int
main(void)
{
int i;
flint_rand_t state;
printf("init/ clear... ");
fflush(stdout);
_randinit(state);
/* Unmanaged element type (long) */
for (i = 0; i < 100; i++)
{
long m, n;
ctx_t ctx;
mat_t A;
m = n_randint(state, 100) + 1;
n = n_randint(state, 100) + 1;
ctx_init_long(ctx);
mat_init(A, m, n, ctx);
mat_randtest(A, state, ctx);
mat_clear(A, ctx);
ctx_clear(ctx);
}
/* Managed element type (mpq_t) */
for (i = 0; i < 100; i++)
{
long m, n;
ctx_t ctx;
mat_t A;
m = n_randint(state, 100) + 1;
n = n_randint(state, 100) + 1;
ctx_init_mpq(ctx);
mat_init(A, m, n, ctx);
mat_randtest(A, state, ctx);
mat_clear(A, ctx);
ctx_clear(ctx);
}
_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
/**
* Main function
*
* @param argc
* @param argv
*/
int main(int argc, char **argv)
{
// create PAPI routines
PapiCounterList papi_routines;
papi_routines.AddRoutine("matvec");
// allocate arrays
float a[ROWS][COLS];
float b[COLS];
float c[ROWS] = {0.0f};
printf("Rows: %d\n", ROWS);
printf("Cols: %d\n", COLS);
printf("Runs: %d\n", RUNS);
// initialize matrix & vector
mat_init(ROWS, COLS, 1.0, a);
vec_init(COLS, 3.0, b);
// do the measurement
papi_routines["matvec"].Start();
for (unsigned i = 0; i < RUNS; i++)
mat_vec_mul(ROWS, COLS, a, b, c);
papi_routines["matvec"].Stop();
// print results
printf("Control sum: %f\n", vec_sum(ROWS, c));
printf("\n");
papi_routines.PrintScreen();
return EXIT_SUCCESS;
}
double second_subproblem_obj (double ** ytwo, double ** z, double ** wtwo, double rho, int N, double* lambda) {
double ** temp = mat_init (N, N);
double ** difftwo = mat_init (N, N);
mat_zeros (difftwo, N, N);
// reg = 0.5 * sum_k max_n | w_nk | -> group-lasso
mat_zeros (temp, N, N);
double * maxn = new double [N];
for (int i = 0; i < N; i ++) { // Ian: need initial
maxn[i] = -INF;
}
for (int i = 0; i < N; i ++) {
for (int j = 0; j < N; j ++) {
if (wtwo[i][j] > maxn[j])
maxn[j] = wtwo[i][j];
}
}
double sumk = 0.0;
for (int i = 0; i < N; i ++) {
sumk += lambda[i]*maxn[i];
}
double group_lasso = sumk;
// sum2 = y_2^T dot (w_2 - z) -> linear
mat_zeros (temp, N, N);
mat_sub (wtwo, z, difftwo, N, N);
mat_tdot (ytwo, difftwo, temp, N, N);
double sum2 = mat_sum (temp, N, N);
// sum3 = 0.5 * rho * || w_2 - z_2 ||^2 -> quadratic mat_zeros (temp, N, N);
mat_sub (wtwo, z, temp, N, N);
double sum3 = 0.5 * rho * mat_norm2 (temp, N, N);
mat_free (temp, N, N);
// ouput values of each components
#ifdef BLOCKWISE_DUMP
cout << "[Blockwise] (group_lasso, linear, quadratic) = ("
<< group_lasso << ", " << sum2 << ", " << sum3
<< ")" << endl;
#endif
//cerr << group_lasso << ", " << sum2 << ", " << sum3 << endl;
return group_lasso + sum2 + sum3;
}
/**
* Main function
*
* @param argc
* @param argv
*/
int main(int argc, char **argv)
{
// allocate matrix
float *A = (float*)_mm_malloc(ROWS * COLS * sizeof(float), 64);
if(A == NULL)
{
fprintf(stderr, "_mm_malloc error !\n");
return EXIT_FAILURE;
}
// allocate vectors
float *B = (float*)_mm_malloc(COLS * sizeof(float), 64);
if(A == NULL)
{
fprintf(stderr, "_mm_malloc error !\n");
_mm_free(A);
return EXIT_FAILURE;
}
float *C = (float*)_mm_malloc(ROWS * sizeof(float), 64);
if(A == NULL)
{
fprintf(stderr, "_mm_malloc error !\n");
_mm_free(A);
_mm_free(B);
return EXIT_FAILURE;
}
printf("Rows: %d\n", ROWS);
printf("Cols: %d\n", COLS);
printf("Runs: %d\n", RUNS);
// initialize matrix & vector
const double tstart = omp_get_wtime();
mat_init(ROWS, COLS, 1.0, A);
vec_init(COLS, 3.0, B);
const double tinit = omp_get_wtime();
// do the measurement
for(unsigned i = 0; i < RUNS; i++)
{
mat_vec_mul(ROWS, COLS, A, B, C);
}
const double tcalc = omp_get_wtime();
// print results
printf("Control sum: %f\n", vec_sum(ROWS, C));
printf("Time Initialization: %0.3f\n", tinit - tstart);
printf("Time Calculation: %0.3f\n", tcalc - tinit);
printf("Time Total: %0.3f\n", tcalc - tstart);
// free memory
_mm_free(A);
_mm_free(B);
_mm_free(C);
return EXIT_SUCCESS;
}
void init_matrix(MatrixType& M,
const std::vector<typename MatrixType::GlobalOrdinalType>& rows,
const std::vector<typename MatrixType::LocalOrdinalType>& row_offsets,
const std::vector<int>& row_coords,
int global_nodes_x,
int global_nodes_y,
int global_nodes_z,
typename MatrixType::GlobalOrdinalType global_nrows,
const simple_mesh_description<typename MatrixType::GlobalOrdinalType>& mesh)
{
MatrixInitOp<MatrixType> mat_init(rows, row_offsets, row_coords,
global_nodes_x, global_nodes_y, global_nodes_z,
global_nrows, mesh, M);
for(int i=0; i<mat_init.n; ++i) {
mat_init(i);
}
}
extern inline Matrix mat_O(int m,int n){
Matrix R;
int i;
srand(time(NULL)+rand());
mat_init(&R,m,n);
for(i=0;i<m*n;i++){
R.body[i]=0.;
}
return R;
}
double first_subproblm_obj (double ** dist_mat, double ** yone, double ** zone, double ** wone, double rho, int N) {
double ** temp = mat_init (N, N);
double ** diffone = mat_init (N, N);
mat_zeros (diffone, N, N);
// sum1 = 0.5 * sum_n sum_k (w_nk * d^2_nk) -> loss
mat_zeros (temp, N, N);
mat_times (wone, dist_mat, temp, N, N);
double sum1 = 0.5 * mat_sum (temp, N, N);
// sum2 = y_1^T dot (w_1 - z) -> linear
mat_zeros (temp, N, N);
mat_sub (wone, zone, diffone, N, N); // temp = w_1 - z_1
mat_tdot (yone, diffone, temp, N, N);
double sum2 = mat_sum (temp, N, N);
// sum3 = 0.5 * rho * || w_1 - z_1 ||^2 -> quadratic
mat_zeros (temp, N, N);
mat_sub (wone, zone, temp, N, N);
double sum3 = 0.5 * rho * mat_norm2 (temp, N, N);
// sum4 = r dot (1 - sum_k w_nk) -> dummy
double * temp_vec = new double [N];
mat_sum_row (wone, temp_vec, N, N);
double dummy_penalty = 0.0;
for (int i = 0; i < N; i ++) {
dummy_penalty += r*(1 - temp_vec[i]);
}
double total = sum1+sum2+sum3+dummy_penalty;
#ifdef FRANK_WOLFE_DUMP
cout << "[Frank_wolfe] (loss, linear, quadratic, dummy, total) = ("
<< sum1 << ", " << sum2 << ", " << sum3 << ", " << dummy_penalty << ", " << total
<< ")" << endl;
#endif
mat_free (temp, N, N);
