PetscErrorCode SNESMonitorJacUpdateSpectrum(SNES snes,PetscInt it,PetscReal fnorm,void *ctx)
{
#if defined(PETSC_MISSING_LAPACK_GEEV)
SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_SUP,"GEEV - Lapack routine is unavailable\nNot able to provide eigen values.");
#elif defined(PETSC_HAVE_ESSL)
SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_SUP,"GEEV - No support for ESSL Lapack Routines");
#else
Vec X;
Mat J,dJ,dJdense;
PetscErrorCode ierr;
PetscErrorCode (*func)(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
PetscInt n,i;
PetscBLASInt nb,lwork;
PetscReal *eigr,*eigi;
MatStructure flg = DIFFERENT_NONZERO_PATTERN;
PetscScalar *work;
PetscScalar *a;
PetscFunctionBegin;
if (it == 0) PetscFunctionReturn(0);
/* create the difference between the current update and the current jacobian */
ierr = SNESGetSolution(snes,&X);CHKERRQ(ierr);
ierr = SNESGetJacobian(snes,&J,NULL,&func,NULL);CHKERRQ(ierr);
ierr = MatDuplicate(J,MAT_COPY_VALUES,&dJ);CHKERRQ(ierr);
ierr = SNESComputeJacobian(snes,X,&dJ,&dJ,&flg);CHKERRQ(ierr);
ierr = MatAXPY(dJ,-1.0,J,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
/* compute the spectrum directly */
ierr = MatConvert(dJ,MATSEQDENSE,MAT_INITIAL_MATRIX,&dJdense);CHKERRQ(ierr);
ierr = MatGetSize(dJ,&n,NULL);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n,&nb);CHKERRQ(ierr);
lwork = 3*nb;
ierr = PetscMalloc(n*sizeof(PetscReal),&eigr);CHKERRQ(ierr);
ierr = PetscMalloc(n*sizeof(PetscReal),&eigi);CHKERRQ(ierr);
ierr = PetscMalloc(lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);
ierr = MatDenseGetArray(dJdense,&a);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
{
PetscBLASInt lierr;
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
PetscStackCall("LAPACKgeev",LAPACKgeev_("N","N",&nb,a,&nb,eigr,eigi,NULL,&nb,NULL,&nb,work,&lwork,&lierr));
if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"geev() error %d",lierr);
ierr = PetscFPTrapPop();CHKERRQ(ierr);
}
#else
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not coded for complex");
#endif
PetscPrintf(PetscObjectComm((PetscObject)snes),"Eigenvalues of J_%d - J_%d:\n",it,it-1);CHKERRQ(ierr);
for (i=0;i<n;i++) {
PetscPrintf(PetscObjectComm((PetscObject)snes),"%5d: %20.5g + %20.5gi\n",i,eigr[i],eigi[i]);CHKERRQ(ierr);
}
ierr = MatDenseRestoreArray(dJdense,&a);CHKERRQ(ierr);
ierr = MatDestroy(&dJ);CHKERRQ(ierr);
ierr = MatDestroy(&dJdense);CHKERRQ(ierr);
ierr = PetscFree(eigr);CHKERRQ(ierr);
ierr = PetscFree(eigi);CHKERRQ(ierr);
ierr = PetscFree(work);CHKERRQ(ierr);
PetscFunctionReturn(0);
#endif
}
/*@
PetscDTGaussQuadrature - create Gauss quadrature
Not Collective
Input Arguments:
+ npoints - number of points
. a - left end of interval (often-1)
- b - right end of interval (often +1)
Output Arguments:
+ x - quadrature points
- w - quadrature weights
Level: intermediate
References:
Golub and Welsch, Calculation of Quadrature Rules, Math. Comp. 23(106), 221--230, 1969.
.seealso: PetscDTLegendreEval()
@*/
PetscErrorCode PetscDTGaussQuadrature(PetscInt npoints,PetscReal a,PetscReal b,PetscReal *x,PetscReal *w)
{
PetscErrorCode ierr;
PetscInt i;
PetscReal *work;
PetscScalar *Z;
PetscBLASInt N,LDZ,info;
PetscFunctionBegin;
/* Set up the Golub-Welsch system */
for (i=0; i<npoints; i++) {
x[i] = 0; /* diagonal is 0 */
if (i) w[i-1] = 0.5 / PetscSqrtReal(1 - 1./PetscSqr(2*i));
}
ierr = PetscRealView(npoints-1,w,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = PetscMalloc2(npoints*npoints,PetscScalar,&Z,PetscMax(1,2*npoints-2),PetscReal,&work);CHKERRQ(ierr);
ierr = PetscBLASIntCast(npoints,&N);CHKERRQ(ierr);
LDZ = N;
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
PetscStackCall("LAPACKsteqr",LAPACKsteqr_("I",&N,x,w,Z,&LDZ,work,&info));
ierr = PetscFPTrapPop();CHKERRQ(ierr);
if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"xSTEQR error");
for (i=0; i<(npoints+1)/2; i++) {
PetscReal y = 0.5 * (-x[i] + x[npoints-i-1]); /* enforces symmetry */
x[i] = (a+b)/2 - y*(b-a)/2;
x[npoints-i-1] = (a+b)/2 + y*(b-a)/2;
w[i] = w[npoints-1-i] = (b-a)*PetscSqr(0.5*PetscAbsScalar(Z[i*npoints] + Z[(npoints-i-1)*npoints]));
}
ierr = PetscFree2(Z,work);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/**************************************xyt.c***********************************/
static PetscErrorCode do_xyt_solve(xyt_ADT xyt_handle, PetscScalar *uc)
{
PetscInt off, len, *iptr;
PetscInt level =xyt_handle->level;
PetscInt n =xyt_handle->info->n;
PetscInt m =xyt_handle->info->m;
PetscInt *stages =xyt_handle->info->stages;
PetscInt *xcol_indices=xyt_handle->info->xcol_indices;
PetscInt *ycol_indices=xyt_handle->info->ycol_indices;
PetscScalar *x_ptr, *y_ptr, *uu_ptr;
PetscScalar *solve_uu=xyt_handle->info->solve_uu;
PetscScalar *solve_w =xyt_handle->info->solve_w;
PetscScalar *x =xyt_handle->info->x;
PetscScalar *y =xyt_handle->info->y;
PetscBLASInt i1 = 1,dlen;
PetscErrorCode ierr;
PetscFunctionBegin;
uu_ptr=solve_uu;
PCTFS_rvec_zero(uu_ptr,m);
/* x = X.Y^T.b */
/* uu = Y^T.b */
for (y_ptr=y,iptr=ycol_indices; *iptr!=-1; y_ptr+=len)
{
off =*iptr++;
len =*iptr++;
ierr = PetscBLASIntCast(len,&dlen);CHKERRQ(ierr);
PetscStackCall("BLASdot",*uu_ptr++ = BLASdot_(&dlen,uc+off,&i1,y_ptr,&i1));
}
/* comunication of beta */
uu_ptr=solve_uu;
if (level) PCTFS_ssgl_radd(uu_ptr, solve_w, level, stages);
PCTFS_rvec_zero(uc,n);
/* x = X.uu */
for (x_ptr=x,iptr=xcol_indices; *iptr!=-1; x_ptr+=len) {
off =*iptr++;
len =*iptr++;
ierr = PetscBLASIntCast(len,&dlen);CHKERRQ(ierr);
PetscStackCall("BLASaxpy",BLASaxpy_(&dlen,uu_ptr++,x_ptr,&i1,uc+off,&i1));
}
PetscFunctionReturn(0);
}
PetscErrorCode MatLUFactorSymbolic_SuperLU_DIST(Mat F,Mat A,IS r,IS c,const MatFactorInfo *info)
{
Mat_SuperLU_DIST *lu = (Mat_SuperLU_DIST*)F->spptr;
PetscInt M = A->rmap->N,N=A->cmap->N;
PetscFunctionBegin;
/* Initialize the SuperLU process grid. */
PetscStackCall("SuperLU_DIST:superlu_gridinit",superlu_gridinit(lu->comm_superlu, lu->nprow, lu->npcol, &lu->grid));
/* Initialize ScalePermstruct and LUstruct. */
PetscStackCall("SuperLU_DIST:ScalePermstructInit",ScalePermstructInit(M, N, &lu->ScalePermstruct));
PetscStackCall("SuperLU_DIST:LUstructInit",LUstructInit(M, N, &lu->LUstruct));
F->ops->lufactornumeric = MatLUFactorNumeric_SuperLU_DIST;
F->ops->solve = MatSolve_SuperLU_DIST;
F->ops->matsolve = MatMatSolve_SuperLU_DIST;
lu->CleanUpSuperLU_Dist = PETSC_TRUE;
PetscFunctionReturn(0);
}
PetscErrorCode MatScale_MPIDense(Mat inA,PetscScalar alpha)
{
Mat_MPIDense *A = (Mat_MPIDense*)inA->data;
Mat_SeqDense *a = (Mat_SeqDense*)A->A->data;
PetscScalar oalpha = alpha;
PetscErrorCode ierr;
PetscBLASInt one = 1,nz;
PetscFunctionBegin;
ierr = PetscBLASIntCast(inA->rmap->n*inA->cmap->N,&nz);CHKERRQ(ierr);
PetscStackCall("BLASscal",BLASscal_(&nz,&oalpha,a->v,&one));
ierr = PetscLogFlops(nz);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode MatDestroy_SuperLU_DIST(Mat A)
{
PetscErrorCode ierr;
Mat_SuperLU_DIST *lu = (Mat_SuperLU_DIST*)A->spptr;
PetscBool flg;
PetscFunctionBegin;
if (lu && lu->CleanUpSuperLU_Dist) {
/* Deallocate SuperLU_DIST storage */
if (lu->MatInputMode == GLOBAL) {
PetscStackCall("SuperLU_DIST:Destroy_CompCol_Matrix_dist",Destroy_CompCol_Matrix_dist(&lu->A_sup));
} else {
PetscStackCall("SuperLU_DIST:Destroy_CompRowLoc_Matrix_dist",Destroy_CompRowLoc_Matrix_dist(&lu->A_sup));
if (lu->options.SolveInitialized) {
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:zSolveFinalize",zSolveFinalize(&lu->options, &lu->SOLVEstruct));
#else
PetscStackCall("SuperLU_DIST:dSolveFinalize",dSolveFinalize(&lu->options, &lu->SOLVEstruct));
#endif
}
}
PetscStackCall("SuperLU_DIST:Destroy_LU",Destroy_LU(A->cmap->N, &lu->grid, &lu->LUstruct));
