static void
do_test(MAP *rmap, MAP *cmap)
{
MAT *A;
VEC *x, *y;
INT i, j, m0, n0;
INT *cols = phgAlloc(cmap->nglobal * sizeof(*cols));
FLOAT *data = phgAlloc(cmap->nglobal * sizeof(*data));
A = phgMapCreateMat(rmap, cmap);
m0 = A->rmap->partition[A->rmap->rank];
n0 = A->cmap->partition[A->cmap->rank];
/* Matrix entries: A(I,J) = 1 + (I-1) + (J-1) */
for (i = m0; i < m0 + A->rmap->nlocal; i++) {
#if 0
/* Test MatAddEntry */
for (j = 0; j < A->cmap->nglobal; j++)
phgMatAddGlobalEntry(A, i, j, 1.0 + i + j);
#else
/* Test MatAddEntries */
for (j = 0; j < A->cmap->nglobal; j++) {
cols[j] = j;
data[j] = 1.0 + i + j;
}
phgMatAddGlobalEntries(A, 1, &i, A->cmap->nglobal, cols, data);
#endif
}
phgFree(cols);
phgFree(data);
phgMatAssemble(A);
phgInfo(-1, "y = A * x\n");
x = phgMapCreateVec(A->cmap, 1);
for (i = 0; i < x->map->nlocal; i++)
x->data[i] = 1.0 + i + n0;
phgVecAssemble(x);
y = phgMatVec(MAT_OP_N, 1.0, A, x, 0.0, NULL);
for (i = 0; i < y->map->nlocal; i++)
phgInfo(-1, " y->data[%d] = %lg\n", i + m0, (double)y->data[i]);
phgVecDestroy(&x);
phgVecDestroy(&y);
phgInfo(-1, "y = A' * x\n");
x = phgMapCreateVec(A->rmap, 1);
for (i = 0; i < x->map->nlocal; i++)
x->data[i] = 1.0 + i + m0;
phgVecAssemble(x);
y = phgMatVec(MAT_OP_T, 1.0, A, x, 0.0, NULL);
for (i = 0; i < y->map->nlocal; i++)
phgInfo(-1, " y->data[%d] = %lg\n", i + n0, (double)y->data[i]);
phgVecDestroy(&x);
phgVecDestroy(&y);
phgMatDestroy(&A);
}
/*
* Jacobi smoother2:
* Implement using details of matvec
* ref: matvec in matvec.c
*
* */
void
mg_Jacobi2(MAT *A, VEC *x, VEC *b, int nsmooth, void *ctx)
{
INT i, j, k, n, *pc, *pc_offp;
FLOAT *pd, *pd_offp, *vx, *vx0, *vb;
FLOAT sum, omega = _p->smooth_damp;;
VEC *x0;
#if USE_MPI
FLOAT *offp_data = NULL;
#endif /* USE_MPI */
MagicCheck(VEC, x);
MagicCheck(VEC, b);
assert(x == NULL || x->nvec == 1);
assert(b == NULL || b->nvec == 1);
if (x != NULL && !x->assembled)
phgVecAssemble(x);
if (b != NULL && !b->assembled)
phgVecAssemble(b);
x0 = phgMapCreateVec(x->map, 1);
assert(A->type != PHG_DESTROYED);
if (!A->assembled)
phgMatAssemble(A);
assert(A->type != PHG_MATRIX_FREE);
phgMatPack(A);
#if USE_MPI
if (A->cmap->nprocs > 1) {
offp_data = phgAlloc(A->cinfo->rsize * sizeof(*offp_data));
}
#endif /* USE_MPI */
if (A->cmap->nlocal != A->rmap->nlocal ||
A->cmap->nlocal != x->map->nlocal ||
A->cmap->nlocal != b->map->nlocal)
phgError(1, "%s:%d: inconsistent matrix-vector.", __FILE__,
__LINE__);
#if USE_MPI
if (A->cmap->nprocs > 1) {
phgMapScatterBegin(A->cinfo, x->nvec, x->data, offp_data);
phgMapScatterEnd(A->cinfo, x->nvec, x->data, offp_data);
}
#endif /* USE_MPI */
/* iteration */
for (k = 0; k < nsmooth; k++) {
phgVecCopy(x, &x0);
/* multiply with local data */
vx = x->data;
vx0 = x0->data;
vb = b->data;
pc = A->packed_cols;
pd = A->packed_data;
if (A->cmap->nprocs > 1) {
pc_offp = A->packed_cols + A->rmap->nlocal + A->nnz_d;
pd_offp = A->packed_data + A->nnz_d;
} else {
pc_offp = NULL;
pd_offp = NULL;
}
for (i = 0; i < A->rmap->nlocal; i++) {
INT jcol;
FLOAT aa = 0., dx;
/* x_i = (b_i - \sum_{j ~= i} a_ij * x_j) / a_ii */
sum = vb[i];
/* local data */
if ((n = *(pc++)) != 0) {
for (j = 0; j < n; j++) {
jcol = *(pc++);
if (jcol != i) {
sum -= *(pd++) * vx0[jcol];
} else {
aa = *(pd++);
assert(fabs(aa) > 1e-14);
}
}
}
/* remote data */
if (pc_offp != NULL && (n = *(pc_offp++)) != 0) {
for (j = 0; j < n; j++) {
jcol = *(pc_offp++);
sum -= *(pd_offp++) * offp_data[jcol];
}
}
dx = sum / aa - vx[i];
vx[i] += omega * dx;
}
#if USE_MPI
if (A->cmap->nprocs > 1) {
phgMapScatterBegin(A->cinfo, x->nvec, x->data, offp_data);