mat_free (diffone, N, N);
delete [] temp_vec;
return total;
}
int main(int argc, char** args)
{
Matrix a;
mat_init(a, HEIGHT_OF_A, WIDTH_OF_A);
Matrix b;
mat_init(b, HEIGHT_OF_B, WIDTH_OF_B);
Matrix c;
mat_init(c, HEIGHT_OF_A, WIDTH_OF_B);
mat_print(a, "The matrix A:\n");
mat_print(b, "The matrix B:\n");
printf("APPLYING KERNEL...\n\n");
MatMul(a, b, c);
// MatMul_Fast(a, b, c);
mat_print(c, "The result:\n");
mat_free(a);
mat_free(b);
mat_free(c);
}
extern inline Matrix mat_I(int m,int n){
Matrix I;
int i,j;
mat_init(&I,m,n);
for(i=0;i<m;i++){
for(j=0;j<m;j++){
if(i==j)
mat_set(I,i,j,1.0);
else
mat_set(I,i,j,0.0);
}
}
return I;
}
int main(void)
{
uint8_t delay1 = 0, delay2 = 0, delay3 = 0;
seg_init();
mat_init();
uart_init();
sei();
uart_puts("\n\n");
uart_puts("/o/i/booting\r\n");
while(1)
{
for(uint8_t i=0; i<3;i++) uart_process();
delay2++;
if(delay2 == 200){
delay2 = 0;
mat_check();
delay1++;
if(delay1 == 200){
delay1 = 0;
mat_debug();
test();
uart_puts("d\r\n");
if(delay3 == 10){
delay3 = 0;
uart_puts("\n");
}
connect(); //checks hastoconnect variable
}
}
_delay_us(5);
}
}
/*
data: N data instance
assignment: N by 1 vector indicating assignment of one atom
*/
void compute_means (vector<Instance*>& data, vector<int>& assignment, int FIX_DIM, vector< vector<double> >& means) {
int N = data.size();
assert (assignment.size() == N);
int nClusters = means.size(); // for 0-index
vector< vector<int> > group_points (nClusters, vector<int>());
for (int i = 0; i < N; i ++)
group_points[assignment[i]].push_back(i);
for (int c = 0; c < nClusters; c++) {
int num_points = group_points[c].size();
if (num_points == 0) {
std::fill(means[c].begin(), means[c].end(), -INF);
continue;
}
std::fill(means[c].begin(), means[c].end(), 0.0);
double ** local_dist_mat = mat_init(num_points, num_points);
for (int x = 0; x < num_points; x++) {
for (int y = 0; y < num_points; y++) {
Instance* a = data[group_points[c][x]];
Instance* b = data[group_points[c][y]];
double dist = L2norm(a, b, FIX_DIM);
local_dist_mat[x][y] = dist * dist;
}
}
double* sum_dist = new double [num_points];
mat_sum_col(local_dist_mat, sum_dist, num_points, num_points);
int min_index = -1;
double min_value = INF;
for (int j = 0; j < num_points; j++)
if (sum_dist[j] < min_value) {
min_index = j;
min_value = sum_dist[j];
}
assert (min_index < num_points);
Instance* new_medoid = data[group_points[c][min_index]];
for (int f = 0; f < new_medoid->fea.size(); f ++)
means[c][new_medoid->fea[f].first-1] = new_medoid->fea[f].second ;
delete [] sum_dist;
mat_free (local_dist_mat, num_points, num_points);
}
}
static void
pdf_gstate_init(pdf_page *p)
{
pdf_prs *s = p->s;
int rotate = p->rotate;
pdf_extgstate *gs;
gs = &s->gs;
gs->th = 1;
mat_init(&gs->ctm, 1, 0, 0, 1, 0, 0);
if (rotate)
{
switch (rotate)
{
case 90:
mat_init(&gs->ctm, 0, -1, 1, 0, 0, p->mediabox.y1);
break;
case 180:
mat_init(&gs->ctm, -1, 0, 0, 1, p->mediabox.x1, 0);
break;
case 270:
mat_init(&gs->ctm, 0, 1, -1, 0, p->mediabox.x1, 0);
break;
case 360:
mat_init(&gs->ctm, 1, 0, 0, -1, 0, p->mediabox.y1);
break;
default:
break;
}
}
mat_init(&gs->txt_ctm, 1, 0, 0, 1, 0, 0);
mat_init(&gs->txt_lm, 1, 0, 0, 1, 0, 0);
// path stack
gs->path_base = p->i->path_stk;
gs->path_top = gs->path_base;
gs->D_n = 0;
gs->D_OFFSET = 0;
}
int main(int argc, char *argv[])
{
double err = 0.0;
struct timeval start;
float time = 0.0;
int n;
nr_nodes = get_nr_nodes();
initial_node = get_node_id () ;
next_node = (initial_node + 1) % nr_nodes ;
nr_migrations = nr_nodes + 1 ;
parse_args(argc, argv);
if (verbose>=2)
{
printf("gram-schmidt 'uni-proc' for %dx%d in", numcols, numrows);
fflush(stdout);
}
time = 0 ;
for (n=0 ; n<numloops ; n++)
{
mat_init(&mat);
timer_start(&start);
up_mgs(&mat);
time += timer_stop(&start);
if (verbose > 2)
printf ("up_gs finished, starting orth_err\n");
if (migration == 1 &&
get_node_id() != initial_node)
migrate_self (initial_node);
err = orth_err(&mat);
printf ("\n Err = %g\n", err);
if ( err < ERROR )
printf ("-- MGS test : PASSED --\n\n\n");
else
{
printf ("-- MGS test : FAILED --\n\n\n");
exit(-1) ;
}
}
/* migration ici = pb */
if (verbose>2)
printf ("up-gs : terminé\n");
if (verbose >= 1)
{
printf("\ntime :");
printf(" %g s (err: %g)\n", time/(float)numloops, err);
}
if (save_matrix)
save_normalized_matrix();
if (verbose>2)
printf ("up_gs termine\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("transpose... ");
fflush(stdout);
_randinit(state);
/* Check aliasing */
/* Unmanaged element type (long) */
for (i = 0; i < 100; i++)
{
long m, n;
ctx_t ctx;
mat_t A, B, C;
m = n_randint(state, 50) + 1;
n = m;
ctx_init_long(ctx);
mat_init(A, m, n, ctx);
mat_init(B, m, n, ctx);
mat_init(C, m, n, ctx);
mat_randtest(A, state, ctx);
mat_set(B, A, ctx);
mat_transpose(C, B, ctx);
mat_transpose(B, B, ctx);
result = mat_equal(B, C, ctx);
if (!result)
{
printf("FAIL:\n\n");
printf("Matrix A\n");
mat_print(A, ctx);
printf("\n");
printf("Matrix B\n");
mat_print(B, ctx);
printf("\n");
printf("Matrix C\n");
mat_print(C, ctx);
printf("\n");
}
mat_clear(A, ctx);
mat_clear(B, ctx);
mat_clear(C, ctx);
ctx_clear(ctx);
}
/* Check that (A^t)^t == A */
/* Unmanaged element type (long) */
for (i = 0; i < 100; i++)
{
long m, n;
ctx_t ctx;
mat_t A, B, C;
m = n_randint(state, 50) + 1;
n = n_randint(state, 50) + 1;
ctx_init_long(ctx);
mat_init(A, m, n, ctx);
mat_init(B, n, m, ctx);
mat_init(C, m, n, ctx);
mat_randtest(A, state, ctx);
mat_transpose(B, A, ctx);
mat_transpose(C, B, ctx);
result = mat_equal(A, C, ctx);
if (!result)
{
printf("FAIL:\n\n");
printf("Matrix A\n");
mat_print(A, ctx);
printf("\n");
printf("Matrix B\n");
mat_print(B, ctx);
printf("\n");
printf("Matrix C\n");
mat_print(C, ctx);
printf("\n");
}
mat_clear(A, ctx);
mat_clear(B, ctx);
mat_clear(C, ctx);
ctx_clear(ctx);
}
_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main (int argc, char ** argv) {