PetscStackCall("SuperLU_DIST:ScalePermstructFree",ScalePermstructFree(&lu->ScalePermstruct));
PetscStackCall("SuperLU_DIST:LUstructFree",LUstructFree(&lu->LUstruct));
/* Release the SuperLU_DIST process grid. */
PetscStackCall("SuperLU_DIST:superlu_gridexit",superlu_gridexit(&lu->grid));
ierr = MPI_Comm_free(&(lu->comm_superlu));CHKERRQ(ierr);
}
ierr = PetscFree(A->spptr);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJ,&flg);CHKERRQ(ierr);
if (flg) {
ierr = MatDestroy_SeqAIJ(A);CHKERRQ(ierr);
} else {
ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode SNESNGMRESFormCombinedSolution_Private(SNES snes,PetscInt l,Vec XM,Vec FM,PetscReal fMnorm,Vec X,Vec XA,Vec FA)
{
SNES_NGMRES *ngmres = (SNES_NGMRES*) snes->data;
PetscInt i,j;
Vec *Fdot = ngmres->Fdot;
Vec *Xdot = ngmres->Xdot;
PetscScalar *beta = ngmres->beta;
PetscScalar *xi = ngmres->xi;
PetscScalar alph_total = 0.;
PetscErrorCode ierr;
PetscReal nu;
Vec Y = snes->work[2];
PetscBool changed_y,changed_w;
PetscFunctionBegin;
nu = fMnorm*fMnorm;
/* construct the right hand side and xi factors */
ierr = VecMDot(FM,l,Fdot,xi);CHKERRQ(ierr);
for (i = 0; i < l; i++) beta[i] = nu - xi[i];
/* construct h */
for (j = 0; j < l; j++) {
for (i = 0; i < l; i++) {
H(i,j) = Q(i,j)-xi[i]-xi[j]+nu;
}
}
if (l == 1) {
/* simply set alpha[0] = beta[0] / H[0, 0] */
if (H(0,0) != 0.) beta[0] = beta[0]/H(0,0);
else beta[0] = 0.;
} else {
#if defined(PETSC_MISSING_LAPACK_GELSS)
SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_SUP,"NGMRES with LS requires the LAPACK GELSS routine.");
#else
ierr = PetscBLASIntCast(l,&ngmres->m);CHKERRQ(ierr);
ierr = PetscBLASIntCast(l,&ngmres->n);CHKERRQ(ierr);
ngmres->info = 0;
ngmres->rcond = -1.;
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("LAPACKgelss",LAPACKgelss_(&ngmres->m,&ngmres->n,&ngmres->nrhs,ngmres->h,&ngmres->lda,ngmres->beta,&ngmres->ldb,ngmres->s,&ngmres->rcond,&ngmres->rank,ngmres->work,&ngmres->lwork,ngmres->rwork,&ngmres->info));
#else
PetscStackCall("LAPACKgelss",LAPACKgelss_(&ngmres->m,&ngmres->n,&ngmres->nrhs,ngmres->h,&ngmres->lda,ngmres->beta,&ngmres->ldb,ngmres->s,&ngmres->rcond,&ngmres->rank,ngmres->work,&ngmres->lwork,&ngmres->info));
#endif
ierr = PetscFPTrapPop();CHKERRQ(ierr);
if (ngmres->info < 0) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_LIB,"Bad argument to GELSS");
if (ngmres->info > 0) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_LIB,"SVD failed to converge");
#endif
}
for (i=0; i<l; i++) {
if (PetscIsInfOrNanScalar(beta[i])) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_LIB,"SVD generated inconsistent output");
}
alph_total = 0.;
for (i = 0; i < l; i++) alph_total += beta[i];
ierr = VecCopy(XM,XA);CHKERRQ(ierr);
ierr = VecScale(XA,1.-alph_total);CHKERRQ(ierr);
ierr = VecMAXPY(XA,l,beta,Xdot);CHKERRQ(ierr);
/* check the validity of the step */
ierr = VecCopy(XA,Y);CHKERRQ(ierr);
ierr = VecAXPY(Y,-1.0,X);CHKERRQ(ierr);
ierr = SNESLineSearchPostCheck(snes->linesearch,X,Y,XA,&changed_y,&changed_w);CHKERRQ(ierr);
if (!ngmres->approxfunc) {ierr = SNESComputeFunction(snes,XA,FA);CHKERRQ(ierr);}
else {
ierr = VecCopy(FM,FA);CHKERRQ(ierr);
ierr = VecScale(FA,1.-alph_total);CHKERRQ(ierr);
ierr = VecMAXPY(FA,l,beta,Fdot);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/* approximately solve the overdetermined system:
2*F(x_i)\cdot F(\x_j)\alpha_i = 0
\alpha_i = 1
Which minimizes the L2 norm of the linearization of:
||F(\sum_i \alpha_i*x_i)||^2
With the constraint that \sum_i\alpha_i = 1
Where x_i is the solution from the ith subsolver.
*/
static PetscErrorCode SNESCompositeApply_AdditiveOptimal(SNES snes,Vec X,Vec B,Vec F,PetscReal *fnorm)
{
PetscErrorCode ierr;
SNES_Composite *jac = (SNES_Composite*)snes->data;
SNES_CompositeLink next = jac->head;
Vec *Xes = jac->Xes,*Fes = jac->Fes;
PetscInt i,j;
PetscScalar tot,total,ftf;
PetscReal min_fnorm;
PetscInt min_i;
SNESConvergedReason reason;
PetscFunctionBegin;
if (!next) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE,"No composite SNESes supplied via SNESCompositeAddSNES() or -snes_composite_sneses");
if (snes->normschedule == SNES_NORM_ALWAYS) {
next = jac->head;
ierr = SNESSetInitialFunction(next->snes,F);CHKERRQ(ierr);
while (next->next) {
next = next->next;
ierr = SNESSetInitialFunction(next->snes,F);CHKERRQ(ierr);
}
}
next = jac->head;
i = 0;
ierr = VecCopy(X,Xes[i]);CHKERRQ(ierr);
ierr = SNESSolve(next->snes,B,Xes[i]);CHKERRQ(ierr);
ierr = SNESGetConvergedReason(next->snes,&reason);CHKERRQ(ierr);
if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
jac->innerFailures++;
if (jac->innerFailures >= snes->maxFailures) {
snes->reason = SNES_DIVERGED_INNER;
PetscFunctionReturn(0);
}
}
while (next->next) {
i++;
next = next->next;
ierr = VecCopy(X,Xes[i]);CHKERRQ(ierr);
ierr = SNESSolve(next->snes,B,Xes[i]);CHKERRQ(ierr);
ierr = SNESGetConvergedReason(next->snes,&reason);CHKERRQ(ierr);
if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
jac->innerFailures++;
if (jac->innerFailures >= snes->maxFailures) {
snes->reason = SNES_DIVERGED_INNER;
PetscFunctionReturn(0);
}
}
}
/* all the solutions are collected; combine optimally */
for (i=0;i<jac->n;i++) {
for (j=0;j<i+1;j++) {
ierr = VecDotBegin(Fes[i],Fes[j],&jac->h[i + j*jac->n]);CHKERRQ(ierr);
}
ierr = VecDotBegin(Fes[i],F,&jac->g[i]);CHKERRQ(ierr);
}
for (i=0;i<jac->n;i++) {
for (j=0;j<i+1;j++) {
ierr = VecDotEnd(Fes[i],Fes[j],&jac->h[i + j*jac->n]);CHKERRQ(ierr);
if (i == j) jac->fnorms[i] = PetscSqrtReal(PetscRealPart(jac->h[i + j*jac->n]));
}
ierr = VecDotEnd(Fes[i],F,&jac->g[i]);CHKERRQ(ierr);
}
ftf = (*fnorm)*(*fnorm);
for (i=0; i<jac->n; i++) {
for (j=i+1;j<jac->n;j++) {
jac->h[i + j*jac->n] = jac->h[j + i*jac->n];
}
}
for (i=0; i<jac->n; i++) {
for (j=0; j<jac->n; j++) {
jac->h[i + j*jac->n] = jac->h[i + j*jac->n] - jac->g[j] - jac->g[i] + ftf;
}
jac->beta[i] = ftf - jac->g[i];
}
#if defined(PETSC_MISSING_LAPACK_GELSS)
SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_SUP,"SNESCOMPOSITE with ADDITIVEOPTIMAL requires the LAPACK GELSS routine.");
#else
jac->info = 0;
jac->rcond = -1.;
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("LAPACKgelss",LAPACKgelss_(&jac->n,&jac->n,&jac->nrhs,jac->h,&jac->lda,jac->beta,&jac->lda,jac->s,&jac->rcond,&jac->rank,jac->work,&jac->lwork,jac->rwork,&jac->info));
#else
PetscStackCall("LAPACKgelss",LAPACKgelss_(&jac->n,&jac->n,&jac->nrhs,jac->h,&jac->lda,jac->beta,&jac->lda,jac->s,&jac->rcond,&jac->rank,jac->work,&jac->lwork,&jac->info));
#endif
ierr = PetscFPTrapPop();CHKERRQ(ierr);
if (jac->info < 0) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_LIB,"Bad argument to GELSS");
if (jac->info > 0) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_LIB,"SVD failed to converge");
#endif
tot = 0.;
total = 0.;
for (i=0; i<jac->n; i++) {
if (snes->errorifnotconverged && PetscIsInfOrNanScalar(jac->beta[i])) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_LIB,"SVD generated inconsistent output");
ierr = PetscInfo2(snes,"%D: %g\n",i,(double)PetscRealPart(jac->beta[i]));CHKERRQ(ierr);
tot += jac->beta[i];
total += PetscAbsScalar(jac->beta[i]);
}
ierr = VecScale(X,(1. - tot));CHKERRQ(ierr);
ierr = VecMAXPY(X,jac->n,jac->beta,Xes);CHKERRQ(ierr);
ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr);
if (snes->xl && snes->xu) {
ierr = SNESVIComputeInactiveSetFnorm(snes, F, X, fnorm);CHKERRQ(ierr);
} else {
ierr = VecNorm(F, NORM_2, fnorm);CHKERRQ(ierr);
}
/* take the minimum-normed candidate if it beats the combination by a factor of rtol or the combination has stagnated */
min_fnorm = jac->fnorms[0];
min_i = 0;
for (i=0; i<jac->n; i++) {
if (jac->fnorms[i] < min_fnorm) {
min_fnorm = jac->fnorms[i];