phgMapScatterEnd(A->cinfo, x->nvec, x->data, offp_data);
}
#endif /* USE_MPI */
}
phgVecDestroy(&x0);
#if USE_MPI
phgFree(offp_data);
#endif /* USE_MPI */
return;
}
/*
* Gauss-Sidel smoother for vector:
*
* As GS:
* 1. exchange off proc data
* 2. smooth local dof
*
* Assumption:
* 1. unknow dof is vector of dim 3
* 2. Matrix block for vector is
* | a1 -b 0 |
* | b a2 0 |
* | 0 0 a3 |
*
* */
void
mg_GaussSidel_vec(MAT *A, VEC *x, VEC *b, int nsmooth, void *ctx)
{
INT i, j, k, l, n, *pc, *pc0, *pc_offp, nlocal;
FLOAT *pd, *pd0, *pd_offp, *vx, *vb;
size_t *ps;
FLOAT sum[Dim], omega = _p->smooth_damp;
#if USE_MPI
FLOAT *offp_data = NULL;
#endif /* USE_MPI */
MagicCheck(VEC, x);
MagicCheck(VEC, b);
assert(x == NULL || x->nvec == 1);
assert(b == NULL || b->nvec == 1);
if (x != NULL && !x->assembled)
phgVecAssemble(x);
if (b != NULL && !b->assembled)
phgVecAssemble(b);
assert(A->type != PHG_DESTROYED);
if (!A->assembled)
phgMatAssemble(A);
assert(A->type != PHG_MATRIX_FREE);
phgMatPack(A);
#if USE_MPI
if (A->cmap->nprocs > 1) {
offp_data = phgAlloc(A->cinfo->rsize * sizeof(*offp_data));
}
#endif /* USE_MPI */
if (A->cmap->nlocal != A->rmap->nlocal ||
A->cmap->nlocal != x->map->nlocal ||
A->cmap->nlocal != b->map->nlocal)
phgError(1, "%s:%d: inconsistent matrix-vector.", __FILE__,
__LINE__);
if (A->cmap->nlocal % Dim != 0)
phgError(1, "%s: assume vector dof of dim 3!\n", __FUNCTION__);
#if USE_MPI
if (A->cmap->nprocs > 1) {
phgMapScatterBegin(A->cinfo, x->nvec, x->data, offp_data);
phgMapScatterEnd(A->cinfo, x->nvec, x->data, offp_data);
}
#endif /* USE_MPI */
/* iteration */
for (l = 0; l < nsmooth; l++) {
INT i_start, i_add;
/* multiply with local data */
vx = x->data;
vb = b->data;
pc0 = A->packed_cols;
pd0 = A->packed_data;
ps = A->packed_ind;
nlocal = A->rmap->nlocal;
/*
* lexicographic order: low to high
* Note: low->high and high->low alternatively does not help.
* */
if (TRUE || l % 2 == 0) {
i_start = 0;
i_add = Dim;
} else {
i_start = nlocal - Dim;
i_add = -Dim;
}
//for (i = i_start; i < A->rmap->nlocal && i >= 0; i += i_add) {
for (i = 0; i < nlocal ; i += Dim) {
INT jcol;
FLOAT aa[Dim][Dim], det, dx[Dim];
memset(aa, 0, sizeof(aa));
sum[0] = vb[i ];
sum[1] = vb[i+1];
sum[2] = vb[i+2];
/* local data */
pc = pc0 + PACK_COL(ps, i);
pd = pd0 + PACK_DAT(ps, i);
for (k = 0; k < Dim; k++) {
if ((n = *(pc++)) != 0) {
for (j = 0; j < n; j++) {
jcol = *(pc++);
if (jcol < i || jcol > i+2) {
sum[k] -= *(pd++) * vx[jcol];
} else { /* offD, jcol = i,i+1,i+2 */
aa[k][jcol - i] = *(pd++);
}
}
}
}
/* remote data */
if (A->cmap->nprocs > 1) {
pc_offp = pc0 + PACK_COL_OFFP(ps, i, nlocal);
pd_offp = pd0 + PACK_DAT_OFFP(ps, i, nlocal);
for (k = 0; k < Dim; k++) {
if ((n = *(pc_offp++)) != 0) {
for (j = 0; j < n; j++) {
jcol = *(pc_offp++);
sum[k] -= *(pd_offp++) * offp_data[jcol];
}
}
}
}
/* solve */
det = (aa[0][0] * aa[1][1] - aa[0][1] * aa[1][0]);
assert(Fabs(det) > 1e-12);
det = 1. / det;
dx[0] = (aa[1][1] * sum[0] - aa[0][1] * sum[1]) * det - vx[i ];
dx[1] = (aa[0][0] * sum[1] - aa[1][0] * sum[1]) * det - vx[i+1];
dx[2] = (1./aa[2][2] * sum[2]) - vx[i+2];
vx[i ] += omega * dx[0];
vx[i+1] += omega * dx[1];
vx[i+2] += omega * dx[2];
}
#if USE_MPI
if (A->cmap->nprocs > 1) {
phgMapScatterBegin(A->cinfo, x->nvec, x->data, offp_data);
phgMapScatterEnd(A->cinfo, x->nvec, x->data, offp_data);
}
#endif /* USE_MPI */
}
#if USE_MPI
phgFree(offp_data);
#endif /* USE_MPI */
return;
}
/*
* Gauss-Sidel smoother2:
*
* 1. interior dof (!REMOTE) is smoothed, and then offp data is updated;
* 2. proc boundary dof (REMOTE) is smoothed, and then offp data is updated.