if (argc < 5) {
cerr << "Usage: " << endl;
cerr << "\tHDP_MEDOIDS [dataFile] [nRuns] [lambda_global] [lambda_local]" << endl;
exit(-1);
}
// PARSE arguments
char* dataFile = argv[1];
int nRuns = atoi(argv[2]);
vector<double> LAMBDAs (2, 0.0);
LAMBDAs[0] = atof(argv[3]); // lambda_global
LAMBDAs[1] = atof(argv[4]); // lambda_local
objmin_trace << "time objective" << endl;
// read in data
int FIX_DIM;
Parser parser;
vector<Instance*>* pdata;
vector<Instance*> data;
pdata = parser.parseSVM(dataFile, FIX_DIM);
data = *pdata;
// init lookup_tables
vector< pair<int,int> > doc_lookup;
get_doc_lookup (data, doc_lookup);
Lookups lookup_tables;
lookup_tables.doc_lookup = &doc_lookup;
lookup_tables.nWords = data.size();
lookup_tables.nDocs = lookup_tables.doc_lookup->size();
int seed = time(NULL);
srand (seed);
cerr << "###########################################" << endl;
cerr << "nDocs = " << lookup_tables.nDocs << endl; // # documents
cerr << "nWords = " << lookup_tables.nWords << endl; // # words
cerr << "lambda_global = " << LAMBDAs[0] << endl;
cerr << "lambda_local = " << LAMBDAs[1] << endl;
cerr << "TRIM_THRESHOLD = " << TRIM_THRESHOLD << endl;
cerr << "seed = " << seed << endl;
cerr << "###########################################" << endl;
// Run sparse convex clustering
int N = lookup_tables.nWords;
int D = lookup_tables.nDocs;
double** W = mat_init (N, N);
// dist_mat computation and output
dist_func df = L2norm;
double** dist_mat = mat_init (N, N);
compute_dist_mat (data, dist_mat, N, FIX_DIM, df, true);
start_time = omp_get_wtime();
double min_obj = INF;
vector< vector<double> > min_means;
for (int j = 0; j < nRuns; j ++) {
vector< vector<double> > means;
// inner-doc shuffle
for (int d = 0; d < D; d++) {
int begin_i = doc_lookup[d].first;
int end_i = doc_lookup[d].second;
random_shuffle(data.begin()+begin_i, data.begin()+end_i);
}
// between-doc shuffle
vector<pair<int,int> > s_doc_lookup (doc_lookup);
random_shuffle(s_doc_lookup.begin(), s_doc_lookup.end());
vector<Instance*> s_data (N, NULL);
int p = 0;
for (int d = 0; d < D; d ++) {
for (int i = s_doc_lookup[d].first; i < s_doc_lookup[d].second; i ++) {
s_data[p] = data[i];
p ++;
}
}
lookup_tables.doc_lookup = &s_doc_lookup;
double obj = HDP_MEDOIDS (s_data, means, &lookup_tables, LAMBDAs, df, FIX_DIM);
lookup_tables.doc_lookup = &doc_lookup;
cerr << "###################################################" << endl;
if (obj < min_obj) {
min_obj = obj;
min_means = means;
}
}
/* Output objective */
output_objective (min_obj);
ofstream model_out ("opt_model");
for (int i = 0; i < min_means.size(); i ++) {
model_out << "mean[" << i << "] ";
for (int j = 0; j < min_means[i].size(); j ++) {
model_out << min_means[i][j] << " " ;
}
model_out << endl;
}
model_out.close();
/* Output cluster centroids */
// output_model (W, &lookup_tables);
/* Output assignment */
// output_assignment (W, &lookup_tables);
/* reallocation */
mat_free (W, N, N);
mat_free (dist_mat, N, N);
objmin_trace.close();
}
void cvx_clustering ( double ** dist_mat, int fw_max_iter, int max_iter, int D, int N, double* lambda, double ** W) {
// parameters
double alpha = 0.1;
double rho = 1;
// iterative optimization
double error = INF;
double ** wone = mat_init (N, N);
double ** wtwo = mat_init (N, N);
double ** yone = mat_init (N, N);
double ** ytwo = mat_init (N, N);
double ** z = mat_init (N, N);
double ** diffzero = mat_init (N, N);
double ** diffone = mat_init (N, N);
double ** difftwo = mat_init (N, N);
mat_zeros (yone, N, N);
mat_zeros (ytwo, N, N);
mat_zeros (z, N, N);
mat_zeros (diffzero, N, N);
mat_zeros (diffone, N, N);
mat_zeros (difftwo, N, N);
int iter = 0; // Ian: usually we count up (instead of count down)
while ( iter < max_iter ) { // stopping criteria
#ifdef SPARSE_CLUSTERING_DUMP
cout << "it is place 0 iteration #" << iter << ", going to get into frank_wolfe" << endl;
#endif
// mat_set (wone, z, N, N);
// mat_set (wtwo, z, N, N);
// mat_zeros (wone, N, N);
// mat_zeros (wtwo, N, N);
// STEP ONE: resolve w_1 and w_2
frank_wolf (dist_mat, yone, z, wone, rho, N, fw_max_iter); // for w_1
#ifdef SPARSE_CLUSTERING_DUMP
cout << "norm2(w_1) = " << mat_norm2 (wone, N, N) << endl;
#endif
blockwise_closed_form (ytwo, z, wtwo, rho, lambda, N); // for w_2
#ifdef SPARSE_CLUSTERING_DUMP
cout << "norm2(w_2) = " << mat_norm2 (wtwo, N, N) << endl;
#endif
// STEP TWO: update z by averaging w_1 and w_2
mat_add (wone, wtwo, z, N, N);
mat_dot (0.5, z, z, N, N);
#ifdef SPARSE_CLUSTERING_DUMP
cout << "norm2(z) = " << mat_norm2 (z, N, N) << endl;
#endif
// STEP THREE: update the y_1 and y_2 by w_1, w_2 and z
mat_sub (wone, z, diffone, N, N);
double trace_wone_minus_z = mat_norm2 (diffone, N, N);
mat_dot (alpha, diffone, diffone, N, N);
mat_add (yone, diffone, yone, N, N);
mat_sub (wtwo, z, difftwo, N, N);
//double trace_wtwo_minus_z = mat_norm2 (difftwo, N, N);
mat_dot (alpha, difftwo, difftwo, N, N);
mat_add (ytwo, difftwo, ytwo, N, N);
// STEP FOUR: trace the objective function
if (iter % 100 == 0) {
error = overall_objective (dist_mat, lambda, N, z);
// get current number of employed centroid
#ifdef NCENTROID_DUMP
int nCentroids = get_nCentroids (z, N, N);
#endif
cout << "[Overall] iter = " << iter
<< ", Overall Error: " << error
#ifdef NCENTROID_DUMP
<< ", nCentroids: " << nCentroids
#endif
<< endl;
}
iter ++;
}
// STEP FIVE: memory recollection
mat_free (wone, N, N);
mat_free (wtwo, N, N);
mat_free (yone, N, N);
mat_free (ytwo, N, N);
mat_free (diffone, N, N);
mat_free (difftwo, N, N);
// STEP SIX: put converged solution to destination W
mat_copy (z, W, N, N);
}
// entry main function
int main (int argc, char ** argv) {
// exception control: illustrate the usage if get input of wrong format
if (argc < 5) {
cerr << "Usage: cvx_clustering [dataFile] [fw_max_iter] [max_iter] [lambda] " << endl;
cerr << "Note: dataFile must be scaled to [0,1] in advance." << endl;