min_i = i;
}
}
/* stagnation or divergence restart to the solution of the solver that failed the least */
if (PetscRealPart(total) < jac->stol || min_fnorm*jac->rtol < *fnorm) {
ierr = VecCopy(jac->Xes[min_i],X);CHKERRQ(ierr);
ierr = VecCopy(jac->Fes[min_i],F);CHKERRQ(ierr);
*fnorm = min_fnorm;
}
PetscFunctionReturn(0);
}
/**************************************xyt.c***********************************/
static PetscInt xyt_generate(xyt_ADT xyt_handle)
{
PetscInt i,j,k,idx;
PetscInt dim, col;
PetscScalar *u, *uu, *v, *z, *w, alpha, alpha_w;
PetscInt *segs;
PetscInt op[] = {GL_ADD,0};
PetscInt off, len;
PetscScalar *x_ptr, *y_ptr;
PetscInt *iptr, flag;
PetscInt start =0, end, work;
PetscInt op2[] = {GL_MIN,0};
PCTFS_gs_ADT PCTFS_gs_handle;
PetscInt *nsep, *lnsep, *fo;
PetscInt a_n =xyt_handle->mvi->n;
PetscInt a_m =xyt_handle->mvi->m;
PetscInt *a_local2global=xyt_handle->mvi->local2global;
PetscInt level;
PetscInt n, m;
PetscInt *xcol_sz, *xcol_indices, *stages;
PetscScalar **xcol_vals, *x;
PetscInt *ycol_sz, *ycol_indices;
PetscScalar **ycol_vals, *y;
PetscInt n_global;
PetscInt xt_nnz =0, xt_max_nnz=0;
PetscInt yt_nnz =0, yt_max_nnz=0;
PetscInt xt_zero_nnz =0;
PetscInt xt_zero_nnz_0=0;
PetscInt yt_zero_nnz =0;
PetscInt yt_zero_nnz_0=0;
PetscBLASInt i1 = 1,dlen;
PetscScalar dm1 = -1.0;
PetscErrorCode ierr;
n =xyt_handle->mvi->n;
nsep =xyt_handle->info->nsep;
lnsep =xyt_handle->info->lnsep;
fo =xyt_handle->info->fo;
end =lnsep[0];
level =xyt_handle->level;
PCTFS_gs_handle=xyt_handle->mvi->PCTFS_gs_handle;
/* is there a null space? */
/* LATER add in ability to detect null space by checking alpha */
for (i=0, j=0; i<=level; i++) j+=nsep[i];
m = j-xyt_handle->ns;
if (m!=j) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"xyt_generate() :: null space exists %D %D %D\n",m,j,xyt_handle->ns);CHKERRQ(ierr);
}
ierr = PetscInfo2(0,"xyt_generate() :: X(%D,%D)\n",n,m);CHKERRQ(ierr);
/* get and initialize storage for x local */
/* note that x local is nxm and stored by columns */
xcol_sz = (PetscInt*) malloc(m*sizeof(PetscInt));
xcol_indices = (PetscInt*) malloc((2*m+1)*sizeof(PetscInt));
xcol_vals = (PetscScalar**) malloc(m*sizeof(PetscScalar*));
for (i=j=0; i<m; i++, j+=2) {
xcol_indices[j]=xcol_indices[j+1]=xcol_sz[i]=-1;
xcol_vals[i] = NULL;
}
xcol_indices[j]=-1;
/* get and initialize storage for y local */
/* note that y local is nxm and stored by columns */
ycol_sz = (PetscInt*) malloc(m*sizeof(PetscInt));
ycol_indices = (PetscInt*) malloc((2*m+1)*sizeof(PetscInt));
ycol_vals = (PetscScalar**) malloc(m*sizeof(PetscScalar*));
for (i=j=0; i<m; i++, j+=2) {
ycol_indices[j]=ycol_indices[j+1]=ycol_sz[i]=-1;
ycol_vals[i] = NULL;
}
ycol_indices[j]=-1;
/* size of separators for each sub-hc working from bottom of tree to top */
/* this looks like nsep[]=segments */
stages = (PetscInt*) malloc((level+1)*sizeof(PetscInt));
segs = (PetscInt*) malloc((level+1)*sizeof(PetscInt));
PCTFS_ivec_zero(stages,level+1);
PCTFS_ivec_copy(segs,nsep,level+1);
for (i=0; i<level; i++) segs[i+1] += segs[i];
stages[0] = segs[0];
/* temporary vectors */
u = (PetscScalar*) malloc(n*sizeof(PetscScalar));
z = (PetscScalar*) malloc(n*sizeof(PetscScalar));
v = (PetscScalar*) malloc(a_m*sizeof(PetscScalar));
uu = (PetscScalar*) malloc(m*sizeof(PetscScalar));
w = (PetscScalar*) malloc(m*sizeof(PetscScalar));
/* extra nnz due to replication of vertices across separators */
for (i=1, j=0; i<=level; i++) j+=nsep[i];
/* storage for sparse x values */
n_global = xyt_handle->info->n_global;
xt_max_nnz = yt_max_nnz = (PetscInt)(2.5*PetscPowReal(1.0*n_global,1.6667) + j*n/2)/PCTFS_num_nodes;
x = (PetscScalar*) malloc(xt_max_nnz*sizeof(PetscScalar));
y = (PetscScalar*) malloc(yt_max_nnz*sizeof(PetscScalar));
/* LATER - can embed next sep to fire in gs */
/* time to make the donuts - generate X factor */
for (dim=i=j=0; i<m; i++) {
/* time to move to the next level? */
while (i==segs[dim]) {
if (dim==level) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"dim about to exceed level\n");
stages[dim++]=i;
end +=lnsep[dim];
}
stages[dim]=i;
/* which column are we firing? */
/* i.e. set v_l */
/* use new seps and do global min across hc to determine which one to fire */
(start<end) ? (col=fo[start]) : (col=INT_MAX);
PCTFS_giop_hc(&col,&work,1,op2,dim);
/* shouldn't need this */
if (col==INT_MAX) {
ierr = PetscInfo(0,"hey ... col==INT_MAX??\n");CHKERRQ(ierr);
continue;
}
/* do I own it? I should */
PCTFS_rvec_zero(v,a_m);
if (col==fo[start]) {
start++;
idx=PCTFS_ivec_linear_search(col, a_local2global, a_n);
if (idx!=-1) {
v[idx] = 1.0;
j++;
} else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"NOT FOUND!\n");
} else {
idx=PCTFS_ivec_linear_search(col, a_local2global, a_m);
if (idx!=-1) v[idx] = 1.0;
}
/* perform u = A.v_l */
PCTFS_rvec_zero(u,n);
do_matvec(xyt_handle->mvi,v,u);
/* uu = X^T.u_l (local portion) */
/* technically only need to zero out first i entries */
/* later turn this into an XYT_solve call ? */
PCTFS_rvec_zero(uu,m);
y_ptr=y;
iptr = ycol_indices;
for (k=0; k<i; k++) {
off = *iptr++;
len = *iptr++;
ierr = PetscBLASIntCast(len,&dlen);CHKERRQ(ierr);
PetscStackCall("BLASdot",uu[k] = BLASdot_(&dlen,u+off,&i1,y_ptr,&i1));
y_ptr+=len;
}
/* uu = X^T.u_l (comm portion) */
PCTFS_ssgl_radd (uu, w, dim, stages);
/* z = X.uu */
PCTFS_rvec_zero(z,n);
x_ptr=x;
iptr = xcol_indices;
for (k=0; k<i; k++) {
off = *iptr++;
len = *iptr++;
ierr = PetscBLASIntCast(len,&dlen);CHKERRQ(ierr);
PetscStackCall("BLASaxpy",BLASaxpy_(&dlen,&uu[k],x_ptr,&i1,z+off,&i1));
x_ptr+=len;
}
/* compute v_l = v_l - z */
PCTFS_rvec_zero(v+a_n,a_m-a_n);
ierr = PetscBLASIntCast(n,&dlen);CHKERRQ(ierr);
PetscStackCall("BLASaxpy",BLASaxpy_(&dlen,&dm1,z,&i1,v,&i1));
/* compute u_l = A.v_l */
if (a_n!=a_m) PCTFS_gs_gop_hc(PCTFS_gs_handle,v,"+\0",dim);
PCTFS_rvec_zero(u,n);
do_matvec(xyt_handle->mvi,v,u);
/* compute sqrt(alpha) = sqrt(u_l^T.u_l) - local portion */
ierr = PetscBLASIntCast(n,&dlen);CHKERRQ(ierr);
PetscStackCall("BLASdot",alpha = BLASdot_(&dlen,u,&i1,u,&i1));
/* compute sqrt(alpha) = sqrt(u_l^T.u_l) - comm portion */
PCTFS_grop_hc(&alpha, &alpha_w, 1, op, dim);
alpha = (PetscScalar) PetscSqrtReal((PetscReal)alpha);
/* check for small alpha */
/* LATER use this to detect and determine null space */
if (fabs(alpha)<1.0e-14) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"bad alpha! %g\n",alpha);
/* compute v_l = v_l/sqrt(alpha) */
PCTFS_rvec_scale(v,1.0/alpha,n);
PCTFS_rvec_scale(u,1.0/alpha,n);
/* add newly generated column, v_l, to X */
flag = 1;
off =len=0;
for (k=0; k<n; k++) {
if (v[k]!=0.0) {
len=k;
if (flag) {off=k; flag=0;}
}
}
len -= (off-1);
if (len>0) {
if ((xt_nnz+len)>xt_max_nnz) {
ierr = PetscInfo(0,"increasing space for X by 2x!\n");CHKERRQ(ierr);
xt_max_nnz *= 2;
x_ptr = (PetscScalar*) malloc(xt_max_nnz*sizeof(PetscScalar));
PCTFS_rvec_copy(x_ptr,x,xt_nnz);
free(x);
x = x_ptr;
x_ptr+=xt_nnz;
}
xt_nnz += len;
PCTFS_rvec_copy(x_ptr,v+off,len);
/* keep track of number of zeros */
if (dim) {
for (k=0; k<len; k++) {
if (x_ptr[k]==0.0) xt_zero_nnz++;
}
} else {
for (k=0; k<len; k++) {
if (x_ptr[k]==0.0) xt_zero_nnz_0++;
}
}
xcol_indices[2*i] = off;
xcol_sz[i] = xcol_indices[2*i+1] = len;
xcol_vals[i] = x_ptr;
} else {
xcol_indices[2*i] = 0;
xcol_sz[i] = xcol_indices[2*i+1] = 0;
xcol_vals[i] = x_ptr;
}
/* add newly generated column, u_l, to Y */
flag = 1;
off =len=0;
for (k=0; k<n; k++) {
if (u[k]!=0.0) {
len=k;
if (flag) { off=k; flag=0; }
}
}
len -= (off-1);
if (len>0) {
if ((yt_nnz+len)>yt_max_nnz) {
ierr = PetscInfo(0,"increasing space for Y by 2x!\n");CHKERRQ(ierr);
yt_max_nnz *= 2;
y_ptr = (PetscScalar*) malloc(yt_max_nnz*sizeof(PetscScalar));
