static PetscErrorCode PCSetUp_LU(PC pc)
{
PetscErrorCode ierr;
PC_LU *dir = (PC_LU*)pc->data;
PetscFunctionBegin;
if (dir->reusefill && pc->setupcalled) ((PC_Factor*)dir)->info.fill = dir->actualfill;
if (dir->inplace) {
if (dir->row && dir->col && dir->row != dir->col) {ierr = ISDestroy(dir->row);CHKERRQ(ierr);}
if (dir->col) {ierr = ISDestroy(dir->col);CHKERRQ(ierr);}
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
if (dir->row) {
ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);
ierr = PetscLogObjectParent(pc,dir->col);CHKERRQ(ierr);
}
ierr = MatLUFactor(pc->pmat,dir->row,dir->col,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
((PC_Factor*)dir)->fact = pc->pmat;
} else {
MatInfo info;
if (!pc->setupcalled) {
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
if (dir->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,dir->nonzerosalongdiagonaltol,dir->row,dir->col);CHKERRQ(ierr);
}
if (dir->row) {
ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);
ierr = PetscLogObjectParent(pc,dir->col);CHKERRQ(ierr);
}
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_LU,&((PC_Factor*)dir)->fact);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,dir->col,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)dir)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
dir->actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent(pc,((PC_Factor*)dir)->fact);CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
if (!dir->reuseordering) {
if (dir->row && dir->col && dir->row != dir->col) {ierr = ISDestroy(dir->row);CHKERRQ(ierr);}
if (dir->col) {ierr = ISDestroy(dir->col);CHKERRQ(ierr);}
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
if (dir->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,dir->nonzerosalongdiagonaltol,dir->row,dir->col);CHKERRQ(ierr);
}
if (dir->row) {
ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);
ierr = PetscLogObjectParent(pc,dir->col);CHKERRQ(ierr);
}
}
ierr = MatDestroy(((PC_Factor*)dir)->fact);CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_LU,&((PC_Factor*)dir)->fact);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,dir->col,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)dir)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
dir->actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent(pc,((PC_Factor*)dir)->fact);CHKERRQ(ierr);
}
ierr = MatLUFactorNumeric(((PC_Factor*)dir)->fact,pc->pmat,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static PetscErrorCode PCSetup_ICC(PC pc)
{
PC_ICC *icc = (PC_ICC*)pc->data;
IS perm,cperm;
PetscErrorCode ierr;
MatInfo info;
PetscFunctionBegin;
ierr = MatGetOrdering(pc->pmat, ((PC_Factor*)icc)->ordering,&perm,&cperm);CHKERRQ(ierr);
if (!pc->setupcalled) {
if (!((PC_Factor*)icc)->fact) {
ierr = MatGetFactor(pc->pmat,((PC_Factor*)icc)->solvertype,MAT_FACTOR_ICC,&((PC_Factor*)icc)->fact);CHKERRQ(ierr);
}
ierr = MatICCFactorSymbolic(((PC_Factor*)icc)->fact,pc->pmat,perm,&((PC_Factor*)icc)->info);CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
ierr = MatDestroy(&((PC_Factor*)icc)->fact);CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)icc)->solvertype,MAT_FACTOR_ICC,&((PC_Factor*)icc)->fact);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(((PC_Factor*)icc)->fact,pc->pmat,perm,&((PC_Factor*)icc)->info);CHKERRQ(ierr);
}
ierr = MatGetInfo(((PC_Factor*)icc)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
icc->actualfill = info.fill_ratio_needed;
ierr = ISDestroy(&cperm);CHKERRQ(ierr);
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatCholeskyFactorNumeric(((PC_Factor*)icc)->fact,pc->pmat,&((PC_Factor*)icc)->info);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Mat C;
PetscInt i,j,m = 5,n = 5,Ii,J;
PetscErrorCode ierr;
PetscScalar v;
IS perm,iperm;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MatCreate(PETSC_COMM_SELF,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
/* create the matrix for the five point stencil, YET AGAIN*/
for (i=0; i<m; i++) {
for (j=0; j<n; j++) {
v = -1.0; Ii = j + n*i;
if (i>0) {J = Ii - n; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (i<m-1) {J = Ii + n; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (j>0) {J = Ii - 1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (j<n-1) {J = Ii + 1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
v = 4.0; ierr = MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatGetOrdering(C,MATORDERINGND,&perm,&iperm);CHKERRQ(ierr);
ierr = ISView(perm,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = ISView(iperm,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = ISDestroy(&iperm);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat C,A;
PetscInt i,j,m = 5,n = 5,Ii,J;
PetscErrorCode ierr;
PetscScalar v,five = 5.0,one = 1.0;
IS isrow,row,col;
Vec x,u,b;
PetscReal norm;
MatFactorInfo info;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,m*n,m*n,5,NULL,&C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
/* create the matrix for the five point stencil, YET AGAIN*/
for (i=0; i<m; i++) {
for (j=0; j<n; j++) {
v = -1.0; Ii = j + n*i;
if (i>0) {J = Ii - n; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (i<m-1) {J = Ii + n; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (j>0) {J = Ii - 1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (j<n-1) {J = Ii + 1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
v = 4.0; ierr = MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,(m*n)/2,0,2,&isrow);CHKERRQ(ierr);
ierr = MatZeroRowsIS(C,isrow,five,0,0);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,m*n,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&x);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecSet(u,one);CHKERRQ(ierr);
ierr = MatMultTranspose(C,u,b);CHKERRQ(ierr);
/* Set default ordering to be Quotient Minimum Degree; also read
orderings from the options database */
ierr = MatGetOrdering(C,MATORDERINGQMD,&row,&col);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
ierr = MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_LU,&A);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(A,C,row,col,&info);CHKERRQ(ierr);
ierr = MatLUFactorNumeric(A,C,&info);CHKERRQ(ierr);
ierr = MatSolveTranspose(A,b,x);CHKERRQ(ierr);
ierr = ISView(row,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = VecAXPY(x,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"Norm of error %g\n",(double)norm);CHKERRQ(ierr);
ierr = ISDestroy(&row);CHKERRQ(ierr);
ierr = ISDestroy(&col);CHKERRQ(ierr);
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat A,LU;
Vec x,y;
PetscInt nnz[4]={2,1,1,1},col[4],i;
PetscErrorCode ierr;
PetscScalar values[4];
IS rowperm,colperm;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MatCreateSeqAIJ(PETSC_COMM_WORLD,4,4,2,nnz,&A);CHKERRQ(ierr);
/* build test matrix */
values[0]=1.0;values[1]=-1.0;
col[0] =0;col[1]=2; i=0;
ierr = MatSetValues(A,1,&i,2,col,values,INSERT_VALUES);CHKERRQ(ierr);
values[0]=1.0;
col[0] =1;i=1;
ierr = MatSetValues(A,1,&i,1,col,values,INSERT_VALUES);CHKERRQ(ierr);
values[0]=-1.0;
col[0] =3;i=2;
ierr = MatSetValues(A,1,&i,1,col,values,INSERT_VALUES);CHKERRQ(ierr);
values[0]=1.0;
col[0] =2;i=3;
ierr = MatSetValues(A,1,&i,1,col,values,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&rowperm,&colperm);CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(A,1.e-12,rowperm,colperm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"column and row perms\n");CHKERRQ(ierr);
ierr = ISView(rowperm,0);CHKERRQ(ierr);
ierr = ISView(colperm,0);CHKERRQ(ierr);
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&LU);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(LU,A,rowperm,colperm,NULL);CHKERRQ(ierr);
ierr = MatLUFactorNumeric(LU,A,NULL);CHKERRQ(ierr);
ierr = MatView(LU,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,PETSC_DECIDE,4);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
values[0]=0;values[1]=1.0;values[2]=-1.0;values[3]=1.0;
for (i=0; i<4; i++) col[i]=i;
ierr = VecSetValues(x,4,col,values,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(x);CHKERRQ(ierr);
ierr = VecAssemblyEnd(x);CHKERRQ(ierr);
ierr = VecView(x,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = MatSolve(LU,x,y);CHKERRQ(ierr);
ierr = VecView(y,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = ISDestroy(&rowperm);CHKERRQ(ierr);
ierr = ISDestroy(&colperm);CHKERRQ(ierr);
ierr = MatDestroy(&LU);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
Example: mpiexec -n <np> ./ex168 -f <matrix binary file> \n\n";
#include <petscmat.h>
int main(int argc,char **args)
{
Mat A,F;
Vec u,x,b;
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt m,n,nfact;
PetscReal norm,tol=1.e-12,Anorm;
IS perm,iperm;
MatFactorInfo info;
PetscBool flg,testMatSolve=PETSC_TRUE;
PetscViewer fd; /* viewer */
char file[PETSC_MAX_PATH_LEN]; /* input file name */
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
/* Determine file from which we read the matrix A */
ierr = PetscOptionsGetString(NULL,NULL,"-f",file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_WORLD,1,"Must indicate binary file with the -f option");
/* Load matrix A */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatLoad(A,fd);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&b);CHKERRQ(ierr);
ierr = VecLoad(b,fd);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
if (m != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%d, %d)", m, n);
ierr = MatNorm(A,NORM_INFINITY,&Anorm);CHKERRQ(ierr);
/* Create vectors */
ierr = VecDuplicate(b,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */
/* Test Cholesky Factorization */
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iperm);CHKERRQ(ierr);
if (!rank) printf(" Clique Cholesky:\n");
ierr = MatGetFactor(A,MATSOLVERCLIQUE,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
info.fill = 5.0;
ierr = MatCholeskyFactorSymbolic(F,A,perm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 1; nfact++) {
if (!rank) printf(" %d-the Cholesky numfactorization \n",nfact);
ierr = MatCholeskyFactorNumeric(F,A,&info);CHKERRQ(ierr);
/* Test MatSolve() */
if (testMatSolve && nfact == 2) {
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the residual */
ierr = MatMult(A,x,u);CHKERRQ(ierr);
ierr = VecAXPY(u,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(u,NORM_INFINITY,&norm);CHKERRQ(ierr);
/* if (norm > tol) { */
if (!rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatSolve: rel residual %g/%g = %g, LU numfact %d\n",norm,Anorm,norm/Anorm,nfact);CHKERRQ(ierr);
}
/*} */
}
}
/* Free data structures */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = ISDestroy(&iperm);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Mat C;
PetscInt i,j,m = 3,n = 3,Ii,J;
PetscErrorCode ierr;
PetscBool flg;
PetscScalar v;
IS perm,iperm;
Vec x,u,b,y;
PetscReal norm,tol=PETSC_SMALL;
MatFactorInfo info;
PetscMPIInt size;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL,"-symmetric",&flg);CHKERRQ(ierr);
if (flg) { /* Treat matrix as symmetric only if we set this flag */
ierr = MatSetOption(C,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetOption(C,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);CHKERRQ(ierr);
}
/* Create the matrix for the five point stencil, YET AGAIN */
for (i=0; i<m; i++) {
for (j=0; j<n; j++) {
v = -1.0; Ii = j + n*i;
if (i>0) {J = Ii - n; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (i<m-1) {J = Ii + n; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (j>0) {J = Ii - 1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (j<n-1) {J = Ii + 1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
v = 4.0; ierr = MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatGetOrdering(C,MATORDERINGRCM,&perm,&iperm);CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = ISView(perm,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,m*n,&u);CHKERRQ(ierr);
ierr = VecSet(u,1.0);CHKERRQ(ierr);
ierr = VecDuplicate(u,&x);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(u,&y);CHKERRQ(ierr);
ierr = MatMult(C,u,b);CHKERRQ(ierr);
ierr = VecCopy(b,y);CHKERRQ(ierr);
ierr = VecScale(y,2.0);CHKERRQ(ierr);
ierr = MatNorm(C,NORM_FROBENIUS,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"Frobenius norm of matrix %g\n",(double)norm);CHKERRQ(ierr);
ierr = MatNorm(C,NORM_1,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"One norm of matrix %g\n",(double)norm);CHKERRQ(ierr);
ierr = MatNorm(C,NORM_INFINITY,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"Infinity norm of matrix %g\n",(double)norm);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
info.fill = 2.0;
info.dtcol = 0.0;
info.zeropivot = 1.e-14;
info.pivotinblocks = 1.0;
ierr = MatLUFactor(C,perm,iperm,&info);CHKERRQ(ierr);
/* Test MatSolve */
ierr = MatSolve(C,b,x);CHKERRQ(ierr);