*
* Note: need types_vec.
* */
void
mg_GaussSidel2(MAT *A, VEC *x, VEC *b, int nsmooth, void *ctx)
{
MG_LEVEL *ml = (MG_LEVEL *)ctx;
INT i, j, k, n, *pc, *pc_offp;
FLOAT *pd, *pd_offp, *vx, *vb;
FLOAT sum, omega = _p->smooth_damp;;
#if USE_MPI
FLOAT *offp_data = NULL;
#endif /* USE_MPI */
MagicCheck(VEC, x);
MagicCheck(VEC, b);
assert(x == NULL || x->nvec == 1);
assert(b == NULL || b->nvec == 1);
if (x != NULL && !x->assembled)
phgVecAssemble(x);
if (b != NULL && !b->assembled)
phgVecAssemble(b);
assert(A->type != PHG_DESTROYED);
if (!A->assembled)
phgMatAssemble(A);
assert(A->type != PHG_MATRIX_FREE);
phgMatPack(A);
#if USE_MPI
if (A->cmap->nprocs > 1) {
offp_data = phgAlloc(A->cinfo->rsize * sizeof(*offp_data));
}
#endif /* USE_MPI */
if (A->cmap->nlocal != A->rmap->nlocal ||
A->cmap->nlocal != x->map->nlocal ||
A->cmap->nlocal != b->map->nlocal)
phgError(1, "%s:%d: inconsistent matrix-vector.", __FILE__,
__LINE__);
#if USE_MPI
if (A->cmap->nprocs > 1) {
phgMapScatterBegin(A->cinfo, x->nvec, x->data, offp_data);
phgMapScatterEnd(A->cinfo, x->nvec, x->data, offp_data);
}
#endif /* USE_MPI */
/* iteration */
for (k = 0; k < nsmooth; k++) {
/* multiply with local data */
vx = x->data;
vb = b->data;
/* First, interior dof (!REMOTE) is smoothed, and then offp data is updated */
pc = A->packed_cols;
pd = A->packed_data;
if (A->cmap->nprocs > 1) {
pc_offp = A->packed_cols + A->rmap->nlocal + A->nnz_d;
pd_offp = A->packed_data + A->nnz_d;
} else {
pc_offp = NULL;
pd_offp = NULL;
}
for (i = 0; i < A->rmap->nlocal; i++) {
INT jcol;
FLOAT aa = 0., dx;
if (ml->types_vec[i] & REMOTE) {
if ((n = *(pc++)) != 0) {
pc += n;
pd += n;
}
if (pc_offp != NULL && (n = *(pc_offp++)) != 0) {
pc_offp += n;
pd_offp += n;
}
continue;
}
sum = vb[i];
/* local data */
if ((n = *(pc++)) != 0) {
for (j = 0; j < n; j++) {
jcol = *(pc++);
if (jcol != i) {
sum -= *(pd++) * vx[jcol];
} else {
aa = *(pd++);
assert(fabs(aa) > 1e-14);
}
}
}
/* remote data */
if (pc_offp != NULL && (n = *(pc_offp++)) != 0) {
for (j = 0; j < n; j++) {
jcol = *(pc_offp++);
sum -= *(pd_offp++) * offp_data[jcol];
}
}
dx = sum / aa - vx[i];
vx[i] += omega * dx;
}
#if USE_MPI
if (A->cmap->nprocs > 1) {
phgMapScatterBegin(A->cinfo, x->nvec, x->data, offp_data);
phgMapScatterEnd(A->cinfo, x->nvec, x->data, offp_data);
}
#endif /* USE_MPI */
/* Second, proc boundary dof (!REMOTE) is smoothed, and then offp data is updated */
pc = A->packed_cols;
pd = A->packed_data;
if (A->cmap->nprocs > 1) {
pc_offp = A->packed_cols + A->rmap->nlocal + A->nnz_d;
pd_offp = A->packed_data + A->nnz_d;
} else {
pc_offp = NULL;
pd_offp = NULL;
}
for (i = 0; i < A->rmap->nlocal; i++) {
INT jcol;
FLOAT aa = 0., dx;
if (!(ml->types_vec[i] & REMOTE)) {
if ((n = *(pc++)) != 0) {
pc += n;
pd += n;
}
if (pc_offp != NULL && (n = *(pc_offp++)) != 0) {
pc_offp += n;
pd_offp += n;
}
continue;
}
sum = vb[i];
/* local data */
if ((n = *(pc++)) != 0) {
for (j = 0; j < n; j++) {
jcol = *(pc++);
if (jcol != i) {
sum -= *(pd++) * vx[jcol];
} else {
aa = *(pd++);
assert(fabs(aa) > 1e-14);
}
}
}
/* remote data */
if (pc_offp != NULL && (n = *(pc_offp++)) != 0) {
for (j = 0; j < n; j++) {
jcol = *(pc_offp++);
sum -= *(pd_offp++) * offp_data[jcol];
}
}
dx = sum / aa - vx[i];
vx[i] += omega * dx;
}
#if USE_MPI
if (A->cmap->nprocs > 1) {
phgMapScatterBegin(A->cinfo, x->nvec, x->data, offp_data);