PCTFS_rvec_copy(y_ptr,y,yt_nnz);
free(y);
y = y_ptr;
y_ptr+=yt_nnz;
}
yt_nnz += len;
PCTFS_rvec_copy(y_ptr,u+off,len);
/* keep track of number of zeros */
if (dim) {
for (k=0; k<len; k++) {
if (y_ptr[k]==0.0) yt_zero_nnz++;
}
} else {
for (k=0; k<len; k++) {
if (y_ptr[k]==0.0) yt_zero_nnz_0++;
}
}
ycol_indices[2*i] = off;
ycol_sz[i] = ycol_indices[2*i+1] = len;
ycol_vals[i] = y_ptr;
} else {
ycol_indices[2*i] = 0;
ycol_sz[i] = ycol_indices[2*i+1] = 0;
ycol_vals[i] = y_ptr;
}
}
/* close off stages for execution phase */
while (dim!=level) {
stages[dim++]=i;
ierr = PetscInfo2(0,"disconnected!!! dim(%D)!=level(%D)\n",dim,level);CHKERRQ(ierr);
}
stages[dim]=i;
xyt_handle->info->n =xyt_handle->mvi->n;
xyt_handle->info->m =m;
xyt_handle->info->nnz =xt_nnz + yt_nnz;
xyt_handle->info->max_nnz =xt_max_nnz + yt_max_nnz;
xyt_handle->info->msg_buf_sz =stages[level]-stages[0];
xyt_handle->info->solve_uu = (PetscScalar*) malloc(m*sizeof(PetscScalar));
xyt_handle->info->solve_w = (PetscScalar*) malloc(m*sizeof(PetscScalar));
xyt_handle->info->x =x;
xyt_handle->info->xcol_vals =xcol_vals;
xyt_handle->info->xcol_sz =xcol_sz;
xyt_handle->info->xcol_indices=xcol_indices;
xyt_handle->info->stages =stages;
xyt_handle->info->y =y;
xyt_handle->info->ycol_vals =ycol_vals;
xyt_handle->info->ycol_sz =ycol_sz;
xyt_handle->info->ycol_indices=ycol_indices;
free(segs);
free(u);
free(v);
free(uu);
free(z);
free(w);
return(0);
}
static PetscErrorCode KSPSolve_BCGSL(KSP ksp)
{
KSP_BCGSL *bcgsl = (KSP_BCGSL*) ksp->data;
PetscScalar alpha, beta, omega, sigma;
PetscScalar rho0, rho1;
PetscReal kappa0, kappaA, kappa1;
PetscReal ghat;
PetscReal zeta, zeta0, rnmax_computed, rnmax_true, nrm0;
PetscBool bUpdateX;
PetscInt maxit;
PetscInt h, i, j, k, vi, ell;
PetscBLASInt ldMZ,bierr;
PetscScalar utb;
PetscReal max_s, pinv_tol;
PetscErrorCode ierr;
PetscFunctionBegin;
/* set up temporary vectors */
vi = 0;
ell = bcgsl->ell;
bcgsl->vB = ksp->work[vi]; vi++;
bcgsl->vRt = ksp->work[vi]; vi++;
bcgsl->vTm = ksp->work[vi]; vi++;
bcgsl->vvR = ksp->work+vi; vi += ell+1;
bcgsl->vvU = ksp->work+vi; vi += ell+1;
bcgsl->vXr = ksp->work[vi]; vi++;
ierr = PetscBLASIntCast(ell+1,&ldMZ);CHKERRQ(ierr);
/* Prime the iterative solver */
ierr = KSPInitialResidual(ksp, VX, VTM, VB, VVR[0], ksp->vec_rhs);CHKERRQ(ierr);
ierr = VecNorm(VVR[0], NORM_2, &zeta0);CHKERRQ(ierr);
rnmax_computed = zeta0;
rnmax_true = zeta0;
ierr = (*ksp->converged)(ksp, 0, zeta0, &ksp->reason, ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) {
ierr = PetscObjectAMSTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its = 0;
ksp->rnorm = zeta0;
ierr = PetscObjectAMSGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
ierr = VecSet(VVU[0],0.0);CHKERRQ(ierr);
alpha = 0.;
rho0 = omega = 1;
if (bcgsl->delta>0.0) {
ierr = VecCopy(VX, VXR);CHKERRQ(ierr);
ierr = VecSet(VX,0.0);CHKERRQ(ierr);
ierr = VecCopy(VVR[0], VB);CHKERRQ(ierr);
} else {
ierr = VecCopy(ksp->vec_rhs, VB);CHKERRQ(ierr);
}
/* Life goes on */
ierr = VecCopy(VVR[0], VRT);CHKERRQ(ierr);
zeta = zeta0;
ierr = KSPGetTolerances(ksp, NULL, NULL, NULL, &maxit);CHKERRQ(ierr);
for (k=0; k<maxit; k += bcgsl->ell) {
ksp->its = k;
ksp->rnorm = zeta;
ierr = KSPLogResidualHistory(ksp, zeta);CHKERRQ(ierr);
ierr = KSPMonitor(ksp, ksp->its, zeta);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp, k, zeta, &ksp->reason, ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason < 0) PetscFunctionReturn(0);
else if (ksp->reason) break;
/* BiCG part */
rho0 = -omega*rho0;
nrm0 = zeta;
for (j=0; j<bcgsl->ell; j++) {
/* rho1 <- r_j' * r_tilde */
ierr = VecDot(VVR[j], VRT, &rho1);CHKERRQ(ierr);
if (rho1 == 0.0) {
ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
PetscFunctionReturn(0);
}
beta = alpha*(rho1/rho0);
rho0 = rho1;
for (i=0; i<=j; i++) {
/* u_i <- r_i - beta*u_i */
ierr = VecAYPX(VVU[i], -beta, VVR[i]);CHKERRQ(ierr);
}
/* u_{j+1} <- inv(K)*A*u_j */
ierr = KSP_PCApplyBAorAB(ksp, VVU[j], VVU[j+1], VTM);CHKERRQ(ierr);
ierr = VecDot(VVU[j+1], VRT, &sigma);CHKERRQ(ierr);
if (sigma == 0.0) {
ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
PetscFunctionReturn(0);
}
alpha = rho1/sigma;
/* x <- x + alpha*u_0 */
ierr = VecAXPY(VX, alpha, VVU[0]);CHKERRQ(ierr);
for (i=0; i<=j; i++) {
/* r_i <- r_i - alpha*u_{i+1} */
ierr = VecAXPY(VVR[i], -alpha, VVU[i+1]);CHKERRQ(ierr);
}
/* r_{j+1} <- inv(K)*A*r_j */
ierr = KSP_PCApplyBAorAB(ksp, VVR[j], VVR[j+1], VTM);CHKERRQ(ierr);
ierr = VecNorm(VVR[0], NORM_2, &nrm0);CHKERRQ(ierr);
if (bcgsl->delta>0.0) {
if (rnmax_computed<nrm0) rnmax_computed = nrm0;
if (rnmax_true<nrm0) rnmax_true = nrm0;
}
/* NEW: check for early exit */
ierr = (*ksp->converged)(ksp, k+j, nrm0, &ksp->reason, ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) {
ierr = PetscObjectAMSTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its = k+j;
ksp->rnorm = nrm0;
ierr = PetscObjectAMSGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
if (ksp->reason < 0) PetscFunctionReturn(0);
}
}
/* Polynomial part */
for (i = 0; i <= bcgsl->ell; ++i) {
ierr = VecMDot(VVR[i], i+1, VVR, &MZa[i*ldMZ]);CHKERRQ(ierr);
}
/* Symmetrize MZa */
for (i = 0; i <= bcgsl->ell; ++i) {
for (j = i+1; j <= bcgsl->ell; ++j) {
MZa[i*ldMZ+j] = MZa[j*ldMZ+i] = PetscConj(MZa[j*ldMZ+i]);
}
}
/* Copy MZa to MZb */
ierr = PetscMemcpy(MZb,MZa,ldMZ*ldMZ*sizeof(PetscScalar));CHKERRQ(ierr);
if (!bcgsl->bConvex || bcgsl->ell==1) {
PetscBLASInt ione = 1,bell;
ierr = PetscBLASIntCast(bcgsl->ell,&bell);CHKERRQ(ierr);
AY0c[0] = -1;
if (bcgsl->pinv) {
#if defined(PETSC_MISSING_LAPACK_GESVD)
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable.");
#else
# if defined(PETSC_USE_COMPLEX)
PetscStackCall("LAPACKgesvd",LAPACKgesvd_("A","A",&bell,&bell,&MZa[1+ldMZ],&ldMZ,bcgsl->s,bcgsl->u,&bell,bcgsl->v,&bell,bcgsl->work,&bcgsl->lwork,bcgsl->realwork,&bierr));
# else
PetscStackCall("LAPACKgesvd",LAPACKgesvd_("A","A",&bell,&bell,&MZa[1+ldMZ],&ldMZ,bcgsl->s,bcgsl->u,&bell,bcgsl->v,&bell,bcgsl->work,&bcgsl->lwork,&bierr));
# endif
#endif
if (bierr!=0) {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
PetscFunctionReturn(0);
}
/* Apply pseudo-inverse */
max_s = bcgsl->s[0];
for (i=1; i<bell; i++) {
if (bcgsl->s[i] > max_s) {
max_s = bcgsl->s[i];
}
}
/* tolerance is hardwired to bell*max(s)*PETSC_MACHINE_EPSILON */
pinv_tol = bell*max_s*PETSC_MACHINE_EPSILON;
ierr = PetscMemzero(&AY0c[1],bell*sizeof(PetscScalar));CHKERRQ(ierr);
for (i=0; i<bell; i++) {
if (bcgsl->s[i] >= pinv_tol) {
utb=0.;
for (j=0; j<bell; j++) {
utb += MZb[1+j]*bcgsl->u[i*bell+j];
}
for (j=0; j<bell; j++) {
AY0c[1+j] += utb/bcgsl->s[i]*bcgsl->v[j*bell+i];
}
}
}
} else {
#if defined(PETSC_MISSING_LAPACK_POTRF)
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"POTRF - Lapack routine is unavailable.");
#else
PetscStackCall("LAPACKpotrf",LAPACKpotrf_("Lower", &bell, &MZa[1+ldMZ], &ldMZ, &bierr));
#endif
if (bierr!=0) {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
PetscFunctionReturn(0);
}
ierr = PetscMemcpy(&AY0c[1],&MZb[1],bcgsl->ell*sizeof(PetscScalar));CHKERRQ(ierr);
PetscStackCall("LAPACKpotrs",LAPACKpotrs_("Lower", &bell, &ione, &MZa[1+ldMZ], &ldMZ, &AY0c[1], &ldMZ, &bierr));
}
} else {
PetscBLASInt ione = 1;
PetscScalar aone = 1.0, azero = 0.0;
PetscBLASInt neqs;
ierr = PetscBLASIntCast(bcgsl->ell-1,&neqs);CHKERRQ(ierr);
#if defined(PETSC_MISSING_LAPACK_POTRF)
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"POTRF - Lapack routine is unavailable.");
#else
PetscStackCall("LAPACKpotrf",LAPACKpotrf_("Lower", &neqs, &MZa[1+ldMZ], &ldMZ, &bierr));
#endif
if (bierr!=0) {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
PetscFunctionReturn(0);
}
