mat mars(Agraph_t* g, struct marsopts opts)
{
int i, j, n = agnnodes(g), k = MIN(n, MAX(opts.k, 2)), iter = 0;
mat dij, u, u_trans, q, r, q_t, tmp, tmp2, z;
double* s = (double*) malloc(sizeof(double)*k);
double* ones = (double*) malloc(sizeof(double)*n);
double* d;
int* anchors = (int*) malloc(sizeof(int)*k);
int* clusters = NULL;
double change = 1, old_stress = -1;
dij = mat_new(k, n);
u = mat_new(n,k);
tmp = mat_new(n,k);
darrset(ones,n,-1);
select_anchors(g, dij, anchors, k);
if(opts.color) {
for(i = 0; i < k; i++) {
Agnode_t* anchor = get_node(anchors[i]);
agset(anchor, "color", "red");
}
}
if(opts.power != 1) {
clusters = graph_cluster(g,dij,anchors);
}
singular_vectors(g, dij, opts.power, u, s);
vec_scalar_mult(s, k, -1);
u_trans = mat_trans(u);
d = mat_mult_for_d(u, s, u_trans, ones);
for(i = 0; i < u->c; i++) {
double* col = mat_col(u,i);
double* b = inv_mul_ax(d,col,u->r);
for(j = 0; j < u->r; j++) {
tmp->m[mindex(j,i,tmp)] = b[j];
}
free(b);
free(col);
}
tmp2 = mat_mult(u_trans,tmp);
for(i = 0; i < k; i++) {
tmp2->m[mindex(i,i,tmp2)] += (1.0/s[i]);
}
q = mat_new(tmp2->r, tmp2->c);
r = mat_new(tmp2->c, tmp2->c);
qr_factorize(tmp2,q,r);
q_t = mat_trans(q);
if(opts.given) {
z = get_positions(g, opts.dim);
} else {
z = mat_rand(n, opts.dim);
}
translate_by_centroid(z);
if(opts.viewer) {
init_viewer(g, opts.max_iter);
append_layout(z);
}
old_stress = stress(z, dij, anchors, opts.power);
while(change > EPSILON && iter < opts.max_iter) {
mat right_side;
double new_stress;
if(opts.power == 1) {
right_side = barnes_hut(z);
} else {
right_side = barnes_hut_cluster(z, dij, clusters, opts.power);
}
for(i = 0; i < opts.dim; i++) {
double sum = 0;
double* x;
double* b = mat_col(right_side,i);
for(j = 0; j < right_side->r; j++) {
sum += b[j];
}
x = inv_mul_full(d, b, right_side->r, u, u_trans, q_t, r);
for(j = 0; j < z->r; j++) {
z->m[mindex(j,i,z)] = x[j] - sum/right_side->r;
}
free(x);
free(b);
}
adjust_anchors(g, anchors, k, z);
update_anchors(z, dij, anchors, opts.power);
translate_by_centroid(z);
if(opts.viewer) {
append_layout(z);
}
new_stress = stress(z, dij, anchors, opts.power);
change = fabs(new_stress-old_stress)/old_stress;
old_stress = new_stress;
mat_free(right_side);
iter++;
}
mat_free(dij);
mat_free(u);
mat_free(u_trans);
mat_free(q);
mat_free(r);
mat_free(q_t);
mat_free(tmp);
mat_free(tmp2);
free(s);
free(ones);
free(d);
free(anchors);
free(clusters);
return z;
}
matrix_t * mpi_mat_rand(
idx_t const mode,
idx_t const nfactors,
permutation_t const * const perm,
rank_info * const rinfo)
{
idx_t const localdim = rinfo->mat_end[mode] - rinfo->mat_start[mode];
matrix_t * mymat = mat_alloc(localdim, nfactors);
MPI_Status status;
/* figure out buffer sizes */
idx_t maxlocaldim = localdim;
if(rinfo->rank == 0) {
MPI_Reduce(MPI_IN_PLACE, &maxlocaldim, 1, SPLATT_MPI_IDX, MPI_MAX, 0,
rinfo->comm_3d);
} else {
MPI_Reduce(&maxlocaldim, NULL, 1, SPLATT_MPI_IDX, MPI_MAX, 0,
rinfo->comm_3d);
}
/* root rank does the heavy lifting */
if(rinfo->rank == 0) {
/* allocate buffers */
idx_t * loc_perm = splatt_malloc(maxlocaldim * sizeof(*loc_perm));
val_t * vbuf = splatt_malloc(maxlocaldim * nfactors * sizeof(*vbuf));
/* allocate initial factor */
matrix_t * full_factor = mat_rand(rinfo->global_dims[mode], nfactors);
/* copy root's own matrix to output */
#pragma omp parallel for schedule(static)
for(idx_t i=0; i < localdim; ++i) {
idx_t const gi = rinfo->mat_start[mode] + perm->iperms[mode][i];
for(idx_t f=0; f < nfactors; ++f) {
mymat->vals[f + (i*nfactors)] = full_factor->vals[f+(gi*nfactors)];
}
}
/* communicate! */
for(int p=1; p < rinfo->npes; ++p) {
/* first receive layer start and permutation info */
idx_t layerstart;
idx_t nrows;
MPI_Recv(&layerstart, 1, SPLATT_MPI_IDX, p, 0, rinfo->comm_3d, &status);
MPI_Recv(&nrows, 1, SPLATT_MPI_IDX, p, 1, rinfo->comm_3d, &status);