exit(-1);
}
// parse arguments
char * dataFile = argv[1];
int fw_max_iter = atoi(argv[2]);
int max_iter = atoi(argv[3]);
double lambda_base = atof(argv[4]);
char * dmatFile = argv[5];
// vector<Instance*> data;
// readFixDim (dataFile, data, FIX_DIM);
// read in data
int FIX_DIM;
Parser parser;
vector<Instance*>* pdata;
vector<Instance*> data;
pdata = parser.parseSVM(dataFile, FIX_DIM);
data = *pdata;
// vector<Instance*> data;
// readFixDim (dataFile, data, FIX_DIM);
// explore the data
int dimensions = -1;
int N = data.size(); // data size
for (int i = 0; i < N; i++) {
vector< pair<int,double> > * f = &(data[i]->fea);
int last_index = f->size()-1;
if (f->at(last_index).first > dimensions) {
dimensions = f->at(last_index).first;
}
}
assert (dimensions == FIX_DIM);
int D = dimensions;
cerr << "D = " << D << endl; // # features
cerr << "N = " << N << endl; // # instances
cerr << "lambda = " << lambda_base << endl;
cerr << "r = " << r << endl;
int seed = time(NULL);
srand (seed);
cerr << "seed = " << seed << endl;
//create lambda with noise
double* lambda = new double[N];
for(int i=0; i<N; i++) {
lambda[i] = lambda_base + noise();
}
// pre-compute distance matrix
dist_func df = L2norm;
double ** dist_mat = mat_init (N, N);
// double ** dist_mat = mat_read (dmatFile, N, N);
mat_zeros (dist_mat, N, N);
compute_dist_mat (data, dist_mat, N, D, df, true);
ofstream dist_mat_out ("dist_mat");
dist_mat_out << mat_toString(dist_mat, N, N);
dist_mat_out.close();
// Run sparse convex clustering
double ** W = mat_init (N, N);
mat_zeros (W, N, N);
cvx_clustering (dist_mat, fw_max_iter, max_iter, D, N, lambda, W);
ofstream W_OUT("w_out");
W_OUT<< mat_toString(W, N, N);
W_OUT.close();
// Output cluster
output_objective(clustering_objective (dist_mat, W, N));
/* Output cluster centroids */
output_model (W, N);
/* Output assignment */
output_assignment (W, data, N);
/* reallocation */
mat_free (dist_mat, N, N);
mat_free (W, N, N);
}
void blockwise_closed_form (double ** ytwo, double ** ztwo, double ** wtwo, double rho, double* lambda, int N) {
// STEP ONE: compute the optimal solution for truncated problem
double ** wbar = mat_init (N, N);
mat_zeros (wbar, N, N);
mat_dot (rho, ztwo, wbar, N, N); // wbar = rho * z_2
mat_sub (wbar, ytwo, wbar, N, N); // wbar = rho * z_2 - y_2
mat_dot (1.0/rho, wbar, wbar, N, N); // wbar = (rho * z_2 - y_2) / rho
// STEP TWO: find the closed-form solution for second subproblem
for (int j = 0; j < N; j ++) {
// 1. bifurcate the set of values
vector< pair<int,double> > alpha_vec;
for (int i = 0; i < N; i ++) {
double value = wbar[i][j];
/*if( wbar[i][j] < 0 ){
cerr << "wbar[" << i << "][" << j << "]" << endl;
exit(0);
}*/
alpha_vec.push_back (make_pair(i, abs(value)));
}
// 2. sorting
std::sort (alpha_vec.begin(), alpha_vec.end(), pairComparator);
/*
for (int i = 0; i < N; i ++) {
if (alpha_vec[i].second != 0)
cout << alpha_vec[i].second << endl;
}
*/
// 3. find mstar
int mstar = 0; // number of elements support the sky
double separator;
double max_term = -INF, new_term;
double sum_alpha = 0.0;
for (int i = 0; i < N; i ++) {
sum_alpha += alpha_vec[i].second;
new_term = (sum_alpha - lambda[j]) / (i + 1.0);
if ( new_term > max_term ) {
separator = alpha_vec[i].second;
max_term = new_term;
mstar = i;
}
}
// 4. assign closed-form solution to wtwo
if( max_term < 0 ) {
for(int i=0; i<N; i++)
wtwo[i][j] = 0.0;
continue;
}
for (int i = 0; i < N; i ++) {
// harness vector of pair
double value = wbar[i][j];
if ( abs(value) >= separator ) {
wtwo[i][j] = max_term;
} else {
// its ranking is above m*, directly inherit the wbar
wtwo[i][j] = max(wbar[i][j],0.0);
}
}
}
// compute value of objective function
double penalty = second_subproblem_obj (ytwo, ztwo, wtwo, rho, N, lambda);
// report the #iter and objective function
/*cout << "[Blockwise] second_subproblem_obj: " << penalty << endl;
cout << endl;*/
// STEP THREE: recollect temporary variable - wbar
mat_free (wbar, N, N);
}
int
adios_read_icee_schedule_read_byid(const ADIOS_FILE *adiosfile,
const ADIOS_SELECTION *sel,
int varid,
int from_steps,
int nsteps,
void *data)
{
int i;
icee_fileinfo_rec_ptr_t fp = (icee_fileinfo_rec_ptr_t) adiosfile->fh;
log_debug("%s (%d:%s)\n", __FUNCTION__, varid, fp->fname);
//assert((varid < fp->nvars) || (fp->nvars == 0));
if (nsteps != 1)
{
adios_error (err_invalid_timestep,
"Only one step can be read from a stream at a time. "
"You requested % steps in adios_schedule_read()\n",
nsteps);
return err_invalid_timestep;
}
icee_varinfo_rec_ptr_t vp = NULL;
vp = icee_varinfo_search_byname(fp->varinfo, adiosfile->var_namelist[varid]);
if (adios_verbose_level > 5) icee_varinfo_print(vp);
if (!vp)
{
adios_error(err_invalid_varid, "Invalid variable id: %d\n", varid);
return adios_errno;
}
while (fp->merge_count != fp->nchunks)
{
log_debug("Waiting the rest of blocks (%d/%d)\n", fp->merge_count, fp->nchunks);
usleep(0.1*1E6);
}
if (sel==0)
memcpy(data, vp->data, vp->varlen);
else
switch(sel->type)
{
case ADIOS_SELECTION_WRITEBLOCK:
{
//DUMP("fp->rank: %d", fp->rank);
//DUMP("u.block.index: %d", sel->u.block.index);
if (fp->comm_rank != sel->u.block.index)
adios_error(err_unspecified,
"Block id missmatch. "
"Not yet supported by ICEE\n");
// Possible memory overwrite
memcpy(data, vp->data, vp->varlen);
break;
}
case ADIOS_SELECTION_BOUNDINGBOX:
{
if (vp->ndims != sel->u.bb.ndim)
adios_error(err_invalid_dimension,
"Dimension mismatch\n");
log_debug("Merging operation (total nvars: %d).\n", fp->nchunks);
if (adios_verbose_level > 5) icee_sel_bb_print(sel);
while (vp != NULL)
{
icee_matrix_t m_sel;
icee_matrix_t m_var;
icee_matrix_view_t v_sel;
icee_matrix_view_t v_var;
uint64_t start[10];
int64_t count[10]; // should be signed to check validity
uint64_t s_offsets[10], v_offsets[10];
int i;
if (adios_verbose_level > 5) icee_varinfo_print(vp);