phgMapScatterEnd(A->cinfo, x->nvec, x->data, offp_data);
}
#endif /* USE_MPI */
}
#if USE_MPI
phgFree(offp_data);
#endif /* USE_MPI */
return;
}
int
main(int argc, char *argv[])
{
MAT *A, *B;
VEC *U = NULL, *x;
FLOAT *C;
SOLVER *solver, *solver1 = NULL;
INT i, j, k, n, *pvt, N = 1000, K = 2;
char *main_opts = NULL, *sub_opts = NULL;
phgOptionsRegisterInt("-n", "N value", &N);
phgOptionsRegisterInt("-k", "K value", &K);
phgOptionsRegisterString("-main_solver_opts", "Options for the main solver",
&main_opts);
phgOptionsRegisterString("-sub_solver_opts", "Options for the subsolver",
&sub_opts);
/* a direct solver is preferable for the sparse matrix */
phgOptionsPreset("-solver mumps");
phgInit(&argc, &argv);
phgPrintf(
"----------------------------------------------------------------------------\n"
"This code solves (A+UU^t)x=b using the Sherman-Morrison-Woodbury formula.\n"
"Note: may use the following to disable use of the Sherman-Morrison-Woodbury\n"
"algorithm and change to the default solver instead:\n"
" -preonly_pc_type solver -preonly_pc_opts \"-solver_maxit 2000\"\n"
"----------------------------------------------------------------------------\n"
);
phgPrintf("Generating the linear system: N = %"dFMT", K = %"dFMT"\n", N, K);
/* A is a distributed NxN SPD tridiagonal matrix (A = [-1, 2, -1]) */
n = N / phgNProcs + (phgRank < (N % phgNProcs) ? 1 : 0);
A = phgMatCreate(phgComm, n, N);
phgPrintf(" Generating matrix A.\n");
for (i = 0; i < n; i++) {
/* diagonal */
phgMatAddEntry(A, i, i, 2.0);
/* diagonal - 1 */
if (i > 0)
phgMatAddEntry(A, i, i - 1, -1.0);
else if (phgRank > 0)
phgMatAddLGEntry(A, i, A->rmap->partition[phgRank] - 1, -1.0);
/* diagonal + 1 */
if (i < n - 1)
phgMatAddEntry(A, i, i + 1, -1.0);
else if (phgRank < phgNProcs - 1)
phgMatAddLGEntry(A, i, A->rmap->partition[phgRank] + n, -1.0);
}
phgMatAssemble(A);
/* U is a K-component vector */
U = phgMapCreateVec(A->rmap, K);
phgVecRandomize(U, 123);
/* solver1 is the solver for A */
phgOptionsPush();
phgOptionsSetOptions(sub_opts);
solver1 = phgMat2Solver(SOLVER_DEFAULT, A);
phgOptionsPop();
/* x is a scratch vector */
x = phgMapCreateVec(A->rmap, 1);
/* C is a KxK dense matrix, pvt is an integer array, they store the LU
* factorization of (I + U^t*inv(A)*U) */
phgPrintf(" Generating the dense matrix I+U^t*inv(A)*U.\n");
C = phgCalloc(K * K, sizeof(*C));
pvt = phgAlloc(K * sizeof(*pvt));
for (i = 0; i < K; i++) {
for (j = 0; j < n; j++) {
solver1->rhs->data[j] = U->data[i * n + j];
x->data[j] = 0.0;
}
solver1->rhs->assembled = TRUE;
phgSolverVecSolve(solver1, FALSE, x);
for (j = 0; j < K; j++)
for (k = 0; k < n; k++)
C[i * K + j] += U->data[j * n + k] * x->data[k];
}
#if USE_MPI
if (U->map->nprocs > 1) {
FLOAT *tmp = phgAlloc(K * K * sizeof(*tmp));
MPI_Allreduce(C, tmp, K * K, PHG_MPI_FLOAT, MPI_SUM, U->map->comm);
phgFree(C);
C = tmp;
}
#endif /* USE_MPI */
for (i = 0; i < K; i++)
C[i * K + i] += 1.0;
phgPrintf(" Factorizing the dense matrix I+U^t*inv(A)*U.\n");
phgSolverDenseLU(K, C, pvt);
/* B is a matrix-free matrix representing A + U*U^t, B->mv_data is used
* to pass A, U, solver1, C and pvt to callback functions */
B = phgMapCreateMatrixFreeMat(A->rmap, A->cmap, funcB,
/* arguments carried over to CB functions */
A, U, solver1, C, pvt, NULL);
/* solver is a PreOnly solver for B whose pc_proc is set to sherman().