ierr = VecView(b,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = VecView(x,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = VecAXPY(x,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatSolve: Norm of error %g\n",(double)norm);CHKERRQ(ierr);
}
/* Test MatSolveAdd */
ierr = MatSolveAdd(C,b,y,x);CHKERRQ(ierr);
ierr = VecAXPY(x,-1.0,y);CHKERRQ(ierr);
ierr = VecAXPY(x,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatSolveAdd(): Norm of error %g\n",(double)norm);CHKERRQ(ierr);
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = ISDestroy(&iperm);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Vec x,y,b;
Mat A; /* linear system matrix */
Mat sA,sC; /* symmetric part of the matrices */
PetscInt n,mbs=16,bs=1,nz=3,prob=1,i,j,col[3],block, row,Ii,J,n1,lvl;
PetscErrorCode ierr;
PetscMPIInt size;
PetscReal norm2,tol=1.e-10,err[10];
PetscScalar neg_one = -1.0,four=4.0,value[3];
IS perm,cperm;
PetscRandom rdm;
PetscBool reorder = PETSC_FALSE,displ = PETSC_FALSE;
MatFactorInfo factinfo;
PetscBool equal;
PetscBool TestAIJ = PETSC_FALSE,TestBAIJ = PETSC_TRUE;
PetscInt TestShift=0;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
ierr = PetscOptionsGetInt(NULL,NULL,"-bs",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-reorder",&reorder,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-testaij",&TestAIJ,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-testShift",&TestShift,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-displ",&displ,NULL);CHKERRQ(ierr);
n = mbs*bs;
if (TestAIJ) { /* A is in aij format */
ierr = MatCreateSeqAIJ(PETSC_COMM_WORLD,n,n,nz,NULL,&A);CHKERRQ(ierr);
TestBAIJ = PETSC_FALSE;
} else { /* A is in baij format */
ierr =MatCreateSeqBAIJ(PETSC_COMM_WORLD,bs,n,n,nz,NULL,&A);CHKERRQ(ierr);
TestAIJ = PETSC_FALSE;
}
/* Assemble matrix */
if (bs == 1) {
ierr = PetscOptionsGetInt(NULL,NULL,"-test_problem",&prob,NULL);CHKERRQ(ierr);
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
value[0]= 0.1; value[1]=-1; value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0; col[0] = 0; col[1] = 1; col[2]=n-1;
value[0] = 2.0; value[1] = -1.0; value[2]=0.1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (PetscInt) (PetscSqrtReal((PetscReal)n) + 0.001);
if (n1*n1 - n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
value[0]=-1.0; value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
value[0]=4.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
col[0]=i; row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
if (TestShift) {
/* set diagonals in the 0-th block as 0 for testing shift numerical factor */
for (i=0; i<bs; i++) {
row = i; col[0] = i; value[0] = 0.0;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatConvert */
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,20,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"A != sA");
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(sA,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ format\n");CHKERRQ(ierr);
}
/* Vectors */
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
/* Test MatReordering() - not work on sbaij matrix */
if (reorder) {
ierr = MatGetOrdering(A,MATORDERINGRCM,&perm,&cperm);CHKERRQ(ierr);
} else {
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&cperm);CHKERRQ(ierr);
}
ierr = ISDestroy(&cperm);CHKERRQ(ierr);
/* initialize factinfo */
ierr = MatFactorInfoInitialize(&factinfo);CHKERRQ(ierr);
if (TestShift == 1) {
factinfo.shifttype = (PetscReal)MAT_SHIFT_NONZERO;
factinfo.shiftamount = 0.1;
} else if (TestShift == 2) {
factinfo.shifttype = (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE;
}
/* Test MatCholeskyFactor(), MatICCFactor() */
/*------------------------------------------*/
/* Test aij matrix A */
if (TestAIJ) {
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"AIJ: \n");CHKERRQ(ierr);
}
i = 0;
for (lvl=-1; lvl<10; lvl++) {
if (lvl==-1) { /* Cholesky factor */
factinfo.fill = 5.0;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
} else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lvl;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,A,&factinfo);CHKERRQ(ierr);
ierr = MatMult(A,x,b);CHKERRQ(ierr);
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD," lvl: %D, error: %g\n", lvl,(double)norm2);CHKERRQ(ierr);
}
err[i++] = norm2;
}
}
/* Test baij matrix A */
if (TestBAIJ) {
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"BAIJ: \n");CHKERRQ(ierr);
}
i = 0;
for (lvl=-1; lvl<10; lvl++) {
if (lvl==-1) { /* Cholesky factor */
factinfo.fill = 5.0;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
} else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lvl;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,A,&factinfo);CHKERRQ(ierr);
ierr = MatMult(A,x,b);CHKERRQ(ierr);
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD," lvl: %D, error: %g\n", lvl,(double)norm2);CHKERRQ(ierr);
}
err[i++] = norm2;
}
}
/* Test sbaij matrix sA */
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"SBAIJ: \n");CHKERRQ(ierr);
}
i = 0;
for (lvl=-1; lvl<10; lvl++) {
if (lvl==-1) { /* Cholesky factor */
factinfo.fill = 5.0;
ierr = MatGetFactor(sA,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,sA,perm,&factinfo);CHKERRQ(ierr);
} else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lvl;
ierr = MatGetFactor(sA,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,sA,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,sA,&factinfo);CHKERRQ(ierr);
if (lvl==0 && bs==1) { /* Test inplace ICC(0) for sbaij sA - does not work for new datastructure */
/*
Mat B;
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&B);CHKERRQ(ierr);
ierr = MatICCFactor(B,perm,&factinfo);CHKERRQ(ierr);
ierr = MatEqual(sC,B,&equal);CHKERRQ(ierr);
if (!equal) {
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"in-place Cholesky factor != out-place Cholesky factor");
}
ierr = MatDestroy(&B);CHKERRQ(ierr);
*/
}
ierr = MatMult(sA,x,b);CHKERRQ(ierr);
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
/* Test MatSolves() */
if (bs == 1) {
Vecs xx,bb;
ierr = VecsCreateSeq(PETSC_COMM_SELF,n,4,&xx);CHKERRQ(ierr);
ierr = VecsDuplicate(xx,&bb);CHKERRQ(ierr);
ierr = MatSolves(sC,bb,xx);CHKERRQ(ierr);
ierr = VecsDestroy(xx);CHKERRQ(ierr);
ierr = VecsDestroy(bb);CHKERRQ(ierr);
}
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD," lvl: %D, error: %g\n", lvl,(double)norm2);CHKERRQ(ierr);
}
err[i] -= norm2;
if (err[i] > tol) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_USER," level: %d, err: %g\n", lvl,(double)err[i]);
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
Example: mpiexec -n <np> ./ex130 -f <matrix binary file> -mat_solver_package 1 -mat_superlu_equil \n\n";
#include <petscmat.h>
int main(int argc,char **args)
{
Mat A,F;
Vec u,x,b;
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt m,n,nfact,ipack=0;
PetscReal norm,tol=1.e-12,Anorm;
IS perm,iperm;
MatFactorInfo info;
PetscBool flg,testMatSolve=PETSC_TRUE;
PetscViewer fd; /* viewer */
char file[PETSC_MAX_PATH_LEN]; /* input file name */
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
/* Determine file from which we read the matrix A */
ierr = PetscOptionsGetString(NULL,NULL,"-f",file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_WORLD,1,"Must indicate binary file with the -f option");
/* Load matrix A */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatLoad(A,fd);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&b);CHKERRQ(ierr);
ierr = VecLoad(b,fd);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
if (m != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%d, %d)", m, n);
ierr = MatNorm(A,NORM_INFINITY,&Anorm);CHKERRQ(ierr);
/* Create vectors */
ierr = VecDuplicate(b,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */
/* Test LU Factorization */
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iperm);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-mat_solver_package",&ipack,NULL);CHKERRQ(ierr);
switch (ipack) {
case 1:
#if defined(PETSC_HAVE_SUPERLU)
if (!rank) printf(" SUPERLU LU:\n");
ierr = MatGetFactor(A,MATSOLVERSUPERLU,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
break;
#endif
case 2:
#if defined(PETSC_HAVE_MUMPS)
if (!rank) printf(" MUMPS LU:\n");
ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
{
/* test mumps options */
PetscInt icntl_7 = 5;
ierr = MatMumpsSetIcntl(F,7,icntl_7);CHKERRQ(ierr);
}
break;
#endif
default:
if (!rank) printf(" PETSC LU:\n");
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
}
info.fill = 5.0;
ierr = MatLUFactorSymbolic(F,A,perm,iperm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 1; nfact++) {
if (!rank) printf(" %d-the LU numfactorization \n",nfact);
ierr = MatLUFactorNumeric(F,A,&info);CHKERRQ(ierr);
/* Test MatSolve() */
if (testMatSolve) {
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the residual */
ierr = MatMult(A,x,u);CHKERRQ(ierr);
ierr = VecAXPY(u,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(u,NORM_INFINITY,&norm);CHKERRQ(ierr);
if (norm > tol) {
if (!rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatSolve: rel residual %g/%g = %g, LU numfact %d\n",norm,Anorm,norm/Anorm,nfact);CHKERRQ(ierr);
}
}
}
}
/* Free data structures */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = ISDestroy(&iperm);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
PetscErrorCode MatSOR_BlockMat_Symmetric(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
{
Mat_BlockMat *a = (Mat_BlockMat*)A->data;
PetscScalar *x;
const Mat *v;
const PetscScalar *b;
PetscErrorCode ierr;
PetscInt n = A->cmap->n,i,mbs = n/A->rmap->bs,j,bs = A->rmap->bs;
const PetscInt *idx;
IS row,col;
MatFactorInfo info;
Vec left = a->left,right = a->right, middle = a->middle;
Mat *diag;
PetscFunctionBegin;
its = its*lits;
if (its <= 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D and local its %D both positive",its,lits);
if (flag & SOR_EISENSTAT) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for Eisenstat");
if (omega != 1.0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for omega not equal to 1.0");
if (fshift) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for fshift");
if ((flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) && !(flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP)) {
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot do backward sweep without forward sweep");
}
if (!a->diags) {
ierr = PetscMalloc1(mbs,&a->diags);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
for (i=0; i<mbs; i++) {
ierr = MatGetOrdering(a->a[a->diag[i]], MATORDERINGND,&row,&col);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(a->diags[i],a->a[a->diag[i]],row,&info);CHKERRQ(ierr);
ierr = MatCholeskyFactorNumeric(a->diags[i],a->a[a->diag[i]],&info);CHKERRQ(ierr);
ierr = ISDestroy(&row);CHKERRQ(ierr);
ierr = ISDestroy(&col);CHKERRQ(ierr);
}
ierr = VecDuplicate(bb,&a->workb);CHKERRQ(ierr);
}
diag = a->diags;
ierr = VecSet(xx,0.0);CHKERRQ(ierr);
ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
/* copy right hand side because it must be modified during iteration */
ierr = VecCopy(bb,a->workb);CHKERRQ(ierr);
ierr = VecGetArrayRead(a->workb,&b);CHKERRQ(ierr);
/* need to add code for when initial guess is zero, see MatSOR_SeqAIJ */
while (its--) {
if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
for (i=0; i<mbs; i++) {
n = a->i[i+1] - a->i[i] - 1;
idx = a->j + a->i[i] + 1;
v = a->a + a->i[i] + 1;
ierr = VecSet(left,0.0);CHKERRQ(ierr);
for (j=0; j<n; j++) {
ierr = VecPlaceArray(right,x + idx[j]*bs);CHKERRQ(ierr);
ierr = MatMultAdd(v[j],right,left,left);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
}
ierr = VecPlaceArray(right,b + i*bs);CHKERRQ(ierr);
ierr = VecAYPX(left,-1.0,right);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
ierr = VecPlaceArray(right,x + i*bs);CHKERRQ(ierr);
ierr = MatSolve(diag[i],left,right);CHKERRQ(ierr);
/* now adjust right hand side, see MatSOR_SeqSBAIJ */
for (j=0; j<n; j++) {
ierr = MatMultTranspose(v[j],right,left);CHKERRQ(ierr);
ierr = VecPlaceArray(middle,b + idx[j]*bs);CHKERRQ(ierr);
ierr = VecAXPY(middle,-1.0,left);CHKERRQ(ierr);
ierr = VecResetArray(middle);CHKERRQ(ierr);
}
ierr = VecResetArray(right);CHKERRQ(ierr);
}
}
if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
for (i=mbs-1; i>=0; i--) {
n = a->i[i+1] - a->i[i] - 1;
idx = a->j + a->i[i] + 1;
v = a->a + a->i[i] + 1;
ierr = VecSet(left,0.0);CHKERRQ(ierr);
for (j=0; j<n; j++) {
ierr = VecPlaceArray(right,x + idx[j]*bs);CHKERRQ(ierr);
ierr = MatMultAdd(v[j],right,left,left);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
}
ierr = VecPlaceArray(right,b + i*bs);CHKERRQ(ierr);
ierr = VecAYPX(left,-1.0,right);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
ierr = VecPlaceArray(right,x + i*bs);CHKERRQ(ierr);
ierr = MatSolve(diag[i],left,right);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
}
}
}
ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(a->workb,&b);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode PCSetUp_ILU(PC pc)
{
PetscErrorCode ierr;
PC_ILU *ilu = (PC_ILU*)pc->data;
MatInfo info;
PetscBool flg;
PetscFunctionBegin;
/* ugly hack to change default, since it is not support by some matrix types */
if (((PC_Factor*)ilu)->info.shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATSEQAIJ,&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATMPIAIJ,&flg);CHKERRQ(ierr);
if (!flg) {
((PC_Factor*)ilu)->info.shifttype = (PetscReal)MAT_SHIFT_INBLOCKS;
PetscInfo(pc,"Changing shift type from NONZERO to INBLOCKS because block matrices do not support NONZERO");CHKERRQ(ierr);
}
}
}
if (ilu->inplace) {
CHKMEMQ;
if (!pc->setupcalled) {
/* In-place factorization only makes sense with the natural ordering,
so we only need to get the ordering once, even if nonzero structure changes */
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent(pc,ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent(pc,ilu->col);CHKERRQ(ierr);}
}
/* In place ILU only makes sense with fill factor of 1.0 because
cannot have levels of fill */
((PC_Factor*)ilu)->info.fill = 1.0;
((PC_Factor*)ilu)->info.diagonal_fill = 0.0;
ierr = MatILUFactor(pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);CHKMEMQ;
((PC_Factor*)ilu)->fact = pc->pmat;
} else {
if (!pc->setupcalled) {
/* first time in so compute reordering and symbolic factorization */
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent(pc,ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent(pc,ilu->col);CHKERRQ(ierr);}
/* Remove zeros along diagonal? */
if (ilu->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);CHKERRQ(ierr);
}
if (!((PC_Factor*)ilu)->fact){
ierr = MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
}
ierr = MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
ilu->actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent(pc,((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
if (!ilu->reuseordering) {
/* compute a new ordering for the ILU */
ierr = ISDestroy(&ilu->row);CHKERRQ(ierr);
ierr = ISDestroy(&ilu->col);CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent(pc,ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent(pc,ilu->col);CHKERRQ(ierr);}
/* Remove zeros along diagonal? */
if (ilu->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);CHKERRQ(ierr);
}
}
ierr = MatDestroy(&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
ierr = MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
ilu->actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent(pc,((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
}
CHKMEMQ;
ierr = MatLUFactorNumeric(((PC_Factor*)ilu)->fact,pc->pmat,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
CHKMEMQ;
}
PetscFunctionReturn(0);
}
#include <petsc/private/fortranimpl.h>
#include <petscmat.h>
#if defined(PETSC_HAVE_FORTRAN_CAPS)
#define matgetordering_ MATGETORDERING
#elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
#define matgetordering_ matgetordering
#endif
PETSC_EXTERN void PETSC_STDCALL matgetordering_(Mat *mat,char* type PETSC_MIXED_LEN(len),IS *rperm,IS *cperm,PetscErrorCode *ierr PETSC_END_LEN(len))
{
char *t;
FIXCHAR(type,len,t);
*ierr = MatGetOrdering(*mat,t,rperm,cperm);
FREECHAR(type,t);
}
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;
}
int main(int argc,char **args)
{
Mat A,RHS,C,F,X;
Vec u,x,b;
PetscErrorCode ierr;
PetscMPIInt rank,nproc;
PetscInt i,m,n,nfact,nsolve,nrhs,ipack=0;
PetscScalar *array,rval;
PetscReal norm,tol=1.e-12;
IS perm,iperm;
MatFactorInfo info;
PetscRandom rand;
PetscBool flg,testMatSolve=PETSC_TRUE,testMatMatSolve=PETSC_TRUE;
PetscViewer fd; /* viewer */
char file[PETSC_MAX_PATH_LEN]; /* input file name */
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &nproc);CHKERRQ(ierr);
/* Determine file from which we read the matrix A */
ierr = PetscOptionsGetString(NULL,"-f",file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_WORLD,1,"Must indicate binary file with the -f option");
/* Load matrix A */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatLoad(A,fd);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
if (m != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%d, %d)", m, n);
/* Create dense matrix C and X; C holds true solution with identical colums */
nrhs = 2;
ierr = PetscOptionsGetInt(NULL,"-nrhs",&nrhs,NULL);CHKERRQ(ierr);
if (!rank) printf("ex125: nrhs %d\n",nrhs);
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,m,PETSC_DECIDE,PETSC_DECIDE,nrhs);CHKERRQ(ierr);
ierr = MatSetType(C,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = MatSetRandom(C,rand);CHKERRQ(ierr);
ierr = MatDuplicate(C,MAT_DO_NOT_COPY_VALUES,&X);CHKERRQ(ierr);
/* Create vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */
/* Test LU Factorization */
ierr = MatGetOrdering(A,MATORDERINGND,&perm,&iperm);CHKERRQ(ierr);
/*ierr = ISView(perm,PETSC_VIEWER_STDOUT_WORLD);*/
/*ierr = ISView(perm,PETSC_VIEWER_STDOUT_SELF);*/
ierr = PetscOptionsGetInt(NULL,"-mat_solver_package",&ipack,NULL);CHKERRQ(ierr);
switch (ipack) {
case 0:
#if defined(PETSC_HAVE_SUPERLU)
if (!rank) printf(" SUPERLU LU:\n");
ierr = MatGetFactor(A,MATSOLVERSUPERLU,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
break;
#endif
case 1:
#if defined(PETSC_HAVE_SUPERLU_DIST)
if (!rank) printf(" SUPERLU_DIST LU:\n");
ierr = MatGetFactor(A,MATSOLVERSUPERLU_DIST,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
break;
#endif
case 2:
#if defined(PETSC_HAVE_MUMPS)
if (!rank) printf(" MUMPS LU:\n");
ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
{
/* test mumps options */
PetscInt icntl_7 = 5;
ierr = MatMumpsSetIcntl(F,7,icntl_7);CHKERRQ(ierr);
}
break;
#endif
default:
if (!rank) printf(" PETSC LU:\n");
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
}
info.fill = 5.0;
ierr = MatLUFactorSymbolic(F,A,perm,iperm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 2; nfact++) {
if (!rank) printf(" %d-the LU numfactorization \n",nfact);
ierr = MatLUFactorNumeric(F,A,&info);CHKERRQ(ierr);
/* Test MatMatSolve() */
/*
if ((ipack == 0 || ipack == 2) && testMatMatSolve) {
printf(" MatMatSolve() is not implemented for this package. Skip the testing.\n");
testMatMatSolve = PETSC_FALSE;
}
*/
if (testMatMatSolve) {
if (!nfact) {
ierr = MatMatMult(A,C,MAT_INITIAL_MATRIX,2.0,&RHS);CHKERRQ(ierr);
} else {
ierr = MatMatMult(A,C,MAT_REUSE_MATRIX,2.0,&RHS);CHKERRQ(ierr);
}
for (nsolve = 0; nsolve < 2; nsolve++) {
if (!rank) printf(" %d-the MatMatSolve \n",nsolve);
ierr = MatMatSolve(F,RHS,X);CHKERRQ(ierr);
/* Check the error */
ierr = MatAXPY(X,-1.0,C,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatNorm(X,NORM_FROBENIUS,&norm);CHKERRQ(ierr);
if (norm > tol) {
if (!rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"1st MatMatSolve: Norm of error %g, nsolve %d\n",norm,nsolve);CHKERRQ(ierr);
}
}
}
}
/* Test MatSolve() */
if (testMatSolve) {
for (nsolve = 0; nsolve < 2; nsolve++) {
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
ierr = MatMult(A,x,b);CHKERRQ(ierr);
if (!rank) printf(" %d-the MatSolve \n",nsolve);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(u,-1.0,x);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = MatMult(A,x,u);CHKERRQ(ierr); /* u = A*x */
PetscReal resi;
ierr = VecAXPY(u,-1.0,b);CHKERRQ(ierr); /* u <- (-1.0)b + u */
ierr = VecNorm(u,NORM_2,&resi);CHKERRQ(ierr);
if (!rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatSolve: Norm of error %g, resi %g, LU numfact %d\n",norm,resi,nfact);CHKERRQ(ierr);
}
}
}
}
}
/* Free data structures */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
ierr = MatDestroy(&X);CHKERRQ(ierr);
if (testMatMatSolve) {
ierr = MatDestroy(&RHS);CHKERRQ(ierr);
}
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = ISDestroy(&iperm);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
PetscErrorCode ierr;
Mat mat,fact,B;
PetscInt ind1[2],ind2[2];
PetscScalar temp[4];
PetscInt nnz[3];
IS perm,colp;
MatFactorInfo info;
PetscMPIInt size;
ierr = PetscInitialize(&argc,&args,0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
nnz[0]=2;nnz[1]=1;nnz[2]=1;
ierr = MatCreateSeqSBAIJ(PETSC_COMM_SELF,2,6,6,0,nnz,&mat);CHKERRQ(ierr);
ind1[0]=0;ind1[1]=1;
temp[0]=3;temp[1]=2;temp[2]=0;temp[3]=3;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ind2[0]=4;ind2[1]=5;
temp[0]=1;temp[1]=1;temp[2]=2;temp[3]=1;
ierr = MatSetValues(mat,2,ind1,2,ind2,temp,INSERT_VALUES);CHKERRQ(ierr);
ind1[0]=2;ind1[1]=3;
temp[0]=4;temp[1]=1;temp[2]=1;temp[3]=5;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ind1[0]=4;ind1[1]=5;
temp[0]=5;temp[1]=1;temp[2]=1;temp[3]=6;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatDuplicate(mat,MAT_SHARE_NONZERO_PATTERN,&B);CHKERRQ(ierr);
ind1[0]=0;ind1[1]=1;
temp[0]=3;temp[1]=2;temp[2]=0;temp[3]=3;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ind2[0]=4;ind2[1]=5;
temp[0]=1;temp[1]=1;temp[2]=2;temp[3]=1;
ierr = MatSetValues(mat,2,ind1,2,ind2,temp,INSERT_VALUES);CHKERRQ(ierr);
ind1[0]=2;ind1[1]=3;
temp[0]=4;temp[1]=1;temp[2]=1;temp[3]=5;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ind1[0]=4;ind1[1]=5;
temp[0]=5;temp[1]=1;temp[2]=1;temp[3]=6;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"mat: \n");CHKERRQ(ierr);
ierr = MatView(mat,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
/* begin cholesky factorization */
ierr = MatGetOrdering(mat,MATORDERINGNATURAL,&perm,&colp);CHKERRQ(ierr);
ierr = ISDestroy(&colp);CHKERRQ(ierr);
info.fill=1.0;
ierr = MatGetFactor(mat,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&fact);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(fact,mat,perm,&info);CHKERRQ(ierr);
ierr = MatCholeskyFactorNumeric(fact,mat,&info);CHKERRQ(ierr);
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&mat);CHKERRQ(ierr);
ierr = MatDestroy(&fact);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
PetscErrorCode MatSOR_BlockMat(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
{
Mat_BlockMat *a = (Mat_BlockMat*)A->data;
PetscScalar *x;
const Mat *v;
const PetscScalar *b;
PetscErrorCode ierr;
PetscInt n = A->cmap->n,i,mbs = n/A->rmap->bs,j,bs = A->rmap->bs;
const PetscInt *idx;
IS row,col;
MatFactorInfo info;
Vec left = a->left,right = a->right;
Mat *diag;
PetscFunctionBegin;
its = its*lits;
if (its <= 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D and local its %D both positive",its,lits);
if (flag & SOR_EISENSTAT) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for Eisenstat");
if (omega != 1.0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for omega not equal to 1.0");
if (fshift) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for fshift");
if (!a->diags) {
ierr = PetscMalloc1(mbs,&a->diags);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
for (i=0; i<mbs; i++) {
ierr = MatGetOrdering(a->a[a->diag[i]], MATORDERINGND,&row,&col);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(a->diags[i],a->a[a->diag[i]],row,col,&info);CHKERRQ(ierr);
ierr = MatLUFactorNumeric(a->diags[i],a->a[a->diag[i]],&info);CHKERRQ(ierr);
ierr = ISDestroy(&row);CHKERRQ(ierr);
ierr = ISDestroy(&col);CHKERRQ(ierr);
}
}
diag = a->diags;
ierr = VecSet(xx,0.0);CHKERRQ(ierr);
ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
/* need to add code for when initial guess is zero, see MatSOR_SeqAIJ */
while (its--) {
if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
for (i=0; i<mbs; i++) {
n = a->i[i+1] - a->i[i];
idx = a->j + a->i[i];
v = a->a + a->i[i];
ierr = VecSet(left,0.0);CHKERRQ(ierr);
for (j=0; j<n; j++) {
if (idx[j] != i) {
ierr = VecPlaceArray(right,x + idx[j]*bs);CHKERRQ(ierr);
ierr = MatMultAdd(v[j],right,left,left);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
}
}
ierr = VecPlaceArray(right,b + i*bs);CHKERRQ(ierr);
ierr = VecAYPX(left,-1.0,right);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
ierr = VecPlaceArray(right,x + i*bs);CHKERRQ(ierr);
ierr = MatSolve(diag[i],left,right);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
}
}
if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
for (i=mbs-1; i>=0; i--) {
n = a->i[i+1] - a->i[i];
idx = a->j + a->i[i];
v = a->a + a->i[i];
ierr = VecSet(left,0.0);CHKERRQ(ierr);
for (j=0; j<n; j++) {
if (idx[j] != i) {
ierr = VecPlaceArray(right,x + idx[j]*bs);CHKERRQ(ierr);
ierr = MatMultAdd(v[j],right,left,left);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
}
}
ierr = VecPlaceArray(right,b + i*bs);CHKERRQ(ierr);
ierr = VecAYPX(left,-1.0,right);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
ierr = VecPlaceArray(right,x + i*bs);CHKERRQ(ierr);
ierr = MatSolve(diag[i],left,right);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
}
}
}
ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode PCSetUp_Cholesky(PC pc)
{
PetscErrorCode ierr;
PetscBool flg;
PC_Cholesky *dir = (PC_Cholesky*)pc->data;
PetscFunctionBegin;