mat_init(&m_sel, vp->typesize, vp->ndims, sel->u.bb.count, data);
mat_init(&m_var, vp->typesize, vp->ndims, vp->ldims, vp->data);
for (i=0; i<vp->ndims; i++)
start[i] = MYMAX(sel->u.bb.start[i], vp->offsets[i]);
for (i=0; i<vp->ndims; i++)
{
count[i] =
MYMIN(sel->u.bb.start[i]+sel->u.bb.count[i],
vp->offsets[i]+vp->ldims[i]) - start[i];
}
for (i=0; i<vp->ndims; i++)
{
if (count[i] <= 0)
{
log_debug("No ROI. Skip\n");
goto next;
}
}
for (i=0; i<vp->ndims; i++)
s_offsets[i] = start[i] - sel->u.bb.start[i];
for (i=0; i<vp->ndims; i++)
v_offsets[i] = start[i] - vp->offsets[i];
view_init (&v_sel, &m_sel, count, s_offsets);
view_init (&v_var, &m_var, count, v_offsets);
view_copy (&v_sel, &v_var);
next:
vp = icee_varinfo_search_byname(vp->next, adiosfile->var_namelist[varid]);
}
break;
}
case ADIOS_SELECTION_AUTO:
{
// Possible memory overwrite
memcpy(data, vp->data, vp->varlen);
break;
}
case ADIOS_SELECTION_POINTS:
{
adios_error(err_operation_not_supported,
"ADIOS_SELECTION_POINTS not yet supported by ICEE.\n");
break;
}
}
return adios_errno;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("zero... ");
fflush(stdout);
_randinit(state);
/* Unmanaged element type (long) */
for (i = 0; i < 100; i++)
{
long m, n;
ctx_t ctx;
mat_t A;
m = n_randint(state, 100) + 1;
n = n_randint(state, 100) + 1;
ctx_init_long(ctx);
mat_init(A, m, n, ctx);
mat_randtest(A, state, ctx);
mat_zero(A, ctx);
result = mat_is_zero(A, ctx);
if (!result)
{
printf("FAIL:\n\n");
printf("Matrix A\n");
mat_print(A, ctx);
printf("\n");
abort();
}
mat_clear(A, ctx);
ctx_clear(ctx);
}
/* Managed element type (mpq_t) */
for (i = 0; i < 100; i++)
{
long m, n;
ctx_t ctx;
mat_t A;
m = n_randint(state, 100) + 1;
n = n_randint(state, 100) + 1;
ctx_init_mpq(ctx);
mat_init(A, m, n, ctx);
mat_randtest(A, state, ctx);
mat_zero(A, ctx);
result = mat_is_zero(A, ctx);
if (!result)
{
printf("FAIL:\n\n");
printf("Matrix A\n");
mat_print(A, ctx);
printf("\n");
abort();
}
mat_clear(A, ctx);
ctx_clear(ctx);
}
_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main(void)
{
char *str; /* String for the input polynomial P */
mpoly_t P; /* Input polynomial P */
int n; /* Number of variables minus one */
long K; /* Required t-adic precision */
long N, Nw;
long b; /* Matrix dimensions */
long i, j, k;
mat_t M;
ctx_t ctxM;
mon_t *rows, *cols;
padic_mat_struct *C;
fmpz_t p;
fmpz_poly_mat_t B;
long vB;
printf("solve... \n");
fflush(stdout);
/* Example 3-1-1 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 1)[1 1 1]"; */
/* Example 3-3-2 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 1)[2 1 0] (2 0 1)[0 2 1] (2 0 1)[1 0 2]"; */
/* Example 4-4-2 */
/* str = "4 [4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] (2 0 1)[3 1 0 0] (2 0 1)[1 0 1 2] (2 0 1)[0 1 0 3]"; */
/* Example ... */
/* str = "4 [4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] (2 0 1)[1 1 1 1]"; */
/* Example from AKR */
str = "4 (1 3)[0 3 0 0] (2 0 3)[0 1 2 0] "
"(2 0 -1)[1 1 1 0] (2 0 3)[1 1 0 1] "
"(2 0 -1)[2 1 0 0] [0 0 3 0] (2 0 -1)[1 0 2 0] "
"(1 2)[0 0 0 3] [3 0 0 0]";
n = atoi(str) - 1;
K = 616;
N = 10;
Nw = 22;
fmpz_init(p);
fmpz_set_ui(p, 5);
ctx_init_fmpz_poly_q(ctxM);
ctxM->print = &__fmpz_poly_q_print_pretty;
mpoly_init(P, n + 1, ctxM);
mpoly_set_str(P, str, ctxM);
printf("P = "), mpoly_print(P, ctxM), printf("\n");
b = gmc_basis_size(n, mpoly_degree(P, -1, ctxM));
mat_init(M, b, b, ctxM);
fmpz_poly_mat_init(B, b, b);
vB = 0;
gmc_compute(M, &rows, &cols, P, ctxM);
mat_print(M, ctxM);
printf("\n");
gmde_solve(&C, K, p, N, Nw, M, ctxM);
gmde_convert_soln(B, &vB, C, K, p);
printf("Solution to (d/dt + M) C = 0:\n");
fmpz_poly_mat_print(B, "t");
printf("vB = %ld\n", vB);
gmde_check_soln(B, vB, p, N, K, M, ctxM);
mpoly_clear(P, ctxM);
mat_clear(M, ctxM);
free(rows);
free(cols);
fmpz_poly_mat_clear(B);
ctx_clear(ctxM);
fmpz_clear(p);
for (i = 0; i < K; i++)
padic_mat_clear(C + i);
free(C);
_fmpz_cleanup();
return EXIT_SUCCESS;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("add... ");
fflush(stdout);
_randinit(state);
/* Check that addition is abelian */
/* Unmanaged element type (long) */
for (i = 0; i < 100; i++)
{
long m, n;
ctx_t ctx;
mat_t A, B, C, D;
m = n_randint(state, 50) + 1;
n = n_randint(state, 50) + 1;
ctx_init_long(ctx);
mat_init(A, m, n, ctx);
mat_init(B, m, n, ctx);
mat_init(C, m, n, ctx);
mat_init(D, m, n, ctx);
mat_randtest(A, state, ctx);
mat_randtest(B, state, ctx);
mat_add(C, A, B, ctx);
mat_add(D, B, A, ctx);
result = mat_equal(C, D, ctx);
if (!result)
{
printf("FAIL:\n\n");
printf("Matrix A\n");
mat_print(A, ctx);
printf("\n");
printf("Matrix A\n");
mat_print(B, ctx);
printf("\n");
}
mat_clear(A, ctx);
mat_clear(B, ctx);
mat_clear(C, ctx);
mat_clear(D, ctx);
ctx_clear(ctx);
}
/* Managed element type (mpq_t) */
for (i = 0; i < 100; i++)
{
long m, n;
ctx_t ctx;
mat_t A, B, C, D;
m = n_randint(state, 50) + 1;
n = n_randint(state, 50) + 1;
ctx_init_mpq(ctx);
mat_init(A, m, n, ctx);
mat_init(B, m, n, ctx);
mat_init(C, m, n, ctx);
mat_init(D, m, n, ctx);
mat_randtest(A, state, ctx);
mat_randtest(B, state, ctx);
mat_add(C, A, B, ctx);
mat_add(D, B, A, ctx);
result = mat_equal(C, D, ctx);
if (!result)
{
printf("FAIL:\n\n");
printf("Matrix A\n");
mat_print(A, ctx);
printf("\n");
printf("Matrix A\n");
mat_print(B, ctx);
printf("\n");
}
mat_clear(A, ctx);
mat_clear(B, ctx);
mat_clear(C, ctx);
mat_clear(D, ctx);
ctx_clear(ctx);
}
/* Check that the zero matrix does what it's supposed to do */
/* Unmanaged element type (long) */
for (i = 0; i < 100; i++)
{
long m, n;
ctx_t ctx;
mat_t A, B, C, D;
m = n_randint(state, 50) + 1;
n = n_randint(state, 50) + 1;
ctx_init_long(ctx);
mat_init(A, m, n, ctx);
mat_init(B, m, n, ctx);
mat_init(C, m, n, ctx);
mat_init(D, m, n, ctx);
mat_randtest(A, state, ctx);
mat_zero(B, ctx);
mat_add(C, A, B, ctx);
mat_add(D, B, A, ctx);
result = mat_equal(A, C, ctx) && mat_equal(C, D, ctx);