*
* Note: can also use pcg, gmres, or petsc for this solver, in this case
* the solution obtained with the Sherman-Morisson formula is iteratively
* refined. */
phgOptionsPush();
phgOptionsSetOptions("-solver preonly");
phgOptionsSetOptions(main_opts);
solver = phgMat2Solver(SOLVER_DEFAULT, B);
phgSolverSetPC(solver, solver, sherman);
phgOptionsPop();
for (i = 0; i < n; i++)
x->data[i] = 1.0;
phgMatVec(MAT_OP_N, 1.0, B, x, 0.0, &solver->rhs);
phgPrintf("Solving the linear system.\n");
/* reset initial solution to zero */
memset(x->data, 0, n * sizeof(*x->data));
phgSolverVecSolve(solver, TRUE, x);
for (i = 0; i < n; i++)
solver->rhs->data[i] = 1.0;
phgVecAXPBY(-1.0, solver->rhs, 1.0, &x);
phgPrintf("Checking the result: |x - x_exact| / |x_exact| = %lg\n",
(double)phgVecNorm2(x, 0, NULL) / sqrt((double)N));
phgSolverDestroy(&solver);
phgSolverDestroy(&solver1);
phgMatDestroy(&A);
phgMatDestroy(&B);
phgVecDestroy(&U);
phgVecDestroy(&x);
phgFree(C);
phgFree(pvt);
phgFinalize();
return 0;
}
static void
build_matrices(MAT *matA, MAT *matM, MAT *matC, MAT *S, FLOAT s,
DOF *u_h, DOF *p_h)
/* S is used to store s*diag(M(p_h))^(-1) */
{
int N = u_h->type->nbas; /* number of basis functions in an element */
int M = p_h->type->nbas;
int i, j;
GRID *g = u_h->g;
ELEMENT *e;
FLOAT A[N][N], B[N][N], C[N][M];
INT I[N], Ip[M];
INT k, n0;
VEC *V = phgMapCreateVec(S->rmap, 1);
phgVecDisassemble(V); /* for phgVecAddEntry */
ForAllElements(g, e) {
for (i = 0; i < N; i++) {
I[i] = phgMapE2L(matA->rmap, 0, e, i);
for (k = 0; k < M; k++) {
/* \int \grad\psi_k\cdot\phi_i */
C[i][k] = phgQuadGradBasDotBas(e, p_h, k, u_h, i, QUAD_DEFAULT);
}
for (j = 0; j <= i; j++) {
/* \int \phi_i\cdot\phi_j */
B[j][i] = B[i][j] =
phgQuadBasDotBas(e, u_h, j, u_h, i, QUAD_DEFAULT);
/* \int \curl\phi_i\cdot\curl\phi_j */
A[j][i] = A[i][j] =
phgQuadCurlBasDotCurlBas(e, u_h, j, u_h, i, QUAD_DEFAULT);
}
}
for (i = 0; i < M; i++) {
Ip[i] = phgMapE2L(matC->cmap, 0, e, i);
if (Ip[i] < 0) /* boundary entry */
continue;
phgVecAddEntry(V, 0, Ip[i],
phgQuadBasDotBas(e, p_h, i, p_h, i, QUAD_DEFAULT));
}
/* loop on basis functions */
for (i = 0; i < N; i++) {
if (phgDofDirichletBC(u_h, e, i, NULL, NULL, NULL, DOF_PROJ_CROSS))
continue;
phgMatAddEntries(matA, 1, I + i, N, I, A[i]);
phgMatAddEntries(matM, 1, I + i, N, I, B[i]);
phgMatAddEntries(matC, 1, I + i, M, Ip, C[i]);
}
}
phgVecAssemble(V);
n0 = V->map->partition[V->map->rank];
for (k = 0; k < V->map->nlocal; k++)
phgMatAddGlobalEntry(S, k + n0, k + n0, s / V->data[k]);
phgVecDestroy(&V);
phgMatAssemble(S);
phgMatSetupDiagonal(S);
phgMatAssemble(matA);
phgMatAssemble(matM);
phgMatAssemble(matC);
}
int
main(int argc, char *argv[])
{
GRID *g;
DOF *u_h;
MAT *A, *A0, *B;
MAP *map;
INT i;
size_t nnz, mem, mem_peak;
VEC *x, *y0, *y1, *y2;
double t0, t1, dnz, dnz1, mflops, mop;
char *fn = "../test/cube.dat";
FLOAT mem_max = 300;
INT refine = 0;
phgOptionsRegisterFilename("-mesh_file", "Mesh file", (char **)&fn);
phgOptionsRegisterInt("-loop_count", "Loop count", &loop_count);
phgOptionsRegisterInt("-refine", "Refinement level", &refine);
phgOptionsRegisterFloat("-mem_max", "Maximum memory", &mem_max);
phgInit(&argc, &argv);
g = phgNewGrid(-1);
if (!phgImport(g, fn, FALSE))
phgError(1, "can't read file \"%s\".\n", fn);
phgRefineAllElements(g, refine);
u_h = phgDofNew(g, DOF_DEFAULT, 1, "u_h", DofNoAction);
while (TRUE) {
phgPrintf("\n");
if (phgBalanceGrid(g, 1.2, 1, NULL, 0.))