ierr = PetscMemcpy(&AY0c[1],&MZb[1],(bcgsl->ell-1)*sizeof(PetscScalar));CHKERRQ(ierr);
PetscStackCall("LAPACKpotrs",LAPACKpotrs_("Lower", &neqs, &ione, &MZa[1+ldMZ], &ldMZ, &AY0c[1], &ldMZ, &bierr));
AY0c[0] = -1;
AY0c[bcgsl->ell] = 0.;
ierr = PetscMemcpy(&AYlc[1],&MZb[1+ldMZ*(bcgsl->ell)],(bcgsl->ell-1)*sizeof(PetscScalar));CHKERRQ(ierr);
PetscStackCall("LAPACKpotrs",LAPACKpotrs_("Lower", &neqs, &ione, &MZa[1+ldMZ], &ldMZ, &AYlc[1], &ldMZ, &bierr));
AYlc[0] = 0.;
AYlc[bcgsl->ell] = -1;
PetscStackCall("BLASgemv",BLASgemv_("NoTr", &ldMZ, &ldMZ, &aone, MZb, &ldMZ, AY0c, &ione, &azero, AYtc, &ione));
kappa0 = PetscRealPart(BLASdot_(&ldMZ, AY0c, &ione, AYtc, &ione));
/* round-off can cause negative kappa's */
if (kappa0<0) kappa0 = -kappa0;
kappa0 = PetscSqrtReal(kappa0);
kappaA = PetscRealPart(BLASdot_(&ldMZ, AYlc, &ione, AYtc, &ione));
PetscStackCall("BLASgemv",BLASgemv_("noTr", &ldMZ, &ldMZ, &aone, MZb, &ldMZ, AYlc, &ione, &azero, AYtc, &ione));
kappa1 = PetscRealPart(BLASdot_(&ldMZ, AYlc, &ione, AYtc, &ione));
if (kappa1<0) kappa1 = -kappa1;
kappa1 = PetscSqrtReal(kappa1);
if (kappa0!=0.0 && kappa1!=0.0) {
if (kappaA<0.7*kappa0*kappa1) {
ghat = (kappaA<0.0) ? -0.7*kappa0/kappa1 : 0.7*kappa0/kappa1;
} else {
ghat = kappaA/(kappa1*kappa1);
}
for (i=0; i<=bcgsl->ell; i++) {
AY0c[i] = AY0c[i] - ghat* AYlc[i];
}
}
}
omega = AY0c[bcgsl->ell];
for (h=bcgsl->ell; h>0 && omega==0.0; h--) omega = AY0c[h];
if (omega==0.0) {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
PetscFunctionReturn(0);
}
ierr = VecMAXPY(VX, bcgsl->ell,AY0c+1, VVR);CHKERRQ(ierr);
for (i=1; i<=bcgsl->ell; i++) AY0c[i] *= -1.0;
ierr = VecMAXPY(VVU[0], bcgsl->ell,AY0c+1, VVU+1);CHKERRQ(ierr);
ierr = VecMAXPY(VVR[0], bcgsl->ell,AY0c+1, VVR+1);CHKERRQ(ierr);
for (i=1; i<=bcgsl->ell; i++) AY0c[i] *= -1.0;
ierr = VecNorm(VVR[0], NORM_2, &zeta);CHKERRQ(ierr);
/* Accurate Update */
if (bcgsl->delta>0.0) {
if (rnmax_computed<zeta) rnmax_computed = zeta;
if (rnmax_true<zeta) rnmax_true = zeta;
bUpdateX = (PetscBool) (zeta<bcgsl->delta*zeta0 && zeta0<=rnmax_computed);
if ((zeta<bcgsl->delta*rnmax_true && zeta0<=rnmax_true) || bUpdateX) {
/* r0 <- b-inv(K)*A*X */
ierr = KSP_PCApplyBAorAB(ksp, VX, VVR[0], VTM);CHKERRQ(ierr);
ierr = VecAYPX(VVR[0], -1.0, VB);CHKERRQ(ierr);
rnmax_true = zeta;
if (bUpdateX) {
ierr = VecAXPY(VXR,1.0,VX);CHKERRQ(ierr);
ierr = VecSet(VX,0.0);CHKERRQ(ierr);
ierr = VecCopy(VVR[0], VB);CHKERRQ(ierr);
rnmax_computed = zeta;
}
}
}
}
if (bcgsl->delta>0.0) {
ierr = VecAXPY(VX,1.0,VXR);CHKERRQ(ierr);
}
ierr = (*ksp->converged)(ksp, k, zeta, &ksp->reason, ksp->cnvP);CHKERRQ(ierr);
if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
PetscFunctionReturn(0);
}
static PetscErrorCode PCSetUp_SVD(PC pc)
{
#if defined(PETSC_MISSING_LAPACK_GESVD)
SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable\nNot able to provide singular value estimates.");
#else
PC_SVD *jac = (PC_SVD*)pc->data;
PetscErrorCode ierr;
PetscScalar *a,*u,*v,*d,*work;
PetscBLASInt nb,lwork;
PetscInt i,n;
PetscMPIInt size;
PetscFunctionBegin;
ierr = MatDestroy(&jac->A);CHKERRQ(ierr);
ierr = MPI_Comm_size(((PetscObject)pc->pmat)->comm,&size);CHKERRQ(ierr);
if (size > 1) {
Mat redmat;
PetscInt M;
ierr = MatGetSize(pc->pmat,&M,NULL);CHKERRQ(ierr);
ierr = MatGetRedundantMatrix(pc->pmat,size,PETSC_COMM_SELF,M,MAT_INITIAL_MATRIX,&redmat);CHKERRQ(ierr);
ierr = MatConvert(redmat,MATSEQDENSE,MAT_INITIAL_MATRIX,&jac->A);CHKERRQ(ierr);
ierr = MatDestroy(&redmat);CHKERRQ(ierr);
} else {
ierr = MatConvert(pc->pmat,MATSEQDENSE,MAT_INITIAL_MATRIX,&jac->A);CHKERRQ(ierr);
}
if (!jac->diag) { /* assume square matrices */
ierr = MatGetVecs(jac->A,&jac->diag,&jac->work);CHKERRQ(ierr);
}
if (!jac->U) {
ierr = MatDuplicate(jac->A,MAT_DO_NOT_COPY_VALUES,&jac->U);CHKERRQ(ierr);
ierr = MatDuplicate(jac->A,MAT_DO_NOT_COPY_VALUES,&jac->Vt);CHKERRQ(ierr);
}
ierr = MatGetSize(pc->pmat,&n,NULL);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n,&nb);CHKERRQ(ierr);
lwork = 5*nb;
ierr = PetscMalloc(lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);
ierr = MatDenseGetArray(jac->A,&a);CHKERRQ(ierr);
ierr = MatDenseGetArray(jac->U,&u);CHKERRQ(ierr);
ierr = MatDenseGetArray(jac->Vt,&v);CHKERRQ(ierr);
ierr = VecGetArray(jac->diag,&d);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
{
PetscBLASInt lierr;
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
PetscStackCall("LAPACKgesvd",LAPACKgesvd_("A","A",&nb,&nb,a,&nb,d,u,&nb,v,&nb,work,&lwork,&lierr));
if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"gesv() error %d",lierr);
ierr = PetscFPTrapPop();CHKERRQ(ierr);
}
#else
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not coded for complex");
#endif
ierr = MatDenseRestoreArray(jac->A,&a);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(jac->U,&u);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(jac->Vt,&v);CHKERRQ(ierr);
for (i=n-1; i>=0; i--) if (PetscRealPart(d[i]) > jac->zerosing) break;
jac->nzero = n-1-i;
if (jac->monitor) {
ierr = PetscViewerASCIIAddTab(jac->monitor,((PetscObject)pc)->tablevel);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(jac->monitor," SVD: condition number %14.12e, %D of %D singular values are (nearly) zero\n",(double)PetscRealPart(d[0]/d[n-1]),jac->nzero,n);CHKERRQ(ierr);
if (n >= 10) { /* print 5 smallest and 5 largest */
ierr = PetscViewerASCIIPrintf(jac->monitor," SVD: smallest singular values: %14.12e %14.12e %14.12e %14.12e %14.12e\n",(double)PetscRealPart(d[n-1]),(double)PetscRealPart(d[n-2]),(double)PetscRealPart(d[n-3]),(double)PetscRealPart(d[n-4]),(double)PetscRealPart(d[n-5]));CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(jac->monitor," SVD: largest singular values : %14.12e %14.12e %14.12e %14.12e %14.12e\n",(double)PetscRealPart(d[4]),(double)PetscRealPart(d[3]),(double)PetscRealPart(d[2]),(double)PetscRealPart(d[1]),(double)PetscRealPart(d[0]));CHKERRQ(ierr);
} else { /* print all singular values */
char buf[256],*p;
size_t left = sizeof(buf),used;
PetscInt thisline;
for (p=buf,i=n-1,thisline=1; i>=0; i--,thisline++) {
ierr = PetscSNPrintfCount(p,left," %14.12e",&used,(double)PetscRealPart(d[i]));CHKERRQ(ierr);
left -= used;
p += used;
if (thisline > 4 || i==0) {
ierr = PetscViewerASCIIPrintf(jac->monitor," SVD: singular values:%s\n",buf);CHKERRQ(ierr);
p = buf;
thisline = 0;
}
}
}
ierr = PetscViewerASCIISubtractTab(jac->monitor,((PetscObject)pc)->tablevel);CHKERRQ(ierr);
}
ierr = PetscInfo2(pc,"Largest and smallest singular values %14.12e %14.12e\n",(double)PetscRealPart(d[0]),(double)PetscRealPart(d[n-1]));CHKERRQ(ierr);
for (i=0; i<n-jac->nzero; i++) d[i] = 1.0/d[i];
for (; i<n; i++) d[i] = 0.0;
if (jac->essrank > 0) for (i=0; i<n-jac->nzero-jac->essrank; i++) d[i] = 0.0; /* Skip all but essrank eigenvalues */
ierr = PetscInfo1(pc,"Number of zero or nearly singular values %D\n",jac->nzero);CHKERRQ(ierr);
ierr = VecRestoreArray(jac->diag,&d);CHKERRQ(ierr);
#if defined(foo)
{
PetscViewer viewer;
ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,"joe",FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
ierr = MatView(jac->A,viewer);CHKERRQ(ierr);
ierr = MatView(jac->U,viewer);CHKERRQ(ierr);
ierr = MatView(jac->Vt,viewer);CHKERRQ(ierr);
ierr = VecView(jac->diag,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
}
#endif
ierr = PetscFree(work);CHKERRQ(ierr);
PetscFunctionReturn(0);
#endif
}
PetscErrorCode MatLUFactorNumeric_SuperLU_DIST(Mat F,Mat A,const MatFactorInfo *info)
{
Mat *tseq,A_seq = NULL;
Mat_SeqAIJ *aa,*bb;
Mat_SuperLU_DIST *lu = (Mat_SuperLU_DIST*)(F)->spptr;
PetscErrorCode ierr;
PetscInt M=A->rmap->N,N=A->cmap->N,i,*ai,*aj,*bi,*bj,nz,rstart,*garray,
m=A->rmap->n, colA_start,j,jcol,jB,countA,countB,*bjj,*ajj;