if (!result)
{
printf("FAIL:\n\n");
printf("Matrix A\n");
mat_print(A, ctx);
printf("\n");
printf("Matrix A\n");
mat_print(B, ctx);
printf("\n");
}
mat_clear(A, ctx);
mat_clear(B, ctx);
mat_clear(C, ctx);
mat_clear(D, ctx);
ctx_clear(ctx);
}
/* Managed element type (mpq_t) */
for (i = 0; i < 100; i++)
{
long m, n;
ctx_t ctx;
mat_t A, B, C, D;
m = n_randint(state, 50) + 1;
n = n_randint(state, 50) + 1;
ctx_init_mpq(ctx);
mat_init(A, m, n, ctx);
mat_init(B, m, n, ctx);
mat_init(C, m, n, ctx);
mat_init(D, m, n, ctx);
mat_randtest(A, state, ctx);
mat_zero(B, ctx);
mat_add(C, A, B, ctx);
mat_add(D, B, A, ctx);
result = mat_equal(A, C, ctx) && mat_equal(C, D, ctx);
if (!result)
{
printf("FAIL:\n\n");
printf("Matrix A\n");
mat_print(A, ctx);
printf("\n");
printf("Matrix A\n");
mat_print(B, ctx);
printf("\n");
}
mat_clear(A, ctx);
mat_clear(B, ctx);
mat_clear(C, ctx);
mat_clear(D, ctx);
ctx_clear(ctx);
}
_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("inv... ");
fflush(stdout);
_randinit(state);
/* Check aliasing */
/* Managed element type (mpq_t) */
for (i = 0; i < 50; i++)
{
long n;
ctx_t ctx;
mat_t A, B, C;
long ansB, ansC;
n = n_randint(state, 20) + 1;
ctx_init_mpq(ctx);
mat_init(A, n, n, ctx);
mat_init(B, n, n, ctx);
mat_init(C, n, n, ctx);
mat_randtest(A, state, ctx);
mat_set(B, A, ctx);
ansC = mat_inv(C, B, ctx);
ansB = mat_inv(B, B, ctx);
result = ((ansB == ansC) && (!ansB || mat_equal(B, C, ctx)));
if (!result)
{
printf("FAIL:\n\n");
printf("A: \n"), mat_print(A, ctx), printf("\n");
printf("B: \n"), mat_print(B, ctx), printf("\n");
printf("C: \n"), mat_print(C, ctx), printf("\n");
printf("ansB = %ld\n", ansB);
printf("ansC = %ld\n", ansC);
}
mat_clear(A, ctx);
mat_clear(B, ctx);
mat_clear(C, ctx);
ctx_clear(ctx);
}
/* Check A * A^{-1} == A^{-1} * A == Id */
/* Managed element type (mpq_t) */
for (i = 0; i < 50; i++)
{
long n;
ctx_t ctx;
mat_t A, B, C, D, I;
long ansB;
n = n_randint(state, 20) + 1;
ctx_init_mpq(ctx);
mat_init(A, n, n, ctx);
mat_init(B, n, n, ctx);
mat_init(C, n, n, ctx);
mat_init(D, n, n, ctx);
mat_init(I, n, n, ctx);
mat_randtest(A, state, ctx);
ansB = mat_inv(B, A, ctx);
if (!ansB)
{
mat_mul(C, A, B, ctx);
mat_mul(D, B, A, ctx);
}
result = (ansB || (mat_equal(C, D, ctx) && mat_is_one(C, ctx)));
if (!result)
{
printf("FAIL:\n\n");
printf("A: \n"), mat_print(A, ctx), printf("\n");
printf("B: \n"), mat_print(B, ctx), printf("\n");
printf("C: \n"), mat_print(C, ctx), printf("\n");
printf("D: \n"), mat_print(D, ctx), printf("\n");
printf("ansB = %ld\n", ansB);
}
mat_clear(A, ctx);
mat_clear(B, ctx);
mat_clear(C, ctx);
mat_clear(D, ctx);
ctx_clear(ctx);
}
_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main(void)
{
char *str; /* String for the input polynomial P */
mpoly_t P; /* Input polynomial P */
long n; /* Number of variables minus one */
long K; /* Required t-adic precision */
long N, Nw;
long i, b;
mat_t M;
ctx_t ctxM;
mon_t *rows, *cols;
padic_mat_struct *C;
fmpz_t p;
printf("valuations... \n");
fflush(stdout);
/* Example 3-1-1 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 1)[1 1 1]"; */
/* Example 4-4-2 */
/* str = "4 [4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] (2 0 1)[3 1 0 0] (2 0 1)[1 0 1 2] (2 0 1)[0 1 0 3]"; */
/* Example 3-3-6 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 314)[2 1 0] (2 0 42)[0 2 1] (2 0 271)[1 0 2] (2 0 -23)[1 1 1]"; */
/* Example 3-3-2 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 1)[2 1 0] (2 0 1)[0 2 1] (2 0 1)[1 0 2]"; */
/* Example ... */
/* str = "4 [4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] (2 0 1)[1 1 1 1]"; */
/* Cubic surface from AKR */
str = "4 (1 3)[0 3 0 0] (2 0 3)[0 1 2 0] "
"(2 0 -1)[1 1 1 0] (2 0 3)[1 1 0 1] "
"(2 0 -1)[2 1 0 0] [0 0 3 0] (2 0 -1)[1 0 2 0] "
"(1 2)[0 0 0 3] [3 0 0 0]";
n = atoi(str) - 1;
N = 10;
Nw = 22;
K = 616;
ctx_init_fmpz_poly_q(ctxM);
mpoly_init(P, n + 1, ctxM);
mpoly_set_str(P, str, ctxM);
printf("P = "), mpoly_print(P, ctxM), printf("\n");
b = gmc_basis_size(n, mpoly_degree(P, -1, ctxM));
mat_init(M, b, b, ctxM);
gmc_compute(M, &rows, &cols, P, ctxM);
mat_print(M, ctxM);
printf("\n");
fmpz_init(p);
fmpz_set_ui(p, 5);
gmde_solve(&C, K, p, N, Nw, M, ctxM);
printf("Valuations\n");
for (i = 0; i < K; i++)
{
long v = padic_mat_val(C + i);
if (v < LONG_MAX)
printf(" i = %ld val = %ld val/log(i) = %f\n", i, v,
(i > 1) ? (double) v / log(i) : 0);
else
printf(" i = %ld val = +infty\n", i);
}
fmpz_clear(p);
mpoly_clear(P, ctxM);
mat_clear(M, ctxM);
for (i = 0; i < K; i++)
padic_mat_clear(C + i);
free(C);
ctx_clear(ctxM);
return EXIT_SUCCESS;
}
void
checkCorrect ()
{
double *A,*B,*C,*cA,*cB,*cC;
int minDim = 1;
int maxDim = 256;
int maxnbytes = sizeof(double) * SQR (maxDim);
int i, j;
A = (double*) malloc (maxnbytes);
B = (double*) malloc (maxnbytes);
C = (double*) malloc (maxnbytes);
cA = (double*) malloc (maxnbytes);
cB = (double*) malloc (maxnbytes);
cC = (double*) malloc (maxnbytes);
fprintf (stderr, "Checking for correctness on sizes:");
#if !RANDOM_TESTS
for (i = 0; i < 2; i++) for (j = 0; j < num_tests[i]; j++)
{
int matdim = test_sizes[i][j];
#else
for (i = 0; i < NUM_CORRECTNESS_CHECKS; i++)
{
int matdim = rrand (minDim, maxDim);
#endif
double err;
int nbytes = sizeof(double) * SQR(matdim);
fprintf (stderr, " %d", matdim);
mat_init (A, matdim, matdim);
mat_init (B, matdim, matdim);
mat_init (C, matdim, matdim);
bcopy ((void*)A, (void*)cA, nbytes);
bcopy ((void*)B, (void*)cB, nbytes);
bcopy ((void*)C, (void*)cC, nbytes);
naive_mm (matdim, matdim, matdim, cA, cB, cC);
MUL_MFMF_MF (matdim, A, B, C);
if (bcmp ((void*)A, (void*)cA, nbytes) != 0 ||
bcmp ((void*)B, (void*)cB, nbytes) != 0)
{
fprintf (stderr, "Source matrices were modified. DISQUALIFIED!!!\n")
;
//exit (0);
}
if ((err = error (C, cC, matdim, matdim)) > MAX_ERROR)
{
fprintf (stderr, "Error for test case %dx%d is %f > %f. DISQUALIFIED!
