/*
Mm_ratio - ration of grid lines between fine and coarse grids.
*/
int main(int argc,char **argv)
{
PetscErrorCode ierr;
AppCtx user;
PetscInt Npx=PETSC_DECIDE,Npy=PETSC_DECIDE,Npz=PETSC_DECIDE;
PetscMPIInt size,rank;
PetscInt m,n,M,N,i,nrows;
PetscScalar one = 1.0;
PetscReal fill=2.0;
Mat A,A_tmp,P,C,C1,C2;
PetscScalar *array,none = -1.0,alpha;
Vec x,v1,v2,v3,v4;
PetscReal norm,norm_tmp,norm_tmp1,tol=100.*PETSC_MACHINE_EPSILON;
PetscRandom rdm;
PetscBool Test_MatMatMult=PETSC_TRUE,Test_MatPtAP=PETSC_TRUE,Test_3D=PETSC_TRUE,flg;
const PetscInt *ia,*ja;
ierr = PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
ierr = PetscOptionsGetReal(NULL,NULL,"-tol",&tol,NULL);CHKERRQ(ierr);
user.ratio = 2;
user.coarse.mx = 20; user.coarse.my = 20; user.coarse.mz = 20;
ierr = PetscOptionsGetInt(NULL,NULL,"-Mx",&user.coarse.mx,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-My",&user.coarse.my,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-Mz",&user.coarse.mz,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-ratio",&user.ratio,NULL);CHKERRQ(ierr);
if (user.coarse.mz) Test_3D = PETSC_TRUE;
user.fine.mx = user.ratio*(user.coarse.mx-1)+1;
user.fine.my = user.ratio*(user.coarse.my-1)+1;
user.fine.mz = user.ratio*(user.coarse.mz-1)+1;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-Npx",&Npx,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-Npy",&Npy,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-Npz",&Npz,NULL);CHKERRQ(ierr);
/* Set up distributed array for fine grid */
if (!Test_3D) {
ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.fine.mx,user.fine.my,Npx,Npy,1,1,NULL,NULL,&user.fine.da);CHKERRQ(ierr);
} else {
ierr = DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.fine.mx,user.fine.my,user.fine.mz,Npx,Npy,Npz,1,1,NULL,NULL,NULL,&user.fine.da);CHKERRQ(ierr);
}
ierr = DMSetFromOptions(user.fine.da);CHKERRQ(ierr);
ierr = DMSetUp(user.fine.da);CHKERRQ(ierr);
/* Test DMCreateMatrix() */
/*------------------------------------------------------------*/
ierr = DMSetMatType(user.fine.da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(user.fine.da,&A);CHKERRQ(ierr);
ierr = DMSetMatType(user.fine.da,MATBAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(user.fine.da,&C);CHKERRQ(ierr);
ierr = MatConvert(C,MATAIJ,MAT_INITIAL_MATRIX,&A_tmp);CHKERRQ(ierr); /* not work for mpisbaij matrix! */
ierr = MatEqual(A,A_tmp,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"A != C");
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&A_tmp);CHKERRQ(ierr);
/*------------------------------------------------------------*/
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
ierr = MatGetSize(A,&M,&N);CHKERRQ(ierr);
/* if (!rank) printf("A %d, %d\n",M,N); */
/* set val=one to A */
if (size == 1) {
ierr = MatGetRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg);CHKERRQ(ierr);
if (flg) {
ierr = MatSeqAIJGetArray(A,&array);CHKERRQ(ierr);
for (i=0; i<ia[nrows]; i++) array[i] = one;
ierr = MatSeqAIJRestoreArray(A,&array);CHKERRQ(ierr);
}
ierr = MatRestoreRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg);CHKERRQ(ierr);
} else {
Mat AA,AB;
ierr = MatMPIAIJGetSeqAIJ(A,&AA,&AB,NULL);CHKERRQ(ierr);
ierr = MatGetRowIJ(AA,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg);CHKERRQ(ierr);
if (flg) {
ierr = MatSeqAIJGetArray(AA,&array);CHKERRQ(ierr);
for (i=0; i<ia[nrows]; i++) array[i] = one;
ierr = MatSeqAIJRestoreArray(AA,&array);CHKERRQ(ierr);
}
ierr = MatRestoreRowIJ(AA,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg);CHKERRQ(ierr);
ierr = MatGetRowIJ(AB,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg);CHKERRQ(ierr);
if (flg) {
ierr = MatSeqAIJGetArray(AB,&array);CHKERRQ(ierr);
for (i=0; i<ia[nrows]; i++) array[i] = one;
ierr = MatSeqAIJRestoreArray(AB,&array);CHKERRQ(ierr);
}
ierr = MatRestoreRowIJ(AB,0,PETSC_FALSE,PETSC_FALSE,&nrows,&ia,&ja,&flg);CHKERRQ(ierr);
}
/* ierr = MatView(A, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */
/* Set up distributed array for coarse grid */
if (!Test_3D) {
ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.coarse.mx,user.coarse.my,Npx,Npy,1,1,NULL,NULL,&user.coarse.da);CHKERRQ(ierr);
} else {
ierr = DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.coarse.mx,user.coarse.my,user.coarse.mz,Npx,Npy,Npz,
1,1,NULL,NULL,NULL,&user.coarse.da);CHKERRQ(ierr);
}
ierr = DMSetFromOptions(user.coarse.da);CHKERRQ(ierr);
ierr = DMSetUp(user.coarse.da);CHKERRQ(ierr);
/* Create interpolation between the fine and coarse grids */
ierr = DMCreateInterpolation(user.coarse.da,user.fine.da,&P,NULL);CHKERRQ(ierr);
ierr = MatGetLocalSize(P,&m,&n);CHKERRQ(ierr);
ierr = MatGetSize(P,&M,&N);CHKERRQ(ierr);
/* if (!rank) printf("P %d, %d\n",M,N); */
/* Create vectors v1 and v2 that are compatible with A */
ierr = VecCreate(PETSC_COMM_WORLD,&v1);CHKERRQ(ierr);
ierr = MatGetLocalSize(A,&m,NULL);CHKERRQ(ierr);
ierr = VecSetSizes(v1,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(v1);CHKERRQ(ierr);
ierr = VecDuplicate(v1,&v2);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
/* Test MatMatMult(): C = A*P */
/*----------------------------*/
if (Test_MatMatMult) {
ierr = MatDuplicate(A,MAT_COPY_VALUES,&A_tmp);CHKERRQ(ierr);
ierr = MatMatMult(A_tmp,P,MAT_INITIAL_MATRIX,fill,&C);CHKERRQ(ierr);
/* Test MAT_REUSE_MATRIX - reuse symbolic C */
alpha=1.0;
for (i=0; i<2; i++) {
alpha -= 0.1;
ierr = MatScale(A_tmp,alpha);CHKERRQ(ierr);
ierr = MatMatMult(A_tmp,P,MAT_REUSE_MATRIX,fill,&C);CHKERRQ(ierr);
}
/* Free intermediate data structures created for reuse of C=Pt*A*P */
ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
/* Test MatDuplicate() */
/*----------------------------*/
ierr = MatDuplicate(C,MAT_COPY_VALUES,&C1);CHKERRQ(ierr);
ierr = MatDuplicate(C1,MAT_COPY_VALUES,&C2);CHKERRQ(ierr);
ierr = MatDestroy(&C1);CHKERRQ(ierr);
ierr = MatDestroy(&C2);CHKERRQ(ierr);
/* Create vector x that is compatible with P */
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = MatGetLocalSize(P,NULL,&n);CHKERRQ(ierr);
ierr = VecSetSizes(x,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
norm = 0.0;
for (i=0; i<10; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = MatMult(P,x,v1);CHKERRQ(ierr);
ierr = MatMult(A_tmp,v1,v2);CHKERRQ(ierr); /* v2 = A*P*x */
ierr = MatMult(C,x,v1);CHKERRQ(ierr); /* v1 = C*x */
ierr = VecAXPY(v1,none,v2);CHKERRQ(ierr);
ierr = VecNorm(v1,NORM_1,&norm_tmp);CHKERRQ(ierr);
ierr = VecNorm(v2,NORM_1,&norm_tmp1);CHKERRQ(ierr);
norm_tmp /= norm_tmp1;
if (norm_tmp > norm) norm = norm_tmp;
}
if (norm >= tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMatMult(), |v1 - v2|/|v2|: %g\n",(double)norm);CHKERRQ(ierr);
}
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&A_tmp);CHKERRQ(ierr);
}
/* Test P^T * A * P - MatPtAP() */
/*------------------------------*/
if (Test_MatPtAP) {
ierr = MatPtAP(A,P,MAT_INITIAL_MATRIX,fill,&C);CHKERRQ(ierr);
ierr = MatGetLocalSize(C,&m,&n);CHKERRQ(ierr);
/* Test MAT_REUSE_MATRIX - reuse symbolic C */
alpha=1.0;
for (i=0; i<1; i++) {
alpha -= 0.1;
ierr = MatScale(A,alpha);CHKERRQ(ierr);
ierr = MatPtAP(A,P,MAT_REUSE_MATRIX,fill,&C);CHKERRQ(ierr);
}
/* Free intermediate data structures created for reuse of C=Pt*A*P */
ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
/* Test MatDuplicate() */
/*----------------------------*/
ierr = MatDuplicate(C,MAT_COPY_VALUES,&C1);CHKERRQ(ierr);
ierr = MatDuplicate(C1,MAT_COPY_VALUES,&C2);CHKERRQ(ierr);
ierr = MatDestroy(&C1);CHKERRQ(ierr);
ierr = MatDestroy(&C2);CHKERRQ(ierr);
/* Create vector x that is compatible with P */
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = MatGetLocalSize(P,&m,&n);CHKERRQ(ierr);
ierr = VecSetSizes(x,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&v3);CHKERRQ(ierr);
ierr = VecSetSizes(v3,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(v3);CHKERRQ(ierr);
ierr = VecDuplicate(v3,&v4);CHKERRQ(ierr);
norm = 0.0;
for (i=0; i<10; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = MatMult(P,x,v1);CHKERRQ(ierr);
ierr = MatMult(A,v1,v2);CHKERRQ(ierr); /* v2 = A*P*x */
ierr = MatMultTranspose(P,v2,v3);CHKERRQ(ierr); /* v3 = Pt*A*P*x */
ierr = MatMult(C,x,v4);CHKERRQ(ierr); /* v3 = C*x */
ierr = VecAXPY(v4,none,v3);CHKERRQ(ierr);
ierr = VecNorm(v4,NORM_1,&norm_tmp);CHKERRQ(ierr);
ierr = VecNorm(v3,NORM_1,&norm_tmp1);CHKERRQ(ierr);
norm_tmp /= norm_tmp1;
if (norm_tmp > norm) norm = norm_tmp;
}
if (norm >= tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatPtAP(), |v3 - v4|/|v3|: %g\n",(double)norm);CHKERRQ(ierr);
}
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = VecDestroy(&v3);CHKERRQ(ierr);
ierr = VecDestroy(&v4);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
}
/* Clean up */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = VecDestroy(&v1);CHKERRQ(ierr);
ierr = VecDestroy(&v2);CHKERRQ(ierr);
ierr = DMDestroy(&user.fine.da);CHKERRQ(ierr);
ierr = DMDestroy(&user.coarse.da);CHKERRQ(ierr);
ierr = MatDestroy(&P);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
/*
PCISSetUp -
*/
PetscErrorCode PCISSetUp(PC pc, PetscBool computesolvers)
{
PC_IS *pcis = (PC_IS*)(pc->data);
Mat_IS *matis;
MatReuse reuse;
PetscErrorCode ierr;
PetscBool flg,issbaij;
Vec counter;
PetscFunctionBegin;
ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"Preconditioner type of Neumann Neumman requires matrix of type MATIS");
matis = (Mat_IS*)pc->pmat->data;
/* first time creation, get info on substructuring */
if (!pc->setupcalled) {
PetscInt n_I;
PetscInt *idx_I_local,*idx_B_local,*idx_I_global,*idx_B_global;
PetscBT bt;
PetscInt i,j;
/* get info on mapping */
ierr = PetscObjectReference((PetscObject)pc->pmat->rmap->mapping);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingDestroy(&pcis->mapping);CHKERRQ(ierr);
pcis->mapping = pc->pmat->rmap->mapping;
ierr = ISLocalToGlobalMappingGetSize(pcis->mapping,&pcis->n);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingGetInfo(pcis->mapping,&(pcis->n_neigh),&(pcis->neigh),&(pcis->n_shared),&(pcis->shared));CHKERRQ(ierr);
/* Identifying interior and interface nodes, in local numbering */
ierr = PetscBTCreate(pcis->n,&bt);CHKERRQ(ierr);
for (i=0;i<pcis->n_neigh;i++)
for (j=0;j<pcis->n_shared[i];j++) {
ierr = PetscBTSet(bt,pcis->shared[i][j]);CHKERRQ(ierr);
}
/* Creating local and global index sets for interior and inteface nodes. */
ierr = PetscMalloc1(pcis->n,&idx_I_local);CHKERRQ(ierr);
ierr = PetscMalloc1(pcis->n,&idx_B_local);CHKERRQ(ierr);
for (i=0, pcis->n_B=0, n_I=0; i<pcis->n; i++) {
if (!PetscBTLookup(bt,i)) {
idx_I_local[n_I] = i;
n_I++;
} else {
idx_B_local[pcis->n_B] = i;
pcis->n_B++;
}
}
/* Getting the global numbering */
idx_B_global = idx_I_local + n_I; /* Just avoiding allocating extra memory, since we have vacant space */
idx_I_global = idx_B_local + pcis->n_B;
ierr = ISLocalToGlobalMappingApply(pcis->mapping,pcis->n_B,idx_B_local,idx_B_global);CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApply(pcis->mapping,n_I,idx_I_local,idx_I_global);CHKERRQ(ierr);
/* Creating the index sets */
ierr = ISCreateGeneral(PETSC_COMM_SELF,pcis->n_B,idx_B_local,PETSC_COPY_VALUES, &pcis->is_B_local);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,pcis->n_B,idx_B_global,PETSC_COPY_VALUES,&pcis->is_B_global);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,n_I,idx_I_local,PETSC_COPY_VALUES, &pcis->is_I_local);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,n_I,idx_I_global,PETSC_COPY_VALUES,&pcis->is_I_global);CHKERRQ(ierr);
/* Freeing memory */
ierr = PetscFree(idx_B_local);CHKERRQ(ierr);
ierr = PetscFree(idx_I_local);CHKERRQ(ierr);
ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
/* Creating work vectors and arrays */
ierr = VecDuplicate(matis->x,&pcis->vec1_N);CHKERRQ(ierr);
ierr = VecDuplicate(pcis->vec1_N,&pcis->vec2_N);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,pcis->n-pcis->n_B,&pcis->vec1_D);CHKERRQ(ierr);
ierr = VecDuplicate(pcis->vec1_D,&pcis->vec2_D);CHKERRQ(ierr);
ierr = VecDuplicate(pcis->vec1_D,&pcis->vec3_D);CHKERRQ(ierr);
ierr = VecDuplicate(pcis->vec1_D,&pcis->vec4_D);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,pcis->n_B,&pcis->vec1_B);CHKERRQ(ierr);
ierr = VecDuplicate(pcis->vec1_B,&pcis->vec2_B);CHKERRQ(ierr);
ierr = VecDuplicate(pcis->vec1_B,&pcis->vec3_B);CHKERRQ(ierr);
ierr = MatCreateVecs(pc->pmat,&pcis->vec1_global,0);CHKERRQ(ierr);
ierr = PetscMalloc1(pcis->n,&pcis->work_N);CHKERRQ(ierr);
/* scaling vector */
if (!pcis->D) { /* it can happen that the user passed in a scaling vector via PCISSetSubdomainDiagonalScaling */
ierr = VecDuplicate(pcis->vec1_B,&pcis->D);CHKERRQ(ierr);
ierr = VecSet(pcis->D,pcis->scaling_factor);CHKERRQ(ierr);
}
/* Creating the scatter contexts */
ierr = VecScatterCreate(pcis->vec1_N,pcis->is_I_local,pcis->vec1_D,(IS)0,&pcis->N_to_D);CHKERRQ(ierr);
ierr = VecScatterCreate(pcis->vec1_global,pcis->is_I_global,pcis->vec1_D,(IS)0,&pcis->global_to_D);CHKERRQ(ierr);
ierr = VecScatterCreate(pcis->vec1_N,pcis->is_B_local,pcis->vec1_B,(IS)0,&pcis->N_to_B);CHKERRQ(ierr);
ierr = VecScatterCreate(pcis->vec1_global,pcis->is_B_global,pcis->vec1_B,(IS)0,&pcis->global_to_B);CHKERRQ(ierr);
/* map from boundary to local */
ierr = ISLocalToGlobalMappingCreateIS(pcis->is_B_local,&pcis->BtoNmap);CHKERRQ(ierr);
}
/*
Extracting the blocks A_II, A_BI, A_IB and A_BB from A. If the numbering
is such that interior nodes come first than the interface ones, we have
[ A_II | A_IB ]
A = [------+------]
[ A_BI | A_BB ]
*/
reuse = MAT_INITIAL_MATRIX;
if (pcis->reusesubmatrices && pc->setupcalled) {
if (pc->flag == SAME_NONZERO_PATTERN) {
reuse = MAT_REUSE_MATRIX;
} else {
reuse = MAT_INITIAL_MATRIX;
}
}
if (reuse == MAT_INITIAL_MATRIX) {
ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
}
ierr = MatGetSubMatrix(matis->A,pcis->is_I_local,pcis->is_I_local,reuse,&pcis->A_II);CHKERRQ(ierr);
ierr = MatGetSubMatrix(matis->A,pcis->is_B_local,pcis->is_B_local,reuse,&pcis->A_BB);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
if (!issbaij) {
ierr = MatGetSubMatrix(matis->A,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
ierr = MatGetSubMatrix(matis->A,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
} else {
Mat newmat;
ierr = MatConvert(matis->A,MATSEQBAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
ierr = MatGetSubMatrix(newmat,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
ierr = MatGetSubMatrix(newmat,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
ierr = MatDestroy(&newmat);CHKERRQ(ierr);
}
/* Creating scaling vector D */
ierr = PetscOptionsGetBool(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_is_use_stiffness_scaling",&pcis->use_stiffness_scaling,NULL);CHKERRQ(ierr);
if (pcis->use_stiffness_scaling) {
ierr = MatGetDiagonal(pcis->A_BB,pcis->D);CHKERRQ(ierr);
}
ierr = MatCreateVecs(pc->pmat,&counter,0);CHKERRQ(ierr); /* temporary auxiliar vector */
ierr = VecSet(counter,0.0);CHKERRQ(ierr);
ierr = VecScatterBegin(pcis->global_to_B,pcis->D,counter,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterEnd(pcis->global_to_B,pcis->D,counter,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterBegin(pcis->global_to_B,counter,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(pcis->global_to_B,counter,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecPointwiseDivide(pcis->D,pcis->D,pcis->vec1_B);CHKERRQ(ierr);
ierr = VecDestroy(&counter);CHKERRQ(ierr);
/* See historical note 01, at the bottom of this file. */
/* Creating the KSP contexts for the local Dirichlet and Neumann problems */
if (computesolvers) {
PC pc_ctx;
pcis->pure_neumann = matis->pure_neumann;
/* Dirichlet */
ierr = KSPCreate(PETSC_COMM_SELF,&pcis->ksp_D);CHKERRQ(ierr);
ierr = KSPSetErrorIfNotConverged(pcis->ksp_D,pc->erroriffailure);CHKERRQ(ierr);
ierr = PetscObjectIncrementTabLevel((PetscObject)pcis->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
ierr = KSPSetOperators(pcis->ksp_D,pcis->A_II,pcis->A_II);CHKERRQ(ierr);
ierr = KSPSetOptionsPrefix(pcis->ksp_D,"is_localD_");CHKERRQ(ierr);
ierr = KSPGetPC(pcis->ksp_D,&pc_ctx);CHKERRQ(ierr);
ierr = PCSetType(pc_ctx,PCLU);CHKERRQ(ierr);
ierr = KSPSetType(pcis->ksp_D,KSPPREONLY);CHKERRQ(ierr);
ierr = KSPSetFromOptions(pcis->ksp_D);CHKERRQ(ierr);
/* the vectors in the following line are dummy arguments, just telling the KSP the vector size. Values are not used */