phgPrintf("Repartition mesh, %d submeshes, load imbalance: %lg\n",
g->nprocs, (double)g->lif);
map = phgMapCreate(u_h, NULL);
A = phgMapCreateMat(map, map);
A->handle_bdry_eqns = TRUE;
build_matrix(A, u_h);
phgMatAssemble(A);
/* Note: A is unsymmetric (A' != A) if boundary entries not removed */
phgMatRemoveBoundaryEntries(A);
#if 0
/* test block matrix operation */
A0 = phgMatCreateBlockMatrix(g->comm, 1, 1, &A, NULL);
#else
A0 = A;
#endif
phgPrintf("%d DOF, %d elems, %d submeshes, matrix size: %d, LIF: %lg\n",
DofGetDataCountGlobal(u_h), g->nleaf_global,
g->nprocs, A->rmap->nglobal, (double)g->lif);
/* test PHG mat-vec multiply */
x = phgMapCreateVec(A->cmap, 1);
y1 = phgMapCreateVec(A->rmap, 1);
phgVecRandomize(x, 123);
phgMatVec(MAT_OP_N, 1.0, A0, x, 0.0, &y1);
phgPerfGetMflops(g, NULL, NULL); /* reset flops counter */
t0 = phgGetTime(NULL);
for (i = 0; i < loop_count; i++) {
phgMatVec(MAT_OP_N, 1.0, A0, x, 0.0, &y1);
}
t1 = phgGetTime(NULL);
mflops = phgPerfGetMflops(g, NULL, NULL);
y0 = phgVecCopy(y1, NULL);
nnz = A->nnz_d + A->nnz_o;
#if USE_MPI
dnz1 = nnz;
MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
dnz = nnz;
#endif
mop = loop_count * (dnz + dnz - A->rmap->nlocal) * 1e-6;
phgPrintf("\n");
t1 -= t0;
phgPrintf(" PHG: time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF)\n",
t1, dnz, mop / (t1 == 0 ? 1. : t1), mflops);
/* test trans(A)*x */
phgPerfGetMflops(g, NULL, NULL); /* reset flops counter */
t0 = phgGetTime(NULL);
for (i = 0; i < loop_count; i++) {
phgMatVec(MAT_OP_T, 1.0, A0, x, 0.0, &y1);
}
t1 = phgGetTime(NULL);
mflops = phgPerfGetMflops(g, NULL, NULL);
t1 -= t0;
phgPrintf(" A'*x: time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
"err: %le\n", t1, dnz, mop / (t1 == 0 ? 1. : t1), mflops,
(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));
/* time A * trans(A) */
phgPerfGetMflops(g, NULL, NULL); /* reset flops counter */
t0 = phgGetTime(NULL);
B = phgMatMat(MAT_OP_N, MAT_OP_N, 1.0, A, A, 0.0, NULL);
t1 = phgGetTime(NULL);
mflops = phgPerfGetMflops(g, NULL, NULL);
nnz = B->nnz_d + B->nnz_o;
#if USE_MPI
dnz1 = nnz;
MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
dnz = nnz;
#endif
/* compare B*x <--> A*A*x */
y2 = phgMatVec(MAT_OP_N, 1.0, B, x, 0.0, NULL);
phgMatVec(MAT_OP_N, 1.0, A0, y0, 0.0, &y1);
phgMatDestroy(&B);
t1 -= t0;
phgPrintf(" A*A: time %0.4lf, nnz %0.16lg, %0.2lfMF, err: %le\n",
t1, dnz, mflops,
(double)phgVecNorm2(phgVecAXPBY(-1.0, y1, 1.0, &y2), 0, NULL));
#if USE_PETSC
{
Mat ma, mb;
MatInfo info;
Vec va, vb, vc;
PetscScalar *vec;
ma = phgPetscCreateMatAIJ(A);
MatGetVecs(ma, PETSC_NULL, &va);
VecDuplicate(va, &vb);
VecGetArray(va, &vec);
memcpy(vec, x->data, x->map->nlocal * sizeof(*vec));
VecRestoreArray(va, &vec);
MatMult(ma, va, vb);
phgPerfGetMflops(g, NULL, NULL); /* reset flops counter */
t0 = phgGetTime(NULL);
for (i = 0; i < loop_count; i++) {
MatMult(ma, va, vb);
}
t1 = phgGetTime(NULL);
mflops = phgPerfGetMflops(g, NULL, NULL);
VecGetArray(vb, &vec);
memcpy(y1->data, vec, x->map->nlocal * sizeof(*vec));
VecRestoreArray(vb, &vec);
MatGetInfo(ma, MAT_GLOBAL_SUM, &info);
/*phgPrintf(" --------------------------------------------"
"-------------------------\n");*/
phgPrintf("\n");
t1 -= t0;
dnz = info.nz_used;
phgPrintf(" PETSc: time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