if (dir->reusefill && pc->setupcalled) ((PC_Factor*)dir)->info.fill = dir->actualfill;
if (dir->inplace) {
if (dir->row && dir->col && (dir->row != dir->col)) {
ierr = ISDestroy(&dir->row);CHKERRQ(ierr);
}
ierr = ISDestroy(&dir->col);CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
if (dir->col && (dir->row != dir->col)) { /* only use row ordering for SBAIJ */
ierr = ISDestroy(&dir->col);CHKERRQ(ierr);
}
if (dir->row) {ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);}
ierr = MatCholeskyFactor(pc->pmat,dir->row,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
((PC_Factor*)dir)->fact = pc->pmat;
} else {
MatInfo info;
if (!pc->setupcalled) {
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
/* check if dir->row == dir->col */
ierr = ISEqual(dir->row,dir->col,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"row and column permutations must equal");
ierr = ISDestroy(&dir->col);CHKERRQ(ierr); /* only pass one ordering into CholeskyFactor */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&flg,PETSC_NULL);CHKERRQ(ierr);
if (flg) {
PetscReal tol = 1.e-10;
ierr = PetscOptionsGetReal(((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&tol,PETSC_NULL);CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(pc->pmat,tol,dir->row,dir->row);CHKERRQ(ierr);
}
if (dir->row) {ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);}
if (!((PC_Factor*)dir)->fact){
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_CHOLESKY,&((PC_Factor*)dir)->fact);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)dir)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
dir->actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent(pc,((PC_Factor*)dir)->fact);CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
if (!dir->reuseordering) {
ierr = ISDestroy(&dir->row);CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
ierr = ISDestroy(&dir->col);CHKERRQ(ierr); /* only use dir->row ordering in CholeskyFactor */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&flg,PETSC_NULL);CHKERRQ(ierr);
if (flg) {
PetscReal tol = 1.e-10;
ierr = PetscOptionsGetReal(((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&tol,PETSC_NULL);CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(pc->pmat,tol,dir->row,dir->row);CHKERRQ(ierr);
}
if (dir->row) {ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);}
}
ierr = MatDestroy(&((PC_Factor*)dir)->fact);CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_CHOLESKY,&((PC_Factor*)dir)->fact);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)dir)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
dir->actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent(pc,((PC_Factor*)dir)->fact);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(((PC_Factor*)dir)->fact,pc->pmat,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static PetscErrorCode PCSetUp_Cholesky(PC pc)
{
PetscErrorCode ierr;
PetscBool flg;
PC_Cholesky *dir = (PC_Cholesky*)pc->data;
const MatSolverPackage stype;
MatFactorError err;
PetscFunctionBegin;
pc->failedreason = PC_NOERROR;
if (dir->hdr.reusefill && pc->setupcalled) ((PC_Factor*)dir)->info.fill = dir->hdr.actualfill;
ierr = MatSetErrorIfFailure(pc->pmat,pc->erroriffailure);
CHKERRQ(ierr);
if (dir->hdr.inplace) {
if (dir->row && dir->col && (dir->row != dir->col)) {
ierr = ISDestroy(&dir->row);
CHKERRQ(ierr);
}
ierr = ISDestroy(&dir->col);
CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);
CHKERRQ(ierr);
if (dir->col && (dir->row != dir->col)) { /* only use row ordering for SBAIJ */
ierr = ISDestroy(&dir->col);
CHKERRQ(ierr);
}
if (dir->row) {
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)dir->row);
CHKERRQ(ierr);
}
ierr = MatCholeskyFactor(pc->pmat,dir->row,&((PC_Factor*)dir)->info);
CHKERRQ(ierr);
ierr = MatFactorGetError(pc->pmat,&err);
CHKERRQ(ierr);
if (err) { /* Factor() fails */
pc->failedreason = (PCFailedReason)err;
PetscFunctionReturn(0);
}
((PC_Factor*)dir)->fact = pc->pmat;
} else {
MatInfo info;
if (!pc->setupcalled) {
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);
CHKERRQ(ierr);
/* check if dir->row == dir->col */
ierr = ISEqual(dir->row,dir->col,&flg);
CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"row and column permutations must equal");
ierr = ISDestroy(&dir->col);
CHKERRQ(ierr); /* only pass one ordering into CholeskyFactor */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&flg,NULL);
CHKERRQ(ierr);
if (flg) {
PetscReal tol = 1.e-10;
ierr = PetscOptionsGetReal(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&tol,NULL);
CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(pc->pmat,tol,dir->row,dir->row);
CHKERRQ(ierr);
}
if (dir->row) {
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)dir->row);
CHKERRQ(ierr);
}
if (!((PC_Factor*)dir)->fact) {
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_CHOLESKY,&((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
}
ierr = MatCholeskyFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,&((PC_Factor*)dir)->info);
CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)dir)->fact,MAT_LOCAL,&info);
CHKERRQ(ierr);
dir->hdr.actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
if (!dir->hdr.reuseordering) {
ierr = ISDestroy(&dir->row);
CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);
CHKERRQ(ierr);
ierr = ISDestroy(&dir->col);
CHKERRQ(ierr); /* only use dir->row ordering in CholeskyFactor */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&flg,NULL);
CHKERRQ(ierr);
if (flg) {
PetscReal tol = 1.e-10;
ierr = PetscOptionsGetReal(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&tol,NULL);
CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(pc->pmat,tol,dir->row,dir->row);
CHKERRQ(ierr);
}
if (dir->row) {
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)dir->row);
CHKERRQ(ierr);
}
}
ierr = MatDestroy(&((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_CHOLESKY,&((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,&((PC_Factor*)dir)->info);
CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)dir)->fact,MAT_LOCAL,&info);
CHKERRQ(ierr);
dir->hdr.actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
} else {
ierr = MatFactorGetError(((PC_Factor*)dir)->fact,&err);
CHKERRQ(ierr);
if (err == MAT_FACTOR_NUMERIC_ZEROPIVOT) {
ierr = MatFactorClearError(((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
pc->failedreason = PC_NOERROR;
}
}
ierr = MatFactorGetError(((PC_Factor*)dir)->fact,&err);
CHKERRQ(ierr);
if (err) { /* FactorSymbolic() fails */
pc->failedreason = (PCFailedReason)err;
PetscFunctionReturn(0);
}
ierr = MatCholeskyFactorNumeric(((PC_Factor*)dir)->fact,pc->pmat,&((PC_Factor*)dir)->info);
CHKERRQ(ierr);
ierr = MatFactorGetError(((PC_Factor*)dir)->fact,&err);
CHKERRQ(ierr);
if (err) { /* FactorNumeric() fails */
pc->failedreason = (PCFailedReason)err;
}
}
ierr = PCFactorGetMatSolverPackage(pc,&stype);
CHKERRQ(ierr);
if (!stype) {
const MatSolverPackage solverpackage;
ierr = MatFactorGetSolverPackage(((PC_Factor*)dir)->fact,&solverpackage);
CHKERRQ(ierr);
ierr = PCFactorSetMatSolverPackage(pc,solverpackage);
CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Mat C,C1,F;
Vec u,x,b;
PetscErrorCode ierr;
PetscMPIInt rank,nproc;
PetscInt i,M = 10,m,n,nfact,nsolve;
PetscScalar *array,rval;
PetscReal norm,tol=1.e-12;
IS perm,iperm;
MatFactorInfo info;
PetscRandom rand;
PetscTruth flg;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &nproc);CHKERRQ(ierr);
/* Create matrix and vectors */
ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,M,M);CHKERRQ(ierr);
ierr = MatSetType(C,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatGetLocalSize(C,&m,&n);CHKERRQ(ierr);
if (m != n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Matrix local size m %d must equal n %d",m,n);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */
/* Assembly */
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = MatGetArray(C,&array);CHKERRQ(ierr);
for (i=0; i<m*M; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = MatRestoreArray(C,&array);CHKERRQ(ierr);
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*if (!rank) {printf("main, C: \n");}
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */
/* Test MatDuplicate() */
ierr = MatDuplicate(C,MAT_COPY_VALUES,&C1);CHKERRQ(ierr);
ierr = MatEqual(C,C1,&flg);CHKERRQ(ierr);
if (!flg){
SETERRQ(PETSC_ERR_ARG_WRONG,"Duplicate C1 != C");
}
/* Test LU Factorization */
ierr = MatGetOrdering(C1,MATORDERING_NATURAL,&perm,&iperm);CHKERRQ(ierr);
if (nproc == 1){
ierr = MatGetFactor(C1,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
} else {
ierr = MatGetFactor(C1,MAT_SOLVER_PLAPACK,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
}
ierr = MatLUFactorSymbolic(F,C1,perm,iperm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 2; nfact++){
if (!rank) printf(" LU nfact %d\n",nfact);
ierr = MatLUFactorNumeric(F,C1,&info);CHKERRQ(ierr);
/* Test MatSolve() */
for (nsolve = 0; nsolve < 5; nsolve++){
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
ierr = MatMult(C,x,b);CHKERRQ(ierr);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(u,-1.0,x);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol){
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: Norm of error %g, LU nfact %d\n",norm,nfact);CHKERRQ(ierr);
}
}
}
}
ierr = MatDestroy(C1);CHKERRQ(ierr);
ierr = MatDestroy(F);CHKERRQ(ierr);
/* Test Cholesky Factorization */
ierr = MatTranspose(C,MAT_INITIAL_MATRIX,&C1);CHKERRQ(ierr); /* C1 = C^T */
ierr = MatAXPY(C,1.0,C1,SAME_NONZERO_PATTERN);CHKERRQ(ierr); /* make C symmetric: C <- C + C^T */
ierr = MatShift(C,M);CHKERRQ(ierr); /* make C positive definite */
ierr = MatDestroy(C1);CHKERRQ(ierr);
ierr = MatSetOption(C,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetOption(C,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);CHKERRQ(ierr);
if (nproc == 1){
ierr = MatGetFactor(C,MAT_SOLVER_PETSC,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
} else {
ierr = MatGetFactor(C,MAT_SOLVER_PLAPACK,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorSymbolic(F,C,perm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 2; nfact++){
if (!rank) printf(" Cholesky nfact %d\n",nfact);
ierr = MatCholeskyFactorNumeric(F,C,&info);CHKERRQ(ierr);
/* Test MatSolve() */
for (nsolve = 0; nsolve < 5; nsolve++){
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
ierr = MatMult(C,x,b);CHKERRQ(ierr);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(u,-1.0,x);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol){
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: Norm of error %g, Cholesky nfact %d\n",norm,nfact);CHKERRQ(ierr);
}
}
}
}
ierr = MatDestroy(F);CHKERRQ(ierr);
/* Free data structures */
ierr = PetscRandomDestroy(rand);CHKERRQ(ierr);
ierr = ISDestroy(perm);CHKERRQ(ierr);
ierr = ISDestroy(iperm);CHKERRQ(ierr);
ierr = VecDestroy(x);CHKERRQ(ierr);
ierr = VecDestroy(b);CHKERRQ(ierr);
ierr = VecDestroy(u);CHKERRQ(ierr);
ierr = MatDestroy(C);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
int main(int argc,char **argv)
{
Mat mat,B;
PetscErrorCode ierr;
PetscInt i,j;
PetscScalar v;
IS isrow,iscol;
PetscViewer viewer;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
/* ------- Assemble matrix, --------- */
ierr = MatCreate(PETSC_COMM_WORLD,&mat);CHKERRQ(ierr);
ierr = MatSetSizes(mat,PETSC_DECIDE,PETSC_DECIDE,4,4);CHKERRQ(ierr);
ierr = MatSetFromOptions(mat);CHKERRQ(ierr);
ierr = MatSetUp(mat);CHKERRQ(ierr);
/* set anti-diagonal of matrix */
v = 1.0;
i = 0; j = 3;
ierr = MatSetValues(mat,1,&i,1,&j,&v,INSERT_VALUES);CHKERRQ(ierr);
v = 2.0;
i = 1; j = 2;
ierr = MatSetValues(mat,1,&i,1,&j,&v,INSERT_VALUES);CHKERRQ(ierr);
v = 3.0;
i = 2; j = 1;
ierr = MatSetValues(mat,1,&i,1,&j,&v,INSERT_VALUES);CHKERRQ(ierr);
v = 4.0;
i = 3; j = 0;
ierr = MatSetValues(mat,1,&i,1,&j,&v,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr);
ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_DENSE);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Original matrix\n");CHKERRQ(ierr);
ierr = MatView(mat,viewer);CHKERRQ(ierr);
ierr = MatGetOrdering(mat,MATORDERINGNATURAL,&isrow,&iscol);CHKERRQ(ierr);
ierr = MatPermute(mat,isrow,iscol,&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Original matrix permuted by identity\n");CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(mat,1.e-8,isrow,iscol);CHKERRQ(ierr);
ierr = MatPermute(mat,isrow,iscol,&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Original matrix permuted by identity + NonzeroDiagonal()\n");CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Row permutation\n");CHKERRQ(ierr);
ierr = ISView(isrow,viewer);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Column permutation\n");CHKERRQ(ierr);
ierr = ISView(iscol,viewer);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
ierr = MatGetOrdering(mat,MATORDERINGND,&isrow,&iscol);CHKERRQ(ierr);