ierr = KSPSetUp(pcis->ksp_D);CHKERRQ(ierr);
/* Neumann */
ierr = KSPCreate(PETSC_COMM_SELF,&pcis->ksp_N);CHKERRQ(ierr);
ierr = KSPSetErrorIfNotConverged(pcis->ksp_N,pc->erroriffailure);CHKERRQ(ierr);
ierr = PetscObjectIncrementTabLevel((PetscObject)pcis->ksp_N,(PetscObject)pc,1);CHKERRQ(ierr);
ierr = KSPSetOperators(pcis->ksp_N,matis->A,matis->A);CHKERRQ(ierr);
ierr = KSPSetOptionsPrefix(pcis->ksp_N,"is_localN_");CHKERRQ(ierr);
ierr = KSPGetPC(pcis->ksp_N,&pc_ctx);CHKERRQ(ierr);
ierr = PCSetType(pc_ctx,PCLU);CHKERRQ(ierr);
ierr = KSPSetType(pcis->ksp_N,KSPPREONLY);CHKERRQ(ierr);
ierr = KSPSetFromOptions(pcis->ksp_N);CHKERRQ(ierr);
{
PetscBool damp_fixed = PETSC_FALSE,
remove_nullspace_fixed = PETSC_FALSE,
set_damping_factor_floating = PETSC_FALSE,
not_damp_floating = PETSC_FALSE,
not_remove_nullspace_floating = PETSC_FALSE;
PetscReal fixed_factor,
floating_factor;
ierr = PetscOptionsGetReal(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_damp_fixed",&fixed_factor,&damp_fixed);CHKERRQ(ierr);
if (!damp_fixed) fixed_factor = 0.0;
ierr = PetscOptionsGetBool(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_damp_fixed",&damp_fixed,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_remove_nullspace_fixed",&remove_nullspace_fixed,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_set_damping_factor_floating",
&floating_factor,&set_damping_factor_floating);CHKERRQ(ierr);
if (!set_damping_factor_floating) floating_factor = 0.0;
ierr = PetscOptionsGetBool(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_set_damping_factor_floating",&set_damping_factor_floating,NULL);CHKERRQ(ierr);
if (!set_damping_factor_floating) floating_factor = 1.e-12;
ierr = PetscOptionsGetBool(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_not_damp_floating",¬_damp_floating,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_not_remove_nullspace_floating",¬_remove_nullspace_floating,NULL);CHKERRQ(ierr);
if (pcis->pure_neumann) { /* floating subdomain */
if (!(not_damp_floating)) {
ierr = PCFactorSetShiftType(pc_ctx,MAT_SHIFT_NONZERO);CHKERRQ(ierr);
ierr = PCFactorSetShiftAmount(pc_ctx,floating_factor);CHKERRQ(ierr);
}
if (!(not_remove_nullspace_floating)) {
MatNullSpace nullsp;
ierr = MatNullSpaceCreate(PETSC_COMM_SELF,PETSC_TRUE,0,NULL,&nullsp);CHKERRQ(ierr);
ierr = MatSetNullSpace(matis->A,nullsp);CHKERRQ(ierr);
ierr = MatNullSpaceDestroy(&nullsp);CHKERRQ(ierr);
}
} else { /* fixed subdomain */
if (damp_fixed) {
ierr = PCFactorSetShiftType(pc_ctx,MAT_SHIFT_NONZERO);CHKERRQ(ierr);
ierr = PCFactorSetShiftAmount(pc_ctx,floating_factor);CHKERRQ(ierr);
}
if (remove_nullspace_fixed) {
MatNullSpace nullsp;
ierr = MatNullSpaceCreate(PETSC_COMM_SELF,PETSC_TRUE,0,NULL,&nullsp);CHKERRQ(ierr);
ierr = MatSetNullSpace(matis->A,nullsp);CHKERRQ(ierr);
ierr = MatNullSpaceDestroy(&nullsp);CHKERRQ(ierr);
}
}
}
/* the vectors in the following line are dummy arguments, just telling the KSP the vector size. Values are not used */
ierr = KSPSetUp(pcis->ksp_N);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode MatISGetMPIXAIJ_IS(Mat mat, MatReuse reuse, Mat *M)
{
Mat_IS *matis = (Mat_IS*)(mat->data);
Mat local_mat;
/* info on mat */
PetscInt bs,rows,cols,lrows,lcols;
PetscInt local_rows,local_cols;
PetscBool isdense,issbaij,isseqaij;
PetscMPIInt nsubdomains;
/* values insertion */
PetscScalar *array;
/* work */
PetscErrorCode ierr;
PetscFunctionBegin;
/* get info from mat */
ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&nsubdomains);CHKERRQ(ierr);
if (nsubdomains == 1) {
if (reuse == MAT_INITIAL_MATRIX) {
ierr = MatDuplicate(matis->A,MAT_COPY_VALUES,&(*M));CHKERRQ(ierr);
} else {
ierr = MatCopy(matis->A,*M,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
ierr = MatGetLocalSize(mat,&lrows,&lcols);CHKERRQ(ierr);
ierr = MatGetSize(matis->A,&local_rows,&local_cols);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQDENSE,&isdense);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
if (reuse == MAT_INITIAL_MATRIX) {
MatType new_mat_type;
PetscBool issbaij_red;
/* determining new matrix type */
ierr = MPIU_Allreduce(&issbaij,&issbaij_red,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
if (issbaij_red) {
new_mat_type = MATSBAIJ;
} else {
if (bs>1) {
new_mat_type = MATBAIJ;
} else {
new_mat_type = MATAIJ;
}
}
ierr = MatCreate(PetscObjectComm((PetscObject)mat),M);CHKERRQ(ierr);
ierr = MatSetSizes(*M,lrows,lcols,rows,cols);CHKERRQ(ierr);
ierr = MatSetBlockSize(*M,bs);CHKERRQ(ierr);
ierr = MatSetType(*M,new_mat_type);CHKERRQ(ierr);
ierr = MatISSetMPIXAIJPreallocation_Private(mat,*M,PETSC_FALSE);CHKERRQ(ierr);
} else {
PetscInt mbs,mrows,mcols,mlrows,mlcols;
/* some checks */
ierr = MatGetBlockSize(*M,&mbs);CHKERRQ(ierr);
ierr = MatGetSize(*M,&mrows,&mcols);CHKERRQ(ierr);
ierr = MatGetLocalSize(*M,&mlrows,&mlcols);CHKERRQ(ierr);
if (mrows != rows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix. Wrong number of rows (%d != %d)",rows,mrows);
if (mcols != cols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix. Wrong number of cols (%d != %d)",cols,mcols);
if (mlrows != lrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix. Wrong number of local rows (%d != %d)",lrows,mlrows);
if (mlcols != lcols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix. Wrong number of local cols (%d != %d)",lcols,mlcols);
if (mbs != bs) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix. Wrong block size (%d != %d)",bs,mbs);
ierr = MatZeroEntries(*M);CHKERRQ(ierr);
}
if (issbaij) {
ierr = MatConvert(matis->A,MATSEQBAIJ,MAT_INITIAL_MATRIX,&local_mat);CHKERRQ(ierr);
} else {
ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
local_mat = matis->A;
}
/* Set values */
ierr = MatSetLocalToGlobalMapping(*M,mat->rmap->mapping,mat->cmap->mapping);CHKERRQ(ierr);
if (isdense) { /* special case for dense local matrices */
PetscInt i,*dummy_rows,*dummy_cols;
if (local_rows != local_cols) {
ierr = PetscMalloc2(local_rows,&dummy_rows,local_cols,&dummy_cols);CHKERRQ(ierr);
for (i=0;i<local_rows;i++) dummy_rows[i] = i;
for (i=0;i<local_cols;i++) dummy_cols[i] = i;
} else {
ierr = PetscMalloc1(local_rows,&dummy_rows);CHKERRQ(ierr);
for (i=0;i<local_rows;i++) dummy_rows[i] = i;
dummy_cols = dummy_rows;
}
ierr = MatSetOption(*M,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
ierr = MatDenseGetArray(local_mat,&array);CHKERRQ(ierr);
ierr = MatSetValuesLocal(*M,local_rows,dummy_rows,local_cols,dummy_cols,array,ADD_VALUES);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(local_mat,&array);CHKERRQ(ierr);
if (dummy_rows != dummy_cols) {
ierr = PetscFree2(dummy_rows,dummy_cols);CHKERRQ(ierr);
} else {
ierr = PetscFree(dummy_rows);CHKERRQ(ierr);
}
} else if (isseqaij) {
PetscInt i,nvtxs,*xadj,*adjncy;
PetscBool done;
ierr = MatGetRowIJ(local_mat,0,PETSC_FALSE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&done);CHKERRQ(ierr);
if (!done) SETERRQ1(PetscObjectComm((PetscObject)local_mat),PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
ierr = MatSeqAIJGetArray(local_mat,&array);CHKERRQ(ierr);
for (i=0;i<nvtxs;i++) {
ierr = MatSetValuesLocal(*M,1,&i,xadj[i+1]-xadj[i],adjncy+xadj[i],array+xadj[i],ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatRestoreRowIJ(local_mat,0,PETSC_FALSE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&done);CHKERRQ(ierr);
if (!done) SETERRQ1(PetscObjectComm((PetscObject)local_mat),PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
ierr = MatSeqAIJRestoreArray(local_mat,&array);CHKERRQ(ierr);
} else { /* very basic values insertion for all other matrix types */
PetscInt i;
for (i=0;i<local_rows;i++) {
PetscInt j;
const PetscInt *local_indices_cols;
ierr = MatGetRow(local_mat,i,&j,&local_indices_cols,(const PetscScalar**)&array);CHKERRQ(ierr);
ierr = MatSetValuesLocal(*M,1,&i,j,local_indices_cols,array,ADD_VALUES);CHKERRQ(ierr);
ierr = MatRestoreRow(local_mat,i,&j,&local_indices_cols,(const PetscScalar**)&array);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(*M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatDestroy(&local_mat);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (isdense) {
ierr = MatSetOption(*M,MAT_ROW_ORIENTED,PETSC_TRUE);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscInt main(PetscInt argc,char **args)
{
Mat A,As;
Vec x,y,ys;
PetscTruth flg,disp_mat=PETSC_FALSE,disp_vec=PETSC_FALSE;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt m,i,j;
PetscScalar v,sigma2;
PetscRandom rctx;
PetscReal h2,sigma1=100.0,norm;
PetscInt dim,Ii,J,n = 3,use_random,rstart,rend;
PetscInitialize(&argc,&args,(char *)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(1,"This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_mat", &disp_mat);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_vec", &disp_vec);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
dim = n*n;
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(A,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr); /* RealPart(sigma2) == 0.0 */
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
for (Ii=rstart; Ii<rend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is symmetric */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_symmetric", &flg);CHKERRQ(ierr);
if (flg) {
Mat Trans;
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
ierr = MatEqual(A, Trans, &flg);
if (!flg) SETERRQ(PETSC_ERR_USER,"A is not symmetric");
ierr = MatDestroy(Trans);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
/* make A complex Hermitian */
Ii = 0; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
Ii = dim-2; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is Hermitian */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_Hermitian", &flg);CHKERRQ(ierr);
if (flg) {
Mat Hermit;
if (disp_mat){
if (!rank) printf(" A:\n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatHermitianTranspose(A,MAT_INITIAL_MATRIX, &Hermit);
if (disp_mat){
if (!rank) printf(" A_Hermitian:\n");
ierr = MatView(Hermit,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatEqual(A, Hermit, &flg);
if (!flg) SETERRQ(PETSC_ERR_USER,"A is not Hermitian");
ierr = MatDestroy(Hermit);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
/* Create a Hermitian matrix As in sbaij format */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&As);CHKERRQ(ierr);
if (disp_mat){
if (!rank) {ierr = PetscPrintf(PETSC_COMM_SELF," As:\n");CHKERRQ(ierr);}
ierr = MatView(As,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
if (use_random){
ierr = VecSetRandom(x,rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(x,1.0);CHKERRQ(ierr);
}
/* Create vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&y);CHKERRQ(ierr);
ierr = VecSetSizes(y,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(y);CHKERRQ(ierr);
ierr = VecDuplicate(y,&ys);CHKERRQ(ierr);
/* Test MatMult */
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMult(As,x,ys);CHKERRQ(ierr);
if (disp_vec){
printf("y = A*x:\n");
ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"ys = As*x:\n");
ierr = VecView(ys,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = VecAXPY(y,-1.0,ys);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_INFINITY,&norm);CHKERRQ(ierr);
if (norm > 1.e-12 || disp_vec){
printf("|| A*x - As*x || = %G\n",norm);
}
/* Free spaces */
if (use_random) {ierr = PetscRandomDestroy(rctx);CHKERRQ(ierr);}
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = MatDestroy(As);CHKERRQ(ierr);
ierr = VecDestroy(x);CHKERRQ(ierr);
ierr = VecDestroy(y);CHKERRQ(ierr);
ierr = VecDestroy(ys);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
static PetscErrorCode PCSetUp_SVD(PC pc)
{
#if defined(PETSC_MISSING_LAPACK_GESVD)
SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable\nNot able to provide singular value estimates.");
#else
PC_SVD *jac = (PC_SVD*)pc->data;
PetscErrorCode ierr;
PetscScalar *a,*u,*v,*d,*work;
PetscBLASInt nb,lwork;
PetscInt i,n;
PetscMPIInt size;
PetscFunctionBegin;
ierr = MatDestroy(&jac->A);CHKERRQ(ierr);
ierr = MPI_Comm_size(((PetscObject)pc->pmat)->comm,&size);CHKERRQ(ierr);
if (size > 1) {
Mat redmat;
PetscInt M;
ierr = MatGetSize(pc->pmat,&M,NULL);CHKERRQ(ierr);
ierr = MatGetRedundantMatrix(pc->pmat,size,PETSC_COMM_SELF,M,MAT_INITIAL_MATRIX,&redmat);CHKERRQ(ierr);
ierr = MatConvert(redmat,MATSEQDENSE,MAT_INITIAL_MATRIX,&jac->A);CHKERRQ(ierr);
ierr = MatDestroy(&redmat);CHKERRQ(ierr);
} else {
ierr = MatConvert(pc->pmat,MATSEQDENSE,MAT_INITIAL_MATRIX,&jac->A);CHKERRQ(ierr);
}
if (!jac->diag) { /* assume square matrices */
ierr = MatGetVecs(jac->A,&jac->diag,&jac->work);CHKERRQ(ierr);
}
if (!jac->U) {
ierr = MatDuplicate(jac->A,MAT_DO_NOT_COPY_VALUES,&jac->U);CHKERRQ(ierr);
ierr = MatDuplicate(jac->A,MAT_DO_NOT_COPY_VALUES,&jac->Vt);CHKERRQ(ierr);
}
ierr = MatGetSize(pc->pmat,&n,NULL);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n,&nb);CHKERRQ(ierr);
lwork = 5*nb;
ierr = PetscMalloc(lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);
ierr = MatDenseGetArray(jac->A,&a);CHKERRQ(ierr);
ierr = MatDenseGetArray(jac->U,&u);CHKERRQ(ierr);
ierr = MatDenseGetArray(jac->Vt,&v);CHKERRQ(ierr);
ierr = VecGetArray(jac->diag,&d);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
{
PetscBLASInt lierr;
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
PetscStackCall("LAPACKgesvd",LAPACKgesvd_("A","A",&nb,&nb,a,&nb,d,u,&nb,v,&nb,work,&lwork,&lierr));
if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"gesv() error %d",lierr);
ierr = PetscFPTrapPop();CHKERRQ(ierr);
}
#else
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not coded for complex");
#endif
ierr = MatDenseRestoreArray(jac->A,&a);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(jac->U,&u);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(jac->Vt,&v);CHKERRQ(ierr);
for (i=n-1; i>=0; i--) if (PetscRealPart(d[i]) > jac->zerosing) break;
jac->nzero = n-1-i;
if (jac->monitor) {
ierr = PetscViewerASCIIAddTab(jac->monitor,((PetscObject)pc)->tablevel);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(jac->monitor," SVD: condition number %14.12e, %D of %D singular values are (nearly) zero\n",(double)PetscRealPart(d[0]/d[n-1]),jac->nzero,n);CHKERRQ(ierr);
if (n >= 10) { /* print 5 smallest and 5 largest */
ierr = PetscViewerASCIIPrintf(jac->monitor," SVD: smallest singular values: %14.12e %14.12e %14.12e %14.12e %14.12e\n",(double)PetscRealPart(d[n-1]),(double)PetscRealPart(d[n-2]),(double)PetscRealPart(d[n-3]),(double)PetscRealPart(d[n-4]),(double)PetscRealPart(d[n-5]));CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(jac->monitor," SVD: largest singular values : %14.12e %14.12e %14.12e %14.12e %14.12e\n",(double)PetscRealPart(d[4]),(double)PetscRealPart(d[3]),(double)PetscRealPart(d[2]),(double)PetscRealPart(d[1]),(double)PetscRealPart(d[0]));CHKERRQ(ierr);
} else { /* print all singular values */
char buf[256],*p;
size_t left = sizeof(buf),used;
PetscInt thisline;
for (p=buf,i=n-1,thisline=1; i>=0; i--,thisline++) {
ierr = PetscSNPrintfCount(p,left," %14.12e",&used,(double)PetscRealPart(d[i]));CHKERRQ(ierr);
left -= used;
p += used;
if (thisline > 4 || i==0) {
ierr = PetscViewerASCIIPrintf(jac->monitor," SVD: singular values:%s\n",buf);CHKERRQ(ierr);
p = buf;
thisline = 0;
}
}
}
ierr = PetscViewerASCIISubtractTab(jac->monitor,((PetscObject)pc)->tablevel);CHKERRQ(ierr);
}
ierr = PetscInfo2(pc,"Largest and smallest singular values %14.12e %14.12e\n",(double)PetscRealPart(d[0]),(double)PetscRealPart(d[n-1]));CHKERRQ(ierr);
for (i=0; i<n-jac->nzero; i++) d[i] = 1.0/d[i];
for (; i<n; i++) d[i] = 0.0;
if (jac->essrank > 0) for (i=0; i<n-jac->nzero-jac->essrank; i++) d[i] = 0.0; /* Skip all but essrank eigenvalues */
ierr = PetscInfo1(pc,"Number of zero or nearly singular values %D\n",jac->nzero);CHKERRQ(ierr);
ierr = VecRestoreArray(jac->diag,&d);CHKERRQ(ierr);
#if defined(foo)
{
PetscViewer viewer;
ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,"joe",FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
ierr = MatView(jac->A,viewer);CHKERRQ(ierr);
ierr = MatView(jac->U,viewer);CHKERRQ(ierr);
ierr = MatView(jac->Vt,viewer);CHKERRQ(ierr);
ierr = VecView(jac->diag,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
}
#endif
ierr = PetscFree(work);CHKERRQ(ierr);
PetscFunctionReturn(0);
#endif
}
/*
GetElasticityMatrix - Forms 3D linear elasticity matrix.
