x, A_.n) ; // x = P2\t
}
x += ncol();
}
if (CasadiOptions::profiling && CasadiOptions::profilingBinary) {
double time_stop = getRealTime(); // Stop timer
profileWriteTime(CasadiOptions::profilingLog, this, 1,
time_stop-time_start,
time_stop-time_start);
profileWriteExit(CasadiOptions::profilingLog, this, time_stop-time_start);
}
}
/* x=A\b where A is unsymmetric; b overwritten with solution */
csi cs_lusol_modifier (csi order, const cs *A, double *b, double *a, double tol)
{
double *x ;
css *S ;
csn *N ;
csi n, ok ;
// if (!CS_CSC (A) || !b) return (0) ; /* check inputs */
n = A->n ;
S = cs_sqr (order, A, 0) ; /* ordering and symbolic analysis */
N = cs_lu (A, S, tol) ; /* numeric LU factorization */
x = cs_malloc (n, sizeof (double)) ; /* get workspace */
// ok = (S && N && x) ;
//if (ok)
//{
cs_ipvec (N->pinv, b, x, n) ; /* x = b(p) */
cs_lsolve (N->L, x) ; /* x = L\x */
cs_usolve (N->U, x) ; /* x = U\x */
cs_ipvec (S->q, x, a, n) ; /* b(q) = x */
// }
cs_free (x) ;
cs_sfree (S) ;
cs_nfree (N) ;
return (ok) ;
}
void luDecomp_sparse(cs* matrixA, double* matrixB, double* matrixX, int size)
{
int i;
css *S;
csn *N;
S=cs_sqr(2,matrixA,0);
N=cs_lu(matrixA,S,1);
cs_spfree(matrixA);
if(found_dc_sweep==0){
cs_ipvec(N->pinv, matrixB, matrixX, size);
cs_lsolve(N->L, matrixX);
cs_usolve(N->U, matrixX);
cs_ipvec(S->q, matrixX, matrixB, size);
printf("X vector \n");
for(i=0;i<size;i++){
printf(" %.6lf ",matrixX[i]);
}
printf("\n");
}
else{
double value;
double *matrixB_temp = (double *)calloc(size,sizeof(double));
if (source > -1) {
for(value=start_value;value<=end_value;value=value+step){
matrixB[source-1]=value;
cs_ipvec(N->pinv, matrixB, matrixX, size);
cs_lsolve(N->L, matrixX);
cs_usolve(N->U, matrixX);
}
}
else {
if (sweep_node1!=0){
matrixB[sweep_node1-1]+=sweep_value-start_value;
}
if(sweep_node2!=0){
matrixB[sweep_node2-1]-=sweep_value+start_value;
}
for(value=start_value;value<=end_value;value=value+step) {
cs_ipvec(N->pinv, matrixB, matrixX, size);
cs_lsolve(N->L, matrixX);
cs_usolve(N->U, matrixX);
cs_ipvec(S->q, matrixX, matrixB_temp, size);
if (sweep_node1!=0){
matrixB[sweep_node1-1]+=sweep_value-start_value;
}
if(sweep_node2!=0){
matrixB[sweep_node2-1]-=sweep_value+start_value;
}
printf("value= %lf Matrix X: \n",value);
for(i=0;i<size;i++){
printf(" %.6lf ",matrixX[i]);
}
printf("\n");
}
}
}
printf("\n");
}
void solveSparse(double time){
int i;
double current_value;
double *B_sparse_temp;
//Adeiasma twn arxeiwn sta opoia tha apothikeutoun ta apotelesmata tis analysis gia tous komvous PLOT
if(TRAN==0)initPlotFiles("Sparse");
if(ITER==0)
{
//LU decomposition
S=cs_sqr(2,C_sparse,0);
N=cs_lu(C_sparse,S,1);
//cs_spfree(C_sparse);
}
B_sparse_temp = (double *)calloc(sizeB,sizeof(double)); //apothikeusi tou apotelesmatos tis LU solve gia to sweep kai to transient
if(dc_sweep==0){ //An den exoume sweep
for(i=0;i<sizeB;i++)B_sparse_temp[i]=B_sparse[i];
if (ITER == 0){ //LU solve
cs_ipvec(N->pinv, B_sparse, x_sparse, sizeB); //seg fault gia choleskyNetlist!LA8OS TO N!ARA ANADROMIKA LA8OS TO C_sparse.Omws C_sparce swsto vash ths CG.