ierr = MatPermute(mat,isrow,iscol,&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Original matrix permuted by ND\n");CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"ND row permutation\n");CHKERRQ(ierr);
ierr = ISView(isrow,viewer);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"ND column permutation\n");CHKERRQ(ierr);
ierr = ISView(iscol,viewer);CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(mat,1.e-8,isrow,iscol);CHKERRQ(ierr);
ierr = MatPermute(mat,isrow,iscol,&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Original matrix permuted by ND + NonzeroDiagonal()\n");CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"ND + NonzeroDiagonal() row permutation\n");CHKERRQ(ierr);
ierr = ISView(isrow,viewer);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"ND + NonzeroDiagonal() column permutation\n");CHKERRQ(ierr);
ierr = ISView(iscol,viewer);CHKERRQ(ierr);
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
ierr = MatGetOrdering(mat,MATORDERINGRCM,&isrow,&iscol);CHKERRQ(ierr);
ierr = MatPermute(mat,isrow,iscol,&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Original matrix permuted by RCM\n");CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"RCM row permutation\n");CHKERRQ(ierr);
ierr = ISView(isrow,viewer);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"RCM column permutation\n");CHKERRQ(ierr);
ierr = ISView(iscol,viewer);CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(mat,1.e-8,isrow,iscol);CHKERRQ(ierr);
ierr = MatPermute(mat,isrow,iscol,&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Original matrix permuted by RCM + NonzeroDiagonal()\n");CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"RCM + NonzeroDiagonal() row permutation\n");CHKERRQ(ierr);
ierr = ISView(isrow,viewer);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"RCM + NonzeroDiagonal() column permutation\n");CHKERRQ(ierr);
ierr = ISView(iscol,viewer);CHKERRQ(ierr);
ierr = MatLUFactor(mat,isrow,iscol,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Factored matrix permuted by RCM + NonzeroDiagonal()\n");CHKERRQ(ierr);
ierr = MatView(mat,viewer);CHKERRQ(ierr);
/* Free data structures */
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
ierr = MatDestroy(&mat);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat C,F,Cpetsc,Csymm;
Vec u,x,b,bpla;
PetscErrorCode ierr;
PetscMPIInt rank,nproc;
PetscInt i,j,k,M = 10,m,nfact,nsolve,Istart,Iend,*im,*in,start,end;
PetscScalar *array,rval;
PetscReal norm,tol=1.e-12;
IS perm,iperm;
MatFactorInfo info;
PetscRandom rand;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &nproc);CHKERRQ(ierr);
/* Test non-symmetric operations */
/*-------------------------------*/
/* Create a Plapack dense matrix C */
ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,M,M);CHKERRQ(ierr);
ierr = MatSetType(C,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
/* Create vectors */
ierr = MatGetOwnershipRange(C,&start,&end);CHKERRQ(ierr);
m = end - start;
/* printf("[%d] C - local size m: %d\n",rank,m); */
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&bpla);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */
/* Create a petsc dense matrix Cpetsc */
ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&Cpetsc);CHKERRQ(ierr);
ierr = MatSetSizes(Cpetsc,m,m,M,M);CHKERRQ(ierr);
ierr = MatSetType(Cpetsc,MATDENSE);CHKERRQ(ierr);
ierr = MatMPIDenseSetPreallocation(Cpetsc,PETSC_NULL);CHKERRQ(ierr);
ierr = MatSetFromOptions(Cpetsc);CHKERRQ(ierr);
ierr = MatSetUp(Cpetsc);CHKERRQ(ierr);
ierr = MatSetOption(Cpetsc,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
ierr = MatSetOption(C,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
/* Assembly */
/* PLAPACK doesn't support INSERT_VALUES mode, zero all entries before calling MatSetValues() */
ierr = MatZeroEntries(C);CHKERRQ(ierr);
ierr = MatZeroEntries(Cpetsc);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(C,&Istart,&Iend);CHKERRQ(ierr);
/* printf(" [%d] C m: %d, Istart/end: %d %d\n",rank,m,Istart,Iend); */
ierr = PetscMalloc((m*M+1)*sizeof(PetscScalar),&array);CHKERRQ(ierr);
ierr = PetscMalloc2(m,PetscInt,&im,M,PetscInt,&in);CHKERRQ(ierr);
k = 0;
for (j=0; j<M; j++){ /* column oriented! */
in[j] = j;
for (i=0; i<m; i++){
im[i] = i+Istart;
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[k++] = rval;
}
}
ierr = MatSetValues(Cpetsc,m,im,M,in,array,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(C,m,im,M,in,array,ADD_VALUES);CHKERRQ(ierr);
ierr = PetscFree(array);CHKERRQ(ierr);
ierr = PetscFree2(im,in);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*
if (!rank) {printf("main, Cpetsc: \n");}
ierr = MatView(Cpetsc,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
*/
ierr = MatGetOrdering(C,MATORDERINGNATURAL,&perm,&iperm);CHKERRQ(ierr);
/* Test nonsymmetric MatMult() */
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = MatMult(Cpetsc,x,b);CHKERRQ(ierr);
ierr = MatMult(C,x,bpla);CHKERRQ(ierr);
ierr = VecAXPY(bpla,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(bpla,NORM_2,&norm);CHKERRQ(ierr);
if (norm > 1.e-12 && !rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Nonsymmetric MatMult_Plapack error: |b_pla - b|= %g\n",norm);CHKERRQ(ierr);
}
/* Test LU Factorization */
if (nproc == 1){
ierr = MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
} else {
ierr = MatGetFactor(C,MATSOLVERPLAPACK,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
}
ierr = MatLUFactorSymbolic(F,C,perm,iperm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 2; nfact++){
if (!rank) printf(" LU nfact %d\n",nfact);
if (nfact>0){ /* change matrix value for testing repeated MatLUFactorNumeric() */
if (!rank){
i = j = 0;
rval = nfact;
ierr = MatSetValues(Cpetsc,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(C,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
} else { /* PLAPACK seems requiring all processors call MatSetValues(), so we add 0.0 on processesses with rank>0! */
i = j = 0;
rval = 0.0;
ierr = MatSetValues(Cpetsc,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(C,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
ierr = MatLUFactorNumeric(F,C,&info);CHKERRQ(ierr);
/* Test MatSolve() */
for (nsolve = 0; nsolve < 2; nsolve++){
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
/* array[i] = rank + 1; */
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
ierr = MatMult(C,x,b);CHKERRQ(ierr);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(u,-1.0,x);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol){
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: Norm of error %g, LU nfact %d\n",norm,nfact);CHKERRQ(ierr);
}
}
}
}
ierr = MatDestroy(&F);CHKERRQ(ierr);
/* Test non-symmetric operations */
/*-------------------------------*/
/* Create a symmetric Plapack dense matrix Csymm */
ierr = MatCreate(PETSC_COMM_WORLD,&Csymm);CHKERRQ(ierr);
ierr = MatSetSizes(Csymm,PETSC_DECIDE,PETSC_DECIDE,M,M);CHKERRQ(ierr);
ierr = MatSetType(Csymm,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(Csymm);CHKERRQ(ierr);
ierr = MatSetUp(Csymm);CHKERRQ(ierr);
ierr = MatSetOption(Csymm,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
ierr = MatSetOption(Csymm,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetOption(Csymm,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatZeroEntries(Csymm);CHKERRQ(ierr);
ierr = MatZeroEntries(Cpetsc);CHKERRQ(ierr);
for (i=Istart; i<Iend; i++){
for (j=0; j<=i; j++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
ierr = MatSetValues(Cpetsc,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(Csymm,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
if (j<i){
/* Although PLAPACK only requires lower triangular entries, we must add all the entries.
MatSetValues_Plapack() will ignore the upper triangular entries AFTER an index map! */
ierr = MatSetValues(Cpetsc,1,&j,1,&i,&rval,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(Csymm,1,&j,1,&i,&rval,ADD_VALUES);CHKERRQ(ierr);
}
}
}
ierr = MatAssemblyBegin(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Csymm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Csymm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test symmetric MatMult() */
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = MatMult(Cpetsc,x,b);CHKERRQ(ierr);
ierr = MatMult(Csymm,x,bpla);CHKERRQ(ierr);
ierr = VecAXPY(bpla,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(bpla,NORM_2,&norm);CHKERRQ(ierr);
if (norm > 1.e-12 && !rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Symmetric MatMult_Plapack error: |b_pla - b|= %g\n",norm);CHKERRQ(ierr);
}
/* Test Cholesky Factorization */
ierr = MatShift(Csymm,M);CHKERRQ(ierr); /* make Csymm positive definite */
if (nproc == 1){
ierr = MatGetFactor(Csymm,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
} else {
ierr = MatGetFactor(Csymm,MATSOLVERPLAPACK,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorSymbolic(F,Csymm,perm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 2; nfact++){
if (!rank) printf(" Cholesky nfact %d\n",nfact);
ierr = MatCholeskyFactorNumeric(F,Csymm,&info);CHKERRQ(ierr);
/* Test MatSolve() */
for (nsolve = 0; nsolve < 2; nsolve++){
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
ierr = MatMult(Csymm,x,b);CHKERRQ(ierr);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(u,-1.0,x);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol){
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: Norm of error %g, Cholesky nfact %d\n",norm,nfact);CHKERRQ(ierr);
}
}
}
}
ierr = MatDestroy(&F);CHKERRQ(ierr);
/* Free data structures */
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = ISDestroy(&iperm);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&bpla);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = MatDestroy(&Cpetsc);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&Csymm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat C,Cperm;
PetscInt i,j,m = 5,n = 5,Ii,J,ncols;
PetscErrorCode ierr;
PetscScalar v;
PetscMPIInt size;
IS rperm,cperm,icperm;
const PetscInt *rperm_ptr,*cperm_ptr,*cols;
const PetscScalar *vals;
PetscBool TestMyorder=PETSC_FALSE;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);
CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
/* create the matrix for the five point stencil, YET AGAIN */
ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,m*n,m*n,5,NULL,&C);
ierr = MatSetUp(C);
CHKERRQ(ierr);
for (i=0; i<m; i++) {
for (j=0; j<n; j++) {
v = -1.0;
Ii = j + n*i;
if (i>0) {
J = Ii - n;
ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);
CHKERRQ(ierr);
}
if (i<m-1) {
J = Ii + n;
ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j<n-1) {
J = Ii + 1;
ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);
CHKERRQ(ierr);
}
v = 4.0;
ierr = MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);
CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatGetOrdering(C,MATORDERINGND,&rperm,&cperm);
CHKERRQ(ierr);
ierr = ISView(rperm,PETSC_VIEWER_STDOUT_SELF);
CHKERRQ(ierr);
ierr = ISDestroy(&rperm);
CHKERRQ(ierr);
ierr = ISDestroy(&cperm);
CHKERRQ(ierr);
ierr = MatGetOrdering(C,MATORDERINGRCM,&rperm,&cperm);
CHKERRQ(ierr);
ierr = ISView(rperm,PETSC_VIEWER_STDOUT_SELF);
CHKERRQ(ierr);
ierr = ISDestroy(&rperm);
CHKERRQ(ierr);
ierr = ISDestroy(&cperm);
CHKERRQ(ierr);
ierr = MatGetOrdering(C,MATORDERINGQMD,&rperm,&cperm);
CHKERRQ(ierr);
ierr = ISView(rperm,PETSC_VIEWER_STDOUT_SELF);
CHKERRQ(ierr);
ierr = ISDestroy(&rperm);
CHKERRQ(ierr);
ierr = ISDestroy(&cperm);
CHKERRQ(ierr);
/* create Cperm = rperm*C*icperm */
ierr = PetscOptionsGetBool(NULL,"-testmyordering",&TestMyorder,NULL);
CHKERRQ(ierr);
if (TestMyorder) {
ierr = MatGetOrdering_myordering(C,MATORDERINGQMD,&rperm,&cperm);
CHKERRQ(ierr);
printf("myordering's rperm:\n");
ierr = ISView(rperm,PETSC_VIEWER_STDOUT_SELF);
CHKERRQ(ierr);
ierr = ISInvertPermutation(cperm,PETSC_DECIDE,&icperm);
CHKERRQ(ierr);
ierr = ISGetIndices(rperm,&rperm_ptr);
CHKERRQ(ierr);
ierr = ISGetIndices(icperm,&cperm_ptr);
CHKERRQ(ierr);
ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,m*n,m*n,5,NULL,&Cperm);
CHKERRQ(ierr);
for (i=0; i<m*n; i++) {
ierr = MatGetRow(C,rperm_ptr[i],&ncols,&cols,&vals);
CHKERRQ(ierr);
for (j=0; j<ncols; j++) {
/* printf(" (%d %d %g)\n",i,cperm_ptr[cols[j]],vals[j]); */
ierr = MatSetValues(Cperm,1,&i,1,&cperm_ptr[cols[j]],&vals[j],INSERT_VALUES);
CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(Cperm,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(Cperm,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = ISRestoreIndices(rperm,&rperm_ptr);
CHKERRQ(ierr);
ierr = ISRestoreIndices(icperm,&cperm_ptr);
CHKERRQ(ierr);
ierr = ISDestroy(&rperm);
CHKERRQ(ierr);
ierr = ISDestroy(&cperm);
CHKERRQ(ierr);
ierr = ISDestroy(&icperm);
CHKERRQ(ierr);
ierr = MatDestroy(&Cperm);
CHKERRQ(ierr);
}
ierr = MatDestroy(&C);
CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Vec x,y,b,s1,s2;
Mat A; /* linear system matrix */
Mat sA; /* symmetric part of the matrices */
PetscInt n,mbs=16,bs=1,nz=3,prob=2,i,j,col[3],row,Ii,J,n1;
const PetscInt *ip_ptr;
PetscScalar neg_one = -1.0,value[3],alpha=0.1;
PetscMPIInt size;
PetscErrorCode ierr;
IS ip, isrow, iscol;
PetscRandom rdm;
PetscBool reorder=PETSC_FALSE;
MatInfo minfo1,minfo2;
PetscReal norm1,norm2,tol=1.e-10;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
ierr = PetscOptionsGetInt(PETSC_NULL,"-bs",&bs,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-mbs",&mbs,PETSC_NULL);CHKERRQ(ierr);
n = mbs*bs;
ierr=MatCreateSeqBAIJ(PETSC_COMM_WORLD,bs,n,n,nz,PETSC_NULL, &A);CHKERRQ(ierr);
ierr=MatCreateSeqSBAIJ(PETSC_COMM_WORLD,bs,n,n,nz,PETSC_NULL, &sA);CHKERRQ(ierr);
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(sA,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ format\n");CHKERRQ(ierr);
}
/* Assemble matrix */
if (bs == 1){
ierr = PetscOptionsGetInt(PETSC_NULL,"-test_problem",&prob,PETSC_NULL);CHKERRQ(ierr);
if (prob == 1){ /* tridiagonal matrix */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
value[0]= 0.1; value[1]=-1; value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0; col[0] = 0; col[1] = 1; col[2]=n-1;
value[0] = 2.0; value[1] = -1.0; value[2]=0.1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
else if (prob ==2){ /* matrix for the five point stencil */
n1 = (int) (PetscSqrtReal((PetscReal)n) + 0.001);
if (n1*n1 - n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
/*
ierr = MatSetValues(A,1,&I,1,&I,&four,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&I,1,&I,&four,INSERT_VALUES);CHKERRQ(ierr);
*/
}
}
}
}
else { /* bs > 1 */
#ifdef DIAGB
for (block=0; block<n/bs; block++){
/* diagonal blocks */
value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
value[0]=-1.0; value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
value[0]=4.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
#endif
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++){
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
col[0]=i; row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* PetscPrintf(PETSC_COMM_SELF,"\n The Matrix: \n");
MatView(A, VIEWER_DRAW_WORLD);
MatView(A, VIEWER_STDOUT_WORLD); */
ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* PetscPrintf(PETSC_COMM_SELF,"\n Symmetric Part of Matrix: \n");
MatView(sA, VIEWER_DRAW_WORLD);
MatView(sA, VIEWER_STDOUT_WORLD);
*/
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_FROBENIUS,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm(), fnorm1-fnorm2=%16.14e\n",norm1);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_INFINITY,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm(), inf_norm1-inf_norm2=%16.14e\n",norm1);CHKERRQ(ierr);
}
/* Test MatGetInfo(), MatGetSize(), MatGetBlockSize() */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sA,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
if (i<0 || j<0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetInfo()\n");CHKERRQ(ierr);
}
ierr = MatGetSize(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetSize(sA,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
PetscPrintf(PETSC_COMM_SELF,"Error: MatGetSize()\n");CHKERRQ(ierr);
}
ierr = MatGetBlockSize(A, &Ii);CHKERRQ(ierr);
ierr = MatGetBlockSize(sA, &i);CHKERRQ(ierr);
if (i-Ii){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetBlockSize()\n");CHKERRQ(ierr);
}
/* Test MatDiagonalScale(), MatGetDiagonal(), MatScale() */
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s2);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = MatDiagonalScale(A,x,x);CHKERRQ(ierr);
ierr = MatDiagonalScale(sA,x,x);CHKERRQ(ierr);
ierr = MatGetDiagonal(A,s1);CHKERRQ(ierr);
ierr = MatGetDiagonal(sA,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetDiagonal() \n");CHKERRQ(ierr);
}
ierr = MatScale(A,alpha);CHKERRQ(ierr);
ierr = MatScale(sA,alpha);CHKERRQ(ierr);
/* Test MatMult(), MatMultAdd() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = MatMult(A,x,s1);CHKERRQ(ierr);
ierr = MatMult(sA,x,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult(), MatDiagonalScale() or MatScale()\n");CHKERRQ(ierr);
}
}
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(y,rdm);CHKERRQ(ierr);
ierr = MatMultAdd(A,x,y,s1);CHKERRQ(ierr);
ierr = MatMultAdd(sA,x,y,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatMultAdd(), MatDiagonalScale() or MatScale() \n");CHKERRQ(ierr);
}
}
/* Test MatReordering() */
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&isrow,&iscol);CHKERRQ(ierr);
ip = isrow;
if (reorder){
IS nip;
PetscInt *nip_ptr;
ierr = PetscMalloc(mbs*sizeof(PetscInt),&nip_ptr);CHKERRQ(ierr);
ierr = ISGetIndices(ip,&ip_ptr);CHKERRQ(ierr);
ierr = PetscMemcpy(nip_ptr,ip_ptr,mbs*sizeof(PetscInt));CHKERRQ(ierr);
i = nip_ptr[1]; nip_ptr[1] = nip_ptr[mbs-2]; nip_ptr[mbs-2] = i;
i = nip_ptr[0]; nip_ptr[0] = nip_ptr[mbs-1]; nip_ptr[mbs-1] = i;
ierr = ISRestoreIndices(ip,&ip_ptr);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,mbs,nip_ptr,PETSC_COPY_VALUES,&nip);CHKERRQ(ierr);
ierr = PetscFree(nip_ptr);CHKERRQ(ierr);
ierr = MatReorderingSeqSBAIJ(sA, ip);CHKERRQ(ierr);
ierr = ISDestroy(&nip);CHKERRQ(ierr);
/* ierr = ISView(ip, VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = MatView(sA,VIEWER_DRAW_SELF);CHKERRQ(ierr); */
}
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
/* ierr = ISDestroy(&isrow);CHKERRQ(ierr);*/
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
static PetscErrorCode PCSetUp_ILU(PC pc)
{
PetscErrorCode ierr;
PC_ILU *ilu = (PC_ILU*)pc->data;
MatInfo info;
PetscBool flg;
const MatSolverPackage stype;
MatFactorError err;
PetscFunctionBegin;
pc->failedreason = PC_NOERROR;
/* ugly hack to change default, since it is not support by some matrix types */
if (((PC_Factor*)ilu)->info.shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATSEQAIJ,&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATMPIAIJ,&flg);CHKERRQ(ierr);
if (!flg) {
((PC_Factor*)ilu)->info.shifttype = (PetscReal)MAT_SHIFT_INBLOCKS;
PetscInfo(pc,"Changing shift type from NONZERO to INBLOCKS because block matrices do not support NONZERO\n");CHKERRQ(ierr);
}
}
}
ierr = MatSetErrorIfFailure(pc->pmat,pc->erroriffailure);CHKERRQ(ierr);
if (ilu->hdr.inplace) {
if (!pc->setupcalled) {
/* In-place factorization only makes sense with the natural ordering,
so we only need to get the ordering once, even if nonzero structure changes */
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);CHKERRQ(ierr);}
}
/* In place ILU only makes sense with fill factor of 1.0 because
cannot have levels of fill */
((PC_Factor*)ilu)->info.fill = 1.0;
((PC_Factor*)ilu)->info.diagonal_fill = 0.0;
ierr = MatILUFactor(pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);CHKERRQ(ierr);
ierr = MatFactorGetError(pc->pmat,&err);CHKERRQ(ierr);
if (err) { /* Factor() fails */
pc->failedreason = (PCFailedReason)err;
PetscFunctionReturn(0);
}
((PC_Factor*)ilu)->fact = pc->pmat;
/* must update the pc record of the matrix state or the PC will attempt to run PCSetUp() yet again */
ierr = PetscObjectStateGet((PetscObject)pc->pmat,&pc->matstate);CHKERRQ(ierr);
} else {
if (!pc->setupcalled) {
/* first time in so compute reordering and symbolic factorization */
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);CHKERRQ(ierr);}
/* Remove zeros along diagonal? */
if (ilu->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);CHKERRQ(ierr);
}
if (!((PC_Factor*)ilu)->fact) {
ierr = MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
}
ierr = MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
ilu->hdr.actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
if (!ilu->hdr.reuseordering) {
/* compute a new ordering for the ILU */
ierr = ISDestroy(&ilu->row);CHKERRQ(ierr);
ierr = ISDestroy(&ilu->col);CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);CHKERRQ(ierr);}
/* Remove zeros along diagonal? */
if (ilu->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);CHKERRQ(ierr);
}
}
ierr = MatDestroy(&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
ierr = MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
ilu->hdr.actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
}
ierr = MatFactorGetError(((PC_Factor*)ilu)->fact,&err);CHKERRQ(ierr);
if (err) { /* FactorSymbolic() fails */
pc->failedreason = (PCFailedReason)err;
PetscFunctionReturn(0);
}
ierr = MatLUFactorNumeric(((PC_Factor*)ilu)->fact,pc->pmat,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
ierr = MatFactorGetError(((PC_Factor*)ilu)->fact,&err);CHKERRQ(ierr);
if (err) { /* FactorNumeric() fails */
pc->failedreason = (PCFailedReason)err;
}
}
ierr = PCFactorGetMatSolverPackage(pc,&stype);CHKERRQ(ierr);
if (!stype) {
const MatSolverPackage solverpackage;
ierr = MatFactorGetSolverPackage(((PC_Factor*)ilu)->fact,&solverpackage);CHKERRQ(ierr);
ierr = PCFactorSetMatSolverPackage(pc,solverpackage);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*
DMDAGetFaceInterpolation - Gets the interpolation for a face based coarse space
*/
PetscErrorCode DMDAGetFaceInterpolation(DM da,PC_Exotic *exotic,Mat Aglobal,MatReuse reuse,Mat *P)
{
PetscErrorCode ierr;
PetscInt dim,i,j,k,m,n,p,dof,Nint,Nface,Nwire,Nsurf,*Iint,*Isurf,cint = 0,csurf = 0,istart,jstart,kstart,*II,N,c = 0;
PetscInt mwidth,nwidth,pwidth,cnt,mp,np,pp,Ntotal,gl[6],*globals,Ng,*IIint,*IIsurf,Nt;
Mat Xint, Xsurf,Xint_tmp;
IS isint,issurf,is,row,col;
ISLocalToGlobalMapping ltg;
MPI_Comm comm;
Mat A,Aii,Ais,Asi,*Aholder,iAii;
MatFactorInfo info;
PetscScalar *xsurf,*xint;
#if defined(PETSC_USE_DEBUG_foo)
PetscScalar tmp;
#endif
PetscTable ht;
PetscFunctionBegin;
ierr = DMDAGetInfo(da,&dim,0,0,0,&mp,&np,&pp,&dof,0,0,0,0,0);
CHKERRQ(ierr);
if (dof != 1) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Only for single field problems");
if (dim != 3) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Only coded for 3d problems");
ierr = DMDAGetCorners(da,0,0,0,&m,&n,&p);
CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(da,&istart,&jstart,&kstart,&mwidth,&nwidth,&pwidth);
CHKERRQ(ierr);
istart = istart ? -1 : 0;
jstart = jstart ? -1 : 0;
kstart = kstart ? -1 : 0;
/*
the columns of P are the interpolation of each coarse grid point (one for each vertex and edge)
to all the local degrees of freedom (this includes the vertices, edges and faces).
Xint are the subset of the interpolation into the interior
Xface are the interpolation onto faces but not into the interior
Xsurf are the interpolation onto the vertices and edges (the surfbasket)
Xint
Symbolically one could write P = (Xface) after interchanging the rows to match the natural ordering on the domain
Xsurf
*/
N = (m - istart)*(n - jstart)*(p - kstart);
Nint = (m-2-istart)*(n-2-jstart)*(p-2-kstart);
Nface = 2*((m-2-istart)*(n-2-jstart) + (m-2-istart)*(p-2-kstart) + (n-2-jstart)*(p-2-kstart));
Nwire = 4*((m-2-istart) + (n-2-jstart) + (p-2-kstart)) + 8;
Nsurf = Nface + Nwire;
ierr = MatCreateSeqDense(MPI_COMM_SELF,Nint,6,NULL,&Xint);
CHKERRQ(ierr);
ierr = MatCreateSeqDense(MPI_COMM_SELF,Nsurf,6,NULL,&Xsurf);
CHKERRQ(ierr);
ierr = MatDenseGetArray(Xsurf,&xsurf);
CHKERRQ(ierr);
/*
Require that all 12 edges and 6 faces have at least one grid point. Otherwise some of the columns of
Xsurf will be all zero (thus making the coarse matrix singular).
*/
if (m-istart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in X direction must be at least 3");
if (n-jstart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in Y direction must be at least 3");
if (p-kstart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in Z direction must be at least 3");
cnt = 0;
for (j=1; j<n-1-jstart; j++) {
for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 0*Nsurf] = 1;
}
for (k=1; k<p-1-kstart; k++) {
for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 1*Nsurf] = 1;
for (j=1; j<n-1-jstart; j++) {
xsurf[cnt++ + 2*Nsurf] = 1;
/* these are the interior nodes */
xsurf[cnt++ + 3*Nsurf] = 1;
}
for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 4*Nsurf] = 1;
}
for (j=1; j<n-1-jstart; j++) {
for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 5*Nsurf] = 1;
}
#if defined(PETSC_USE_DEBUG_foo)
for (i=0; i<Nsurf; i++) {
tmp = 0.0;
for (j=0; j<6; j++) tmp += xsurf[i+j*Nsurf];
if (PetscAbsScalar(tmp-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong Xsurf interpolation at i %D value %g",i,(double)PetscAbsScalar(tmp));
}
#endif
ierr = MatDenseRestoreArray(Xsurf,&xsurf);
CHKERRQ(ierr);
/* ierr = MatView(Xsurf,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);*/
/*
I are the indices for all the needed vertices (in global numbering)
Iint are the indices for the interior values, I surf for the surface values
(This is just for the part of the global matrix obtained with MatGetSubMatrix(), it
is NOT the local DMDA ordering.)