*/
PetscErrorCode GetElasticityMatrix(PetscInt m,Mat *newmat)
{
PetscInt i,j,k,i1,i2,j_1,j2,k1,k2,h1,h2,shiftx,shifty,shiftz;
PetscInt ict,nz,base,r1,r2,N,*rowkeep,nstart;
PetscErrorCode ierr;
IS iskeep;
PetscReal **K,norm;
Mat mat,submat = 0,*submatb;
MatType type = MATSEQBAIJ;
m /= 2; /* This is done just to be consistent with the old example */
N = 3*(2*m+1)*(2*m+1)*(2*m+1);
ierr = PetscPrintf(PETSC_COMM_SELF,"m = %D, N=%D\n",m,N);CHKERRQ(ierr);
ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,80,PETSC_NULL,&mat);CHKERRQ(ierr);
/* Form stiffness for element */
ierr = PetscMalloc(81*sizeof(PetscReal *),&K);CHKERRQ(ierr);
for (i=0; i<81; i++) {
ierr = PetscMalloc(81*sizeof(PetscReal),&K[i]);CHKERRQ(ierr);
}
ierr = Elastic20Stiff(K);CHKERRQ(ierr);
/* Loop over elements and add contribution to stiffness */
shiftx = 3; shifty = 3*(2*m+1); shiftz = 3*(2*m+1)*(2*m+1);
for (k=0; k<m; k++) {
for (j=0; j<m; j++) {
for (i=0; i<m; i++) {
h1 = 0;
base = 2*k*shiftz + 2*j*shifty + 2*i*shiftx;
for (k1=0; k1<3; k1++) {
for (j_1=0; j_1<3; j_1++) {
for (i1=0; i1<3; i1++) {
h2 = 0;
r1 = base + i1*shiftx + j_1*shifty + k1*shiftz;
for (k2=0; k2<3; k2++) {
for (j2=0; j2<3; j2++) {
for (i2=0; i2<3; i2++) {
r2 = base + i2*shiftx + j2*shifty + k2*shiftz;
ierr = AddElement(mat,r1,r2,K,h1,h2);CHKERRQ(ierr);
h2 += 3;
}
}
}
h1 += 3;
}
}
}
}
}
}
for (i=0; i<81; i++) {
ierr = PetscFree(K[i]);CHKERRQ(ierr);
}
ierr = PetscFree(K);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Exclude any superfluous rows and columns */
nstart = 3*(2*m+1)*(2*m+1);
ict = 0;
ierr = PetscMalloc((N-nstart)*sizeof(PetscInt),&rowkeep);CHKERRQ(ierr);
for (i=nstart; i<N; i++) {
ierr = MatGetRow(mat,i,&nz,0,0);CHKERRQ(ierr);
if (nz) rowkeep[ict++] = i;
ierr = MatRestoreRow(mat,i,&nz,0,0);CHKERRQ(ierr);
}
ierr = ISCreateGeneral(PETSC_COMM_SELF,ict,rowkeep,PETSC_COPY_VALUES,&iskeep);CHKERRQ(ierr);
ierr = MatGetSubMatrices(mat,1,&iskeep,&iskeep,MAT_INITIAL_MATRIX,&submatb);CHKERRQ(ierr);
submat = *submatb;
ierr = PetscFree(submatb);CHKERRQ(ierr);
ierr = PetscFree(rowkeep);CHKERRQ(ierr);
ierr = ISDestroy(&iskeep);CHKERRQ(ierr);
ierr = MatDestroy(&mat);CHKERRQ(ierr);
/* Convert storage formats -- just to demonstrate conversion to various
formats (in particular, block diagonal storage). This is NOT the
recommended means to solve such a problem. */
ierr = MatConvert(submat,type,MAT_INITIAL_MATRIX,newmat);CHKERRQ(ierr);
ierr = MatDestroy(&submat);CHKERRQ(ierr);
ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO);CHKERRQ(ierr);
ierr = MatView(*newmat,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatNorm(*newmat,NORM_1,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"matrix 1 norm = %G\n",norm);CHKERRQ(ierr);
return 0;
}
static PetscErrorCode MatPartitioningApply_Parmetis_Private(MatPartitioning part, PetscBool useND, IS *partitioning)
{
MatPartitioning_Parmetis *pmetis = (MatPartitioning_Parmetis*)part->data;
PetscErrorCode ierr;
PetscInt *locals = NULL;
Mat mat = part->adj,amat,pmat;
PetscBool flg;
PetscInt bs = 1;
PetscFunctionBegin;
ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIADJ,&flg);CHKERRQ(ierr);
if (flg) {
amat = mat;
ierr = PetscObjectReference((PetscObject)amat);CHKERRQ(ierr);
} else {
/* bs indicates if the converted matrix is "reduced" from the original and hence the
resulting partition results need to be stretched to match the original matrix */
ierr = MatConvert(mat,MATMPIADJ,MAT_INITIAL_MATRIX,&amat);CHKERRQ(ierr);
if (amat->rmap->n > 0) bs = mat->rmap->n/amat->rmap->n;
}
ierr = MatMPIAdjCreateNonemptySubcommMat(amat,&pmat);CHKERRQ(ierr);
ierr = MPI_Barrier(PetscObjectComm((PetscObject)part));CHKERRQ(ierr);
if (pmat) {
MPI_Comm pcomm,comm;
Mat_MPIAdj *adj = (Mat_MPIAdj*)pmat->data;
PetscInt *vtxdist = pmat->rmap->range;
PetscInt *xadj = adj->i;
PetscInt *adjncy = adj->j;
PetscInt *NDorder = NULL;
PetscInt itmp = 0,wgtflag=0, numflag=0, ncon=1, nparts=part->n, options[24], i, j;
real_t *tpwgts,*ubvec,itr=0.1;
int status;
ierr = PetscObjectGetComm((PetscObject)pmat,&pcomm);CHKERRQ(ierr);
#if defined(PETSC_USE_DEBUG)
/* check that matrix has no diagonal entries */
{
PetscInt rstart;
ierr = MatGetOwnershipRange(pmat,&rstart,NULL);CHKERRQ(ierr);
for (i=0; i<pmat->rmap->n; i++) {
for (j=xadj[i]; j<xadj[i+1]; j++) {
if (adjncy[j] == i+rstart) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Row %d has diagonal entry; Parmetis forbids diagonal entry",i+rstart);
}
}
}
#endif
ierr = PetscMalloc1(pmat->rmap->n,&locals);CHKERRQ(ierr);
if (adj->values && !part->vertex_weights)
wgtflag = 1;
if (part->vertex_weights && !adj->values)
wgtflag = 2;
if (part->vertex_weights && adj->values)
wgtflag = 3;
if (PetscLogPrintInfo) {itmp = pmetis->printout; pmetis->printout = 127;}
ierr = PetscMalloc1(ncon*nparts,&tpwgts);CHKERRQ(ierr);
for (i=0; i<ncon; i++) {
for (j=0; j<nparts; j++) {
if (part->part_weights) {
tpwgts[i*nparts+j] = part->part_weights[i*nparts+j];
} else {
tpwgts[i*nparts+j] = 1./nparts;
}
}
}
ierr = PetscMalloc1(ncon,&ubvec);CHKERRQ(ierr);
for (i=0; i<ncon; i++) {
ubvec[i] = 1.05;
}
/* This sets the defaults */
options[0] = 0;
for (i=1; i<24; i++) {
options[i] = -1;
}
/* Duplicate the communicator to be sure that ParMETIS attribute caching does not interfere with PETSc. */
ierr = MPI_Comm_dup(pcomm,&comm);CHKERRQ(ierr);
if (useND) {
PetscInt *sizes, *seps, log2size, subd, *level;
PetscMPIInt size;
idx_t mtype = PARMETIS_MTYPE_GLOBAL, rtype = PARMETIS_SRTYPE_2PHASE, p_nseps = 1, s_nseps = 1;
real_t ubfrac = 1.05;
ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
ierr = PetscMalloc1(pmat->rmap->n,&NDorder);CHKERRQ(ierr);
ierr = PetscMalloc3(2*size,&sizes,4*size,&seps,size,&level);CHKERRQ(ierr);
PetscStackCallParmetis(ParMETIS_V32_NodeND,((idx_t*)vtxdist,(idx_t*)xadj,(idx_t*)adjncy,(idx_t*)part->vertex_weights,(idx_t*)&numflag,&mtype,&rtype,&p_nseps,&s_nseps,&ubfrac,NULL/* seed */,NULL/* dbglvl */,(idx_t*)NDorder,(idx_t*)(sizes),&comm));
log2size = PetscLog2Real(size);
subd = PetscPowInt(2,log2size);
ierr = MatPartitioningSizesToSep_Private(subd,sizes,seps,level);CHKERRQ(ierr);
for (i=0;i<pmat->rmap->n;i++) {
PetscInt loc;
ierr = PetscFindInt(NDorder[i],2*subd,seps,&loc);CHKERRQ(ierr);
if (loc < 0) {
loc = -(loc+1);
if (loc%2) { /* part of subdomain */
locals[i] = loc/2;
} else {
ierr = PetscFindInt(NDorder[i],2*(subd-1),seps+2*subd,&loc);CHKERRQ(ierr);
loc = loc < 0 ? -(loc+1)/2 : loc/2;
locals[i] = level[loc];
}
} else locals[i] = loc/2;
}
ierr = PetscFree3(sizes,seps,level);CHKERRQ(ierr);
} else {
if (pmetis->repartition) {
PetscStackCallParmetis(ParMETIS_V3_AdaptiveRepart,((idx_t*)vtxdist,(idx_t*)xadj,(idx_t*)adjncy,(idx_t*)part->vertex_weights,(idx_t*)part->vertex_weights,(idx_t*)adj->values,(idx_t*)&wgtflag,(idx_t*)&numflag,(idx_t*)&ncon,(idx_t*)&nparts,tpwgts,ubvec,&itr,(idx_t*)options,(idx_t*)&pmetis->cuts,(idx_t*)locals,&comm));
} else {
PetscStackCallParmetis(ParMETIS_V3_PartKway,((idx_t*)vtxdist,(idx_t*)xadj,(idx_t*)adjncy,(idx_t*)part->vertex_weights,(idx_t*)adj->values,(idx_t*)&wgtflag,(idx_t*)&numflag,(idx_t*)&ncon,(idx_t*)&nparts,tpwgts,ubvec,(idx_t*)options,(idx_t*)&pmetis->cuts,(idx_t*)locals,&comm));
}
}
ierr = MPI_Comm_free(&comm);CHKERRQ(ierr);
ierr = PetscFree(tpwgts);CHKERRQ(ierr);
ierr = PetscFree(ubvec);CHKERRQ(ierr);
if (PetscLogPrintInfo) pmetis->printout = itmp;
if (bs > 1) {
PetscInt i,j,*newlocals;
ierr = PetscMalloc1(bs*pmat->rmap->n,&newlocals);CHKERRQ(ierr);
for (i=0; i<pmat->rmap->n; i++) {
for (j=0; j<bs; j++) {
newlocals[bs*i + j] = locals[i];
}
}
ierr = PetscFree(locals);CHKERRQ(ierr);
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),bs*pmat->rmap->n,newlocals,PETSC_OWN_POINTER,partitioning);CHKERRQ(ierr);
} else {
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),pmat->rmap->n,locals,PETSC_OWN_POINTER,partitioning);CHKERRQ(ierr);
}
if (useND) {
IS ndis;
if (bs > 1) {
ierr = ISCreateBlock(PetscObjectComm((PetscObject)part),bs,pmat->rmap->n,NDorder,PETSC_OWN_POINTER,&ndis);CHKERRQ(ierr);
} else {
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),pmat->rmap->n,NDorder,PETSC_OWN_POINTER,&ndis);CHKERRQ(ierr);
}
ierr = ISSetPermutation(ndis);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject)(*partitioning),"_petsc_matpartitioning_ndorder",(PetscObject)ndis);CHKERRQ(ierr);
ierr = ISDestroy(&ndis);CHKERRQ(ierr);
}
} else {
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),0,NULL,PETSC_COPY_VALUES,partitioning);CHKERRQ(ierr);
if (useND) {
IS ndis;
if (bs > 1) {
ierr = ISCreateBlock(PetscObjectComm((PetscObject)part),bs,0,NULL,PETSC_COPY_VALUES,&ndis);CHKERRQ(ierr);
} else {
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),0,NULL,PETSC_COPY_VALUES,&ndis);CHKERRQ(ierr);
}
ierr = ISSetPermutation(ndis);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject)(*partitioning),"_petsc_matpartitioning_ndorder",(PetscObject)ndis);CHKERRQ(ierr);
ierr = ISDestroy(&ndis);CHKERRQ(ierr);
}
}
ierr = MatDestroy(&pmat);CHKERRQ(ierr);
ierr = MatDestroy(&amat);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
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;
PetscInt reorder=0,displ=0;
MatFactorInfo factinfo;
PetscBool equal;
PetscBool TestAIJ =PETSC_FALSE,TestBAIJ=PETSC_TRUE;
PetscInt TestShift=0;
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(NULL,"-bs",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-reorder",&reorder,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,"-testaij",&TestAIJ,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-testShift",&TestShift,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(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,"-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");
}
/* 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>0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"AIJ: \n");
}
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>0) {
ierr = PetscPrintf(PETSC_COMM_SELF," lvl: %D, error: %g\n", lvl,(double)norm2);
}
err[i++] = norm2;
}
}
/* Test baij matrix A */
if (TestBAIJ) {
if (displ>0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"BAIJ: \n");
}
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>0) {
ierr = PetscPrintf(PETSC_COMM_SELF," lvl: %D, error: %g\n", lvl,(double)norm2);
}
err[i++] = norm2;
}
}
/* Test sbaij matrix sA */
if (displ>0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"SBAIJ: \n");
}
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>0) {
ierr = PetscPrintf(PETSC_COMM_SELF," lvl: %D, error: %g\n", lvl,(double)norm2);
}
err[i] -= norm2;
if (err[i] > tol) SETERRQ2(PETSC_COMM_SELF,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 0;
}
int main(int argc,char **args)
{
User user;
Mat A,S;
PetscScalar *data,diag = 1.3;
PetscReal tol = PETSC_SMALL;
PetscInt i,j,m = PETSC_DECIDE,n = PETSC_DECIDE,M = 17,N = 15,s1,s2;
PetscInt test, ntest = 2;
PetscMPIInt rank,size;
PetscBool nc = PETSC_FALSE, cong;
PetscBool ronl = PETSC_TRUE;
PetscBool randomize = PETSC_FALSE;
PetscBool keep = PETSC_FALSE;
PetscBool testzerorows = PETSC_TRUE, testdiagscale = PETSC_TRUE, testgetdiag = PETSC_TRUE;
PetscBool testshift = PETSC_TRUE, testscale = PETSC_TRUE, testdup = PETSC_TRUE, testreset = PETSC_TRUE;
PetscErrorCode ierr;
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);
ierr = PetscOptionsGetInt(NULL,NULL,"-M",&M,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-N",&N,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-ml",&m,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-nl",&n,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-square_nc",&nc,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-rows_only",&ronl,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-randomize",&randomize,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-test_zerorows",&testzerorows,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-test_diagscale",&testdiagscale,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-test_getdiag",&testgetdiag,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-test_shift",&testshift,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-test_scale",&testscale,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-test_dup",&testdup,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-test_reset",&testreset,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-loop",&ntest,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,NULL,"-tol",&tol,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetScalar(NULL,NULL,"-diag",&diag,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-keep",&keep,NULL);CHKERRQ(ierr);
/* This tests square matrices with different row/col layout */
if (nc && size > 1) {
M = PetscMax(PetscMax(N,M),1);
N = M;
m = n = 0;
if (rank == 0) { m = M-1; n = 1; }
else if (rank == 1) { m = 1; n = N-1; }
}
ierr = MatCreateDense(PETSC_COMM_WORLD,m,n,M,N,NULL,&A);CHKERRQ(ierr);
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
ierr = MatGetSize(A,&M,&N);CHKERRQ(ierr);
ierr = MatHasCongruentLayouts(A,&cong);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&s1,NULL);CHKERRQ(ierr);
s2 = 1;
while (s2 < M) s2 *= 10;
ierr = MatDenseGetArray(A,&data);CHKERRQ(ierr);
for (j = 0; j < N; j++) {
for (i = 0; i < m; i++) {
data[j*m + i] = s2*j + i + s1 + 1;
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatConvert(A,MATAIJ,MAT_INPLACE_MATRIX,&A);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,keep);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)A,"initial");CHKERRQ(ierr);
ierr = MatViewFromOptions(A,NULL,"-view_mat");CHKERRQ(ierr);
ierr = PetscNew(&user);CHKERRQ(ierr);
ierr = MatCreateShell(PETSC_COMM_WORLD,m,n,M,N,user,&S);CHKERRQ(ierr);
ierr = MatShellSetOperation(S,MATOP_MULT,(void (*)(void))MatMult_User);CHKERRQ(ierr);
ierr = MatShellSetOperation(S,MATOP_MULT_TRANSPOSE,(void (*)(void))MatMultTranspose_User);CHKERRQ(ierr);
if (cong) {
ierr = MatShellSetOperation(S,MATOP_GET_DIAGONAL,(void (*)(void))MatGetDiagonal_User);CHKERRQ(ierr);
}
ierr = MatDuplicate(A,MAT_COPY_VALUES,&user->B);CHKERRQ(ierr);
/* Square and rows only scaling */
ronl = cong ? ronl : PETSC_TRUE;
for (test = 0; test < ntest; test++) {
PetscReal err;
if (testzerorows) {
Mat ST,B,C,BT,BTT;
IS zr;
Vec x = NULL, b1 = NULL, b2 = NULL;
PetscInt *idxs = NULL, nr = 0;
if (rank == (test%size)) {
nr = 1;
ierr = PetscMalloc1(nr,&idxs);CHKERRQ(ierr);
if (test%2) {
idxs[0] = (2*M - 1 - test/2)%M;
} else {
idxs[0] = (test/2)%M;
}
idxs[0] = PetscMax(idxs[0],0);
}
ierr = ISCreateGeneral(PETSC_COMM_WORLD,nr,idxs,PETSC_OWN_POINTER,&zr);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)zr,"ZR");CHKERRQ(ierr);
ierr = ISViewFromOptions(zr,NULL,"-view_is");CHKERRQ(ierr);
ierr = MatCreateVecs(A,&x,&b1);CHKERRQ(ierr);
if (randomize) {
ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
ierr = VecSetRandom(b1,NULL);CHKERRQ(ierr);
} else {
ierr = VecSet(x,11.4);CHKERRQ(ierr);
ierr = VecSet(b1,-14.2);CHKERRQ(ierr);
}
ierr = VecDuplicate(b1,&b2);CHKERRQ(ierr);
ierr = VecCopy(b1,b2);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)b1,"A_B1");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)b2,"A_B2");CHKERRQ(ierr);
if (size > 1 && !cong) { /* MATMPIAIJ ZeroRows and ZeroRowsColumns are buggy in this case */
ierr = VecDestroy(&b1);CHKERRQ(ierr);
}
if (ronl) {
ierr = MatZeroRowsIS(A,zr,diag,x,b1);CHKERRQ(ierr);
ierr = MatZeroRowsIS(S,zr,diag,x,b2);CHKERRQ(ierr);
} else {
ierr = MatZeroRowsColumnsIS(A,zr,diag,x,b1);CHKERRQ(ierr);
ierr = MatZeroRowsColumnsIS(S,zr,diag,x,b2);CHKERRQ(ierr);
ierr = ISDestroy(&zr);CHKERRQ(ierr);
/* Mix zerorows and zerorowscols */
nr = 0;
idxs = NULL;
if (!rank) {
nr = 1;
ierr = PetscMalloc1(nr,&idxs);CHKERRQ(ierr);
if (test%2) {
idxs[0] = (3*M - 2 - test/2)%M;
} else {
idxs[0] = (test/2+1)%M;
}
idxs[0] = PetscMax(idxs[0],0);
}
ierr = ISCreateGeneral(PETSC_COMM_WORLD,nr,idxs,PETSC_OWN_POINTER,&zr);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)zr,"ZR2");CHKERRQ(ierr);
ierr = ISViewFromOptions(zr,NULL,"-view_is");CHKERRQ(ierr);
ierr = MatZeroRowsIS(A,zr,diag*2.0+PETSC_SMALL,NULL,NULL);CHKERRQ(ierr);
ierr = MatZeroRowsIS(S,zr,diag*2.0+PETSC_SMALL,NULL,NULL);CHKERRQ(ierr);
}
ierr = ISDestroy(&zr);CHKERRQ(ierr);
if (b1) {
Vec b;
ierr = VecViewFromOptions(b1,NULL,"-view_b");CHKERRQ(ierr);
ierr = VecViewFromOptions(b2,NULL,"-view_b");CHKERRQ(ierr);
ierr = VecDuplicate(b1,&b);CHKERRQ(ierr);
ierr = VecCopy(b1,b);CHKERRQ(ierr);
ierr = VecAXPY(b,-1.0,b2);CHKERRQ(ierr);
ierr = VecNorm(b,NORM_INFINITY,&err);CHKERRQ(ierr);
if (err >= tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"[test %D] Error b %g\n",test,(double)err);CHKERRQ(ierr);
}
ierr = VecDestroy(&b);CHKERRQ(ierr);
}
ierr = VecDestroy(&b1);CHKERRQ(ierr);
ierr = VecDestroy(&b2);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = MatConvert(S,MATDENSE,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);
ierr = MatCreateTranspose(S,&ST);CHKERRQ(ierr);
ierr = MatComputeOperator(ST,MATDENSE,&BT);CHKERRQ(ierr);
ierr = MatTranspose(BT,MAT_INITIAL_MATRIX,&BTT);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)B,"S");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)BTT,"STT");CHKERRQ(ierr);
ierr = MatConvert(A,MATDENSE,MAT_INITIAL_MATRIX,&C);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)C,"A");CHKERRQ(ierr);
ierr = MatViewFromOptions(C,NULL,"-view_mat");CHKERRQ(ierr);
ierr = MatViewFromOptions(B,NULL,"-view_mat");CHKERRQ(ierr);
ierr = MatViewFromOptions(BTT,NULL,"-view_mat");CHKERRQ(ierr);
ierr = MatAXPY(C,-1.0,B,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatNorm(C,NORM_FROBENIUS,&err);CHKERRQ(ierr);
if (err >= tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"[test %D] Error mat mult %g\n",test,(double)err);CHKERRQ(ierr);
}
ierr = MatConvert(A,MATDENSE,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
ierr = MatAXPY(C,-1.0,BTT,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatNorm(C,NORM_FROBENIUS,&err);CHKERRQ(ierr);
if (err >= tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"[test %D] Error mat mult transpose %g\n",test,(double)err);CHKERRQ(ierr);
}
ierr = MatDestroy(&ST);CHKERRQ(ierr);
ierr = MatDestroy(&BTT);CHKERRQ(ierr);
ierr = MatDestroy(&BT);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
}
if (testdiagscale) { /* MatDiagonalScale() */
Vec vr,vl;
ierr = MatCreateVecs(A,&vr,&vl);CHKERRQ(ierr);
if (randomize) {
ierr = VecSetRandom(vr,NULL);CHKERRQ(ierr);
ierr = VecSetRandom(vl,NULL);CHKERRQ(ierr);
} else {
ierr = VecSet(vr,test%2 ? 0.15 : 1.0/0.15);CHKERRQ(ierr);
ierr = VecSet(vl,test%2 ? -1.2 : 1.0/-1.2);CHKERRQ(ierr);
}
ierr = MatDiagonalScale(A,vl,vr);CHKERRQ(ierr);
ierr = MatDiagonalScale(S,vl,vr);CHKERRQ(ierr);
ierr = VecDestroy(&vr);CHKERRQ(ierr);
ierr = VecDestroy(&vl);CHKERRQ(ierr);
}
if (testscale) { /* MatScale() */
ierr = MatScale(A,test%2 ? 1.4 : 1.0/1.4);CHKERRQ(ierr);
ierr = MatScale(S,test%2 ? 1.4 : 1.0/1.4);CHKERRQ(ierr);
}