!!\n",
matdim, matdim, err, MAX_ERROR);
//exit (0);
}
}
fprintf (stderr,"\n");
free (A); free (B); free (C);
free (cA); free (cB); free (cC);
}
void
timeIt ()
{
double *A, *B, *C;
double *oA[TEST_RUNS], *oB[TEST_RUNS], *oC[TEST_RUNS];
int i, j, k;
int test;
for (k = 0; k < 2; k++)
{
if (k > 0) printf ("\n");
for (test = 0; test < num_tests[k]; test++)
{
int matdim = test_sizes[k][test];
const int num_iters = CALC_ITERS (matdim);
double max_mflops = 0.0;
int run;
/* make sure these are quad-word (i.e., 16-byte) aligned */
#if 0
A = oA = (double*) malloc ((SQR(matdim)+1) * sizeof(double));
B = oB = (double*) malloc ((SQR(matdim)+1) * sizeof(double));
C = oC = (double*) malloc ((SQR(matdim)+1) * sizeof(double));
#endif
for (run = 0; run < TEST_RUNS; run++)
{
int iter;
double mflops;
double utime;
/* use different matricies for each trial so that the OS page map
ping */
/* won't affect the results... */
A = oA[run] = (double*) malloc ((SQR(matdim)+rrand(1,10)) * sizeof(double));
B = oB[run] = (double*) malloc ((SQR(matdim)+rrand(1,10)) * sizeof(double));
C = oC[run] = (double*) malloc ((SQR(matdim)+rrand(1,10)) * sizeof(double));
if (((unsigned)A) & 0x8) A = (double*)(((unsigned)A)+0x8);
if (((unsigned)B) & 0x8) B = (double*)(((unsigned)B)+0x8);
if (((unsigned)C) & 0x8) C = (double*)(((unsigned)C)+0x8);
mat_init (A, matdim, matdim);
mat_init (B, matdim, matdim);
mat_init (C, matdim, matdim);
START_TIMING;
for (iter=0;iter<num_iters;iter++)
{
// iteratively accumulate into C
MUL_MFMF_MF (matdim, A, B, C);
}
STOP_TIMING;
utime = reportTiming();
// (2 * n^3) FLOPs (n^3 mul-adds)
mflops = 2.0 * CUBE(matdim) * num_iters * 1e-6 / utime;
max_mflops = MAX (max_mflops, mflops);
}
printf("%d %.0f\n", matdim, max_mflops);
fflush(stdout);
for (run = 0; run < TEST_RUNS; run++)
{
free (oA[run]);
free (oB[run]);
free (oC[run]);
}
}
}
}
void frob(const mpoly_t P, const ctx_t ctxFracQt,
const qadic_t t1, const qadic_ctx_t Qq,
prec_t *prec, const prec_t *prec_in,
int verbose)
{
const padic_ctx_struct *Qp = &Qq->pctx;
const fmpz *p = Qp->p;
const long a = qadic_ctx_degree(Qq);
const long n = P->n - 1;
const long d = mpoly_degree(P, -1, ctxFracQt);
const long b = gmc_basis_size(n, d);
long i, j, k;
/* Diagonal fibre */
padic_mat_t F0;
/* Gauss--Manin Connection */
mat_t M;
mon_t *bR, *bC;
fmpz_poly_t r;
/* Local solution */
fmpz_poly_mat_t C, Cinv;
long vC, vCinv;
/* Frobenius */
fmpz_poly_mat_t F;
long vF;
fmpz_poly_mat_t F1;
long vF1;
fmpz_poly_t cp;
clock_t c0, c1;
double c;
if (verbose)
{
printf("Input:\n");
printf(" P = "), mpoly_print(P, ctxFracQt), printf("\n");
printf(" p = "), fmpz_print(p), printf("\n");
printf(" t1 = "), qadic_print_pretty(t1, Qq), printf("\n");
printf("\n");
fflush(stdout);
}
/* Step 1 {M, r} *********************************************************/
c0 = clock();
mat_init(M, b, b, ctxFracQt);
fmpz_poly_init(r);
gmc_compute(M, &bR, &bC, P, ctxFracQt);
{
fmpz_poly_t t;
fmpz_poly_init(t);
fmpz_poly_set_ui(r, 1);
for (i = 0; i < M->m; i++)
for (j = 0; j < M->n; j++)
{
fmpz_poly_lcm(t, r, fmpz_poly_q_denref(
(fmpz_poly_q_struct *) mat_entry(M, i, j, ctxFracQt)));
fmpz_poly_swap(r, t);
}
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Gauss-Manin connection:\n");
printf(" r(t) = "), fmpz_poly_print_pretty(r, "t"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
{
qadic_t t;
qadic_init2(t, 1);
fmpz_poly_evaluate_qadic(t, r, t1, Qq);
if (qadic_is_zero(t))
{
printf("Exception (deformation_frob).\n");
printf("The resultant r evaluates to zero (mod p) at t1.\n");
abort();
}
qadic_clear(t);
}
/* Precisions ************************************************************/
if (prec_in != NULL)
{
*prec = *prec_in;
}
else
{
deformation_precisions(prec, p, a, n, d, fmpz_poly_degree(r));
}
if (verbose)
{
printf("Precisions:\n");
printf(" N0 = %ld\n", prec->N0);
printf(" N1 = %ld\n", prec->N1);
printf(" N2 = %ld\n", prec->N2);
printf(" N3 = %ld\n", prec->N3);
printf(" N3i = %ld\n", prec->N3i);
printf(" N3w = %ld\n", prec->N3w);
printf(" N3iw = %ld\n", prec->N3iw);
printf(" N4 = %ld\n", prec->N4);
printf(" m = %ld\n", prec->m);
printf(" K = %ld\n", prec->K);
printf(" r = %ld\n", prec->r);
printf(" s = %ld\n", prec->s);
printf("\n");
fflush(stdout);
}
/* Initialisation ********************************************************/
padic_mat_init2(F0, b, b, prec->N4);
fmpz_poly_mat_init(C, b, b);
fmpz_poly_mat_init(Cinv, b, b);
fmpz_poly_mat_init(F, b, b);
vF = 0;
fmpz_poly_mat_init(F1, b, b);
vF1 = 0;
fmpz_poly_init(cp);
/* Step 2 {F0} ***********************************************************/
{
padic_ctx_t pctx_F0;
fmpz *t;
padic_ctx_init(pctx_F0, p, FLINT_MIN(prec->N4 - 10, 0), prec->N4, PADIC_VAL_UNIT);
t = _fmpz_vec_init(n + 1);
c0 = clock();
mpoly_diagonal_fibre(t, P, ctxFracQt);
diagfrob(F0, t, n, d, prec->N4, pctx_F0, 0);
padic_mat_transpose(F0, F0);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Diagonal fibre:\n");
printf(" P(0) = {"), _fmpz_vec_print(t, n + 1), printf("}\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
_fmpz_vec_clear(t, n + 1);
padic_ctx_clear(pctx_F0);
}
/* Step 3 {C, Cinv} ******************************************************/
/*
Compute C as a matrix over Z_p[[t]]. A is the same but as a series
of matrices over Z_p. Mt is the matrix -M^t, and Cinv is C^{-1}^t,
the local solution of the differential equation replacing M by Mt.