int sinfo; /* SuperLU_Dist info flag is always an int even with long long indices */
PetscMPIInt size;
SuperLUStat_t stat;
double *berr=0;
IS isrow;
Mat F_diag=NULL;
#if defined(PETSC_USE_COMPLEX)
doublecomplex *av, *bv;
#else
double *av, *bv;
#endif
PetscFunctionBegin;
ierr = MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);CHKERRQ(ierr);
if (lu->MatInputMode == GLOBAL) { /* global mat input */
if (size > 1) { /* convert mpi A to seq mat A */
ierr = ISCreateStride(PETSC_COMM_SELF,M,0,1,&isrow);CHKERRQ(ierr);
ierr = MatGetSubMatrices(A,1,&isrow,&isrow,MAT_INITIAL_MATRIX,&tseq);CHKERRQ(ierr);
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
A_seq = *tseq;
ierr = PetscFree(tseq);CHKERRQ(ierr);
aa = (Mat_SeqAIJ*)A_seq->data;
} else {
PetscBool flg;
ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
if (flg) {
Mat_MPIAIJ *At = (Mat_MPIAIJ*)A->data;
A = At->A;
}
aa = (Mat_SeqAIJ*)A->data;
}
/* Convert Petsc NR matrix to SuperLU_DIST NC.
Note: memories of lu->val, col and row are allocated by CompRow_to_CompCol_dist()! */
if (lu->options.Fact != DOFACT) {/* successive numeric factorization, sparsity pattern is reused. */
PetscStackCall("SuperLU_DIST:Destroy_CompCol_Matrix_dist",Destroy_CompCol_Matrix_dist(&lu->A_sup));
if (lu->FactPattern == SamePattern_SameRowPerm) {
lu->options.Fact = SamePattern_SameRowPerm; /* matrix has similar numerical values */
} else { /* lu->FactPattern == SamePattern */
PetscStackCall("SuperLU_DIST:Destroy_LU",Destroy_LU(N, &lu->grid, &lu->LUstruct));
lu->options.Fact = SamePattern;
}
}
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:zCompRow_to_CompCol_dist",zCompRow_to_CompCol_dist(M,N,aa->nz,(doublecomplex*)aa->a,(int_t*)aa->j,(int_t*)aa->i,&lu->val,&lu->col, &lu->row));
#else
PetscStackCall("SuperLU_DIST:dCompRow_to_CompCol_dist",dCompRow_to_CompCol_dist(M,N,aa->nz,aa->a,(int_t*)aa->j,(int_t*)aa->i,&lu->val, &lu->col, &lu->row));
#endif
/* Create compressed column matrix A_sup. */
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:zCreate_CompCol_Matrix_dist",zCreate_CompCol_Matrix_dist(&lu->A_sup, M, N, aa->nz, lu->val, lu->col, lu->row, SLU_NC, SLU_Z, SLU_GE));
#else
PetscStackCall("SuperLU_DIST:dCreate_CompCol_Matrix_dist",dCreate_CompCol_Matrix_dist(&lu->A_sup, M, N, aa->nz, lu->val, lu->col, lu->row, SLU_NC, SLU_D, SLU_GE));
#endif
} else { /* distributed mat input */
Mat_MPIAIJ *mat = (Mat_MPIAIJ*)A->data;
aa=(Mat_SeqAIJ*)(mat->A)->data;
bb=(Mat_SeqAIJ*)(mat->B)->data;
ai=aa->i; aj=aa->j;
bi=bb->i; bj=bb->j;
#if defined(PETSC_USE_COMPLEX)
av=(doublecomplex*)aa->a;
bv=(doublecomplex*)bb->a;
#else
av=aa->a;
bv=bb->a;
#endif
rstart = A->rmap->rstart;
nz = aa->nz + bb->nz;
garray = mat->garray;
if (lu->options.Fact == DOFACT) { /* first numeric factorization */
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:zallocateA_dist",zallocateA_dist(m, nz, &lu->val, &lu->col, &lu->row));
#else
PetscStackCall("SuperLU_DIST:dallocateA_dist",dallocateA_dist(m, nz, &lu->val, &lu->col, &lu->row));
#endif
} else { /* successive numeric factorization, sparsity pattern and perm_c are reused. */
/* Destroy_CompRowLoc_Matrix_dist(&lu->A_sup); */ /* this leads to crash! However, see SuperLU_DIST_2.5/EXAMPLE/pzdrive2.c */
if (lu->FactPattern == SamePattern_SameRowPerm) {
lu->options.Fact = SamePattern_SameRowPerm; /* matrix has similar numerical values */
} else {
PetscStackCall("SuperLU_DIST:Destroy_LU",Destroy_LU(N, &lu->grid, &lu->LUstruct)); /* Deallocate storage associated with the L and U matrices. */
lu->options.Fact = SamePattern;
}
}
nz = 0;
for (i=0; i<m; i++) {
lu->row[i] = nz;
countA = ai[i+1] - ai[i];
countB = bi[i+1] - bi[i];
ajj = aj + ai[i]; /* ptr to the beginning of this row */
bjj = bj + bi[i];
/* B part, smaller col index */
colA_start = rstart + ajj[0]; /* the smallest global col index of A */
jB = 0;
for (j=0; j<countB; j++) {
jcol = garray[bjj[j]];
if (jcol > colA_start) {
jB = j;
break;
}
lu->col[nz] = jcol;
lu->val[nz++] = *bv++;
if (j==countB-1) jB = countB;
}
/* A part */
for (j=0; j<countA; j++) {
lu->col[nz] = rstart + ajj[j];
lu->val[nz++] = *av++;
}
/* B part, larger col index */
for (j=jB; j<countB; j++) {
lu->col[nz] = garray[bjj[j]];
lu->val[nz++] = *bv++;
}
}
lu->row[m] = nz;
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:zCreate_CompRowLoc_Matrix_dist",zCreate_CompRowLoc_Matrix_dist(&lu->A_sup, M, N, nz, m, rstart,lu->val, lu->col, lu->row, SLU_NR_loc, SLU_Z, SLU_GE));
#else
PetscStackCall("SuperLU_DIST:dCreate_CompRowLoc_Matrix_dist",dCreate_CompRowLoc_Matrix_dist(&lu->A_sup, M, N, nz, m, rstart,lu->val, lu->col, lu->row, SLU_NR_loc, SLU_D, SLU_GE));
#endif
}
/* Factor the matrix. */
PetscStackCall("SuperLU_DIST:PStatInit",PStatInit(&stat)); /* Initialize the statistics variables. */
if (lu->MatInputMode == GLOBAL) { /* global mat input */
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:pzgssvx_ABglobal",pzgssvx_ABglobal(&lu->options, &lu->A_sup, &lu->ScalePermstruct, 0, M, 0,&lu->grid, &lu->LUstruct, berr, &stat, &sinfo));
#else
PetscStackCall("SuperLU_DIST:pdgssvx_ABglobal",pdgssvx_ABglobal(&lu->options, &lu->A_sup, &lu->ScalePermstruct, 0, M, 0,&lu->grid, &lu->LUstruct, berr, &stat, &sinfo));
#endif
} else { /* distributed mat input */
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:pzgssvx",pzgssvx(&lu->options, &lu->A_sup, &lu->ScalePermstruct, 0, m, 0, &lu->grid,&lu->LUstruct, &lu->SOLVEstruct, berr, &stat, &sinfo));
if (sinfo) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"pzgssvx fails, info: %d\n",sinfo);
#else
PetscStackCall("SuperLU_DIST:pdgssvx",pdgssvx(&lu->options, &lu->A_sup, &lu->ScalePermstruct, 0, m, 0, &lu->grid,&lu->LUstruct, &lu->SOLVEstruct, berr, &stat, &sinfo));
if (sinfo) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"pdgssvx fails, info: %d\n",sinfo);
#endif
}
if (lu->MatInputMode == GLOBAL && size > 1) {
ierr = MatDestroy(&A_seq);CHKERRQ(ierr);
}
if (lu->options.PrintStat) {
PStatPrint(&lu->options, &stat, &lu->grid); /* Print the statistics. */
}
PStatFree(&stat);
if (size > 1) {
F_diag = ((Mat_MPIAIJ*)(F)->data)->A;
F_diag->assembled = PETSC_TRUE;
}
(F)->assembled = PETSC_TRUE;
(F)->preallocated = PETSC_TRUE;
lu->options.Fact = FACTORED; /* The factored form of A is supplied. Local option used by this func. only */
PetscFunctionReturn(0);
}
PetscErrorCode MatMatSolve_SuperLU_DIST(Mat A,Mat B_mpi,Mat X)
{
Mat_SuperLU_DIST *lu = (Mat_SuperLU_DIST*)A->spptr;
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt M=A->rmap->N,m=A->rmap->n,nrhs;
SuperLUStat_t stat;
double berr[1];
PetscScalar *bptr;
int info; /* SuperLU_Dist info code is ALWAYS an int, even with long long indices */
PetscBool flg;
PetscFunctionBegin;
if (lu->options.Fact != FACTORED) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"SuperLU_DIST options.Fact mush equal FACTORED");
ierr = PetscObjectTypeCompareAny((PetscObject)B_mpi,&flg,MATSEQDENSE,MATMPIDENSE,NULL);CHKERRQ(ierr);
if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Matrix B must be MATDENSE matrix");
ierr = PetscObjectTypeCompareAny((PetscObject)X,&flg,MATSEQDENSE,MATMPIDENSE,NULL);CHKERRQ(ierr);
if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Matrix X must be MATDENSE matrix");
ierr = MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);CHKERRQ(ierr);
if (size > 1 && lu->MatInputMode == GLOBAL) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatInputMode=GLOBAL for nproc %d>1 is not supported",size);
/* size==1 or distributed mat input */
if (lu->options.SolveInitialized && !lu->matmatsolve_iscalled) {
/* communication pattern of SOLVEstruct is unlikely created for matmatsolve,
thus destroy it and create a new SOLVEstruct.