if (testshift && cong) { /* MatShift() : MATSHELL shift is broken when row/cols layout are not congruent and left/right scaling have been applied */
ierr = MatShift(A,test%2 ? -77.5 : 77.5);CHKERRQ(ierr);
ierr = MatShift(S,test%2 ? -77.5 : 77.5);CHKERRQ(ierr);
}
if (testgetdiag && cong) { /* MatGetDiagonal() */
Vec dA,dS;
ierr = MatCreateVecs(A,&dA,NULL);CHKERRQ(ierr);
ierr = MatCreateVecs(S,&dS,NULL);CHKERRQ(ierr);
ierr = MatGetDiagonal(A,dA);CHKERRQ(ierr);
ierr = MatGetDiagonal(S,dS);CHKERRQ(ierr);
ierr = VecAXPY(dA,-1.0,dS);CHKERRQ(ierr);
ierr = VecNorm(dA,NORM_INFINITY,&err);CHKERRQ(ierr);
if (err >= tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"[test %D] Error diag %g\n",test,(double)err);CHKERRQ(ierr);
}
ierr = VecDestroy(&dA);CHKERRQ(ierr);
ierr = VecDestroy(&dS);CHKERRQ(ierr);
}
if (testdup && !test) {
Mat A2, S2;
ierr = MatDuplicate(A,MAT_COPY_VALUES,&A2);CHKERRQ(ierr);
ierr = MatDuplicate(S,MAT_COPY_VALUES,&S2);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&S);CHKERRQ(ierr);
A = A2;
S = S2;
}
if (testreset && (ntest == 1 || test == ntest-2)) {
/* reset MATSHELL */
ierr = MatAssemblyBegin(S,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(S,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* reset A */
ierr = MatCopy(user->B,A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
}
}
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&user->B);CHKERRQ(ierr);
ierr = MatDestroy(&S);CHKERRQ(ierr);
ierr = PetscFree(user);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
static PetscErrorCode MatPartitioningApply_Party(MatPartitioning part,IS *partitioning)
{
PetscErrorCode ierr;
PetscInt i,*parttab,*locals,nb_locals,M,N;
PetscMPIInt size,rank;
Mat mat = part->adj,matAdj,matSeq,*A;
Mat_MPIAdj *adj;
MatPartitioning_Party *party = (MatPartitioning_Party*)part->data;
PetscBool flg;
IS isrow, iscol;
int n,*edge_p,*edge,*vertex_w,p,*part_party,cutsize,redl,rec;
const char *redm,*redo;
char *mesg_log;
#if defined(PETSC_HAVE_UNISTD_H)
int fd_stdout,fd_pipe[2],count,err;
#endif
PetscFunctionBegin;
ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIADJ,&flg);CHKERRQ(ierr);
if (size>1) {
if (flg) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Distributed matrix format MPIAdj is not supported for sequential partitioners");
ierr = PetscInfo(part,"Converting distributed matrix to sequential: this could be a performance loss\n");CHKERRQ(ierr);
ierr = MatGetSize(mat,&M,&N);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,M,0,1,&isrow);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,N,0,1,&iscol);CHKERRQ(ierr);
ierr = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
matSeq = *A;
ierr = PetscFree(A);CHKERRQ(ierr);
} else {
ierr = PetscObjectReference((PetscObject)mat);CHKERRQ(ierr);
matSeq = mat;
}
if (!flg) { /* convert regular matrix to MPIADJ */
ierr = MatConvert(matSeq,MATMPIADJ,MAT_INITIAL_MATRIX,&matAdj);CHKERRQ(ierr);
} else {
ierr = PetscObjectReference((PetscObject)matSeq);CHKERRQ(ierr);
matAdj = matSeq;
}
adj = (Mat_MPIAdj*)matAdj->data; /* finaly adj contains adjacency graph */
/* arguments for Party library */
n = mat->rmap->N; /* number of vertices in full graph */
edge_p = adj->i; /* start of edge list for each vertex */
edge = adj->j; /* edge list data */
vertex_w = part->vertex_weights; /* weights for all vertices */
p = part->n; /* number of parts to create */
redl = party->nbvtxcoarsed; /* how many vertices to coarsen down to? */
rec = party->recursive ? 1 : 0; /* recursive bisection */
redm = party->redm ? "lam" : ""; /* matching method */
redo = party->redo ? "w3" : ""; /* matching optimization method */
ierr = PetscMalloc1(mat->rmap->N,&part_party);CHKERRQ(ierr);
/* redirect output to buffer */
#if defined(PETSC_HAVE_UNISTD_H)
fd_stdout = dup(1);
if (pipe(fd_pipe)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SYS,"Could not open pipe");
close(1);
dup2(fd_pipe[1],1);
ierr = PetscMalloc1(SIZE_LOG,&mesg_log);CHKERRQ(ierr);
#endif
/* library call */
party_lib_times_start();
ierr = party_lib(n,vertex_w,NULL,NULL,NULL,edge_p,edge,NULL,p,part_party,&cutsize,redl,(char*)redm,(char*)redo,party->global,party->local,rec,1);
party_lib_times_output(1);
part_info(n,vertex_w,edge_p,edge,NULL,p,part_party,1);
#if defined(PETSC_HAVE_UNISTD_H)
err = fflush(stdout);
if (err) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SYS,"fflush() failed on stdout");
count = read(fd_pipe[0],mesg_log,(SIZE_LOG-1)*sizeof(char));
if (count<0) count = 0;
mesg_log[count] = 0;
close(1);
dup2(fd_stdout,1);
close(fd_stdout);
close(fd_pipe[0]);
close(fd_pipe[1]);
if (party->verbose) {
ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),mesg_log);
}
ierr = PetscFree(mesg_log);CHKERRQ(ierr);
#endif
if (ierr) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Party failed");
ierr = PetscMalloc1(mat->rmap->N,&parttab);CHKERRQ(ierr);
for (i=0; i<mat->rmap->N; i++) parttab[i] = part_party[i];
/* creation of the index set */
nb_locals = mat->rmap->N / size;
locals = parttab + rank*nb_locals;
if (rank < mat->rmap->N % size) {
nb_locals++;
locals += rank;
} else locals += mat->rmap->N % size;
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),nb_locals,locals,PETSC_COPY_VALUES,partitioning);CHKERRQ(ierr);
/* clean up */
ierr = PetscFree(parttab);CHKERRQ(ierr);
ierr = PetscFree(part_party);CHKERRQ(ierr);
ierr = MatDestroy(&matSeq);CHKERRQ(ierr);
ierr = MatDestroy(&matAdj);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode MatPartitioningApply_Scotch(MatPartitioning part, IS * partitioning)
{
PetscErrorCode ierr;
int *parttab, *locals = PETSC_NULL, rank, i, size;
size_t j;
Mat mat = part->adj, matMPI, matSeq;
int nb_locals = mat->rmap->n;
Mat_MPIAdj *adj = (Mat_MPIAdj *) mat->data;
MatPartitioning_Scotch *scotch = (MatPartitioning_Scotch *) part->data;
PetscTruth flg;
#ifdef PETSC_HAVE_UNISTD_H
int fd_stdout, fd_pipe[2], count,err;
#endif
PetscFunctionBegin;
/* check if the matrix is sequential, use MatGetSubMatrices if necessary */
ierr = MPI_Comm_size(((PetscObject)mat)->comm, &size);CHKERRQ(ierr);
ierr = PetscTypeCompare((PetscObject) mat, MATMPIADJ, &flg);CHKERRQ(ierr);
if (size > 1) {
int M, N;
IS isrow, iscol;
Mat *A;
if (flg) {
SETERRQ(0, "Distributed matrix format MPIAdj is not supported for sequential partitioners");
}
PetscPrintf(((PetscObject)part)->comm, "Converting distributed matrix to sequential: this could be a performance loss\n");CHKERRQ(ierr);
ierr = MatGetSize(mat, &M, &N);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF, M, 0, 1, &isrow);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF, N, 0, 1, &iscol);CHKERRQ(ierr);
ierr = MatGetSubMatrices(mat, 1, &isrow, &iscol, MAT_INITIAL_MATRIX, &A);CHKERRQ(ierr);
matSeq = *A;
ierr = PetscFree(A);CHKERRQ(ierr);
ierr = ISDestroy(isrow);CHKERRQ(ierr);
ierr = ISDestroy(iscol);CHKERRQ(ierr);
} else
matSeq = mat;
/* convert the the matrix to MPIADJ type if necessary */
if (!flg) {
ierr = MatConvert(matSeq, MATMPIADJ, MAT_INITIAL_MATRIX, &matMPI);CHKERRQ(ierr);
} else {
matMPI = matSeq;
}
adj = (Mat_MPIAdj *) matMPI->data; /* finaly adj contains adjacency graph */
ierr = MPI_Comm_rank(((PetscObject)part)->comm, &rank);CHKERRQ(ierr);
{
/* definition of Scotch library arguments */
SCOTCH_Strat stratptr; /* scotch strategy */
SCOTCH_Graph grafptr; /* scotch graph */
#if defined(DOES_NOT_COMPILE_DUE_TO_BROKEN_INTERFACE)
int vertnbr = mat->rmap->N; /* number of vertices in full graph */
int *verttab = adj->i; /* start of edge list for each vertex */
int *edgetab = adj->j; /* edge list data */
int edgenbr = adj->nz; /* number of edges */
int *velotab = NULL; /* not used by petsc interface */
int *vlbltab = NULL;
int *edlotab = NULL;
int flagval = 3; /* (cf doc scotch no weight edge & vertices) */
#endif
int baseval = 0; /* 0 for C array indexing */
char strategy[256];
ierr = PetscMalloc((mat->rmap->N) * sizeof(int), &parttab);CHKERRQ(ierr);
/* redirect output to buffer scotch -> mesg_log */
#ifdef PETSC_HAVE_UNISTD_H
fd_stdout = dup(1);
pipe(fd_pipe);
close(1);
dup2(fd_pipe[1], 1);
ierr = PetscMalloc(SIZE_LOG * sizeof(char), &(scotch->mesg_log));CHKERRQ(ierr);
#endif
/* library call */
/* Construction of the scotch graph object */
ierr = SCOTCH_graphInit(&grafptr);
#if defined(DOES_NOT_COMPILE_DUE_TO_BROKEN_INTERFACE)
ierr = SCOTCH_graphBuild((SCOTCH_Graph *) &grafptr,
(const SCOTCH_Num) vertnbr,
(const SCOTCH_Num) verttab,
(const SCOTCH_Num *)velotab,
(const SCOTCH_Num *)vlbltab,
(const SCOTCH_Num *)edgenbr,
(const SCOTCH_Num *)edgetab,
(const SCOTCH_Num) edlotab,
(const SCOTCH_Num *)baseval,
(const SCOTCH_Num *)flagval);CHKERRQ(ierr);
#else
SETERRQ(PETSC_ERR_SUP,"Scotch interface currently broken");
#endif
ierr = SCOTCH_graphCheck(&grafptr);CHKERRQ(ierr);
/* Construction of the strategy */
if (scotch->strategy[0] != 0) {
ierr = PetscStrcpy(strategy, scotch->strategy);CHKERRQ(ierr);
} else {
PetscStrcpy(strategy, "b{strat=");
if (scotch->multilevel) {
/* PetscStrcat(strategy,"m{vert=");
sprintf(strategy+strlen(strategy),"%d",scotch->nbvtxcoarsed);
PetscStrcat(strategy,",asc="); */
sprintf(strategy, "b{strat=m{vert=%d,asc=",
scotch->nbvtxcoarsed);
} else
PetscStrcpy(strategy, "b{strat=");
switch (scotch->global_method) {
case MP_SCOTCH_GREEDY:
PetscStrcat(strategy, "h");
break;
case MP_SCOTCH_GPS:
PetscStrcat(strategy, "g");
break;
case MP_SCOTCH_GR_GPS:
PetscStrcat(strategy, "g|h");
}
switch (scotch->local_method) {
case MP_SCOTCH_KERNIGHAN_LIN:
if (scotch->multilevel)
PetscStrcat(strategy, ",low=f}");
else
PetscStrcat(strategy, " f");
break;
case MP_SCOTCH_NONE:
if (scotch->multilevel)
PetscStrcat(strategy, ",asc=x}");
default:
break;
}
PetscStrcat(strategy, " x}");
}
PetscPrintf(((PetscObject)part)->comm, "strategy=[%s]\n", strategy);
ierr = SCOTCH_stratInit(&stratptr);CHKERRQ(ierr);
/*
TODO: Correct this part
Commented because this doesn't exists anymore
ierr = SCOTCH_stratMap(&stratptr, strategy);CHKERRQ(ierr);
*/
/* check for option mapping */
if (!scotch->map) {
/* ********************************************
* *
* TODO: Correct this part *
* *
* Won't work with this tmp SCOTCH_Strat... *
* *
* I just modified it to make scotch compile, *
* to be able to use PaStiX... *
* *
**********************************************/
#if defined (DOES_NOT_COMPILE_DUE_TO_BROKEN_INTERFACE)
SCOTCH_Strat tmp;
ierr = SCOTCH_graphPart((const SCOTCH_Graph *)&grafptr,
(const SCOTCH_Num) &stratptr,
(const SCOTCH_Strat *)&tmp, /* The Argument changed from scotch 3.04 it was part->n, */
(SCOTCH_Num *) parttab);CHKERRQ(ierr);
#else
SETERRQ(PETSC_ERR_SUP,"Scotch interface currently broken");
#endif
ierr = PetscPrintf(PETSC_COMM_SELF, "Partition simple without mapping\n");
} else {
SCOTCH_Graph grafarch;
SCOTCH_Num *listtab;
SCOTCH_Num listnbr = 0;
SCOTCH_Arch archptr; /* file in scotch architecture format */
SCOTCH_Strat archstrat;
int arch_total_size, *parttab_tmp,err;
int cpt;
char buf[256];
FILE *file1, *file2;
char host_buf[256];
/* generate the graph that represents the arch */
file1 = fopen(scotch->arch, "r");
if (!file1) SETERRQ1(PETSC_ERR_FILE_OPEN, "Scotch: unable to open architecture file %s", scotch->arch);
ierr = SCOTCH_graphInit(&grafarch);CHKERRQ(ierr);
ierr = SCOTCH_graphLoad(&grafarch, file1, baseval, 3);CHKERRQ(ierr);
ierr = SCOTCH_graphCheck(&grafarch);CHKERRQ(ierr);
SCOTCH_graphSize(&grafarch, &arch_total_size, &cpt);
err = fclose(file1);
if (err) SETERRQ(PETSC_ERR_SYS,"fclose() failed on file");
printf("total size = %d\n", arch_total_size);
/* generate the list of nodes currently working */
ierr = PetscGetHostName(host_buf, 256);CHKERRQ(ierr);
ierr = PetscStrlen(host_buf, &j);CHKERRQ(ierr);
file2 = fopen(scotch->host_list, "r");
if (!file2) SETERRQ1(PETSC_ERR_FILE_OPEN, "Scotch: unable to open host list file %s", scotch->host_list);
i = -1;
flg = PETSC_FALSE;
while (!feof(file2) && !flg) {
i++;
fgets(buf, 256, file2);
PetscStrncmp(buf, host_buf, j, &flg);
}
err = fclose(file2);
if (err) SETERRQ(PETSC_ERR_SYS,"fclose() failed on file");
if (!flg) SETERRQ1(PETSC_ERR_LIB, "Scotch: unable to find '%s' in host list file", host_buf);
listnbr = size;
ierr = PetscMalloc(sizeof(SCOTCH_Num) * listnbr, &listtab);CHKERRQ(ierr);
ierr = MPI_Allgather(&i, 1, MPI_INT, listtab, 1, MPI_INT, ((PetscObject)part)->comm);CHKERRQ(ierr);
printf("listnbr = %d, listtab = ", listnbr);
for (i = 0; i < listnbr; i++)
printf("%d ", listtab[i]);
printf("\n");
err = fflush(stdout);
if (err) SETERRQ(PETSC_ERR_SYS,"fflush() failed on file");
ierr = SCOTCH_stratInit(&archstrat);CHKERRQ(ierr);
/**************************************************************
* *
* TODO: Correct this part *
* *
* Commented because this doesn't exists anymore *
* *
* ierr = SCOTCH_stratBipart(&archstrat, "fx");CHKERRQ(ierr); *
**************************************************************/
ierr = SCOTCH_archInit(&archptr);CHKERRQ(ierr);
ierr = SCOTCH_archBuild(&archptr, &grafarch, listnbr, listtab,
&archstrat);CHKERRQ(ierr);
ierr = PetscMalloc((mat->rmap->N) * sizeof(int), &parttab_tmp);CHKERRQ(ierr);
/************************************************************************************
* *
* TODO: Correct this part *
* *
* Commented because this doesn't exists anymore *
* *
* ierr = SCOTCH_mapInit(&mappptr, &grafptr, &archptr, parttab_tmp);CHKERRQ(ierr); *
* *
* ierr = SCOTCH_mapCompute(&mappptr, &stratptr);CHKERRQ(ierr); *
* *
* ierr = SCOTCH_mapView(&mappptr, stdout);CHKERRQ(ierr); *
************************************************************************************/
/* now we have to set in the real parttab at the good place */
/* because the ranks order are different than position in */
/* the arch graph */
for (i = 0; i < mat->rmap->N; i++) {
parttab[i] = parttab_tmp[i];
}
ierr = PetscFree(listtab);CHKERRQ(ierr);
SCOTCH_archExit(&archptr);
/*************************************************
* TODO: Correct this part *
* *
* Commented because this doesn't exists anymore *
* SCOTCH_mapExit(&mappptr); *
*************************************************/
SCOTCH_stratExit(&archstrat);
}
/* dump to mesg_log... */
#ifdef PETSC_HAVE_UNISTD_H
err = fflush(stdout);
if (err) SETERRQ(PETSC_ERR_SYS,"fflush() failed on stdout");
count = read(fd_pipe[0], scotch->mesg_log, (SIZE_LOG - 1) * sizeof(char));
if (count < 0)
count = 0;
scotch->mesg_log[count] = 0;
close(1);
dup2(fd_stdout, 1);
close(fd_stdout);
close(fd_pipe[0]);
close(fd_pipe[1]);
#endif
SCOTCH_graphExit(&grafptr);
SCOTCH_stratExit(&stratptr);
}
if (ierr)
SETERRQ(PETSC_ERR_LIB, scotch->mesg_log);
/* Creation of the index set */
ierr = MPI_Comm_rank(((PetscObject)part)->comm, &rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(((PetscObject)part)->comm, &size);CHKERRQ(ierr);
nb_locals = mat->rmap->N / size;
locals = parttab + rank * nb_locals;
if (rank < mat->rmap->N % size) {
nb_locals++;
locals += rank;
} else
locals += mat->rmap->N % size;
ierr = ISCreateGeneral(((PetscObject)part)->comm, nb_locals, locals, partitioning);CHKERRQ(ierr);
/* destroying old objects */
ierr = PetscFree(parttab);CHKERRQ(ierr);
if (matSeq != mat) {
ierr = MatDestroy(matSeq);CHKERRQ(ierr);
}
if (matMPI != mat) {
ierr = MatDestroy(matMPI);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Mat A,B,MA;
PetscViewer fd;
char file[PETSC_MAX_PATH_LEN];
PetscInt m,n,M,N,dof=1;
PetscMPIInt rank,size;
PetscErrorCode ierr;
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,&size);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
SETERRQ(1,"This example does not work with complex numbers");
#else
/* Load aij matrix A */
ierr = PetscOptionsGetString(PETSC_NULL,"-f",file,PETSC_MAX_PATH_LEN-1,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_ERR_USER,"Must indicate binary file with the -f option");
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
ierr = MatLoad(fd,MATAIJ,&A);CHKERRQ(ierr);
ierr = PetscViewerDestroy(fd);CHKERRQ(ierr);
/* Get dof, then create maij matrix MA */
ierr = PetscOptionsGetInt(PETSC_NULL,"-dof",&dof,PETSC_NULL);CHKERRQ(ierr);
ierr = MatCreateMAIJ(A,dof,&MA);CHKERRQ(ierr);
ierr = MatGetLocalSize(MA,&m,&n);CHKERRQ(ierr);
ierr = MatGetSize(MA,&M,&N);CHKERRQ(ierr);
if (size == 1){
ierr = MatConvert(MA,MATSEQAIJ,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);
} else {
ierr = MatConvert(MA,MATMPIAIJ,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);
}
/* Test MatMult() */
ierr = MatMultEqual(MA,B,10,&flg);CHKERRQ(ierr);
if (!flg){
SETERRQ(PETSC_ERR_CONV_FAILED,"Error: MatMul() for MAIJ matrix");
}
/* Test MatMultAdd() */
ierr = MatMultAddEqual(MA,B,10,&flg);CHKERRQ(ierr);
if (!flg){
SETERRQ(PETSC_ERR_CONV_FAILED,"Error: MatMulAdd() for MAIJ matrix");
}
/* Test MatMultTranspose() */
ierr = MatMultTransposeEqual(MA,B,10,&flg);CHKERRQ(ierr);
if (!flg){
SETERRQ(PETSC_ERR_CONV_FAILED,"Error: MatMulAdd() for MAIJ matrix");
}
/* Test MatMultTransposeAdd() */
ierr = MatMultTransposeAddEqual(MA,B,10,&flg);CHKERRQ(ierr);
if (!flg){
SETERRQ(PETSC_ERR_CONV_FAILED,"Error: MatMulTransposeAdd() for MAIJ matrix");
}
ierr = MatDestroy(MA);CHKERRQ(ierr);
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = MatDestroy(B);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
#endif
return 0;
}
int main(int argc,char **args)
{
Mat Cdense,B,C,Ct;
Vec d;
PetscInt i,j,m = 5,n,nrows,ncols;
const PetscInt *rows,*cols;
IS isrows,iscols;
PetscErrorCode ierr;
PetscScalar *v;
PetscMPIInt rank,size;
PetscReal Cnorm;
PetscBool flg,mats_view=PETSC_FALSE;
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);
ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
CHKERRQ(ierr);
n = m;
ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL,"-mats_view",&mats_view);
CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&C);
CHKERRQ(ierr);
ierr = MatSetSizes(C,m,n,PETSC_DECIDE,PETSC_DECIDE);
CHKERRQ(ierr);
ierr = MatSetType(C,MATELEMENTAL);
CHKERRQ(ierr);
ierr = MatSetFromOptions(C);
CHKERRQ(ierr);
ierr = MatSetUp(C);
CHKERRQ(ierr);
ierr = MatGetOwnershipIS(C,&isrows,&iscols);
CHKERRQ(ierr);
ierr = ISGetLocalSize(isrows,&nrows);
CHKERRQ(ierr);
ierr = ISGetIndices(isrows,&rows);
CHKERRQ(ierr);
ierr = ISGetLocalSize(iscols,&ncols);
CHKERRQ(ierr);
ierr = ISGetIndices(iscols,&cols);
CHKERRQ(ierr);
ierr = PetscMalloc1(nrows*ncols,&v);
CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
PetscRandom rand;
PetscScalar rval;
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);
CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);
CHKERRQ(ierr);
for (i=0; i<nrows; i++) {
for (j=0; j<ncols; j++) {
ierr = PetscRandomGetValue(rand,&rval);
CHKERRQ(ierr);
v[i*ncols+j] = rval;
}
}
ierr = PetscRandomDestroy(&rand);
CHKERRQ(ierr);
#else
for (i=0; i<nrows; i++) {
for (j=0; j<ncols; j++) {
v[i*ncols+j] = (PetscReal)(10000*rank+100*rows[i]+cols[j]);
}
}
#endif
ierr = MatSetValues(C,nrows,rows,ncols,cols,v,INSERT_VALUES);
CHKERRQ(ierr);
ierr = ISRestoreIndices(isrows,&rows);
CHKERRQ(ierr);
ierr = ISRestoreIndices(iscols,&cols);
CHKERRQ(ierr);
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = ISDestroy(&isrows);
CHKERRQ(ierr);