"err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));
phgPerfGetMflops(g, NULL, NULL); /* reset flops counter */
t0 = phgGetTime(NULL);
for (i = 0; i < loop_count; i++) {
MatMultTranspose(ma, va, vb);
}
t1 = phgGetTime(NULL);
mflops = phgPerfGetMflops(g, NULL, NULL);
VecGetArray(vb, &vec);
memcpy(y1->data, vec, x->map->nlocal * sizeof(*vec));
VecRestoreArray(vb, &vec);
t1 -= t0;
phgPrintf(" A'*x: time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
"err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));
phgPerfGetMflops(g, NULL, NULL); /* reset flops counter */
t0 = phgGetTime(NULL);
MatMatMult(ma, ma, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &mb);
t1 = phgGetTime(NULL);
mflops = phgPerfGetMflops(g, NULL, NULL);
t1 -= t0;
MatGetInfo(mb, MAT_GLOBAL_SUM, &info);
dnz = info.nz_used;
VecDuplicate(va, &vc);
/* compare B*x <--> A*A*x */
MatMult(ma, vb, vc);
MatMult(mb, va, vb);
VecGetArray(vb, &vec);
memcpy(y1->data, vec, x->map->nlocal * sizeof(*vec));
VecRestoreArray(vb, &vec);
VecGetArray(vc, &vec);
memcpy(y2->data, vec, x->map->nlocal * sizeof(*vec));
VecRestoreArray(vc, &vec);
phgPrintf(" A*A: time %0.4lf, nnz %0.16lg, %0.2lfMF, err: %le\n",
t1, dnz, mflops,
(double)phgVecNorm2(phgVecAXPBY(-1.0, y1, 1.0, &y2), 0, NULL));
phgPetscMatDestroy(&mb);
phgPetscMatDestroy(&ma);
phgPetscVecDestroy(&va);
phgPetscVecDestroy(&vb);
phgPetscVecDestroy(&vc);
}
#endif /* USE_PETSC */
#if USE_HYPRE
{
HYPRE_IJMatrix ma;
HYPRE_IJVector va, vb, vc;
HYPRE_ParCSRMatrix par_ma;
hypre_ParCSRMatrix *par_mb;
HYPRE_ParVector par_va, par_vb, par_vc;
HYPRE_Int offset, *ni, start, end;
assert(sizeof(INT)==sizeof(int) && sizeof(FLOAT)==sizeof(double));
setup_hypre_mat(A, &ma);
ni = phgAlloc(2 * A->rmap->nlocal * sizeof(*ni));
offset = A->cmap->partition[A->cmap->rank];
for (i = 0; i < A->rmap->nlocal; i++)
ni[i] = i + offset;
HYPRE_IJVectorCreate(g->comm, offset, offset + A->rmap->nlocal - 1,
&va);
HYPRE_IJVectorCreate(g->comm, offset, offset + A->rmap->nlocal - 1,
&vb);
HYPRE_IJVectorCreate(g->comm, offset, offset + A->rmap->nlocal - 1,
&vc);
HYPRE_IJVectorSetObjectType(va, HYPRE_PARCSR);
HYPRE_IJVectorSetObjectType(vb, HYPRE_PARCSR);
HYPRE_IJVectorSetObjectType(vc, HYPRE_PARCSR);
HYPRE_IJVectorSetMaxOffProcElmts(va, 0);
HYPRE_IJVectorSetMaxOffProcElmts(vb, 0);
HYPRE_IJVectorSetMaxOffProcElmts(vc, 0);
HYPRE_IJVectorInitialize(va);
HYPRE_IJVectorInitialize(vb);
HYPRE_IJVectorInitialize(vc);
HYPRE_IJMatrixGetObject(ma, (void **)(void *)&par_ma);
HYPRE_IJVectorGetObject(va, (void **)(void *)&par_va);
HYPRE_IJVectorGetObject(vb, (void **)(void *)&par_vb);
HYPRE_IJVectorGetObject(vc, (void **)(void *)&par_vc);
HYPRE_IJVectorSetValues(va, A->cmap->nlocal, ni, (double *)x->data);
HYPRE_IJVectorAssemble(va);
HYPRE_IJVectorAssemble(vb);
HYPRE_IJVectorAssemble(vc);
HYPRE_IJMatrixGetRowCounts(ma, A->cmap->nlocal,
ni, ni + A->rmap->nlocal);
for (i = 0, nnz = 0; i < A->rmap->nlocal; i++)
nnz += ni[A->rmap->nlocal + i];
#if USE_MPI
dnz1 = nnz;
MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
dnz = nnz;
#endif
HYPRE_ParCSRMatrixMatvec(1.0, par_ma, par_va, 0.0, par_vb);
phgPerfGetMflops(g, NULL, NULL); /* reset flops counter */
t0 = phgGetTime(NULL);
for (i = 0; i < loop_count; i++) {
HYPRE_ParCSRMatrixMatvec(1.0, par_ma, par_va, 0.0, par_vb);