cs_lsolve(N->L, x_sparse);
cs_usolve(N->U, x_sparse);
cs_ipvec(S->q, x_sparse, B_sparse, sizeB);
//printf("\n ----- SPARSE LU decomposition ----- \n");
for(i=0;i<sizeB;i++){x_sparse[i]=B_sparse[i];}
cs_nfree(N);
cs_sfree(S);
}else{
bi_conjugate_gradient_sparse(C_sparse,B_sparse, sizeB, x_sparse, itol_value);
//printf("\n");
//printf("---- BI-CG SPARSE ----\n");
}
/*
printf("X = \n");
for(i=0;i<sizeB;i++){
printf(" %.6lf \n",x_sparse[i]);
}
printf("----------------------\n");
printf("\n");
*/
if(TRAN==0){
plotFiles("Sparse", x_sparse, -1.0, "Analysis: DC");
}else{
plotFiles("Sparse", x_sparse, time, "Analysis: TRAN");
}
for(i=0;i<sizeB;i++)B_sparse[i]=B_sparse_temp[i]; //epanafora tou B_sparse gia xrisi sto transient
}
else //DC_SWEEP != 0
{
if(sweep_source!=-1){ //pigi tashs ginetai sweep
for(current_value=start_value; current_value<=end_value+EPS; current_value+=sweep_step){
B_sparse[sweep_source-1]=current_value;
if(ITER == 0){
cs_ipvec(N->pinv, B_sparse, x_sparse, sizeB);
cs_lsolve(N->L, x_sparse);
cs_usolve(N->U, x_sparse);
cs_ipvec(S->q, x_sparse, B_sparse_temp, sizeB);
}else{
bi_conjugate_gradient_sparse(C_sparse,B_sparse, sizeB, x_sparse, itol_value);
}
//Apothikeusi twn apotelesmatwn tis analysis gia tous komvous PLOT
plotFiles("Sparse", (ITER ? x_sparse:B_sparse_temp), current_value, "Sweep source voltage at");
}
}else{ //pigi reumatos ginetai sweep
//Anairesi twn praksewn + kai - apo tin arxiki timi tis pigis ston pinaka B
//kai praksi + kai - me to start_value
if(sweep_posNode!=0){
B_sparse[sweep_posNode-1]+=sweep_value_I-start_value;
}
if(sweep_negNode!=0){
B_sparse[sweep_negNode-1]-=sweep_value_I+start_value;
}
for(current_value=start_value;current_value<=end_value+EPS;current_value+=sweep_step){
if(ITER == 0){
cs_ipvec(N->pinv, B_sparse, x_sparse, sizeB);
cs_lsolve(N->L, x_sparse);
cs_usolve(N->U, x_sparse);
cs_ipvec(S->q, x_sparse, B_sparse_temp,sizeB);
}else{
bi_conjugate_gradient_sparse(C_sparse,B_sparse, sizeB, x_sparse, itol_value);
}
//Allagi twn timwn ston pinaka B gia to epomeno vima tou sweep
if(sweep_posNode!=0){
B_sparse[sweep_posNode-1]-=sweep_step;
}
if(sweep_negNode!=0){
B_sparse[sweep_negNode-1]+=sweep_step;
}
//Apothikeusi twn apotelesmatwn tis analysis gia tous komvous PLOT se arxeia
plotFiles("Sparse", (ITER ? x_sparse:B_sparse_temp), current_value, "Sweep source current at");
}
printf("\n");
}
}
free(B_sparse_temp);
}