ierr = ISDestroy(&iscols);
CHKERRQ(ierr);
/* Test MatView(), MatDuplicate() and out-of-place MatConvert() */
ierr = MatDuplicate(C,MAT_COPY_VALUES,&B);
CHKERRQ(ierr);
if (mats_view) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Duplicated C:\n");
CHKERRQ(ierr);
ierr = MatView(B,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
}
ierr = MatDestroy(&B);
CHKERRQ(ierr);
ierr = MatConvert(C,MATMPIDENSE,MAT_INITIAL_MATRIX,&Cdense);
CHKERRQ(ierr);
ierr = MatMultEqual(C,Cdense,5,&flg);
CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Cdense != C. MatConvert() fails");
/* Test MatNorm() */
ierr = MatNorm(C,NORM_1,&Cnorm);
CHKERRQ(ierr);
/* Test MatTranspose(), MatZeroEntries() and MatGetDiagonal() */
ierr = MatTranspose(C,MAT_INITIAL_MATRIX,&Ct);
CHKERRQ(ierr);
ierr = MatConjugate(Ct);
CHKERRQ(ierr);
if (mats_view) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"C's Transpose Conjugate:\n");
CHKERRQ(ierr);
ierr = MatView(Ct,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
}
ierr = MatZeroEntries(Ct);
CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&d);
CHKERRQ(ierr);
ierr = VecSetSizes(d,m>n ? n : m,PETSC_DECIDE);
CHKERRQ(ierr);
ierr = VecSetFromOptions(d);
CHKERRQ(ierr);
ierr = MatGetDiagonal(C,d);
CHKERRQ(ierr);
if (mats_view) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Diagonal of C:\n");
CHKERRQ(ierr);
ierr = VecView(d,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
}
if (m>n) {
ierr = MatDiagonalScale(C,NULL,d);
CHKERRQ(ierr);
} else {
ierr = MatDiagonalScale(C,d,NULL);
CHKERRQ(ierr);
}
if (mats_view) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Diagonal Scaled C:\n");
CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
}
/* Test MatAXPY(), MatAYPX() and in-place MatConvert() */
ierr = MatCreate(PETSC_COMM_WORLD,&B);
CHKERRQ(ierr);
ierr = MatSetSizes(B,m,n,PETSC_DECIDE,PETSC_DECIDE);
CHKERRQ(ierr);
ierr = MatSetType(B,MATELEMENTAL);
CHKERRQ(ierr);
ierr = MatSetFromOptions(B);
CHKERRQ(ierr);
ierr = MatSetUp(B);
CHKERRQ(ierr);
ierr = MatGetOwnershipIS(B,&isrows,&iscols);
CHKERRQ(ierr);
ierr = ISGetLocalSize(isrows,&nrows);
CHKERRQ(ierr);
ierr = ISGetIndices(isrows,&rows);
CHKERRQ(ierr);
ierr = ISGetLocalSize(iscols,&ncols);
CHKERRQ(ierr);
ierr = ISGetIndices(iscols,&cols);
CHKERRQ(ierr);
for (i=0; i<nrows; i++) {
for (j=0; j<ncols; j++) {
v[i*ncols+j] = (PetscReal)(1000*rows[i]+cols[j]);
}
}
ierr = MatSetValues(B,nrows,rows,ncols,cols,v,INSERT_VALUES);
CHKERRQ(ierr);
ierr = PetscFree(v);
CHKERRQ(ierr);
ierr = ISRestoreIndices(isrows,&rows);
CHKERRQ(ierr);
ierr = ISRestoreIndices(iscols,&cols);
CHKERRQ(ierr);
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAXPY(B,2.5,C,SAME_NONZERO_PATTERN);
CHKERRQ(ierr);
ierr = MatAYPX(B,3.75,C,SAME_NONZERO_PATTERN);
CHKERRQ(ierr);
ierr = MatConvert(B,MATDENSE,MAT_INPLACE_MATRIX,&B);
CHKERRQ(ierr);
if (mats_view) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"B after MatAXPY and MatAYPX:\n");
CHKERRQ(ierr);
ierr = MatView(B,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
}
ierr = ISDestroy(&isrows);
CHKERRQ(ierr);
ierr = ISDestroy(&iscols);
CHKERRQ(ierr);
ierr = MatDestroy(&B);
CHKERRQ(ierr);
/* Test MatMatTransposeMult(): B = C*C^T */
ierr = MatMatTransposeMult(C,C,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&B);
CHKERRQ(ierr);
if (mats_view) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"C MatMatTransposeMult C:\n");
CHKERRQ(ierr);
ierr = MatView(B,PETSC_VIEWER_STDOUT_WORLD);
CHKERRQ(ierr);
}
ierr = MatDestroy(&Cdense);
CHKERRQ(ierr);
ierr = PetscFree(v);
CHKERRQ(ierr);
ierr = MatDestroy(&B);
CHKERRQ(ierr);
ierr = MatDestroy(&C);
CHKERRQ(ierr);
ierr = MatDestroy(&Ct);
CHKERRQ(ierr);
ierr = VecDestroy(&d);
CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
/*@
MatSchurComplementComputeExplicitOperator - Compute the Schur complement matrix explicitly
Collective on Mat
Input Parameter:
. M - the matrix obtained with MatCreateSchurComplement()
Output Parameter:
. S - the Schur complement matrix
Note: This can be expensive, so it is mainly for testing
Level: advanced
.seealso: MatCreateSchurComplement(), MatSchurComplementUpdate()
@*/
PetscErrorCode MatSchurComplementComputeExplicitOperator(Mat M, Mat *S)
{
Mat B, C, D;
KSP ksp;
PC pc;
PetscBool isLU, isILU;
PetscReal fill = 2.0;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);CHKERRQ(ierr);
ierr = MatSchurComplementGetKSP(M, &ksp);CHKERRQ(ierr);
ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);CHKERRQ(ierr);
if (isLU || isILU) {
Mat fact, Bd, AinvB, AinvBd;
PetscReal eps = 1.0e-10;
/* This can be sped up for banded LU */
ierr = KSPSetUp(ksp);CHKERRQ(ierr);
ierr = PCFactorGetMatrix(pc, &fact);CHKERRQ(ierr);
ierr = MatConvert(B, MATDENSE, MAT_INITIAL_MATRIX, &Bd);CHKERRQ(ierr);
ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
ierr = MatMatSolve(fact, Bd, AinvBd);CHKERRQ(ierr);
ierr = MatDestroy(&Bd);CHKERRQ(ierr);
ierr = MatChop(AinvBd, eps);CHKERRQ(ierr);
ierr = MatConvert(AinvBd, MATAIJ, MAT_INITIAL_MATRIX, &AinvB);CHKERRQ(ierr);
ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
ierr = MatMatMult(C, AinvB, MAT_INITIAL_MATRIX, fill, S);CHKERRQ(ierr);
ierr = MatDestroy(&AinvB);CHKERRQ(ierr);
} else {
Mat Ainvd, Ainv;
ierr = PCComputeExplicitOperator(pc, &Ainvd);CHKERRQ(ierr);
ierr = MatConvert(Ainvd, MATAIJ, MAT_INITIAL_MATRIX, &Ainv);CHKERRQ(ierr);
ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
#if 0
/* Symmetric version */
ierr = MatPtAP(Ainv, B, MAT_INITIAL_MATRIX, fill, S);CHKERRQ(ierr);
#else
/* Nonsymmetric version */
ierr = MatMatMatMult(C, Ainv, B, MAT_INITIAL_MATRIX, fill, S);CHKERRQ(ierr);
#endif
ierr = MatDestroy(&Ainv);CHKERRQ(ierr);
}
ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD, PETSC_VIEWER_ASCII_INFO);CHKERRQ(ierr);
ierr = MatView(*S, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
if (D) {
MatInfo info;
PetscReal norm;
ierr = MatGetInfo(D, MAT_GLOBAL_SUM, &info);CHKERRQ(ierr);
if (info.nz_used) {
ierr = MatNorm(D, NORM_INFINITY, &norm);CHKERRQ(ierr);
if (norm > PETSC_MACHINE_EPSILON) SETERRQ(PetscObjectComm((PetscObject) M), PETSC_ERR_SUP, "Not yet implemented for Schur complements with non-vanishing D");
}
}
PetscFunctionReturn(0);
}
Modified from the code contributed by Yaning Liu @lbl.gov \n\n";
/*
Example:
mpiexec -n <np> ./ex103
mpiexec -n <np> ./ex103 -mat_type elemental -mat_view
mpiexec -n <np> ./ex103 -mat_type aij
*/
#include <petscmat.h>
#undef __FUNCT__
#define __FUNCT__ "main"
int main(int argc, char** argv)
{
Mat A,A_elemental;
PetscInt i,j,M=10,N=5,nrows,ncols;
PetscErrorCode ierr;
PetscMPIInt rank,size;
IS isrows,iscols;
const PetscInt *rows,*cols;
PetscScalar *v;
MatType type;
PetscBool isDense,isAIJ,flg;
ierr = PetscInitialize(&argc, &argv, (char*)0, help);if (ierr) return ierr;
#if !defined(PETSC_HAVE_ELEMENTAL)
SETERRQ(PETSC_COMM_WORLD,1,"This example requires ELEMENTAL");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
/* Creat a matrix */
ierr = PetscOptionsGetInt(NULL,NULL,"-M",&M,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-N",&N,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD, &A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
/* Set local matrix entries */
ierr = MatGetOwnershipIS(A,&isrows,&iscols);CHKERRQ(ierr);
ierr = ISGetLocalSize(isrows,&nrows);CHKERRQ(ierr);
ierr = ISGetIndices(isrows,&rows);CHKERRQ(ierr);
ierr = ISGetLocalSize(iscols,&ncols);CHKERRQ(ierr);
ierr = ISGetIndices(iscols,&cols);CHKERRQ(ierr);
ierr = PetscMalloc1(nrows*ncols,&v);CHKERRQ(ierr);
for (i=0; i<nrows; i++) {
for (j=0; j<ncols; j++) {
if (size == 1) {
v[i*ncols+j] = (PetscScalar)(i+j);
} else {
v[i*ncols+j] = (PetscScalar)rank+j*0.1;
}
}
}
ierr = MatSetValues(A,nrows,rows,ncols,cols,v,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
//ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%D] local nrows %D, ncols %D\n",rank,nrows,ncols);CHKERRQ(ierr);
//ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);CHKERRQ(ierr);
/* Test MatSetValues() by converting A to A_elemental */
ierr = MatGetType(A,&type);CHKERRQ(ierr);
if (size == 1) {
ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&isDense);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJ,&isAIJ);CHKERRQ(ierr);
} else {
ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIDENSE,&isDense);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&isAIJ);CHKERRQ(ierr);
}
if (isDense || isAIJ) {
Mat Aexplicit;
ierr = MatConvert(A, MATELEMENTAL, MAT_INITIAL_MATRIX, &A_elemental);CHKERRQ(ierr);
ierr = MatComputeExplicitOperator(A_elemental,&Aexplicit);CHKERRQ(ierr);
ierr = MatMultEqual(Aexplicit,A_elemental,5,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Aexplicit != A_elemental.");
ierr = MatDestroy(&Aexplicit);CHKERRQ(ierr);
/* Test MAT_REUSE_MATRIX which is only supported for inplace conversion */
ierr = MatConvert(A, MATELEMENTAL, MAT_INPLACE_MATRIX, &A);CHKERRQ(ierr);
ierr = MatMultEqual(A_elemental,A,5,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"A_elemental != A.");
ierr = MatDestroy(&A_elemental);CHKERRQ(ierr);
}
ierr = ISRestoreIndices(isrows,&rows);CHKERRQ(ierr);
ierr = ISRestoreIndices(iscols,&cols);CHKERRQ(ierr);
ierr = ISDestroy(&isrows);CHKERRQ(ierr);
ierr = ISDestroy(&iscols);CHKERRQ(ierr);
ierr = PetscFree(v);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Mat A;
Vec min,max,maxabs;
PetscInt m,n;
PetscInt imin[M],imax[M],imaxabs[M],indices[N],row;
PetscScalar values[N];
PetscErrorCode ierr;
MatType type;
PetscMPIInt size;
PetscBool doTest=PETSC_TRUE;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
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 = MatSetUp(A);CHKERRQ(ierr);
row = 0;
indices[0] = 0; indices[1] = 1; indices[2] = 2; indices[3] = 3; indices[4] = 4; indices[5] = 5;
values[0] = -1.0; values[1] = 0.0; values[2] = 1.0; values[3] = 3.0; values[4] = 4.0; values[5] = -5.0;
ierr = MatSetValues(A,1,&row,6,indices,values,INSERT_VALUES);CHKERRQ(ierr);
row = 1;
ierr = MatSetValues(A,1,&row,3,indices,values,INSERT_VALUES);CHKERRQ(ierr);
row = 4;
ierr = MatSetValues(A,1,&row,1,indices+4,values+4,INSERT_VALUES);CHKERRQ(ierr);
row = 4;
ierr = MatSetValues(A,1,&row,2,indices+4,values+4,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_WORLD);CHKERRQ(ierr);
ierr = MatGetLocalSize(A, &m,&n);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&min);CHKERRQ(ierr);
ierr = VecSetSizes(min,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(min);CHKERRQ(ierr);
ierr = VecDuplicate(min,&max);CHKERRQ(ierr);
ierr = VecDuplicate(min,&maxabs);CHKERRQ(ierr);
/* Test MatGetRowMin, MatGetRowMax and MatGetRowMaxAbs */
if (size == 1) {
ierr = MatGetRowMin(A,min,imin);CHKERRQ(ierr);
ierr = MatGetRowMax(A,max,imax);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(A,maxabs,imaxabs);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Row Minimums\n");CHKERRQ(ierr);
ierr = VecView(min,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscIntView(5,imin,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Row Maximums\n");CHKERRQ(ierr);
ierr = VecView(max,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscIntView(5,imax,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Row Maximum Absolute Values\n");CHKERRQ(ierr);
ierr = VecView(maxabs,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscIntView(5,imaxabs,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
} else {
ierr = MatGetType(A,&type);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nMatrix type: %s\n",type);CHKERRQ(ierr);
/* AIJ */
ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&doTest);CHKERRQ(ierr);
if (doTest) {
ierr = MatGetRowMaxAbs(A,maxabs,NULL);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(A,maxabs,imaxabs);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Row Maximum Absolute Values:\n");CHKERRQ(ierr);
ierr = VecView(maxabs,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* BAIJ */
ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIBAIJ,&doTest);CHKERRQ(ierr);
if (doTest) {
ierr = MatGetRowMaxAbs(A,maxabs,NULL);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(A,maxabs,imaxabs);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Row Maximum Absolute Values:\n");CHKERRQ(ierr);
ierr = VecView(maxabs,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
}
if (size == 1) {
ierr = MatConvert(A,MATDENSE,MAT_INPLACE_MATRIX,&A);CHKERRQ(ierr);
ierr = MatGetRowMin(A,min,imin);CHKERRQ(ierr);
ierr = MatGetRowMax(A,max,imax);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(A,maxabs,imaxabs);CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Row Minimums\n");CHKERRQ(ierr);
ierr = VecView(min,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscIntView(5,imin,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Row Maximums\n");CHKERRQ(ierr);
ierr = VecView(max,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscIntView(5,imax,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Row Maximum Absolute Values\n");CHKERRQ(ierr);
ierr = VecView(maxabs,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscIntView(5,imaxabs,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = VecDestroy(&min);CHKERRQ(ierr);
ierr = VecDestroy(&max);CHKERRQ(ierr);
ierr = VecDestroy(&maxabs);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
PetscInt main(PetscInt argc,char **args)
{
Mat A,A_dense,B;
Vec *evecs;
PetscBool flg,TestZHEEV=PETSC_TRUE,TestZHEEVX=PETSC_FALSE,TestZHEGV=PETSC_FALSE,TestZHEGVX=PETSC_FALSE;
PetscErrorCode ierr;
PetscBool isSymmetric;
PetscScalar sigma,*arrayA,*arrayB,*evecs_array=NULL,*work;
PetscReal *evals,*rwork;
PetscMPIInt size;
PetscInt m,i,j,nevs,il,iu,cklvl=2;
PetscReal vl,vu,abstol=1.e-8;
PetscBLASInt *iwork,*ifail,lwork,lierr,bn;
PetscReal tols[2];
PetscInt nzeros[2],nz;
PetscReal ratio;
PetscScalar v,none = -1.0,sigma2,pfive = 0.5,*xa;
PetscRandom rctx;
PetscReal h2,sigma1 = 100.0;
PetscInt dim,Ii,J,Istart,Iend,n = 6,its,use_random,one=1;
PetscInitialize(&argc,&args,(char*)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex numbers");
#endif
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 = PetscOptionsHasName(NULL, "-test_zheevx", &flg);CHKERRQ(ierr);
if (flg) {
TestZHEEV = PETSC_FALSE;
TestZHEEVX = PETSC_TRUE;
}
ierr = PetscOptionsHasName(NULL, "-test_zhegv", &flg);CHKERRQ(ierr);
if (flg) {
TestZHEEV = PETSC_FALSE;
TestZHEGV = PETSC_TRUE;
}
ierr = PetscOptionsHasName(NULL, "-test_zhegvx", &flg);CHKERRQ(ierr);
if (flg) {
TestZHEEV = PETSC_FALSE;
TestZHEGVX = PETSC_TRUE;
}
ierr = PetscOptionsGetReal(NULL,"-sigma1",&sigma1,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
dim = n*n;
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-norandom",&flg);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
for (Ii=0; Ii<dim; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (use_random) {ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
/* make A complex Hermitian */
v = sigma2*h2;
Ii = 0; J = 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
m = n = dim;
/* Check whether A is symmetric */
ierr = PetscOptionsHasName(NULL, "-check_symmetry", &flg);CHKERRQ(ierr);
if (flg) {
Mat Trans;
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
ierr = MatEqual(A, Trans, &isSymmetric);
if (!isSymmetric) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"A must be symmetric");
ierr = MatDestroy(&Trans);CHKERRQ(ierr);
}
/* Convert aij matrix to MatSeqDense for LAPACK */
ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&flg);CHKERRQ(ierr);
if (flg) {
ierr = MatDuplicate(A,MAT_COPY_VALUES,&A_dense);CHKERRQ(ierr);
} else {
ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&A_dense);CHKERRQ(ierr);
}
ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
ierr = MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(B,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(B);CHKERRQ(ierr);
v = 1.0;
for (Ii=0; Ii<dim; Ii++) {
ierr = MatSetValues(B,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
/* Solve standard eigenvalue problem: A*x = lambda*x */
/*===================================================*/
ierr = PetscBLASIntCast(2*n,&lwork);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n,&bn);CHKERRQ(ierr);
ierr = PetscMalloc(n*sizeof(PetscReal),&evals);CHKERRQ(ierr);
ierr = PetscMalloc(lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);
ierr = MatDenseGetArray(A_dense,&arrayA);CHKERRQ(ierr);
if (TestZHEEV) { /* test zheev() */
printf(" LAPACKsyev: compute all %d eigensolutions...\n",m);
ierr = PetscMalloc((3*n-2)*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
LAPACKsyev_("V","U",&bn,arrayA,&bn,evals,work,&lwork,rwork,&lierr);
ierr = PetscFree(rwork);CHKERRQ(ierr);
evecs_array = arrayA;
nevs = m;
il =1; iu=m;
}
if (TestZHEEVX) {
il = 1;
ierr = PetscBLASIntCast((0.2*m),&iu);CHKERRQ(ierr);
printf(" LAPACKsyevx: compute %d to %d-th eigensolutions...\n",il,iu);
ierr = PetscMalloc((m*n+1)*sizeof(PetscScalar),&evecs_array);CHKERRQ(ierr);
ierr = PetscMalloc((7*n+1)*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
ierr = PetscMalloc((5*n+1)*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
ierr = PetscMalloc((n+1)*sizeof(PetscBLASInt),&ifail);CHKERRQ(ierr);
/* in the case "I", vl and vu are not referenced */
vl = 0.0; vu = 8.0;
LAPACKsyevx_("V","I","U",&bn,arrayA,&bn,&vl,&vu,&il,&iu,&abstol,&nevs,evals,evecs_array,&n,work,&lwork,rwork,iwork,ifail,&lierr);
ierr = PetscFree(iwork);CHKERRQ(ierr);
ierr = PetscFree(ifail);CHKERRQ(ierr);
ierr = PetscFree(rwork);CHKERRQ(ierr);
}
if (TestZHEGV) {
printf(" LAPACKsygv: compute all %d eigensolutions...\n",m);
ierr = PetscMalloc((3*n+1)*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
ierr = MatDenseGetArray(B,&arrayB);CHKERRQ(ierr);
LAPACKsygv_(&one,"V","U",&bn,arrayA,&bn,arrayB,&bn,evals,work,&lwork,rwork,&lierr);
evecs_array = arrayA;
nevs = m;
il = 1; iu=m;
ierr = MatDenseRestoreArray(B,&arrayB);CHKERRQ(ierr);
ierr = PetscFree(rwork);CHKERRQ(ierr);
}
if (TestZHEGVX) {
il = 1;
ierr = PetscBLASIntCast((0.2*m),&iu);CHKERRQ(ierr);
printf(" LAPACKsygv: compute %d to %d-th eigensolutions...\n",il,iu);
ierr = PetscMalloc((m*n+1)*sizeof(PetscScalar),&evecs_array);CHKERRQ(ierr);
ierr = PetscMalloc((6*n+1)*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
ifail = iwork + 5*n;
ierr = PetscMalloc((7*n+1)*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
ierr = MatDenseGetArray(B,&arrayB);CHKERRQ(ierr);
vl = 0.0; vu = 8.0;
LAPACKsygvx_(&one,"V","I","U",&bn,arrayA,&bn,arrayB,&bn,&vl,&vu,&il,&iu,&abstol,&nevs,evals,evecs_array,&n,work,&lwork,rwork,iwork,ifail,&lierr);
ierr = MatDenseRestoreArray(B,&arrayB);CHKERRQ(ierr);
ierr = PetscFree(iwork);CHKERRQ(ierr);
ierr = PetscFree(rwork);CHKERRQ(ierr);
}
ierr = MatDenseRestoreArray(A_dense,&arrayA);CHKERRQ(ierr);
if (nevs <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED, "nev=%d, no eigensolution has found", nevs);
/* View evals */
ierr = PetscOptionsHasName(NULL, "-eig_view", &flg);CHKERRQ(ierr);
if (flg) {
printf(" %d evals: \n",nevs);