IIint and IIsurf are the same as the Iint, Isurf except they are in the global numbering
*/
#define Endpoint(a,start,b) (a == 0 || a == (b-1-start))
ierr = PetscMalloc3(N,&II,Nint,&Iint,Nsurf,&Isurf);
CHKERRQ(ierr);
ierr = PetscMalloc2(Nint,&IIint,Nsurf,&IIsurf);
CHKERRQ(ierr);
for (k=0; k<p-kstart; k++) {
for (j=0; j<n-jstart; j++) {
for (i=0; i<m-istart; i++) {
II[c++] = i + j*mwidth + k*mwidth*nwidth;
if (!Endpoint(i,istart,m) && !Endpoint(j,jstart,n) && !Endpoint(k,kstart,p)) {
IIint[cint] = i + j*mwidth + k*mwidth*nwidth;
Iint[cint++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
} else {
IIsurf[csurf] = i + j*mwidth + k*mwidth*nwidth;
Isurf[csurf++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
}
}
}
}
if (c != N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"c != N");
if (cint != Nint) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"cint != Nint");
if (csurf != Nsurf) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csurf != Nsurf");
ierr = DMGetLocalToGlobalMapping(da,<g);
CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApply(ltg,N,II,II);
CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApply(ltg,Nint,IIint,IIint);
CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApply(ltg,Nsurf,IIsurf,IIsurf);
CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)da,&comm);
CHKERRQ(ierr);
ierr = ISCreateGeneral(comm,N,II,PETSC_COPY_VALUES,&is);
CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,Nint,Iint,PETSC_COPY_VALUES,&isint);
CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,Nsurf,Isurf,PETSC_COPY_VALUES,&issurf);
CHKERRQ(ierr);
ierr = PetscFree3(II,Iint,Isurf);
CHKERRQ(ierr);
ierr = ISSort(is);
CHKERRQ(ierr);
ierr = MatGetSubMatrices(Aglobal,1,&is,&is,MAT_INITIAL_MATRIX,&Aholder);
CHKERRQ(ierr);
A = *Aholder;
ierr = PetscFree(Aholder);
CHKERRQ(ierr);
ierr = MatGetSubMatrix(A,isint,isint,MAT_INITIAL_MATRIX,&Aii);
CHKERRQ(ierr);
ierr = MatGetSubMatrix(A,isint,issurf,MAT_INITIAL_MATRIX,&Ais);
CHKERRQ(ierr);
ierr = MatGetSubMatrix(A,issurf,isint,MAT_INITIAL_MATRIX,&Asi);
CHKERRQ(ierr);
/*
Solve for the interpolation onto the interior Xint
*/
ierr = MatMatMult(Ais,Xsurf,MAT_INITIAL_MATRIX,PETSC_DETERMINE,&Xint_tmp);
CHKERRQ(ierr);
ierr = MatScale(Xint_tmp,-1.0);
CHKERRQ(ierr);
if (exotic->directSolve) {
ierr = MatGetFactor(Aii,MATSOLVERPETSC,MAT_FACTOR_LU,&iAii);
CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);
CHKERRQ(ierr);
ierr = MatGetOrdering(Aii,MATORDERINGND,&row,&col);
CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(iAii,Aii,row,col,&info);
CHKERRQ(ierr);
ierr = ISDestroy(&row);
CHKERRQ(ierr);
ierr = ISDestroy(&col);
CHKERRQ(ierr);
ierr = MatLUFactorNumeric(iAii,Aii,&info);
CHKERRQ(ierr);
ierr = MatMatSolve(iAii,Xint_tmp,Xint);
CHKERRQ(ierr);
ierr = MatDestroy(&iAii);
CHKERRQ(ierr);
} else {
Vec b,x;
PetscScalar *xint_tmp;
ierr = MatDenseGetArray(Xint,&xint);
CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&x);
CHKERRQ(ierr);
ierr = MatDenseGetArray(Xint_tmp,&xint_tmp);
CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&b);
CHKERRQ(ierr);
ierr = KSPSetOperators(exotic->ksp,Aii,Aii);
CHKERRQ(ierr);
for (i=0; i<6; i++) {
ierr = VecPlaceArray(x,xint+i*Nint);
CHKERRQ(ierr);
ierr = VecPlaceArray(b,xint_tmp+i*Nint);
CHKERRQ(ierr);
ierr = KSPSolve(exotic->ksp,b,x);
CHKERRQ(ierr);
ierr = VecResetArray(x);
CHKERRQ(ierr);
ierr = VecResetArray(b);
CHKERRQ(ierr);
}
ierr = MatDenseRestoreArray(Xint,&xint);
CHKERRQ(ierr);
ierr = MatDenseRestoreArray(Xint_tmp,&xint_tmp);
CHKERRQ(ierr);
ierr = VecDestroy(&x);
CHKERRQ(ierr);
ierr = VecDestroy(&b);
CHKERRQ(ierr);
}
ierr = MatDestroy(&Xint_tmp);
CHKERRQ(ierr);
#if defined(PETSC_USE_DEBUG_foo)
ierr = MatDenseGetArray(Xint,&xint);
CHKERRQ(ierr);
for (i=0; i<Nint; i++) {
tmp = 0.0;
for (j=0; j<6; j++) tmp += xint[i+j*Nint];
if (PetscAbsScalar(tmp-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong Xint interpolation at i %D value %g",i,(double)PetscAbsScalar(tmp));
}
ierr = MatDenseRestoreArray(Xint,&xint);
CHKERRQ(ierr);
/* ierr =MatView(Xint,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */
#endif
/* total faces */
Ntotal = mp*np*(pp+1) + mp*pp*(np+1) + np*pp*(mp+1);
/*
For each vertex, edge, face on process (in the same orderings as used above) determine its local number including ghost points
*/
cnt = 0;
{
gl[cnt++] = mwidth+1;
}
{
{
gl[cnt++] = mwidth*nwidth+1;
}
{
gl[cnt++] = mwidth*nwidth + mwidth; /* these are the interior nodes */ gl[cnt++] = mwidth*nwidth + mwidth+m-istart-1;
}
{
gl[cnt++] = mwidth*nwidth+mwidth*(n-jstart-1)+1;
}
}
{
gl[cnt++] = mwidth*nwidth*(p-kstart-1) + mwidth+1;
}
/* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
/* convert that to global numbering and get them on all processes */
ierr = ISLocalToGlobalMappingApply(ltg,6,gl,gl);
CHKERRQ(ierr);
/* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
ierr = PetscMalloc1(6*mp*np*pp,&globals);
CHKERRQ(ierr);
ierr = MPI_Allgather(gl,6,MPIU_INT,globals,6,MPIU_INT,PetscObjectComm((PetscObject)da));
CHKERRQ(ierr);
/* Number the coarse grid points from 0 to Ntotal */
ierr = MatGetSize(Aglobal,&Nt,NULL);
CHKERRQ(ierr);
ierr = PetscTableCreate(Ntotal/3,Nt+1,&ht);
CHKERRQ(ierr);
for (i=0; i<6*mp*np*pp; i++) {
ierr = PetscTableAddCount(ht,globals[i]+1);
CHKERRQ(ierr);
}
ierr = PetscTableGetCount(ht,&cnt);
CHKERRQ(ierr);
if (cnt != Ntotal) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Hash table size %D not equal to total number coarse grid points %D",cnt,Ntotal);
ierr = PetscFree(globals);
CHKERRQ(ierr);
for (i=0; i<6; i++) {
ierr = PetscTableFind(ht,gl[i]+1,&gl[i]);
CHKERRQ(ierr);
gl[i]--;
}
ierr = PetscTableDestroy(&ht);
CHKERRQ(ierr);
/* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
/* construct global interpolation matrix */
ierr = MatGetLocalSize(Aglobal,&Ng,NULL);
CHKERRQ(ierr);
if (reuse == MAT_INITIAL_MATRIX) {
ierr = MatCreateAIJ(PetscObjectComm((PetscObject)da),Ng,PETSC_DECIDE,PETSC_DECIDE,Ntotal,Nint+Nsurf,NULL,Nint,NULL,P);
CHKERRQ(ierr);
} else {
ierr = MatZeroEntries(*P);
CHKERRQ(ierr);
}
ierr = MatSetOption(*P,MAT_ROW_ORIENTED,PETSC_FALSE);
CHKERRQ(ierr);
ierr = MatDenseGetArray(Xint,&xint);
CHKERRQ(ierr);
ierr = MatSetValues(*P,Nint,IIint,6,gl,xint,INSERT_VALUES);
CHKERRQ(ierr);
ierr = MatDenseRestoreArray(Xint,&xint);
CHKERRQ(ierr);
ierr = MatDenseGetArray(Xsurf,&xsurf);
CHKERRQ(ierr);
ierr = MatSetValues(*P,Nsurf,IIsurf,6,gl,xsurf,INSERT_VALUES);
CHKERRQ(ierr);
ierr = MatDenseRestoreArray(Xsurf,&xsurf);
CHKERRQ(ierr);
ierr = MatAssemblyBegin(*P,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(*P,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = PetscFree2(IIint,IIsurf);
CHKERRQ(ierr);
#if defined(PETSC_USE_DEBUG_foo)
{
Vec x,y;
PetscScalar *yy;
ierr = VecCreateMPI(PetscObjectComm((PetscObject)da),Ng,PETSC_DETERMINE,&y);
CHKERRQ(ierr);
ierr = VecCreateMPI(PetscObjectComm((PetscObject)da),PETSC_DETERMINE,Ntotal,&x);
CHKERRQ(ierr);
ierr = VecSet(x,1.0);
CHKERRQ(ierr);
ierr = MatMult(*P,x,y);
CHKERRQ(ierr);
ierr = VecGetArray(y,&yy);
CHKERRQ(ierr);
for (i=0; i<Ng; i++) {
if (PetscAbsScalar(yy[i]-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong p interpolation at i %D value %g",i,(double)PetscAbsScalar(yy[i]));
}
ierr = VecRestoreArray(y,&yy);
CHKERRQ(ierr);
ierr = VecDestroy(x);
CHKERRQ(ierr);
ierr = VecDestroy(y);
CHKERRQ(ierr);
}
#endif
ierr = MatDestroy(&Aii);
CHKERRQ(ierr);
ierr = MatDestroy(&Ais);
CHKERRQ(ierr);
ierr = MatDestroy(&Asi);
CHKERRQ(ierr);
ierr = MatDestroy(&A);
CHKERRQ(ierr);
ierr = ISDestroy(&is);
CHKERRQ(ierr);
ierr = ISDestroy(&isint);
CHKERRQ(ierr);
ierr = ISDestroy(&issurf);
CHKERRQ(ierr);
ierr = MatDestroy(&Xint);
CHKERRQ(ierr);
ierr = MatDestroy(&Xsurf);
CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
PetscMPIInt size;
PetscErrorCode ierr;
Vec x,y,b,s1,s2;
Mat A; /* linear system matrix */
Mat sA,sB,sC; /* symmetric part of the matrices */
PetscInt n,mbs=16,bs=1,nz=3,prob=1,i,j,k1,k2,col[3],lf,block, row,Ii,J,n1,inc;
PetscReal norm1,norm2,rnorm,tol=PETSC_SMALL;
PetscScalar neg_one = -1.0,four=4.0,value[3];
IS perm, iscol;
PetscRandom rdm;
PetscBool doIcc=PETSC_TRUE,equal;
MatInfo minfo1,minfo2;
MatFactorInfo factinfo;
MatType type;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
ierr = PetscOptionsGetInt(NULL,"-bs",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
n = mbs*bs;
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQBAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSeqBAIJSetPreallocation(A,bs,nz,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_SELF,&sA);CHKERRQ(ierr);
ierr = MatSetSizes(sA,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(sA,MATSEQSBAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(sA);CHKERRQ(ierr);
ierr = MatGetType(sA,&type);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)sA,MATSEQSBAIJ,&doIcc);CHKERRQ(ierr);
ierr = MatSeqSBAIJSetPreallocation(sA,bs,nz,NULL);CHKERRQ(ierr);
ierr = MatSetOption(sA,MAT_IGNORE_LOWER_TRIANGULAR,PETSC_TRUE);CHKERRQ(ierr);
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(sA,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ format\n");CHKERRQ(ierr);
}
/* Assemble matrix */
if (bs == 1) {
ierr = PetscOptionsGetInt(NULL,"-test_problem",&prob,NULL);CHKERRQ(ierr);
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
value[0]= 0.1; value[1]=-1; value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0;
col[0] = n-1; col[1] = 1; col[2] = 0;
value[0] = 0.1; value[1] = -1.0; value[2] = 2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (PetscInt) (PetscSqrtReal((PetscReal)n) + 0.001);
if (n1*n1 - n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
value[0]=-1.0; value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
value[0]=4.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
col[0]=i; row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatGetInfo() of A and sA */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sA,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("A matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("sA matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error (compare A and sA): MatGetInfo()\n");CHKERRQ(ierr);
}
/* Test MatDuplicate() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&sB);CHKERRQ(ierr);
ierr = MatEqual(sA,sB,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDuplicate()");
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_FROBENIUS,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS, NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_INFINITY,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_1,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
/* Test MatGetInfo(), MatGetSize(), MatGetBlockSize() */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sB,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error(compare A and sB): MatGetInfo()\n");CHKERRQ(ierr);
}
ierr = MatGetSize(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetSize(sB,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
PetscPrintf(PETSC_COMM_SELF,"Error: MatGetSize()\n");CHKERRQ(ierr);
}
ierr = MatGetBlockSize(A, &Ii);CHKERRQ(ierr);
ierr = MatGetBlockSize(sB, &i);CHKERRQ(ierr);
if (i-Ii) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetBlockSize()\n");CHKERRQ(ierr);
}
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s2);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
/* Test MatDiagonalScale(), MatGetDiagonal(), MatScale() */
#if !defined(PETSC_USE_COMPLEX)
/* Scaling matrix with complex numbers results non-spd matrix,
causing crash of MatForwardSolve() and MatBackwardSolve() */
ierr = MatDiagonalScale(A,x,x);CHKERRQ(ierr);
ierr = MatDiagonalScale(sB,x,x);CHKERRQ(ierr);
ierr = MatMultEqual(A,sB,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDiagonalScale");
ierr = MatGetDiagonal(A,s1);CHKERRQ(ierr);
ierr = MatGetDiagonal(sB,s2);CHKERRQ(ierr);
ierr = VecAXPY(s2,neg_one,s1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm1);CHKERRQ(ierr);
if (norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetDiagonal(), ||s1-s2||=%G\n",norm1);CHKERRQ(ierr);
}
{
PetscScalar alpha=0.1;
ierr = MatScale(A,alpha);CHKERRQ(ierr);
ierr = MatScale(sB,alpha);CHKERRQ(ierr);
}
#endif
/* Test MatGetRowMaxAbs() */
ierr = MatGetRowMaxAbs(A,s1,NULL);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(sB,s2,NULL);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetRowMaxAbs() \n");CHKERRQ(ierr);
}
/* Test MatMult() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = MatMult(A,x,s1);CHKERRQ(ierr);
ierr = MatMult(sB,x,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
}
}
/* MatMultAdd() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(y,rdm);CHKERRQ(ierr);
ierr = MatMultAdd(A,x,y,s1);CHKERRQ(ierr);
ierr = MatMultAdd(sB,x,y,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatMultAdd(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
}
}
/* Test MatCholeskyFactor(), MatICCFactor() with natural ordering */
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iscol);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
norm1 = tol;
inc = bs;
/* initialize factinfo */
ierr = PetscMemzero(&factinfo,sizeof(MatFactorInfo));CHKERRQ(ierr);
for (lf=-1; lf<10; lf += inc) {
if (lf==-1) { /* Cholesky factor of sB (duplicate sA) */
factinfo.fill = 5.0;
ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
} else if (!doIcc) break;
else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lf;
ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,sB,&factinfo);CHKERRQ(ierr);
/* MatView(sC, PETSC_VIEWER_DRAW_WORLD); */
/* test MatGetDiagonal on numeric factor */
/*
if (lf == -1) {
ierr = MatGetDiagonal(sC,s1);CHKERRQ(ierr);
printf(" in ex74.c, diag: \n");
ierr = VecView(s1,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
*/
ierr = MatMult(sB,x,b);CHKERRQ(ierr);
/* test MatForwardSolve() and MatBackwardSolve() */
if (lf == -1) {
ierr = MatForwardSolve(sC,b,s1);CHKERRQ(ierr);
ierr = MatBackwardSolve(sC,s1,s2);CHKERRQ(ierr);
ierr = VecAXPY(s2,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&norm2);CHKERRQ(ierr);
if (10*norm1 < norm2) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%G, bs=%d\n",norm2,bs);CHKERRQ(ierr);
}
}
/* test MatSolve() */
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
/* printf("lf: %d, error: %G\n", lf,norm2); */
if (10*norm1 < norm2 && lf-inc != -1) {
ierr = PetscPrintf(PETSC_COMM_SELF,"lf=%D, %D, Norm of error=%G, %G\n",lf-inc,lf,norm1,norm2);CHKERRQ(ierr);
}
norm1 = norm2;
if (norm2 < tol && lf != -1) break;
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sB);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
const int iM11=0, iM12=1, iL11=2, iL22=3, iL21=4, ix=5;
Mat M11,M12,L11,L22,L21; /* matrix */
Vec x,y; /* input and output vectors */
Vec omg1,omg2,omg3,omg4; /* temporary vectors for the operation y=Ax */
KSP ksp; /* linear solver context */
PetscViewer fd[5]; /* viewer */
char file[6][PETSC_MAX_PATH_LEN]; /* input file name */
PetscErrorCode ierr;
PetscInt M, N; /* number of rows and columns of the GLOBAL matrices (they should be the same) */
PetscInt m, n; /* number of rows and columns of the LOCAL matrices */
PetscInt istart, iend; /* ownership row range of the process using GLOBAL indexes */
PetscScalar one=1.0;
PetscMPIInt rank, size;
PetscBool flg[6];
PetscInitialize(&argc,&args,(char *)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
PetscPrintf(PETSC_COMM_WORLD, "Number of processes size=%d\n", size);
// ************ READ MATRICES AND VECTOR x FROM INPUT *****
// M11 and M12
ierr = PetscOptionsGetString(PETSC_NULL,"-m11",file[iM11],PETSC_MAX_PATH_LEN,&flg[iM11]);CHKERRQ(ierr);
ierr = PetscOptionsGetString(PETSC_NULL,"-m12",file[iM12],PETSC_MAX_PATH_LEN,&flg[iM12]);CHKERRQ(ierr);
// L11 L22 and L21
ierr = PetscOptionsGetString(PETSC_NULL,"-l11",file[iL11],PETSC_MAX_PATH_LEN,&flg[iL11]);CHKERRQ(ierr);
ierr = PetscOptionsGetString(PETSC_NULL,"-l22",file[iL22],PETSC_MAX_PATH_LEN,&flg[iL22]);CHKERRQ(ierr);
ierr = PetscOptionsGetString(PETSC_NULL,"-l21",file[iL21],PETSC_MAX_PATH_LEN,&flg[iL21]);CHKERRQ(ierr);
// All of the matrix have to be defined by the user.