Otherwise it may result in memory corruption or incorrect solution
See src/mat/examples/tests/ex125.c */
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:zSolveFinalize",zSolveFinalize(&lu->options, &lu->SOLVEstruct));
#else
PetscStackCall("SuperLU_DIST:dSolveFinalize",dSolveFinalize(&lu->options, &lu->SOLVEstruct));
#endif
lu->options.SolveInitialized = NO;
}
ierr = MatCopy(B_mpi,X,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatGetSize(B_mpi,NULL,&nrhs);CHKERRQ(ierr);
PetscStackCall("SuperLU_DIST:PStatInit",PStatInit(&stat)); /* Initialize the statistics variables. */
ierr = MatDenseGetArray(X,&bptr);CHKERRQ(ierr);
if (lu->MatInputMode == GLOBAL) { /* size == 1 */
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:pzgssvx_ABglobal",pzgssvx_ABglobal(&lu->options, &lu->A_sup, &lu->ScalePermstruct,(doublecomplex*)bptr, M, nrhs,&lu->grid, &lu->LUstruct, berr, &stat, &info));
#else
PetscStackCall("SuperLU_DIST:pdgssvx_ABglobal",pdgssvx_ABglobal(&lu->options, &lu->A_sup, &lu->ScalePermstruct,bptr, M, nrhs, &lu->grid, &lu->LUstruct, berr, &stat, &info));
#endif
} else { /* distributed mat input */
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:pzgssvx",pzgssvx(&lu->options,&lu->A_sup,&lu->ScalePermstruct,(doublecomplex*)bptr,m,nrhs,&lu->grid, &lu->LUstruct,&lu->SOLVEstruct,berr,&stat,&info));
#else
PetscStackCall("SuperLU_DIST:pdgssvx",pdgssvx(&lu->options,&lu->A_sup,&lu->ScalePermstruct,bptr,m,nrhs,&lu->grid,&lu->LUstruct,&lu->SOLVEstruct,berr,&stat,&info));
#endif
}
if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"pdgssvx fails, info: %d\n",info);
ierr = MatDenseRestoreArray(X,&bptr);CHKERRQ(ierr);
if (lu->options.PrintStat) PStatPrint(&lu->options, &stat, &lu->grid); /* Print the statistics. */
PetscStackCall("SuperLU_DIST:PStatFree",PStatFree(&stat));
lu->matsolve_iscalled = PETSC_FALSE;
lu->matmatsolve_iscalled = PETSC_TRUE;
PetscFunctionReturn(0);
}
PetscErrorCode MatSolve_SuperLU_DIST(Mat A,Vec b_mpi,Vec x)
{
Mat_SuperLU_DIST *lu = (Mat_SuperLU_DIST*)A->spptr;
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt m=A->rmap->n,M=A->rmap->N,N=A->cmap->N;
SuperLUStat_t stat;
double berr[1];
PetscScalar *bptr;
PetscInt nrhs=1;
Vec x_seq;
IS iden;
VecScatter scat;
int info; /* SuperLU_Dist info code is ALWAYS an int, even with long long indices */
static PetscBool cite = PETSC_FALSE;
PetscFunctionBegin;
ierr = PetscCitationsRegister("@article{lidemmel03,\n author = {Xiaoye S. Li and James W. Demmel},\n title = {{SuperLU_DIST}: A Scalable Distributed-Memory Sparse Direct\n Solver for Unsymmetric Linear Systems},\n journal = {ACM Trans. Mathematical Software},\n volume = {29},\n number = {2},\n pages = {110-140},\n year = 2003\n}\n",&cite);CHKERRQ(ierr);
ierr = MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);CHKERRQ(ierr);
if (size > 1 && lu->MatInputMode == GLOBAL) {
/* global mat input, convert b to x_seq */
ierr = VecCreateSeq(PETSC_COMM_SELF,N,&x_seq);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,N,0,1,&iden);CHKERRQ(ierr);
ierr = VecScatterCreate(b_mpi,iden,x_seq,iden,&scat);CHKERRQ(ierr);
ierr = ISDestroy(&iden);CHKERRQ(ierr);
ierr = VecScatterBegin(scat,b_mpi,x_seq,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(scat,b_mpi,x_seq,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecGetArray(x_seq,&bptr);CHKERRQ(ierr);
} else { /* size==1 || distributed mat input */
if (lu->options.SolveInitialized && !lu->matsolve_iscalled) {
/* see comments in MatMatSolve() */
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:zSolveFinalize",zSolveFinalize(&lu->options, &lu->SOLVEstruct));
#else
PetscStackCall("SuperLU_DIST:dSolveFinalize",dSolveFinalize(&lu->options, &lu->SOLVEstruct));
#endif
lu->options.SolveInitialized = NO;
}
ierr = VecCopy(b_mpi,x);CHKERRQ(ierr);
ierr = VecGetArray(x,&bptr);CHKERRQ(ierr);
}
if (lu->options.Fact != FACTORED) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"SuperLU_DIST options.Fact mush equal FACTORED");
PetscStackCall("SuperLU_DIST:PStatInit",PStatInit(&stat)); /* Initialize the statistics variables. */
if (lu->MatInputMode == GLOBAL) {
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:pzgssvx_ABglobal",pzgssvx_ABglobal(&lu->options,&lu->A_sup,&lu->ScalePermstruct,(doublecomplex*)bptr,M,nrhs,&lu->grid,&lu->LUstruct,berr,&stat,&info));
#else
PetscStackCall("SuperLU_DIST:pdgssvx_ABglobal",pdgssvx_ABglobal(&lu->options, &lu->A_sup, &lu->ScalePermstruct,bptr,M,nrhs,&lu->grid,&lu->LUstruct,berr,&stat,&info));
#endif
} else { /* distributed mat input */
#if defined(PETSC_USE_COMPLEX)
PetscStackCall("SuperLU_DIST:pzgssvx",pzgssvx(&lu->options,&lu->A_sup,&lu->ScalePermstruct,(doublecomplex*)bptr,m,nrhs,&lu->grid,&lu->LUstruct,&lu->SOLVEstruct,berr,&stat,&info));
#else
PetscStackCall("SuperLU_DIST:pdgssvx",pdgssvx(&lu->options,&lu->A_sup,&lu->ScalePermstruct,bptr,m,nrhs,&lu->grid,&lu->LUstruct,&lu->SOLVEstruct,berr,&stat,&info));
#endif
}
if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"pdgssvx fails, info: %d\n",info);
if (lu->options.PrintStat) PStatPrint(&lu->options, &stat, &lu->grid); /* Print the statistics. */
PetscStackCall("SuperLU_DIST:PStatFree",PStatFree(&stat));
if (size > 1 && lu->MatInputMode == GLOBAL) {
/* convert seq x to mpi x */
ierr = VecRestoreArray(x_seq,&bptr);CHKERRQ(ierr);
ierr = VecScatterBegin(scat,x_seq,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterEnd(scat,x_seq,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterDestroy(&scat);CHKERRQ(ierr);
ierr = VecDestroy(&x_seq);CHKERRQ(ierr);
} else {
ierr = VecRestoreArray(x,&bptr);CHKERRQ(ierr);
lu->matsolve_iscalled = PETSC_TRUE;
lu->matmatsolve_iscalled = PETSC_FALSE;
}
PetscFunctionReturn(0);
}
int main(int argc, char **args)
{
Mat A, L;
AppCtx ctx;
PetscViewer viewer;
PetscErrorCode ierr;
ierr = PetscInitialize(&argc, &args, (char *) 0, help);CHKERRQ(ierr);
ierr = ProcessOptions(&ctx);CHKERRQ(ierr);
/* Load matrix */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD, ctx.matFilename, FILE_MODE_READ, &viewer);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD, &A);CHKERRQ(ierr);
ierr = MatLoad(A, viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
/* Make graph Laplacian from matrix */
ierr = MatLaplacian(A, 1.0e-12, &L);CHKERRQ(ierr);
/* Check Laplacian */
PetscReal norm;
Vec x, y;
ierr = MatGetVecs(L, &x, NULL);CHKERRQ(ierr);
ierr = VecDuplicate(x, &y);CHKERRQ(ierr);
ierr = VecSet(x, 1.0);CHKERRQ(ierr);
ierr = MatMult(L, x, y);CHKERRQ(ierr);
ierr = VecNorm(y, NORM_INFINITY, &norm);CHKERRQ(ierr);
if (norm > 1.0e-10) SETERRQ(PetscObjectComm((PetscObject) y), PETSC_ERR_PLIB, "Invalid graph Laplacian");
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
/* Compute Fiedler vector, and perhaps more vectors */
Mat LD;
PetscScalar *a, *realpart, *imagpart, *eigvec, *work, sdummy;
PetscBLASInt bn, bN, lwork, lierr, idummy;
PetscInt n, i;
ierr = MatConvert(L, MATDENSE, MAT_INITIAL_MATRIX, &LD);CHKERRQ(ierr);
ierr = MatGetLocalSize(LD, &n, NULL);CHKERRQ(ierr);
ierr = MatDenseGetArray(LD, &a);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n, &bn);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n, &bN);CHKERRQ(ierr);