for (i=0; i<nevs; i++) printf("%d %G\n",i+il,evals[i]);
}
/* Check residuals and orthogonality */
ierr = PetscMalloc((nevs+1)*sizeof(Vec),&evecs);CHKERRQ(ierr);
for (i=0; i<nevs; i++) {
ierr = VecCreate(PETSC_COMM_SELF,&evecs[i]);CHKERRQ(ierr);
ierr = VecSetSizes(evecs[i],PETSC_DECIDE,n);CHKERRQ(ierr);
ierr = VecSetFromOptions(evecs[i]);CHKERRQ(ierr);
ierr = VecPlaceArray(evecs[i],evecs_array+i*n);CHKERRQ(ierr);
}
tols[0] = 1.e-8; tols[1] = 1.e-8;
ierr = CkEigenSolutions(cklvl,A,il-1,iu-1,evals,evecs,tols);CHKERRQ(ierr);
for (i=0; i<nevs; i++) { ierr = VecDestroy(&evecs[i]);CHKERRQ(ierr);}
ierr = PetscFree(evecs);CHKERRQ(ierr);
/* Free work space. */
if (TestZHEEVX || TestZHEGVX) {
ierr = PetscFree(evecs_array);CHKERRQ(ierr);
}
ierr = PetscFree(evals);CHKERRQ(ierr);
ierr = PetscFree(work);CHKERRQ(ierr);
ierr = MatDestroy(&A_dense);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
static PetscErrorCode MatPartitioningApply_Parmetis(MatPartitioning part,IS *partitioning)
{
MatPartitioning_Parmetis *parmetis = (MatPartitioning_Parmetis*)part->data;
PetscErrorCode ierr;
PetscInt *locals = PETSC_NULL;
Mat mat = part->adj,amat,pmat;
PetscBool flg;
PetscInt bs = 1;
PetscFunctionBegin;
ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIADJ,&flg);CHKERRQ(ierr);
if (flg) {
amat = mat;
PetscObjectReference((PetscObject)amat);CHKERRQ(ierr);
} else {
/* bs indicates if the converted matrix is "reduced" from the original and hence the
resulting partition results need to be stretched to match the original matrix */
ierr = MatConvert(mat,MATMPIADJ,MAT_INITIAL_MATRIX,&amat);CHKERRQ(ierr);
if (amat->rmap->n > 0) bs = mat->rmap->n/amat->rmap->n;
}
ierr = MatMPIAdjCreateNonemptySubcommMat(amat,&pmat);CHKERRQ(ierr);
ierr = MPI_Barrier(((PetscObject)part)->comm);CHKERRQ(ierr);
if (pmat) {
MPI_Comm pcomm = ((PetscObject)pmat)->comm,comm_pmetis;
Mat_MPIAdj *adj = (Mat_MPIAdj*)pmat->data;
PetscInt *vtxdist = pmat->rmap->range;
PetscInt *xadj = adj->i;
PetscInt *adjncy = adj->j;
PetscInt itmp = 0,wgtflag=0, numflag=0, ncon=1, nparts=part->n, options[24], i, j;
real_t *tpwgts,*ubvec;
int status;
#if defined(PETSC_USE_DEBUG)
/* check that matrix has no diagonal entries */
{
PetscInt rstart;
ierr = MatGetOwnershipRange(pmat,&rstart,PETSC_NULL);CHKERRQ(ierr);
for (i=0; i<pmat->rmap->n; i++) {
for (j=xadj[i]; j<xadj[i+1]; j++) {
if (adjncy[j] == i+rstart) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Row %d has diagonal entry; Parmetis forbids diagonal entry",i+rstart);
}
}
}
#endif
ierr = PetscMalloc(amat->rmap->n*sizeof(PetscInt),&locals);CHKERRQ(ierr);
if (PetscLogPrintInfo) {itmp = parmetis->printout; parmetis->printout = 127;}
ierr = PetscMalloc(ncon*nparts*sizeof(real_t),&tpwgts);CHKERRQ(ierr);
for (i=0; i<ncon; i++) {
for (j=0; j<nparts; j++) {
if (part->part_weights) {
tpwgts[i*nparts+j] = part->part_weights[i*nparts+j];
} else {
tpwgts[i*nparts+j] = 1./nparts;
}
}
}
ierr = PetscMalloc(ncon*sizeof(real_t),&ubvec);CHKERRQ(ierr);
for (i=0; i<ncon; i++) {
ubvec[i] = 1.05;
}
/* This sets the defaults */
options[0] = 0;
for (i=1; i<24; i++) {
options[i] = -1;
}
/* Duplicate the communicator to be sure that ParMETIS attribute caching does not interfere with PETSc. */
ierr = MPI_Comm_dup(pcomm,&comm_pmetis);CHKERRQ(ierr);
status = ParMETIS_V3_PartKway(vtxdist,xadj,adjncy,part->vertex_weights,adj->values,&wgtflag,&numflag,&ncon,&nparts,tpwgts,ubvec,options,&parmetis->cuts,locals,&comm_pmetis);CHKERRQPARMETIS(status);
ierr = MPI_Comm_free(&comm_pmetis);CHKERRQ(ierr);
ierr = PetscFree(tpwgts);CHKERRQ(ierr);
ierr = PetscFree(ubvec);CHKERRQ(ierr);
if (PetscLogPrintInfo) {parmetis->printout = itmp;}
}
if (bs > 1) {
PetscInt i,j,*newlocals;
ierr = PetscMalloc(bs*amat->rmap->n*sizeof(PetscInt),&newlocals);CHKERRQ(ierr);
for (i=0; i<amat->rmap->n; i++) {
for (j=0; j<bs; j++) {
newlocals[bs*i + j] = locals[i];
}
}
ierr = PetscFree(locals);CHKERRQ(ierr);
ierr = ISCreateGeneral(((PetscObject)part)->comm,bs*amat->rmap->n,newlocals,PETSC_OWN_POINTER,partitioning);CHKERRQ(ierr);
} else {
ierr = ISCreateGeneral(((PetscObject)part)->comm,amat->rmap->n,locals,PETSC_OWN_POINTER,partitioning);CHKERRQ(ierr);
}
ierr = MatDestroy(&pmat);CHKERRQ(ierr);
ierr = MatDestroy(&amat);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscInt main(PetscInt argc,char **args)
{
Mat A,As;
PetscBool flg,disp_mat=PETSC_FALSE;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt i,j;
PetscScalar v,sigma2;
PetscRandom rctx;
PetscReal h2,sigma1=100.0;
PetscInt dim,Ii,J,n = 3,use_random,rstart,rend;
KSP ksp;
PC pc;
Mat F;
PetscInt nneg, nzero, npos;
PetscInitialize(&argc,&args,(char *)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_mat", &disp_mat);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
dim = n*n;
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(A,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr); /* RealPart(sigma2) == 0.0 */
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
for (Ii=rstart; Ii<rend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is symmetric */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_symmetric", &flg);CHKERRQ(ierr);
if (flg) {
Mat Trans;
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
ierr = MatEqual(A, Trans, &flg);
if (!flg) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"A is not symmetric");
ierr = MatDestroy(&Trans);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
/* make A complex Hermitian */
Ii = 0; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
Ii = dim-2; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is Hermitian */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_Hermitian", &flg);CHKERRQ(ierr);
if (flg) {
Mat Hermit;
if (disp_mat){
if (!rank) printf(" A:\n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatHermitianTranspose(A,MAT_INITIAL_MATRIX, &Hermit);
if (disp_mat){
if (!rank) printf(" A_Hermitian:\n");
ierr = MatView(Hermit,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatEqual(A, Hermit, &flg);
if (!flg) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"A is not Hermitian");
ierr = MatDestroy(&Hermit);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
/* Create a Hermitian matrix As in sbaij format */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&As);CHKERRQ(ierr);
if (disp_mat){
if (!rank) {ierr = PetscPrintf(PETSC_COMM_SELF," As:\n");CHKERRQ(ierr);}
ierr = MatView(As,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Test MatGetInertia() */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,As,As,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCCHOLESKY);CHKERRQ(ierr);
ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
ierr = PCSetUp(pc);CHKERRQ(ierr);
ierr = PCFactorGetMatrix(pc,&F);CHKERRQ(ierr);
ierr = MatGetInertia(F,&nneg,&nzero,&npos);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF," MatInertia: nneg: %D, nzero: %D, npos: %D\n",nneg,nzero,npos);CHKERRQ(ierr);
}
/* Free spaces */
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&As);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat A,RHS,C,F,X,S;
Vec u,x,b;
Vec xschur,bschur,uschur;
IS is_schur;
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt isolver=0,size_schur,m,n,nfact,nsolve,nrhs;
PetscReal norm,tol=PETSC_SQRT_MACHINE_EPSILON;
PetscRandom rand;
PetscBool data_provided,herm,symm,use_lu;
PetscReal sratio = 5.1/12.;
PetscViewer fd; /* viewer */
char solver[256];
char file[PETSC_MAX_PATH_LEN]; /* input file name */
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 test");
/* Determine which type of solver we want to test for */
herm = PETSC_FALSE;
symm = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,NULL,"-symmetric_solve",&symm,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-hermitian_solve",&herm,NULL);CHKERRQ(ierr);
if (herm) symm = PETSC_TRUE;
/* Determine file from which we read the matrix A */
ierr = PetscOptionsGetString(NULL,NULL,"-f",file,PETSC_MAX_PATH_LEN,&data_provided);CHKERRQ(ierr);
if (!data_provided) { /* get matrices from PETSc distribution */
sprintf(file,PETSC_DIR);
ierr = PetscStrcat(file,"/share/petsc/datafiles/matrices/");CHKERRQ(ierr);
if (symm) {
#if defined (PETSC_USE_COMPLEX)
ierr = PetscStrcat(file,"hpd-complex-");CHKERRQ(ierr);
#else
ierr = PetscStrcat(file,"spd-real-");CHKERRQ(ierr);
#endif
} else {
#if defined (PETSC_USE_COMPLEX)
ierr = PetscStrcat(file,"nh-complex-");CHKERRQ(ierr);
#else
ierr = PetscStrcat(file,"ns-real-");CHKERRQ(ierr);
#endif
}
#if defined(PETSC_USE_64BIT_INDICES)
ierr = PetscStrcat(file,"int64-");CHKERRQ(ierr);
#else
ierr = PetscStrcat(file,"int32-");CHKERRQ(ierr);
#endif
#if defined (PETSC_USE_REAL_SINGLE)
ierr = PetscStrcat(file,"float32");CHKERRQ(ierr);
#else
ierr = PetscStrcat(file,"float64");CHKERRQ(ierr);
#endif
}
/* 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 = MatGetSize(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,NULL,"-nrhs",&nrhs,NULL);CHKERRQ(ierr);
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 */
ierr = PetscOptionsGetInt(NULL,NULL,"-solver",&isolver,NULL);CHKERRQ(ierr);
switch (isolver) {
#if defined(PETSC_HAVE_MUMPS)
case 0:
ierr = PetscStrcpy(solver,MATSOLVERMUMPS);CHKERRQ(ierr);
break;
#endif
#if defined(PETSC_HAVE_MKL_PARDISO)
case 1:
ierr = PetscStrcpy(solver,MATSOLVERMKL_PARDISO);CHKERRQ(ierr);
break;
#endif
default:
ierr = PetscStrcpy(solver,MATSOLVERPETSC);CHKERRQ(ierr);
break;
}
#if defined (PETSC_USE_COMPLEX)
if (isolver == 0 && symm && !data_provided) { /* MUMPS (5.0.0) does not have support for hermitian matrices, so make them symmetric */
PetscScalar im = PetscSqrtScalar((PetscScalar)-1.);
PetscScalar val = -1.0;
val = val + im;
ierr = MatSetValue(A,1,0,val,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
#endif
ierr = PetscOptionsGetReal(NULL,NULL,"-schur_ratio",&sratio,NULL);CHKERRQ(ierr);
if (sratio < 0. || sratio > 1.) {
SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "Invalid ratio for schur degrees of freedom %f", sratio);
}
size_schur = (PetscInt)(sratio*m);
ierr = PetscPrintf(PETSC_COMM_SELF,"Solving with %s: nrhs %d, sym %d, herm %d, size schur %d, size mat %d\n",solver,nrhs,symm,herm,size_schur,m);CHKERRQ(ierr);
/* Test LU/Cholesky Factorization */
use_lu = PETSC_FALSE;
if (!symm) use_lu = PETSC_TRUE;
#if defined (PETSC_USE_COMPLEX)
if (isolver == 1) use_lu = PETSC_TRUE;
#endif
if (herm && !use_lu) { /* test also conversion routines inside the solver packages */
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatConvert(A,MATSEQSBAIJ,MAT_INPLACE_MATRIX,&A);CHKERRQ(ierr);
}
if (use_lu) {
ierr = MatGetFactor(A,solver,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
} else {
if (herm) {
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
} else {
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_SPD,PETSC_FALSE);CHKERRQ(ierr);
}
ierr = MatGetFactor(A,solver,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
}
ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,m-size_schur,1,&is_schur);CHKERRQ(ierr);
ierr = MatFactorSetSchurIS(F,is_schur);CHKERRQ(ierr);
ierr = ISDestroy(&is_schur);CHKERRQ(ierr);
if (use_lu) {
ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
} else {
ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
}
for (nfact = 0; nfact < 3; nfact++) {
Mat AD;
if (!nfact) {
ierr = VecSetRandom(x,rand);CHKERRQ(ierr);
if (symm && herm) {
ierr = VecAbs(x);CHKERRQ(ierr);
}
ierr = MatDiagonalSet(A,x,ADD_VALUES);CHKERRQ(ierr);
}
if (use_lu) {
ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
} else {
ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
}
ierr = MatFactorCreateSchurComplement(F,&S);CHKERRQ(ierr);
ierr = MatCreateVecs(S,&xschur,&bschur);CHKERRQ(ierr);
ierr = VecDuplicate(xschur,&uschur);CHKERRQ(ierr);
if (nfact == 1) {
ierr = MatFactorInvertSchurComplement(F);CHKERRQ(ierr);
}
for (nsolve = 0; nsolve < 2; nsolve++) {
ierr = VecSetRandom(x,rand);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
if (nsolve) {
ierr = MatMult(A,x,b);CHKERRQ(ierr);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
} else {
ierr = MatMultTranspose(A,x,b);CHKERRQ(ierr);
ierr = MatSolveTranspose(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) {
PetscReal resi;
if (nsolve) {
ierr = MatMult(A,x,u);CHKERRQ(ierr); /* u = A*x */
} else {
ierr = MatMultTranspose(A,x,u);CHKERRQ(ierr); /* u = A*x */
}
ierr = VecAXPY(u,-1.0,b);CHKERRQ(ierr); /* u <- (-1.0)b + u */
ierr = VecNorm(u,NORM_2,&resi);CHKERRQ(ierr);
if (nsolve) {
ierr = PetscPrintf(PETSC_COMM_SELF,"(f %d, s %d) MatSolve error: Norm of error %g, residual %f\n",nfact,nsolve,norm,resi);CHKERRQ(ierr);
} else {
ierr = PetscPrintf(PETSC_COMM_SELF,"(f %d, s %d) MatSolveTranspose error: Norm of error %g, residual %f\n",nfact,nsolve,norm,resi);CHKERRQ(ierr);
}
}
ierr = VecSetRandom(xschur,rand);CHKERRQ(ierr);
ierr = VecCopy(xschur,uschur);CHKERRQ(ierr);
if (nsolve) {
ierr = MatMult(S,xschur,bschur);CHKERRQ(ierr);
ierr = MatFactorSolveSchurComplement(F,bschur,xschur);CHKERRQ(ierr);
} else {
ierr = MatMultTranspose(S,xschur,bschur);CHKERRQ(ierr);
ierr = MatFactorSolveSchurComplementTranspose(F,bschur,xschur);CHKERRQ(ierr);
}
/* Check the error */
ierr = VecAXPY(uschur,-1.0,xschur);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(uschur,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
PetscReal resi;
if (nsolve) {
ierr = MatMult(S,xschur,uschur);CHKERRQ(ierr); /* u = A*x */
} else {
ierr = MatMultTranspose(S,xschur,uschur);CHKERRQ(ierr); /* u = A*x */
}
ierr = VecAXPY(uschur,-1.0,bschur);CHKERRQ(ierr); /* u <- (-1.0)b + u */
ierr = VecNorm(uschur,NORM_2,&resi);CHKERRQ(ierr);
if (nsolve) {
ierr = PetscPrintf(PETSC_COMM_SELF,"(f %d, s %d) MatFactorSolveSchurComplement error: Norm of error %g, residual %f\n",nfact,nsolve,norm,resi);CHKERRQ(ierr);
} else {
ierr = PetscPrintf(PETSC_COMM_SELF,"(f %d, s %d) MatFactorSolveSchurComplementTranspose error: Norm of error %g, residual %f\n",nfact,nsolve,norm,resi);CHKERRQ(ierr);
}
}
}
ierr = MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&AD);
if (!nfact) {
ierr = MatMatMult(AD,C,MAT_INITIAL_MATRIX,2.0,&RHS);CHKERRQ(ierr);
} else {
ierr = MatMatMult(AD,C,MAT_REUSE_MATRIX,2.0,&RHS);CHKERRQ(ierr);
}
ierr = MatDestroy(&AD);CHKERRQ(ierr);
for (nsolve = 0; nsolve < 2; 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) {
ierr = PetscPrintf(PETSC_COMM_SELF,"(f %D, s %D) MatMatSolve: Norm of error %g\n",nfact,nsolve,norm);CHKERRQ(ierr);
}
}
ierr = MatDestroy(&S);CHKERRQ(ierr);
ierr = VecDestroy(&xschur);CHKERRQ(ierr);
ierr = VecDestroy(&bschur);CHKERRQ(ierr);
ierr = VecDestroy(&uschur);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);
ierr = MatDestroy(&RHS);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);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 **argv)
{
PetscErrorCode ierr;
KSP ksp;
PC pc;
Vec x,b;
DA da;
Mat A,Atrans;
PetscInt dof=1,M=-8;
PetscTruth flg,trans=PETSC_FALSE;
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-dof",&dof,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetTruth(PETSC_NULL,"-trans",&trans,PETSC_NULL);CHKERRQ(ierr);
ierr = DACreate(PETSC_COMM_WORLD,&da);CHKERRQ(ierr);
ierr = DASetDim(da,3);CHKERRQ(ierr);
ierr = DASetPeriodicity(da,DA_NONPERIODIC);CHKERRQ(ierr);
ierr = DASetStencilType(da,DA_STENCIL_STAR);CHKERRQ(ierr);
ierr = DASetSizes(da,M,M,M);CHKERRQ(ierr);
ierr = DASetNumProcs(da,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = DASetDof(da,dof);CHKERRQ(ierr);
ierr = DASetStencilWidth(da,1);CHKERRQ(ierr);
ierr = DASetVertexDivision(da,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
ierr = DASetFromOptions(da);CHKERRQ(ierr);
ierr = DACreateGlobalVector(da,&x);CHKERRQ(ierr);
ierr = DACreateGlobalVector(da,&b);CHKERRQ(ierr);
ierr = ComputeRHS(da,b);CHKERRQ(ierr);
ierr = DAGetMatrix(da,MATBAIJ,&A);CHKERRQ(ierr);
ierr = ComputeMatrix(da,A);CHKERRQ(ierr);
/* A is non-symmetric. Make A = 0.5*(A + Atrans) symmetric for testing icc and cholesky */
ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&Atrans);CHKERRQ(ierr);
ierr = MatAXPY(A,1.0,Atrans,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatScale(A,0.5);CHKERRQ(ierr);
ierr = MatDestroy(Atrans);CHKERRQ(ierr);
/* Test sbaij matrix */
flg = PETSC_FALSE;
ierr = PetscOptionsGetTruth(PETSC_NULL, "-test_sbaij1", &flg,PETSC_NULL);CHKERRQ(ierr);
if (flg){
Mat sA;
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
ierr = MatDestroy(A);CHKERRQ(ierr);
A = sA;
}
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,A,A,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetDA(pc,da);CHKERRQ(ierr);
if (trans) {
ierr = KSPSolveTranspose(ksp,b,x);CHKERRQ(ierr);
} else {
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
}
/* check final residual */
flg = PETSC_FALSE;
ierr = PetscOptionsGetTruth(PETSC_NULL, "-check_final_residual", &flg,PETSC_NULL);CHKERRQ(ierr);
if (flg){
Vec b1;
PetscReal norm;
ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
ierr = VecDuplicate(b,&b1);CHKERRQ(ierr);
ierr = MatMult(A,x,b1);CHKERRQ(ierr);
ierr = VecAXPY(b1,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(b1,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Final residual %g\n",norm);CHKERRQ(ierr);
ierr = VecDestroy(b1);CHKERRQ(ierr);
}
ierr = KSPDestroy(ksp);CHKERRQ(ierr);
ierr = VecDestroy(x);CHKERRQ(ierr);
ierr = VecDestroy(b);CHKERRQ(ierr);
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = DADestroy(da);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
static PetscErrorCode MatPartitioningApply_Chaco(MatPartitioning part,IS *partitioning)
{
PetscErrorCode ierr;
PetscInt *parttab,*locals,i,nb_locals,M,N;
PetscMPIInt size,rank;
Mat mat = part->adj,matAdj,matSeq,*A;
Mat_MPIAdj *adj;
MatPartitioning_Chaco *chaco = (MatPartitioning_Chaco*)part->data;
PetscBool flg;
IS isrow, iscol;
int nvtxs,*start,*adjacency,*vwgts,architecture,ndims_tot;
int mesh_dims[3],global_method,local_method,rqi_flag,vmax,ndims;
short *assignment;
double eigtol;
long seed;
char *mesg_log;
#if defined(PETSC_HAVE_UNISTD_H)
int fd_stdout,fd_pipe[2],count,err;
#endif
PetscFunctionBegin;
FREE_GRAPH = 0; /* otherwise Chaco will attempt to free memory for adjacency graph */
ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIADJ,&flg);CHKERRQ(ierr);
if (size>1) {
if (flg) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Distributed matrix format MPIAdj is not supported for sequential partitioners");
ierr = PetscInfo(part,"Converting distributed matrix to sequential: this could be a performance loss\n");CHKERRQ(ierr);
ierr = MatGetSize(mat,&M,&N);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,M,0,1,&isrow);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,N,0,1,&iscol);CHKERRQ(ierr);
ierr = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
matSeq = *A;
ierr = PetscFree(A);CHKERRQ(ierr);
} else {
ierr = PetscObjectReference((PetscObject)mat);CHKERRQ(ierr);
matSeq = mat;
}
if (!flg) { /* convert regular matrix to MPIADJ */