MPI_Recv(loc_perm, nrows, SPLATT_MPI_IDX, p, 2, rinfo->comm_3d, &status);
/* fill buffer */
#pragma omp parallel for schedule(static)
for(idx_t i=0; i < nrows; ++i) {
idx_t const gi = layerstart + loc_perm[i];
for(idx_t f=0; f < nfactors; ++f) {
vbuf[f + (i*nfactors)] = full_factor->vals[f+(gi*nfactors)];
}
}
/* send to rank p */
MPI_Send(vbuf, nrows * nfactors, SPLATT_MPI_VAL, p, 3, rinfo->comm_3d);
}
mat_free(full_factor);
splatt_free(loc_perm);
splatt_free(vbuf);
/* other ranks just send/recv */
} else {
/* send permutation info to root */
MPI_Send(&(rinfo->layer_starts[mode]), 1, SPLATT_MPI_IDX, 0, 0, rinfo->comm_3d);
MPI_Send(&localdim, 1, SPLATT_MPI_IDX, 0, 1, rinfo->comm_3d);
MPI_Send(perm->iperms[mode] + rinfo->mat_start[mode], localdim,
SPLATT_MPI_IDX, 0, 2, rinfo->comm_3d);
/* receive factor */
MPI_Recv(mymat->vals, mymat->I * mymat->J, SPLATT_MPI_VAL, 0, 3,
rinfo->comm_3d, &status);
}
return mymat;
}
int main(int argc, char **argv) {
srand(time(NULL));
Cache cache;
double max_runtime;
/* Overly slow ones commented out by default. */
MatMul mat_mul_funcs[] = {
/*mat_mul_cpu,*/
mat_mul_cpu_trans,
mat_mul_cpu_trans_vec,
mat_mul_cpu_block,
mat_mul_cpu_cblas,
/*mat_mul_cl,*/
mat_mul_cl_row_priv,
mat_mul_cl_row_local,
mat_mul_cl_row_priv_col_local,
mat_mul_cl_row_priv_cols_local,
/* TODO broken for larger matrics, some cells contain trash.
* Likey some memory overflow problem. */
/*mat_mul_cl_block,*/
mat_mul_cl_clblas,
};
int first, func_done[NELEMS(mat_mul_funcs)] = {0};
size_t f, i;
size_t mat_sizeof;
/* CLI args. */
if (argc > 1) {
max_runtime = strtod(argv[1], NULL);
} else {
max_runtime = 1.0;
}
common_init(&(cache.common), NULL);
/* Unit test 2x2. */
{
const F A[] = {
1.0, 2.0,
3.0, 4.0
};
const F B[] = {
5.0, 6.0,
7.0, 8.0
};
enum N { n = 2 };
F C[n*n];
const F C_ref[] = {
19.0, 22.0,
43.0, 50.0
};
cl_buf_init(&cache, n * n * sizeof(F));
for (f = 0; f < sizeof(mat_mul_funcs)/sizeof(mat_mul_funcs[0]); ++f) {
mat_zero(C, n);
mat_mul_funcs[f](A, B, C, n, &cache);
mat_assert_eq(C, C_ref, n);
}
cl_buf_deinit(&cache);
}
/* Unit test 4x4. */
{
const F A[] = {
1.0, 2.0, 3.0, 4.0,
5.0, 6.0, 7.0, 8.0,
9.0, 10.0, 11.0, 12.0,
13.0, 14.0, 15.0, 16.0,
};
const F B[] = {
17.0, 18.0, 19.0, 20.0,
21.0, 22.0, 23.0, 24.0,
25.0, 26.0, 27.0, 28.0,
29.0, 30.0, 31.0, 32.0,
};
const F C_ref[] = {
250.0, 260.0, 270.0, 280.0,
618.0, 644.0, 670.0, 696.0,
986.0, 1028.0, 1070.0, 1112.0,
1354.0, 1412.0, 1470.0, 1528.0,
};
enum N { n = 4 };
F C[n*n];
cl_buf_init(&cache, n * n * sizeof(F));
for (f = 0; f < NELEMS(mat_mul_funcs); ++f) {
mat_zero(C, n);
mat_mul_funcs[f](A, B, C, n, &cache);
mat_assert_eq(C, C_ref, n);
}
cl_buf_deinit(&cache);
}
/* Benchmarks. */
{
double dt;
F *A = NULL, *B = NULL, *C = NULL, *C_ref = NULL, *dst = NULL, *ref = NULL;
int done;
size_t n = 2;
puts("#matmul");
done = 0;
while(1) {
printf("%zu ", (size_t)log2(n));
mat_sizeof = n * n * sizeof(F);
/* CPU setup. */
A = aligned_alloc(VECTOR_SIZEOF, mat_sizeof);
B = aligned_alloc(VECTOR_SIZEOF, mat_sizeof);
C = aligned_alloc(VECTOR_SIZEOF, mat_sizeof);
C_ref = aligned_alloc(VECTOR_SIZEOF, mat_sizeof);
if (NULL == A || NULL == B || NULL == C) {
printf("error: could not allocate memory for n = %zu", n);
break;
}
mat_rand(A, n);
mat_rand(B, n);
cl_buf_init(&cache, mat_sizeof);
first = 1;
for (f = 0; f < NELEMS(mat_mul_funcs); ++f) {
if (func_done[f]) {
printf("%*s", 10, "");
} else {
if (first) {
dst = C_ref;
ref = NULL;
first = 0;
} else {
dst = C;
ref = C_ref;
}
dt = bench(mat_mul_funcs[f], A, B, dst, ref, n, &cache);
if (dt > max_runtime)
func_done[f] = 1;
}
}
puts("");
done = 1;
for (i = 0; i < NELEMS(mat_mul_funcs); ++i) {
if (!func_done[i]) {
done = 0;
break;
}
}
if (done)
break;
n *= 2;
/* CPU deinit. */
free(A);
free(B);
free(C);
free(C_ref);
cl_buf_deinit(&cache);
}
common_deinit(&cache.common);
}
return EXIT_SUCCESS;
}