}
t1 = phgGetTime(NULL);
mflops = phgPerfGetMflops(g, NULL, NULL);
HYPRE_IJVectorGetValues(vb, A->rmap->nlocal, ni, (double*)y1->data);
/*phgPrintf(" --------------------------------------------"
"-------------------------\n");*/
phgPrintf("\n");
t1 -= t0;
phgPrintf(" HYPRE: time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
"err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));
phgPerfGetMflops(g, NULL, NULL); /* reset flops counter */
t0 = phgGetTime(NULL);
for (i = 0; i < loop_count; i++) {
HYPRE_ParCSRMatrixMatvecT(1.0, par_ma, par_va, 0.0, par_vb);
}
t1 = phgGetTime(NULL);
mflops = phgPerfGetMflops(g, NULL, NULL);
HYPRE_IJVectorGetValues(vb, A->rmap->nlocal, ni, (double*)y1->data);
t1 -= t0;
phgPrintf(" A'*x: time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
"err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));
phgPerfGetMflops(g, NULL, NULL); /* reset flops counter */
t0 = phgGetTime(NULL);
/* Note: 'HYPRE_ParCSRMatrix' is currently typedef'ed to
* 'hypre_ParCSRMatrix *' */
par_mb = hypre_ParMatmul((hypre_ParCSRMatrix *)par_ma,
(hypre_ParCSRMatrix *)par_ma);
t1 = phgGetTime(NULL);
mflops = phgPerfGetMflops(g, NULL, NULL);
start = hypre_ParCSRMatrixFirstRowIndex(par_mb);
end = hypre_ParCSRMatrixLastRowIndex(par_mb) + 1;
for (i = start, nnz = 0; i < end; i++) {
HYPRE_Int ncols;
hypre_ParCSRMatrixGetRow(par_mb, i, &ncols, NULL, NULL);
hypre_ParCSRMatrixRestoreRow(par_mb, i, &ncols, NULL, NULL);
nnz += ncols;
}
#if USE_MPI
dnz1 = nnz;
MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
dnz = nnz;
#endif
/* compare B*x <--> A*A*x */
HYPRE_ParCSRMatrixMatvec(1.0, par_ma, par_vb, 0.0, par_vc);
HYPRE_ParCSRMatrixMatvec(1.0, (void *)par_mb, par_va, 0.0, par_vb);
HYPRE_IJVectorGetValues(vb, A->rmap->nlocal, ni, (double*)y1->data);
HYPRE_IJVectorGetValues(vc, A->rmap->nlocal, ni, (double*)y2->data);
hypre_ParCSRMatrixDestroy((par_mb));
t1 -= t0;
phgPrintf(" A*A: time %0.4lf, nnz %0.16lg, %0.2lfMF, err: %le\n",
t1, dnz, mflops,
(double)phgVecNorm2(phgVecAXPBY(-1.0, y1, 1.0, &y2), 0, NULL));
phgFree(ni);
HYPRE_IJMatrixDestroy(ma);
HYPRE_IJVectorDestroy(va);
HYPRE_IJVectorDestroy(vb);
HYPRE_IJVectorDestroy(vc);
}
#endif /* USE_HYPRE */
if (A0 != A)
phgMatDestroy(&A0);
#if 0
if (A->rmap->nglobal > 1000) {
VEC *v = phgMapCreateVec(A->rmap, 3);
for (i = 0; i < v->map->nlocal; i++) {
v->data[i + 0 * v->map->nlocal] = 1 * (i + v->map->partition[g->rank]);
v->data[i + 1 * v->map->nlocal] = 2 * (i + v->map->partition[g->rank]);
v->data[i + 2 * v->map->nlocal] = 3 * (i + v->map->partition[g->rank]);
}
phgMatDumpMATLAB(A, "A", "A.m");
phgVecDumpMATLAB(v, "v", "v.m");
phgFinalize();
exit(0);
}
#endif
phgMatDestroy(&A);
phgVecDestroy(&x);
phgVecDestroy(&y0);
phgVecDestroy(&y1);
phgVecDestroy(&y2);
phgMapDestroy(&map);
mem = phgMemoryUsage(g, &mem_peak);
dnz = mem / (1024.0 * 1024.0);
dnz1 = mem_peak / (1024.0 * 1024.0);
/*phgPrintf(" --------------------------------------------"
"-------------------------\n");*/
phgPrintf("\n");
phgPrintf(" Memory: current %0.4lgMB, peak %0.4lgMB\n", dnz, dnz1);
#if 0
{
static int loop_count = 0;
if (++loop_count == 4)
break;
}
#endif
if (mem_peak > 1024 * (size_t)1024 * mem_max)
break;
phgRefineAllElements(g, 1);
}
phgDofFree(&u_h);
phgFreeGrid(&g);
phgFinalize();
return 0;
}