ierr = MatConvert(matSeq,MATMPIADJ,MAT_INITIAL_MATRIX,&matAdj);CHKERRQ(ierr);
} else {
ierr = PetscObjectReference((PetscObject)matSeq);CHKERRQ(ierr);
matAdj = matSeq;
}
adj = (Mat_MPIAdj*)matAdj->data; /* finaly adj contains adjacency graph */
/* arguments for Chaco library */
nvtxs = mat->rmap->N; /* number of vertices in full graph */
start = adj->i; /* start of edge list for each vertex */
vwgts = part->vertex_weights; /* weights for all vertices */
architecture = 1; /* 0 => hypercube, d => d-dimensional mesh */
ndims_tot = 0; /* total number of cube dimensions to divide */
mesh_dims[0] = part->n; /* dimensions of mesh of processors */
global_method = chaco->global_method; /* global partitioning algorithm */
local_method = chaco->local_method; /* local partitioning algorithm */
rqi_flag = chaco->eigen_method; /* should I use RQI/Symmlq eigensolver? */
vmax = chaco->nbvtxcoarsed; /* how many vertices to coarsen down to? */
ndims = chaco->eignum; /* number of eigenvectors (2^d sets) */
eigtol = chaco->eigtol; /* tolerance on eigenvectors */
seed = 123636512; /* for random graph mutations */
ierr = PetscMalloc((mat->rmap->N)*sizeof(short),&assignment);CHKERRQ(ierr);
ierr = PetscMalloc(sizeof(int)*start[nvtxs],&adjacency);CHKERRQ(ierr);
for (i=0; i<start[nvtxs]; i++) adjacency[i] = (adj->j)[i] + 1; /* 1-based indexing */
/* redirect output to buffer */
#if defined(PETSC_HAVE_UNISTD_H)
fd_stdout = dup(1);
if (pipe(fd_pipe)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SYS,"Could not open pipe");
close(1);
dup2(fd_pipe[1],1);
ierr = PetscMalloc(SIZE_LOG*sizeof(char),&mesg_log);CHKERRQ(ierr);
#endif
/* library call */
ierr = interface(nvtxs,start,adjacency,vwgts,NULL,NULL,NULL,NULL,
NULL,NULL,assignment,architecture,ndims_tot,mesh_dims,
NULL,global_method,local_method,rqi_flag,vmax,ndims,eigtol,seed);
#if defined(PETSC_HAVE_UNISTD_H)
err = fflush(stdout);
if (err) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SYS,"fflush() failed on stdout");
count = read(fd_pipe[0],mesg_log,(SIZE_LOG-1)*sizeof(char));
if (count<0) count = 0;
mesg_log[count] = 0;
close(1);
dup2(fd_stdout,1);
close(fd_stdout);
close(fd_pipe[0]);
close(fd_pipe[1]);
if (chaco->verbose) {
ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),mesg_log);
}
ierr = PetscFree(mesg_log);CHKERRQ(ierr);
#endif
if (ierr) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Chaco failed");
ierr = PetscMalloc((mat->rmap->N)*sizeof(PetscInt),&parttab);CHKERRQ(ierr);
for (i=0; i<nvtxs; i++) parttab[i] = assignment[i];
/* creation of the index set */
nb_locals = mat->rmap->N / size;
locals = parttab + rank*nb_locals;
if (rank < mat->rmap->N % size) {
nb_locals++;
locals += rank;
} else locals += mat->rmap->N % size;
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),nb_locals,locals,PETSC_COPY_VALUES,partitioning);CHKERRQ(ierr);
/* clean up */
ierr = PetscFree(parttab);CHKERRQ(ierr);
ierr = PetscFree(adjacency);CHKERRQ(ierr);
ierr = PetscFree(assignment);CHKERRQ(ierr);
ierr = MatDestroy(&matSeq);CHKERRQ(ierr);
ierr = MatDestroy(&matAdj);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode TaoSolve_Test(Tao tao)
{
Mat A = tao->hessian,B;
Vec x = tao->solution,g1,g2;
PetscErrorCode ierr;
PetscInt i;
PetscReal nrm,gnorm,hcnorm,fdnorm;
MPI_Comm comm;
Tao_Test *fd = (Tao_Test*)tao->data;
PetscFunctionBegin;
comm = ((PetscObject)tao)->comm;
if (fd->check_gradient) {
ierr = VecDuplicate(x,&g1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&g2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Testing hand-coded gradient (hc) against finite difference gradient (fd), if the ratio ||fd - hc|| / ||hc|| is\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"0 (1.e-8), the hand-coded gradient is probably correct.\n");CHKERRQ(ierr);
if (!fd->complete_print) {
ierr = PetscPrintf(comm,"Run with -tao_test_display to show difference\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"between hand-coded and finite difference gradient.\n");CHKERRQ(ierr);
}
for (i=0; i<3; i++) {
if (i == 1) {ierr = VecSet(x,-1.0);CHKERRQ(ierr);}
else if (i == 2) {ierr = VecSet(x,1.0);CHKERRQ(ierr);}
/* Compute both version of gradient */
ierr = TaoComputeGradient(tao,x,g1);CHKERRQ(ierr);
ierr = TaoDefaultComputeGradient(tao,x,g2,NULL);CHKERRQ(ierr);
if (fd->complete_print) {
MPI_Comm gcomm;
PetscViewer viewer;
ierr = PetscPrintf(comm,"Finite difference gradient\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)g2,&gcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(gcomm,&viewer);CHKERRQ(ierr);
ierr = VecView(g2,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Hand-coded gradient\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)g1,&gcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(gcomm,&viewer);CHKERRQ(ierr);
ierr = VecView(g1,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"\n");CHKERRQ(ierr);
}
ierr = VecAXPY(g2,-1.0,g1);CHKERRQ(ierr);
ierr = VecNorm(g1,NORM_2,&hcnorm);CHKERRQ(ierr);
ierr = VecNorm(g2,NORM_2,&fdnorm);CHKERRQ(ierr);
if (!hcnorm) hcnorm=1.0e-20;
ierr = PetscPrintf(comm,"ratio ||fd-hc||/||hc|| = %g, difference ||fd-hc|| = %g\n", (double)(fdnorm/hcnorm), (double)fdnorm);CHKERRQ(ierr);
}
ierr = VecDestroy(&g1);CHKERRQ(ierr);
ierr = VecDestroy(&g2);CHKERRQ(ierr);
}
if (fd->check_hessian) {
if (A != tao->hessian_pre) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot test with alternative preconditioner");
ierr = PetscPrintf(comm,"Testing hand-coded Hessian (hc) against finite difference Hessian (fd). If the ratio is\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"O (1.e-8), the hand-coded Hessian is probably correct.\n");CHKERRQ(ierr);
if (!fd->complete_print) {
ierr = PetscPrintf(comm,"Run with -tao_test_display to show difference\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"of hand-coded and finite difference Hessian.\n");CHKERRQ(ierr);
}
for (i=0;i<3;i++) {
/* compute both versions of Hessian */
ierr = TaoComputeHessian(tao,x,A,A);CHKERRQ(ierr);
if (!i) {ierr = MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);}
ierr = TaoDefaultComputeHessian(tao,x,B,B,tao->user_hessP);CHKERRQ(ierr);
if (fd->complete_print) {
MPI_Comm bcomm;
PetscViewer viewer;
ierr = PetscPrintf(comm,"Finite difference Hessian\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)B,&bcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(bcomm,&viewer);CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
}
/* compare */
ierr = MatAYPX(B,-1.0,A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_FROBENIUS,&nrm);CHKERRQ(ierr);
ierr = MatNorm(A,NORM_FROBENIUS,&gnorm);CHKERRQ(ierr);
if (fd->complete_print) {
MPI_Comm hcomm;
PetscViewer viewer;
ierr = PetscPrintf(comm,"Hand-coded Hessian\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)B,&hcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(hcomm,&viewer);CHKERRQ(ierr);
ierr = MatView(A,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Hand-coded minus finite difference Hessian\n");CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
}
if (!gnorm) gnorm = 1.0e-20;
ierr = PetscPrintf(comm,"ratio ||fd-hc||/||hc|| = %g, difference ||fd-hc|| = %g\n",(double)(nrm/gnorm),(double)nrm);CHKERRQ(ierr);
}
ierr = MatDestroy(&B);CHKERRQ(ierr);
}
tao->reason = TAO_CONVERGED_USER;
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Mat A,Atrans,sA,*submatA,*submatsA;
PetscInt bs=1,m=43,ov=1,i,j,k,*rows,*cols,M,nd=5,*idx,mm,nn;
PetscErrorCode ierr;
PetscMPIInt size;
PetscScalar *vals,rval,one=1.0;
IS *is1,*is2;
PetscRandom rand;
Vec xx,s1,s2;
PetscReal s1norm,s2norm,rnorm,tol = 1.e-10;
PetscBool flg;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-mat_block_size",&bs,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-mat_size",&m,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-ov",&ov,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-nd",&nd,PETSC_NULL);CHKERRQ(ierr);
/* create a SeqBAIJ matrix A */
M = m*bs;
ierr = MatCreateSeqBAIJ(PETSC_COMM_SELF,bs,M,M,1,PETSC_NULL,&A);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = PetscMalloc(bs*sizeof(PetscInt),&rows);CHKERRQ(ierr);
ierr = PetscMalloc(bs*sizeof(PetscInt),&cols);CHKERRQ(ierr);
ierr = PetscMalloc(bs*bs*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
ierr = PetscMalloc(M*sizeof(PetscScalar),&idx);CHKERRQ(ierr);
/* Now set blocks of random values */
/* first, set diagonal blocks as zero */
for (j=0; j<bs*bs; j++) vals[j] = 0.0;
for (i=0; i<m; i++){
cols[0] = i*bs; rows[0] = i*bs;
for (j=1; j<bs; j++) {
rows[j] = rows[j-1]+1;
cols[j] = cols[j-1]+1;
}
ierr = MatSetValues(A,bs,rows,bs,cols,vals,ADD_VALUES);CHKERRQ(ierr);
}
/* second, add random blocks */
for (i=0; i<20*bs; i++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
cols[0] = bs*(int)(PetscRealPart(rval)*m);
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
rows[0] = bs*(int)(PetscRealPart(rval)*m);
for (j=1; j<bs; j++) {
rows[j] = rows[j-1]+1;
cols[j] = cols[j-1]+1;
}
for (j=0; j<bs*bs; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
vals[j] = rval;
}
ierr = MatSetValues(A,bs,rows,bs,cols,vals,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* make A a symmetric matrix: A <- A^T + A */
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Atrans);CHKERRQ(ierr);
ierr = MatAXPY(A,one,Atrans,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatDestroy(&Atrans);CHKERRQ(ierr);
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Atrans);
ierr = MatEqual(A, Atrans, &flg);
if (!flg) {
SETERRQ(PETSC_COMM_SELF,1,"A+A^T is non-symmetric");
}
ierr = MatDestroy(&Atrans);CHKERRQ(ierr);
/* create a SeqSBAIJ matrix sA (= A) */
ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
/* Test sA==A through MatMult() */
for (i=0; i<nd; i++) {
ierr = MatGetSize(A,&mm,&nn);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,mm,&xx);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s2);CHKERRQ(ierr);
for (j=0; j<3; j++) {
ierr = VecSetRandom(xx,rand);CHKERRQ(ierr);
ierr = MatMult(A,xx,s1);CHKERRQ(ierr);
ierr = MatMult(sA,xx,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatMult - Norm1=%16.14e Norm2=%16.14e\n",s1norm,s2norm);CHKERRQ(ierr);
}
}
ierr = VecDestroy(&xx);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
}
/* Test MatIncreaseOverlap() */
ierr = PetscMalloc(nd*sizeof(IS **),&is1);CHKERRQ(ierr);
ierr = PetscMalloc(nd*sizeof(IS **),&is2);CHKERRQ(ierr);
for (i=0; i<nd; i++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
size = (int)(PetscRealPart(rval)*m);
for (j=0; j<size; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
idx[j*bs] = bs*(int)(PetscRealPart(rval)*m);
for (k=1; k<bs; k++) idx[j*bs+k] = idx[j*bs]+k;
}
ierr = ISCreateGeneral(PETSC_COMM_SELF,size*bs,idx,PETSC_COPY_VALUES,is1+i);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,size*bs,idx,PETSC_COPY_VALUES,is2+i);CHKERRQ(ierr);
}
/* for debugging */
/*
ierr = MatView(A,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = MatView(sA,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
*/
ierr = MatIncreaseOverlap(A,nd,is1,ov);CHKERRQ(ierr);
ierr = MatIncreaseOverlap(sA,nd,is2,ov);CHKERRQ(ierr);
for (i=0; i<nd; ++i) {
ierr = ISSort(is1[i]);CHKERRQ(ierr);
ierr = ISSort(is2[i]);CHKERRQ(ierr);
}
for (i=0; i<nd; ++i) {
ierr = ISEqual(is1[i],is2[i],&flg);CHKERRQ(ierr);
if (!flg){
/* ISView(is1[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ISView(is2[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); */
SETERRQ1(PETSC_COMM_SELF,1,"i=%d, is1 != is2",i);
}
}
ierr = MatGetSubMatrices(A,nd,is1,is1,MAT_INITIAL_MATRIX,&submatA);CHKERRQ(ierr);
ierr = MatGetSubMatrices(sA,nd,is2,is2,MAT_INITIAL_MATRIX,&submatsA);CHKERRQ(ierr);
/* Test MatMult() */
for (i=0; i<nd; i++) {
ierr = MatGetSize(submatA[i],&mm,&nn);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,mm,&xx);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s2);CHKERRQ(ierr);
for (j=0; j<3; j++) {
ierr = VecSetRandom(xx,rand);CHKERRQ(ierr);
ierr = MatMult(submatA[i],xx,s1);CHKERRQ(ierr);
ierr = MatMult(submatsA[i],xx,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatMult - Norm1=%16.14e Norm2=%16.14e\n",s1norm,s2norm);CHKERRQ(ierr);
}
}
ierr = VecDestroy(&xx);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
}
/* Now test MatGetSubmatrices with MAT_REUSE_MATRIX option */
ierr = MatGetSubMatrices(A,nd,is1,is1,MAT_REUSE_MATRIX,&submatA);CHKERRQ(ierr);
ierr = MatGetSubMatrices(sA,nd,is2,is2,MAT_REUSE_MATRIX,&submatsA);CHKERRQ(ierr);
/* Test MatMult() */
for (i=0; i<nd; i++) {
ierr = MatGetSize(submatA[i],&mm,&nn);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,mm,&xx);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s2);CHKERRQ(ierr);
for (j=0; j<3; j++) {
ierr = VecSetRandom(xx,rand);CHKERRQ(ierr);
ierr = MatMult(submatA[i],xx,s1);CHKERRQ(ierr);
ierr = MatMult(submatsA[i],xx,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatMult - Norm1=%16.14e Norm2=%16.14e\n",s1norm,s2norm);CHKERRQ(ierr);
}
}
ierr = VecDestroy(&xx);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
}
/* Free allocated memory */
for (i=0; i<nd; ++i) {
ierr = ISDestroy(&is1[i]);CHKERRQ(ierr);
ierr = ISDestroy(&is2[i]);CHKERRQ(ierr);
ierr = MatDestroy(&submatA[i]);CHKERRQ(ierr);
ierr = MatDestroy(&submatsA[i]);CHKERRQ(ierr);
}
ierr = PetscFree(submatA);CHKERRQ(ierr);
ierr = PetscFree(submatsA);CHKERRQ(ierr);
ierr = PetscFree(is1);CHKERRQ(ierr);
ierr = PetscFree(is2);CHKERRQ(ierr);
ierr = PetscFree(idx);CHKERRQ(ierr);
ierr = PetscFree(rows);CHKERRQ(ierr);
ierr = PetscFree(cols);CHKERRQ(ierr);
ierr = PetscFree(vals);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat C;
PetscMPIInt rank,size;
PetscInt i,m = 5,N,start,end,M,its;
PetscScalar val,Ke[16],r[4];
PetscReal x,y,h,norm,tol=1.e-14;
PetscErrorCode ierr;
PetscInt idx[4],count,*rows;
Vec u,ustar,b;
KSP ksp;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
N = (m+1)*(m+1); /* dimension of matrix */
M = m*m; /* number of elements */
h = 1.0/m; /* mesh width */
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
/* Create stiffness matrix */
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
end = start + M/size + ((M%size) > rank);
/* Assemble matrix */
ierr = FormElementStiffness(h*h,Ke); /* element stiffness for Laplacian */
for (i=start; i<end; i++) {
/* location of lower left corner of element */
x = h*(i % m); y = h*(i/m);
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
ierr = MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Create right-hand-side and solution vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,N);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)u,"Approx. Solution");CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)b,"Right hand side");CHKERRQ(ierr);
ierr = VecDuplicate(b,&ustar);CHKERRQ(ierr);
ierr = VecSet(u,0.0);CHKERRQ(ierr);
ierr = VecSet(b,0.0);CHKERRQ(ierr);
/* Assemble right-hand-side vector */
for (i=start; i<end; i++) {
/* location of lower left corner of element */
x = h*(i % m); y = h*(i/m);
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
ierr = FormElementRhs(x,y,h*h,r);CHKERRQ(ierr);
ierr = VecSetValues(b,4,idx,r,ADD_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
/* Modify matrix and right-hand-side for Dirichlet boundary conditions */
ierr = PetscMalloc1(4*m,&rows);CHKERRQ(ierr);
for (i=0; i<m+1; i++) {
rows[i] = i; /* bottom */
rows[3*m - 1 +i] = m*(m+1) + i; /* top */
}
count = m+1; /* left side */
for (i=m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
count = 2*m; /* left side */
for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
for (i=0; i<4*m; i++) {
x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
val = y;
ierr = VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatZeroRows(C,4*m,rows,1.0,0,0);CHKERRQ(ierr);
ierr = PetscFree(rows);CHKERRQ(ierr);
ierr = VecAssemblyBegin(u);CHKERRQ(ierr);
ierr = VecAssemblyEnd(u);CHKERRQ(ierr);
ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
{ Mat A;
ierr = MatConvert(C,MATSAME,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&C);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
}
/* Solve linear system */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,u);CHKERRQ(ierr);
/* Check error */
ierr = VecGetOwnershipRange(ustar,&start,&end);CHKERRQ(ierr);
for (i=start; i<end; i++) {
x = h*(i % (m+1)); y = h*(i/(m+1));
val = y;
ierr = VecSetValues(ustar,1,&i,&val,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(ustar);CHKERRQ(ierr);
ierr = VecAssemblyEnd(ustar);CHKERRQ(ierr);
ierr = VecAXPY(u,-1.0,ustar);CHKERRQ(ierr);
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G Iterations %D\n",norm*h,its);CHKERRQ(ierr);
}
/* Free work space */
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&ustar);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv) {
Mat pA,P,aijP;
PetscScalar pa[]={1.,-1.,0.,0.,1.,-1.,0.,0.,1.};
PetscInt pij[]={0,1,2};
PetscInt aij[3][3]={{0,1,2},{3,4,5},{6,7,8}};
Mat A,mC,C;
PetscScalar one=1.;
PetscErrorCode ierr;
PetscInitialize(&argc,&argv,(char *)0,help);
/* Create MAIJ matrix, P */
ierr = MatCreate(PETSC_COMM_SELF,&pA);CHKERRQ(ierr);
ierr = MatSetSizes(pA,3,3,3,3);CHKERRQ(ierr);
ierr = MatSetType(pA,MATSEQAIJ);CHKERRQ(ierr);
ierr = MatSetOption(pA,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetValues(pA,3,pij,3,pij,pa,ADD_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(pA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(pA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatCreateMAIJ(pA,3,&P);CHKERRQ(ierr);
ierr = MatDestroy(pA);
/* Create AIJ equivalent matrix, aijP, for comparison testing */
ierr = MatConvert(P,MATSEQAIJ,MAT_INITIAL_MATRIX,&aijP);
/* Create AIJ matrix, A */
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,9,9,9,9);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQAIJ);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetValues(A,3,aij[0],3,aij[0],pa,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(A,3,aij[1],3,aij[1],pa,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(A,3,aij[2],3,aij[2],pa,ADD_VALUES);CHKERRQ(ierr);
{int i;
for (i=0;i<9;i++) {
ierr = MatSetValue(A,i,i,one,ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Perform SeqAIJ_SeqMAIJ PtAP */
ierr = MatPtAP(A,P,MAT_INITIAL_MATRIX,1.,&mC);CHKERRQ(ierr);
ierr = MatView(mC,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
/* Perform SeqAIJ_SeqAIJ PtAP for comparison testing */
ierr = MatPtAP(A,aijP,MAT_INITIAL_MATRIX,1.,&C);CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
/* Perform diff of two matrices */
ierr = MatAXPY(C,-1.0,mC,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
/* Note: We should be able to use SAME_NONZERO_PATTERN on the line above, */
/* but don't because this flag doesn't assist testing. */
ierr = MatView(C,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
/* Cleanup */
ierr = MatDestroy(P);
ierr = MatDestroy(aijP);
ierr = MatDestroy(A);
ierr = MatDestroy(C);
ierr = MatDestroy(mC);
PetscFinalize();
return(0);
}
int main(int argc,char **args)
{