*/
c0 = clock();
{
const long K = prec->K;
padic_mat_struct *A;
gmde_solve(&A, K, p, prec->N3, prec->N3w, M, ctxFracQt);
gmde_convert_soln(C, &vC, A, K, p);
for(i = 0; i < K; i++)
padic_mat_clear(A + i);
free(A);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Local solution:\n");
printf(" Time for C = %f\n", c);
fflush(stdout);
}
c0 = clock();
{
const long K = (prec->K + (*p) - 1) / (*p);
mat_t Mt;
padic_mat_struct *Ainv;
mat_init(Mt, b, b, ctxFracQt);
mat_transpose(Mt, M, ctxFracQt);
mat_neg(Mt, Mt, ctxFracQt);
gmde_solve(&Ainv, K, p, prec->N3i, prec->N3iw, Mt, ctxFracQt);
gmde_convert_soln(Cinv, &vCinv, Ainv, K, p);
fmpz_poly_mat_transpose(Cinv, Cinv);
fmpz_poly_mat_compose_pow(Cinv, Cinv, *p);
for(i = 0; i < K; i++)
padic_mat_clear(Ainv + i);
free(Ainv);
mat_clear(Mt, ctxFracQt);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf(" Time for C^{-1} = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 4 {F(t) := C(t) F(0) C(t^p)^{-1}} ********************************/
/*
Computes the product C(t) F(0) C(t^p)^{-1} modulo (p^{N_2}, t^K).
This is done by first computing the unit part of the product
exactly over the integers modulo t^K.
*/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
for (i = 0; i < b; i++)
{
/* Find the unique k s.t. F0(i,k) is non-zero */
for (k = 0; k < b; k++)
if (!fmpz_is_zero(padic_mat_entry(F0, i, k)))
break;
if (k == b)
{
printf("Exception (frob). F0 is singular.\n\n");
abort();
}
for (j = 0; j < b; j++)
{
fmpz_poly_scalar_mul_fmpz(fmpz_poly_mat_entry(T, i, j),
fmpz_poly_mat_entry(Cinv, k, j),
padic_mat_entry(F0, i, k));
}
}
fmpz_poly_mat_mul(F, C, T);
fmpz_poly_mat_truncate(F, prec->K);
vF = vC + padic_mat_val(F0) + vCinv;
/* Canonicalise (F, vF) */
{
long v = fmpz_poly_mat_ord_p(F, p);
if (v == LONG_MAX)
{
printf("ERROR (deformation_frob). F(t) == 0.\n");
abort();
}
else if (v > 0)
{
fmpz_pow_ui(pN, p, v);
fmpz_poly_mat_scalar_divexact_fmpz(F, F, pN);
vF = vF + v;
}
}
/* Reduce (F, vF) modulo p^{N2} */
fmpz_pow_ui(pN, p, prec->N2 - vF);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Matrix for F(t):\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 5 {G = r(t)^m F(t)} **********************************************/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_t t;
fmpz_init(pN);
fmpz_poly_init(t);
fmpz_pow_ui(pN, p, prec->N2 - vF);
/* Compute r(t)^m mod p^{N2-vF} */
if (prec->denR == NULL)
{
fmpz_mod_poly_t _t;
fmpz_mod_poly_init(_t, pN);
fmpz_mod_poly_set_fmpz_poly(_t, r);
fmpz_mod_poly_pow(_t, _t, prec->m);
fmpz_mod_poly_get_fmpz_poly(t, _t);
fmpz_mod_poly_clear(_t);
}
else
{
/* TODO: We don't really need a copy */
fmpz_poly_set(t, prec->denR);
}
fmpz_poly_mat_scalar_mul_fmpz_poly(F, F, t);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
/* TODO: This should not be necessary? */
fmpz_poly_mat_truncate(F, prec->K);
fmpz_clear(pN);
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Analytic continuation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Steps 6 and 7 *********************************************************/
if (a == 1)
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t f, g, t, pN;
fmpz_init(f);
fmpz_init(g);
fmpz_init(t);
fmpz_init(pN);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_padic_teichmuller(f, t1->coeffs + 0, p, N);
if (prec->denR == NULL)
{
_fmpz_mod_poly_evaluate_fmpz(g, r->coeffs, r->length, f, pN);
fmpz_powm_ui(t, g, prec->m, pN);
}
else
{
_fmpz_mod_poly_evaluate_fmpz(t, prec->denR->coeffs, prec->denR->length, f, pN);
}
_padic_inv(g, t, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
if (len == 0)
{
fmpz_poly_zero(fmpz_poly_mat_entry(F1, i, j));
}
else
{
fmpz_poly_fit_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_mod_poly_evaluate_fmpz(t, poly->coeffs, len, f, pN);
fmpz_mul(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, g, t);
fmpz_mod(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0,
fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, pN);
_fmpz_poly_set_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_poly_normalise(fmpz_poly_mat_entry(F1, i, j));
}
}
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(f);
fmpz_clear(g);
fmpz_clear(t);
fmpz_clear(pN);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
else
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t pN;
fmpz *f, *g, *t;
fmpz_init(pN);
f = _fmpz_vec_init(a);
g = _fmpz_vec_init(2 * a - 1);
t = _fmpz_vec_init(2 * a - 1);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_qadic_teichmuller(f, t1->coeffs, t1->length, Qq->a, Qq->j, Qq->len, p, N);
if (prec->denR == NULL)
{
fmpz_t e;
fmpz_init_set_ui(e, prec->m);
_fmpz_mod_poly_compose_smod(g, r->coeffs, r->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
_qadic_pow(t, g, a, e, Qq->a, Qq->j, Qq->len, pN);
fmpz_clear(e);
}
else
{
_fmpz_mod_poly_reduce(prec->denR->coeffs, prec->denR->length, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_normalise(prec->denR);
_fmpz_mod_poly_compose_smod(t, prec->denR->coeffs, prec->denR->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
}
_qadic_inv(g, t, a, Qq->a, Qq->j, Qq->len, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
fmpz_poly_struct *poly2 = fmpz_poly_mat_entry(F1, i, j);
if (len == 0)
{
fmpz_poly_zero(poly2);
}
else
{
_fmpz_mod_poly_compose_smod(t, poly->coeffs, len, f, a,
Qq->a, Qq->j, Qq->len, pN);
fmpz_poly_fit_length(poly2, 2 * a - 1);
_fmpz_poly_mul(poly2->coeffs, g, a, t, a);
_fmpz_mod_poly_reduce(poly2->coeffs, 2 * a - 1, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_set_length(poly2, a);
_fmpz_poly_normalise(poly2);
}
}
/* Now the matrix for p^{-1} F_p at t=t_1 is (F1, vF1). */
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
_fmpz_vec_clear(f, a);
_fmpz_vec_clear(g, 2 * a - 1);
_fmpz_vec_clear(t, 2 * a - 1);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 7 {Norm} *****************************************************/
/*
Computes the matrix for $q^{-1} F_q$ at $t = t_1$ as the
product $F \sigma(F) \dotsm \sigma^{a-1}(F)$ up appropriate
transpositions because our convention of columns vs rows is
the opposite of that used by Gerkmann.
Note that, in any case, transpositions do not affect
the characteristic polynomial.
*/
c0 = clock();
{
const long N = prec->N1 - a * vF1;
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
fmpz_pow_ui(pN, p, N);
fmpz_poly_mat_frobenius(T, F1, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
for (i = 2; i < a; i++)
{
fmpz_poly_mat_frobenius(T, T, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
}
vF1 = a * vF1;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Norm:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
/* Step 8 {Reverse characteristic polynomial} ****************************/
c0 = clock();
deformation_revcharpoly(cp, F1, vF1, n, d, prec->N0, prec->r, prec->s, Qq);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Reverse characteristic polynomial:\n");
printf(" p(T) = "), fmpz_poly_print_pretty(cp, "T"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Clean up **************************************************************/
padic_mat_clear(F0);
mat_clear(M, ctxFracQt);
free(bR);
free(bC);
fmpz_poly_clear(r);
fmpz_poly_mat_clear(C);
fmpz_poly_mat_clear(Cinv);
fmpz_poly_mat_clear(F);
fmpz_poly_mat_clear(F1);
fmpz_poly_clear(cp);
}