// If the user don't specify none of them, it will generate laplacian matrices.
if (flg[iM11] && flg[iM12] && flg[iL11] && flg[iL22] && flg[iL21]){
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[iM11],FILE_MODE_READ,\
&fd[iM11]);CHKERRQ(ierr);
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[iM12],FILE_MODE_READ,\
&fd[iM12]);CHKERRQ(ierr);
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[iL11],FILE_MODE_READ,\
&fd[iL11]);CHKERRQ(ierr);
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[iL22],FILE_MODE_READ,\
&fd[iL22]);CHKERRQ(ierr);
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[iL21],FILE_MODE_READ,\
&fd[iL21]);CHKERRQ(ierr);
// Load the matrix and vector; then destroy the viewer.
// M11 and M12
ierr = MatCreate(PETSC_COMM_WORLD,&M11);CHKERRQ(ierr);
ierr = MatSetType(M11,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(M11);CHKERRQ(ierr);
ierr = MatLoad(M11,fd[iM11]);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&M12);CHKERRQ(ierr);
ierr = MatSetType(M12,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(M12);CHKERRQ(ierr);
ierr = MatLoad(M12,fd[iM12]);CHKERRQ(ierr);
// L11 L22 and L21
ierr = MatCreate(PETSC_COMM_WORLD,&L11);CHKERRQ(ierr);
ierr = MatSetType(L11,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(L11);CHKERRQ(ierr);
ierr = MatLoad(L11,fd[iL11]);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&L22);CHKERRQ(ierr);
ierr = MatSetType(L22,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(L22);CHKERRQ(ierr);
ierr = MatLoad(L22,fd[iL22]);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&L21);CHKERRQ(ierr);
ierr = MatSetType(L21,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(L21);CHKERRQ(ierr);
ierr = MatLoad(L21,fd[iL21]);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd[iM11]);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd[iM12]);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd[iL11]);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd[iL22]);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd[iL21]);CHKERRQ(ierr);
}
else if(!flg[iM11] && !flg[iM12] && !flg[iL11] && !flg[iL22] && !flg[iL21]){
// ******************* CREATING FAKE MATRICES *****************
PetscInt i,col[3];
M = N = 100;
PetscScalar value[3];
ierr = MatCreate(PETSC_COMM_WORLD,&M11);CHKERRQ(ierr);
ierr = MatSetSizes(M11,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(M11);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&M12);CHKERRQ(ierr);
ierr = MatSetSizes(M12,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(M12);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&L11);CHKERRQ(ierr);
ierr = MatSetSizes(L11,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(L11);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&L22);CHKERRQ(ierr);
ierr = MatSetSizes(L22,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(L22);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&L21);CHKERRQ(ierr);
ierr = MatSetSizes(L21,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(L21);CHKERRQ(ierr);
// Set values for them
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=1; i<M-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(M11,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(M12,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(L11,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(L22,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(L21,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = N - 1; col[0] = N - 2; col[1] = N - 1;
ierr = MatSetValues(M11,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(M12,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(L11,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(L22,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(L21,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
ierr = MatSetValues(M11,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(M12,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(L11,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(L22,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(L21,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(M11,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M11,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(M12,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M12,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(L11,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(L11,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(L22,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(L22,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(L21,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(L21,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
// ******************** END CREATING FAKE MATRICES *************
}
else{
SETERRQ(PETSC_COMM_WORLD,1,"You must either indicate the ascii file for each matrix M11 M12 L11 L22 L21 using the option -m11 -m12 .... or without any of these options.");
PetscFinalize();
return 1;
}
// Get some information about the partitioning of the matrix
ierr = MatGetSize(M11,&M,&N);CHKERRQ(ierr);
printf("Global dimension of the matrix M11 M=%d N=%d\n",M,N);
ierr = MatGetLocalSize(M11,&m,&n);
printf("Local dimension of the matrix M11 m=%d n=%d\n",m,n);
ierr = MatGetOwnershipRange(M11,&istart,&iend);
printf("Ownership range of the rows for process %d istart=%d iend=%d\n",rank,istart,iend);
// Read vector x from input. If it's not specified by the user, the vector x will be a unitary vector.
ierr = PetscOptionsGetString(PETSC_NULL,"-x",file[ix],PETSC_MAX_PATH_LEN,&flg[ix]);CHKERRQ(ierr);
if(!flg[ix]){
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,PETSC_DECIDE,M);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecSet(x,one);CHKERRQ(ierr);
/*ierr = VecAssemblyBegin(x);CHKERRQ(ierr);*/
/*ierr = VecAssemblyEnd(x);CHKERRQ(ierr);*/
}
else{
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[ix],FILE_MODE_READ,&fd[ix]);CHKERRQ(ierr);
ierr = VecLoad(x,fd[ix]);CHKERRQ(ierr);
}
ierr = PetscObjectSetName((PetscObject) x, "The input vector");CHKERRQ(ierr);
// ************ END READ MATRICES AND VECTOR x FROM INPUT *****
// Create the temporary vectors and y
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecDuplicate(x,&omg1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&omg2);CHKERRQ(ierr);
ierr = VecDuplicate(x,&omg3);CHKERRQ(ierr);
ierr = VecDuplicate(x,&omg4);CHKERRQ(ierr);
// ****************** COMPUTE y=Ax *******************
// Set the Krylov object
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
// Set operators. Here the matrix that defines the linear system
// also serves as the preconditioning matrix.
ierr = KSPSetOperators(ksp,L22,L22,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
// Set runtime options, e.g.,
// -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
// These options will override those specified above as long as
// KSPSetFromOptions() is called _after_ any other customization
// routines.
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
// Multiplication y = A*x
// omg1 = M11*x
// omg2 = L21*x
// L22*omg3 = omg2
// omg4 = omg1 + M12*omg3
// L11*y = omg4
ierr = MatMult(M11, x, omg1);CHKERRQ(ierr);
ierr = MatMult(L21, x, omg2);CHKERRQ(ierr);
ierr = KSPSolve(ksp,omg2,omg3);CHKERRQ(ierr);
ierr = MatMult(M12, omg3, omg4);CHKERRQ(ierr);
ierr = VecAXPY(omg4, one, omg1);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,L11,L11,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSolve(ksp,omg4,y);CHKERRQ(ierr);
// ****************** END COMPUTE y=Ax **************************
/*ierr = VecView(y, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);*/
PetscBool test = PETSC_FALSE;
ierr = PetscOptionsGetBool(PETSC_NULL,"-test",&test,PETSC_NULL);CHKERRQ(ierr);
if(test){
// ******************** TESTING *********************************
// the testing doesn't work if the number of process are more than one
// because the type of the matrices must be different from matmpiaij. Let's try matseqaij
Mat L11_inv, L22_inv, I;
Mat A;
Mat M11_d;
Vec y2;
PetscInt i;
PetscScalar val;
// Create identity matrix
ierr = MatCreate(PETSC_COMM_WORLD,&I);CHKERRQ(ierr);
ierr = MatSetType(I, MATDENSE);
ierr = MatSetSizes(I,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(I);CHKERRQ(ierr);
val = 1.0;
for (i=0; i<M; i++) {
ierr = MatSetValues(I,1,&i,1,&i,&val,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(I,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(I,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
// Create L11_inv
ierr = MatCreate(PETSC_COMM_WORLD,&L11_inv);CHKERRQ(ierr);
ierr = MatSetType(L11_inv, MATDENSE);
ierr = MatSetSizes(L11_inv,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(L11_inv);CHKERRQ(ierr);
ierr = MatAssemblyBegin(L11_inv,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(L11_inv,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
// Create L22_inv
ierr = MatCreate(PETSC_COMM_WORLD,&L22_inv);CHKERRQ(ierr);
ierr = MatSetType(L22_inv, MATDENSE);
ierr = MatSetSizes(L22_inv,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(L22_inv);CHKERRQ(ierr);
ierr = MatAssemblyBegin(L22_inv,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(L22_inv,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
// Create A
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
// Define M11_d
ierr = MatCreate(PETSC_COMM_WORLD,&M11_d);CHKERRQ(ierr);
ierr = MatSetType(M11_d, MATDENSE);
ierr = MatSetSizes(M11_d,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(M11_d);CHKERRQ(ierr);
ierr = MatAssemblyBegin(M11_d,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(M11_d,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
// Calculate A = L11^{-1}*(M11 + M12*L22^{-1}*L21)
IS perm, iperm;
MatFactorInfo info;
ierr = MatGetOrdering(L11,MATORDERINGNATURAL,&perm,&iperm);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info); CHKERRQ(ierr);
ierr = MatLUFactor(L11, perm, iperm, &info); CHKERRQ(ierr);
ierr = MatMatSolve(L11, I, L11_inv);CHKERRQ(ierr);
// TODO try to convert L11_inv to be sparse such as matseqaij
// ierr = MatView(L11_inv, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = MatGetOrdering(L22,MATORDERINGNATURAL,&perm,&iperm);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info); CHKERRQ(ierr);
ierr = MatLUFactor(L22, perm, iperm, &info); CHKERRQ(ierr);
ierr = MatMatSolve(L22, I, L22_inv);CHKERRQ(ierr);
ierr = MatMatMult(M12, L22_inv, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &A);CHKERRQ(ierr);
ierr = MatMatMult(A, L21, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &A);CHKERRQ(ierr);
ierr = MatConvert(M11, MATDENSE, MAT_INITIAL_MATRIX, &M11_d);
ierr = MatAXPY(A,1.0,M11_d,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatMatMult(L11_inv, A, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &A);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y2);CHKERRQ(ierr);
ierr = MatMult(A, x, y2);CHKERRQ(ierr);
/*ierr = VecView(y2, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);*/
// Check the error
PetscReal norm;
ierr = VecAXPY(y2,-1.0,y);CHKERRQ(ierr);
ierr = VecNorm(y2,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A\n",
norm);CHKERRQ(ierr);
// ******************** END TESTING *****************************
}
PetscFinalize();
return 0;
}