Mat A,Atrans,sA,*submatA,*submatsA;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt bs=1,mbs=10,ov=1,i,j,k,*rows,*cols,nd=2,*idx,rstart,rend,sz,M,N,Mbs;
PetscScalar *vals,rval,one=1.0;
IS *is1,*is2;
PetscRandom rand;
PetscBool flg,TestOverlap,TestSubMat,TestAllcols,test_sorted=PETSC_FALSE;
PetscInt vid = -1;
#if defined(PETSC_USE_LOG)
PetscLogStage stages[2];
#endif
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-mat_block_size",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-mat_mbs",&mbs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-ov",&ov,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-nd",&nd,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-view_id",&vid,NULL);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL, "-test_overlap", &TestOverlap);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL, "-test_submat", &TestSubMat);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL, "-test_allcols", &TestAllcols);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-test_sorted",&test_sorted,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,mbs*bs,mbs*bs,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(A,MATBAIJ);CHKERRQ(ierr);
ierr = MatSeqBAIJSetPreallocation(A,bs,PETSC_DEFAULT,NULL);CHKERRQ(ierr);
ierr = MatMPIBAIJSetPreallocation(A,bs,PETSC_DEFAULT,NULL,PETSC_DEFAULT,NULL);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
ierr = MatGetSize(A,&M,&N);CHKERRQ(ierr);
Mbs = M/bs;
ierr = PetscMalloc1(bs,&rows);CHKERRQ(ierr);
ierr = PetscMalloc1(bs,&cols);CHKERRQ(ierr);
ierr = PetscMalloc1(bs*bs,&vals);CHKERRQ(ierr);
ierr = PetscMalloc1(M,&idx);CHKERRQ(ierr);
/* Now set blocks of values */
for (j=0; j<bs*bs; j++) vals[j] = 0.0;
for (i=0; i<Mbs; i++) {
cols[0] = i*bs; rows[0] = i*bs;
for (j=1; j<bs; j++) {
rows[j] = rows[j-1]+1;
cols[j] = cols[j-1]+1;
}
ierr = MatSetValues(A,bs,rows,bs,cols,vals,ADD_VALUES);CHKERRQ(ierr);
}
/* second, add random blocks */
for (i=0; i<20*bs; i++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
cols[0] = bs*(PetscInt)(PetscRealPart(rval)*Mbs);
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
rows[0] = rstart + bs*(PetscInt)(PetscRealPart(rval)*mbs);
for (j=1; j<bs; j++) {
rows[j] = rows[j-1]+1;
cols[j] = cols[j-1]+1;
}
for (j=0; j<bs*bs; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
vals[j] = rval;
}
ierr = MatSetValues(A,bs,rows,bs,cols,vals,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* make A a symmetric matrix: A <- A^T + A */
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Atrans);CHKERRQ(ierr);
ierr = MatAXPY(A,one,Atrans,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatDestroy(&Atrans);CHKERRQ(ierr);
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Atrans);CHKERRQ(ierr);
ierr = MatEqual(A, Atrans, &flg);CHKERRQ(ierr);
if (flg) {
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
} else SETERRQ(PETSC_COMM_SELF,1,"A+A^T is non-symmetric");
ierr = MatDestroy(&Atrans);CHKERRQ(ierr);
/* create a SeqSBAIJ matrix sA (= A) */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
if (vid >= 0 && vid < size) {
if (!rank) printf("A: \n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
if (!rank) printf("sA: \n");
ierr = MatView(sA,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Test sA==A through MatMult() */
ierr = MatMultEqual(A,sA,10,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Error in MatConvert(): A != sA");
/* Test MatIncreaseOverlap() */
ierr = PetscMalloc1(nd,&is1);CHKERRQ(ierr);
ierr = PetscMalloc1(nd,&is2);CHKERRQ(ierr);
for (i=0; i<nd; i++) {
if (!TestAllcols) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
sz = (PetscInt)((0.5+0.2*PetscRealPart(rval))*mbs); /* 0.5*mbs < sz < 0.7*mbs */
for (j=0; j<sz; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
idx[j*bs] = bs*(PetscInt)(PetscRealPart(rval)*Mbs);
for (k=1; k<bs; k++) idx[j*bs+k] = idx[j*bs]+k;
}
ierr = ISCreateGeneral(PETSC_COMM_SELF,sz*bs,idx,PETSC_COPY_VALUES,is1+i);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,sz*bs,idx,PETSC_COPY_VALUES,is2+i);CHKERRQ(ierr);
if (rank == vid) {
ierr = PetscPrintf(PETSC_COMM_SELF," [%d] IS sz[%d]: %d\n",rank,i,sz);CHKERRQ(ierr);
ierr = ISView(is2[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
} else { /* Test all rows and colums */
sz = M;
ierr = ISCreateStride(PETSC_COMM_SELF,sz,0,1,is1+i);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,sz,0,1,is2+i);CHKERRQ(ierr);
if (rank == vid) {
PetscBool colflag;
ierr = ISIdentity(is2[i],&colflag);CHKERRQ(ierr);
printf("[%d] is2[%d], colflag %d\n",rank,(int)i,(int)colflag);
ierr = ISView(is2[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
}
}
ierr = PetscLogStageRegister("MatOv_SBAIJ",&stages[0]);CHKERRQ(ierr);
ierr = PetscLogStageRegister("MatOv_BAIJ",&stages[1]);CHKERRQ(ierr);
/* Test MatIncreaseOverlap */
if (TestOverlap) {
ierr = PetscLogStagePush(stages[0]);CHKERRQ(ierr);
ierr = MatIncreaseOverlap(sA,nd,is2,ov);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
ierr = PetscLogStagePush(stages[1]);CHKERRQ(ierr);
ierr = MatIncreaseOverlap(A,nd,is1,ov);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
if (rank == vid) {
printf("\n[%d] IS from BAIJ:\n",rank);
ierr = ISView(is1[0],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
printf("\n[%d] IS from SBAIJ:\n",rank);
ierr = ISView(is2[0],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
for (i=0; i<nd; ++i) {
ierr = ISEqual(is1[i],is2[i],&flg);CHKERRQ(ierr);
if (!flg) {
if (!rank) {
ierr = ISSort(is1[i]);CHKERRQ(ierr);
/* ISView(is1[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); */
ierr = ISSort(is2[i]);CHKERRQ(ierr);
/* ISView(is2[i],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); */
}
SETERRQ1(PETSC_COMM_SELF,1,"i=%D, is1 != is2",i);
}
}
}
/* Test MatCreateSubmatrices */
if (TestSubMat) {
if (test_sorted) {
for (i = 0; i < nd; ++i) {
ierr = ISSort(is1[i]);CHKERRQ(ierr);
}
}
ierr = MatCreateSubMatrices(A,nd,is1,is1,MAT_INITIAL_MATRIX,&submatA);CHKERRQ(ierr);
ierr = MatCreateSubMatrices(sA,nd,is1,is1,MAT_INITIAL_MATRIX,&submatsA);CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,10,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A != sA");
/* Now test MatCreateSubmatrices with MAT_REUSE_MATRIX option */
ierr = MatCreateSubMatrices(A,nd,is1,is1,MAT_REUSE_MATRIX,&submatA);CHKERRQ(ierr);
ierr = MatCreateSubMatrices(sA,nd,is1,is1,MAT_REUSE_MATRIX,&submatsA);CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,10,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatCreateSubmatrices(): A != sA");
ierr = MatDestroySubMatrices(nd,&submatA);CHKERRQ(ierr);
ierr = MatDestroySubMatrices(nd,&submatsA);CHKERRQ(ierr);
}
/* Free allocated memory */
for (i=0; i<nd; ++i) {
ierr = ISDestroy(&is1[i]);CHKERRQ(ierr);
ierr = ISDestroy(&is2[i]);CHKERRQ(ierr);
}
ierr = PetscFree(is1);CHKERRQ(ierr);
ierr = PetscFree(is2);CHKERRQ(ierr);
ierr = PetscFree(idx);CHKERRQ(ierr);
ierr = PetscFree(rows);CHKERRQ(ierr);
ierr = PetscFree(cols);CHKERRQ(ierr);
ierr = PetscFree(vals);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Mat C,A;
PetscInt i,j,m = 3,n = 2,Ii,J,rstart,rend,nz;
PetscMPIInt rank,size;
PetscErrorCode ierr;
const PetscInt *idx;
PetscScalar v;
const PetscScalar *values;
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);
n = 2*size;
/* create the matrix for the five point stencil, YET AGAIN*/
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 = MatMPIAIJSetPreallocation(C,5,NULL,5,NULL);CHKERRQ(ierr);
ierr = MatSeqAIJSetPreallocation(C,5,NULL);CHKERRQ(ierr);
for (i=0; i<m; i++) {
for (j=2*rank; j<2*rank+2; 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 = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO);CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
for (i=rstart; i<rend; i++) {
ierr = MatGetRow(C,i,&nz,&idx,&values);CHKERRQ(ierr);
ierr = PetscSynchronizedFPrintf(PETSC_COMM_WORLD,stdout,"[%d] get row %D: ",rank,i);CHKERRQ(ierr);
for (j=0; j<nz; j++) {
ierr = PetscSynchronizedFPrintf(PETSC_COMM_WORLD,stdout,"%D %G ",idx[j],PetscRealPart(values[j]));CHKERRQ(ierr);
}
ierr = PetscSynchronizedFPrintf(PETSC_COMM_WORLD,stdout,"\n");CHKERRQ(ierr);
ierr = MatRestoreRow(C,i,&nz,&idx,&values);CHKERRQ(ierr);
}
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,stdout);CHKERRQ(ierr);CHKERRQ(ierr);
ierr = MatConvert(C,MATSAME,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO);CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
KSP ksp;
PC pc;
Vec x,b;
DM da;
Mat A;
PetscInt dof=1;
PetscBool flg;
PetscScalar zero=0.0;
PetscInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-dof",&dof,NULL);CHKERRQ(ierr);
ierr = DMDACreate(PETSC_COMM_WORLD,&da);CHKERRQ(ierr);
ierr = DMDASetDim(da,3);CHKERRQ(ierr);
ierr = DMDASetBoundaryType(da,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE);CHKERRQ(ierr);
ierr = DMDASetStencilType(da,DMDA_STENCIL_STAR);CHKERRQ(ierr);
ierr = DMDASetSizes(da,3,3,3);CHKERRQ(ierr);
ierr = DMDASetNumProcs(da,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = DMDASetDof(da,dof);CHKERRQ(ierr);
ierr = DMDASetStencilWidth(da,1);CHKERRQ(ierr);
ierr = DMDASetOwnershipRanges(da,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMSetUp(da);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&b);CHKERRQ(ierr);
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&A);CHKERRQ(ierr);
ierr = VecSet(b,zero);CHKERRQ(ierr);
/* Test sbaij matrix */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-test_sbaij",&flg,NULL);CHKERRQ(ierr);
if (flg) {
Mat sA;
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
A = sA;
}
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,A,A,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetDM(pc,(DM)da);CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* check final residual */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL, "-check_final_residual", &flg,NULL);CHKERRQ(ierr);
if (flg) {
Vec b1;
PetscReal norm;
ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
ierr = VecDuplicate(b,&b1);CHKERRQ(ierr);
ierr = MatMult(A,x,b1);CHKERRQ(ierr);
ierr = VecAXPY(b1,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(b1,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Final residual %g\n",norm);CHKERRQ(ierr);
ierr = VecDestroy(&b1);CHKERRQ(ierr);
}
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc, char **args)
{
Mat A, L;
AppCtx ctx;
PetscViewer viewer;
PetscErrorCode ierr;
ierr = PetscInitialize(&argc, &args, (char *) 0, help);CHKERRQ(ierr);
ierr = ProcessOptions(&ctx);CHKERRQ(ierr);
/* Load matrix */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD, ctx.matFilename, FILE_MODE_READ, &viewer);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD, &A);CHKERRQ(ierr);
ierr = MatLoad(A, viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
/* Make graph Laplacian from matrix */
ierr = MatLaplacian(A, 1.0e-12, &L);CHKERRQ(ierr);
/* Check Laplacian */
PetscReal norm;
Vec x, y;
ierr = MatGetVecs(L, &x, NULL);CHKERRQ(ierr);
ierr = VecDuplicate(x, &y);CHKERRQ(ierr);
ierr = VecSet(x, 1.0);CHKERRQ(ierr);
ierr = MatMult(L, x, y);CHKERRQ(ierr);
ierr = VecNorm(y, NORM_INFINITY, &norm);CHKERRQ(ierr);
if (norm > 1.0e-10) SETERRQ(PetscObjectComm((PetscObject) y), PETSC_ERR_PLIB, "Invalid graph Laplacian");
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
/* Compute Fiedler vector, and perhaps more vectors */
Mat LD;
PetscScalar *a, *realpart, *imagpart, *eigvec, *work, sdummy;
PetscBLASInt bn, bN, lwork, lierr, idummy;
PetscInt n, i;
ierr = MatConvert(L, MATDENSE, MAT_INITIAL_MATRIX, &LD);CHKERRQ(ierr);
ierr = MatGetLocalSize(LD, &n, NULL);CHKERRQ(ierr);
ierr = MatDenseGetArray(LD, &a);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n, &bn);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n, &bN);CHKERRQ(ierr);
ierr = PetscBLASIntCast(5*n,&lwork);CHKERRQ(ierr);
ierr = PetscBLASIntCast(1,&idummy);CHKERRQ(ierr);
ierr = PetscMalloc4(n,PetscScalar,&realpart,n,PetscScalar,&imagpart,n*n,PetscScalar,&eigvec,lwork,PetscScalar,&work);CHKERRQ(ierr);
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
PetscStackCall("LAPACKgeev", LAPACKgeev_("N","V",&bn,a,&bN,realpart,imagpart,&sdummy,&idummy,eigvec,&bN,work,&lwork,&lierr));
if (lierr) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in LAPACK routine %d", (int) lierr);
ierr = PetscFPTrapPop();CHKERRQ(ierr);
PetscReal *r, *c;
PetscInt *perm;
ierr = PetscMalloc3(n,PetscInt,&perm,n,PetscReal,&r,n,PetscReal,&c);CHKERRQ(ierr);
for (i = 0; i < n; ++i) perm[i] = i;
ierr = PetscSortRealWithPermutation(n,realpart,perm);CHKERRQ(ierr);
for (i = 0; i < n; ++i) {
r[i] = realpart[perm[i]];
c[i] = imagpart[perm[i]];
}
for (i = 0; i < n; ++i) {
realpart[i] = r[i];
imagpart[i] = c[i];
}
/* Output spectrum */
if (ctx.showSpectrum) {
ierr = PetscPrintf(PETSC_COMM_SELF, "Spectrum\n");CHKERRQ(ierr);
for (i = 0; i < n; ++i) {ierr = PetscPrintf(PETSC_COMM_SELF, "%d: Real %g Imag %g\n", i, realpart[i], imagpart[i]);CHKERRQ(ierr);}
}
/* Check lowest eigenvalue and eigenvector */
PetscInt evInd = perm[0];
if ((realpart[0] > 1.0e-12) || (imagpart[0] > 1.0e-12)) SETERRQ(PetscObjectComm((PetscObject) L), PETSC_ERR_PLIB, "Graph Laplacian must have lowest eigenvalue 0");
for (i = 0; i < n; ++i) {
if (fabs(eigvec[evInd*n+i] - eigvec[evInd*n+0]) > 1.0e-10) SETERRQ3(PetscObjectComm((PetscObject) L), PETSC_ERR_PLIB, "Graph Laplacian must have constant lowest eigenvector ev_%d %g != ev_0 %g", i, eigvec[evInd*n+i], eigvec[evInd*n+0]);
}
/* Output Fiedler vector */
evInd = perm[1];
if (ctx.showFiedler) {
ierr = PetscPrintf(PETSC_COMM_SELF, "Fiedler vector, Re{ev} %g\n", realpart[1]);CHKERRQ(ierr);
for (i = 0; i < n; ++i) {ierr = PetscPrintf(PETSC_COMM_SELF, "%d: %g\n", i, eigvec[evInd*n+i]);CHKERRQ(ierr);}
}
/* Construct Fiedler partition */
IS fIS, fIS2;
PetscInt *fperm, *fperm2, pos, neg, posSize = 0;
ierr = PetscMalloc(n * sizeof(PetscInt), &fperm);CHKERRQ(ierr);
for (i = 0; i < n; ++i) {
if (eigvec[evInd*n+i] > 0.0) ++posSize;
}
ierr = PetscMalloc(n * sizeof(PetscInt), &fperm2);CHKERRQ(ierr);
for (i = 0; i < n; ++i) fperm[i] = i;
ierr = PetscSortRealWithPermutation(n, &eigvec[evInd*n], fperm);CHKERRQ(ierr);
for (i = 0; i < n; ++i) fperm2[n-1-i] = fperm[i];
for (i = 0, pos = 0, neg = posSize; i < n; ++i) {
if (eigvec[evInd*n+i] > 0.0) fperm[pos++] = i;
else fperm[neg++] = i;
}
ierr = ISCreateGeneral(PetscObjectComm((PetscObject) L), n, fperm, PETSC_OWN_POINTER, &fIS);CHKERRQ(ierr);
ierr = ISSetPermutation(fIS);CHKERRQ(ierr);
ierr = ISCreateGeneral(PetscObjectComm((PetscObject) L), n, fperm2, PETSC_OWN_POINTER, &fIS2);CHKERRQ(ierr);
ierr = ISSetPermutation(fIS2);CHKERRQ(ierr);
ierr = PetscFree3(perm,r,c);CHKERRQ(ierr);
ierr = PetscFree4(realpart,imagpart,eigvec,work);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(LD, &a);CHKERRQ(ierr);
ierr = MatDestroy(&LD);CHKERRQ(ierr);
ierr = MatDestroy(&L);CHKERRQ(ierr);
/* Permute matrix */
Mat AR, AR2;
ierr = MatPermute(A, fIS, fIS, &AR);CHKERRQ(ierr);
ierr = MatView(A, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(AR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = ISDestroy(&fIS);CHKERRQ(ierr);
ierr = MatPermute(A, fIS2, fIS2, &AR2);CHKERRQ(ierr);
ierr = MatView(AR2, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = ISDestroy(&fIS2);CHKERRQ(ierr);
ierr = MatDestroy(&AR);CHKERRQ(ierr);
AR = AR2;
/* Extract blocks and reorder */
Mat AP, AN, APR, ANR;
IS ispos, isneg, rpermpos, cpermpos, rpermneg, cpermneg;
PetscInt bw, bwr;
ierr = ISCreateStride(PETSC_COMM_SELF, posSize, 0, 1, &ispos);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF, n - posSize, posSize, 1, &isneg);CHKERRQ(ierr);
ierr = MatGetSubMatrix(AR, ispos, ispos, MAT_INITIAL_MATRIX, &AP);CHKERRQ(ierr);
ierr = MatGetSubMatrix(AR, isneg, isneg, MAT_INITIAL_MATRIX, &AN);CHKERRQ(ierr);
ierr = ISDestroy(&ispos);CHKERRQ(ierr);
ierr = ISDestroy(&isneg);CHKERRQ(ierr);
ierr = MatGetOrdering(AP, ctx.matOrdtype, &rpermpos, &cpermpos);CHKERRQ(ierr);
ierr = MatGetOrdering(AN, ctx.matOrdtype, &rpermneg, &cpermneg);CHKERRQ(ierr);
ierr = MatPermute(AP, rpermpos, cpermpos, &APR);CHKERRQ(ierr);
ierr = MatComputeBandwidth(AP, 0.0, &bw);CHKERRQ(ierr);
ierr = MatComputeBandwidth(APR, 0.0, &bwr);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Reduced positive bandwidth from %d to %d\n", bw, bwr);CHKERRQ(ierr);
ierr = MatPermute(AN, rpermneg, cpermneg, &ANR);CHKERRQ(ierr);
ierr = MatComputeBandwidth(AN, 0.0, &bw);CHKERRQ(ierr);
ierr = MatComputeBandwidth(ANR, 0.0, &bwr);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Reduced negative bandwidth from %d to %d\n", bw, bwr);CHKERRQ(ierr);
ierr = MatView(AP, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(APR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(AN, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(ANR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
/* Reorder original matrix */
Mat ARR;
IS rperm, cperm;
PetscInt *idx;
const PetscInt *cidx;
ierr = PetscMalloc(n * sizeof(PetscInt), &idx);CHKERRQ(ierr);
ierr = ISGetIndices(rpermpos, &cidx);CHKERRQ(ierr);
for (i = 0; i < posSize; ++i) idx[i] = cidx[i];
ierr = ISRestoreIndices(rpermpos, &cidx);CHKERRQ(ierr);
ierr = ISGetIndices(rpermneg, &cidx);CHKERRQ(ierr);
for (i = posSize; i < n; ++i) idx[i] = cidx[i-posSize] + posSize;
ierr = ISRestoreIndices(rpermneg, &cidx);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF, n, idx, PETSC_OWN_POINTER, &rperm);CHKERRQ(ierr);
ierr = ISSetPermutation(rperm);CHKERRQ(ierr);
ierr = PetscMalloc(n * sizeof(PetscInt), &idx);CHKERRQ(ierr);
ierr = ISGetIndices(cpermpos, &cidx);CHKERRQ(ierr);
for (i = 0; i < posSize; ++i) idx[i] = cidx[i];
ierr = ISRestoreIndices(cpermpos, &cidx);CHKERRQ(ierr);
ierr = ISGetIndices(cpermneg, &cidx);CHKERRQ(ierr);
for (i = posSize; i < n; ++i) idx[i] = cidx[i-posSize] + posSize;
ierr = ISRestoreIndices(cpermneg, &cidx);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF, n, idx, PETSC_OWN_POINTER, &cperm);CHKERRQ(ierr);
ierr = ISSetPermutation(cperm);CHKERRQ(ierr);
ierr = MatPermute(AR, rperm, cperm, &ARR);CHKERRQ(ierr);
ierr = MatView(ARR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = ISDestroy(&rperm);CHKERRQ(ierr);
ierr = ISDestroy(&cperm);CHKERRQ(ierr);
ierr = ISDestroy(&rpermpos);CHKERRQ(ierr);
ierr = ISDestroy(&cpermpos);CHKERRQ(ierr);
ierr = ISDestroy(&rpermneg);CHKERRQ(ierr);
ierr = ISDestroy(&cpermneg);CHKERRQ(ierr);
ierr = MatDestroy(&AP);CHKERRQ(ierr);
ierr = MatDestroy(&AN);CHKERRQ(ierr);
ierr = MatDestroy(&APR);CHKERRQ(ierr);
ierr = MatDestroy(&ANR);CHKERRQ(ierr);
/* Compare bands */
Mat B, BR;
ierr = MatCreateSubMatrixBanded(A, 50, 0.95, &B);CHKERRQ(ierr);
ierr = MatCreateSubMatrixBanded(ARR, 50, 0.95, &BR);CHKERRQ(ierr);
ierr = MatView(B, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(BR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = MatDestroy(&BR);CHKERRQ(ierr);
/* Cleanup */
ierr = MatDestroy(&ARR);CHKERRQ(ierr);
ierr = MatDestroy(&AR);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
