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;
}
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);
}