ierr = PetscBLASIntCast(5*n,&lwork);CHKERRQ(ierr);
ierr = PetscBLASIntCast(1,&idummy);CHKERRQ(ierr);
ierr = PetscMalloc4(n,PetscScalar,&realpart,n,PetscScalar,&imagpart,n*n,PetscScalar,&eigvec,lwork,PetscScalar,&work);CHKERRQ(ierr);
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
PetscStackCall("LAPACKgeev", LAPACKgeev_("N","V",&bn,a,&bN,realpart,imagpart,&sdummy,&idummy,eigvec,&bN,work,&lwork,&lierr));
if (lierr) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in LAPACK routine %d", (int) lierr);
ierr = PetscFPTrapPop();CHKERRQ(ierr);
PetscReal *r, *c;
PetscInt *perm;
ierr = PetscMalloc3(n,PetscInt,&perm,n,PetscReal,&r,n,PetscReal,&c);CHKERRQ(ierr);
for (i = 0; i < n; ++i) perm[i] = i;
ierr = PetscSortRealWithPermutation(n,realpart,perm);CHKERRQ(ierr);
for (i = 0; i < n; ++i) {
r[i] = realpart[perm[i]];
c[i] = imagpart[perm[i]];
}
for (i = 0; i < n; ++i) {
realpart[i] = r[i];
imagpart[i] = c[i];
}
/* Output spectrum */
if (ctx.showSpectrum) {
ierr = PetscPrintf(PETSC_COMM_SELF, "Spectrum\n");CHKERRQ(ierr);
for (i = 0; i < n; ++i) {ierr = PetscPrintf(PETSC_COMM_SELF, "%d: Real %g Imag %g\n", i, realpart[i], imagpart[i]);CHKERRQ(ierr);}
}
/* Check lowest eigenvalue and eigenvector */
PetscInt evInd = perm[0];
if ((realpart[0] > 1.0e-12) || (imagpart[0] > 1.0e-12)) SETERRQ(PetscObjectComm((PetscObject) L), PETSC_ERR_PLIB, "Graph Laplacian must have lowest eigenvalue 0");
for (i = 0; i < n; ++i) {
if (fabs(eigvec[evInd*n+i] - eigvec[evInd*n+0]) > 1.0e-10) SETERRQ3(PetscObjectComm((PetscObject) L), PETSC_ERR_PLIB, "Graph Laplacian must have constant lowest eigenvector ev_%d %g != ev_0 %g", i, eigvec[evInd*n+i], eigvec[evInd*n+0]);
}
/* Output Fiedler vector */
evInd = perm[1];
if (ctx.showFiedler) {
ierr = PetscPrintf(PETSC_COMM_SELF, "Fiedler vector, Re{ev} %g\n", realpart[1]);CHKERRQ(ierr);
for (i = 0; i < n; ++i) {ierr = PetscPrintf(PETSC_COMM_SELF, "%d: %g\n", i, eigvec[evInd*n+i]);CHKERRQ(ierr);}
}
/* Construct Fiedler partition */
IS fIS, fIS2;
PetscInt *fperm, *fperm2, pos, neg, posSize = 0;
ierr = PetscMalloc(n * sizeof(PetscInt), &fperm);CHKERRQ(ierr);
for (i = 0; i < n; ++i) {
if (eigvec[evInd*n+i] > 0.0) ++posSize;
}
ierr = PetscMalloc(n * sizeof(PetscInt), &fperm2);CHKERRQ(ierr);
for (i = 0; i < n; ++i) fperm[i] = i;
ierr = PetscSortRealWithPermutation(n, &eigvec[evInd*n], fperm);CHKERRQ(ierr);
for (i = 0; i < n; ++i) fperm2[n-1-i] = fperm[i];
for (i = 0, pos = 0, neg = posSize; i < n; ++i) {
if (eigvec[evInd*n+i] > 0.0) fperm[pos++] = i;
else fperm[neg++] = i;
}
ierr = ISCreateGeneral(PetscObjectComm((PetscObject) L), n, fperm, PETSC_OWN_POINTER, &fIS);CHKERRQ(ierr);
ierr = ISSetPermutation(fIS);CHKERRQ(ierr);
ierr = ISCreateGeneral(PetscObjectComm((PetscObject) L), n, fperm2, PETSC_OWN_POINTER, &fIS2);CHKERRQ(ierr);
ierr = ISSetPermutation(fIS2);CHKERRQ(ierr);
ierr = PetscFree3(perm,r,c);CHKERRQ(ierr);
ierr = PetscFree4(realpart,imagpart,eigvec,work);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(LD, &a);CHKERRQ(ierr);
ierr = MatDestroy(&LD);CHKERRQ(ierr);
ierr = MatDestroy(&L);CHKERRQ(ierr);
/* Permute matrix */
Mat AR, AR2;
ierr = MatPermute(A, fIS, fIS, &AR);CHKERRQ(ierr);
ierr = MatView(A, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(AR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = ISDestroy(&fIS);CHKERRQ(ierr);
ierr = MatPermute(A, fIS2, fIS2, &AR2);CHKERRQ(ierr);
ierr = MatView(AR2, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = ISDestroy(&fIS2);CHKERRQ(ierr);
ierr = MatDestroy(&AR);CHKERRQ(ierr);
AR = AR2;
/* Extract blocks and reorder */
Mat AP, AN, APR, ANR;
IS ispos, isneg, rpermpos, cpermpos, rpermneg, cpermneg;
PetscInt bw, bwr;
ierr = ISCreateStride(PETSC_COMM_SELF, posSize, 0, 1, &ispos);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF, n - posSize, posSize, 1, &isneg);CHKERRQ(ierr);
ierr = MatGetSubMatrix(AR, ispos, ispos, MAT_INITIAL_MATRIX, &AP);CHKERRQ(ierr);
ierr = MatGetSubMatrix(AR, isneg, isneg, MAT_INITIAL_MATRIX, &AN);CHKERRQ(ierr);
ierr = ISDestroy(&ispos);CHKERRQ(ierr);
ierr = ISDestroy(&isneg);CHKERRQ(ierr);
ierr = MatGetOrdering(AP, ctx.matOrdtype, &rpermpos, &cpermpos);CHKERRQ(ierr);
ierr = MatGetOrdering(AN, ctx.matOrdtype, &rpermneg, &cpermneg);CHKERRQ(ierr);
ierr = MatPermute(AP, rpermpos, cpermpos, &APR);CHKERRQ(ierr);
ierr = MatComputeBandwidth(AP, 0.0, &bw);CHKERRQ(ierr);
ierr = MatComputeBandwidth(APR, 0.0, &bwr);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Reduced positive bandwidth from %d to %d\n", bw, bwr);CHKERRQ(ierr);
ierr = MatPermute(AN, rpermneg, cpermneg, &ANR);CHKERRQ(ierr);
ierr = MatComputeBandwidth(AN, 0.0, &bw);CHKERRQ(ierr);
ierr = MatComputeBandwidth(ANR, 0.0, &bwr);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Reduced negative bandwidth from %d to %d\n", bw, bwr);CHKERRQ(ierr);
ierr = MatView(AP, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(APR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(AN, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(ANR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
/* Reorder original matrix */
Mat ARR;
IS rperm, cperm;
PetscInt *idx;
const PetscInt *cidx;
ierr = PetscMalloc(n * sizeof(PetscInt), &idx);CHKERRQ(ierr);
ierr = ISGetIndices(rpermpos, &cidx);CHKERRQ(ierr);
for (i = 0; i < posSize; ++i) idx[i] = cidx[i];
ierr = ISRestoreIndices(rpermpos, &cidx);CHKERRQ(ierr);
ierr = ISGetIndices(rpermneg, &cidx);CHKERRQ(ierr);
for (i = posSize; i < n; ++i) idx[i] = cidx[i-posSize] + posSize;
ierr = ISRestoreIndices(rpermneg, &cidx);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF, n, idx, PETSC_OWN_POINTER, &rperm);CHKERRQ(ierr);
ierr = ISSetPermutation(rperm);CHKERRQ(ierr);
ierr = PetscMalloc(n * sizeof(PetscInt), &idx);CHKERRQ(ierr);
ierr = ISGetIndices(cpermpos, &cidx);CHKERRQ(ierr);
for (i = 0; i < posSize; ++i) idx[i] = cidx[i];
ierr = ISRestoreIndices(cpermpos, &cidx);CHKERRQ(ierr);
ierr = ISGetIndices(cpermneg, &cidx);CHKERRQ(ierr);
for (i = posSize; i < n; ++i) idx[i] = cidx[i-posSize] + posSize;
ierr = ISRestoreIndices(cpermneg, &cidx);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF, n, idx, PETSC_OWN_POINTER, &cperm);CHKERRQ(ierr);
ierr = ISSetPermutation(cperm);CHKERRQ(ierr);
ierr = MatPermute(AR, rperm, cperm, &ARR);CHKERRQ(ierr);
ierr = MatView(ARR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = ISDestroy(&rperm);CHKERRQ(ierr);
ierr = ISDestroy(&cperm);CHKERRQ(ierr);
ierr = ISDestroy(&rpermpos);CHKERRQ(ierr);
ierr = ISDestroy(&cpermpos);CHKERRQ(ierr);
ierr = ISDestroy(&rpermneg);CHKERRQ(ierr);
ierr = ISDestroy(&cpermneg);CHKERRQ(ierr);
ierr = MatDestroy(&AP);CHKERRQ(ierr);
ierr = MatDestroy(&AN);CHKERRQ(ierr);
ierr = MatDestroy(&APR);CHKERRQ(ierr);
ierr = MatDestroy(&ANR);CHKERRQ(ierr);
/* Compare bands */
Mat B, BR;
ierr = MatCreateSubMatrixBanded(A, 50, 0.95, &B);CHKERRQ(ierr);
ierr = MatCreateSubMatrixBanded(ARR, 50, 0.95, &BR);CHKERRQ(ierr);
ierr = MatView(B, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(BR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = MatDestroy(&BR);CHKERRQ(ierr);
/* Cleanup */
ierr = MatDestroy(&ARR);CHKERRQ(ierr);
ierr = MatDestroy(&AR);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
