static double multigrid_recurse(struct element **sel, double ****f,
double ****x, int var, int level, double eps,
void (*opeval) ())
{
if (level == (*sel)->precon->nlevels - 1)
return conjugate_gradient(sel, f, x, var, opeval,
jacobi_preconditioner, eps, 500);
const int m = 15;
const int n1 = (*sel)->basis->n;
const int n2 = (*sel)->precon->nmg[level + 1];
double ****r = new_4d_array(n1, n1, n1, (*sel)->nel);
double ****fn = new_4d_array(n2, n2, n2, (*sel)->nel);
double ****e = new_4d_array(n2, n2, n2, (*sel)->nel);
if (level == 0)
compute_residual(sel, x, f, r, var, opeval);
else
copy_array(***f, ***r, n1 * n1 * n1 * (*sel)->nel);
switch_multigrid_level(sel, level + 1);
multigrid_restriction(sel, r, fn, level + 1);
multigrid_recurse(sel, fn, e, var, level + 1, eps, opeval);
switch_multigrid_level(sel, level);
multigrid_prolongation(sel, e, r, level);
add_array(***r, ***x, n1 * n1 * n1 * (*sel)->nel, 1.0);
double err = conjugate_gradient(sel, f, x, var, opeval,
jacobi_preconditioner, eps, m);
free_4d_array(r);
free_4d_array(fn);
free_4d_array(e);
return err;
}
void
FMultiGrid::compute_residual (MultiFab & phi,
MultiFab & rhs,
MultiFab & res)
{
PArray<MultiFab> phi_p;
PArray<MultiFab> rhs_p;
PArray<MultiFab> res_p;
Copy(phi_p, phi);
Copy(rhs_p, rhs);
Copy(res_p, res);
compute_residual(phi_p, rhs_p, res_p);
}
double* inner_outer_gauss_seidel_alg_vecs(
Graph g, double alpha, double tol, int maxit,
double *v, double *x, double *y, double *f,
double beta, double itol, bool resid, bool normed)
{
size_t n = (size_t)size(g);
stime_struct start; simple_time_clock(&start);
printf("inoutgs(%6.4f,%6.4f,%8e,%1i) with tol=%8e and maxit=%6i iterations\n",
alpha, beta, itol, resid, tol, maxit); fflush(stdout);
double odelta, sumy=0.0, dtx, nx, ndiff, ltol=log(tol), la=log(alpha), dt;
if (dangling_mult(g, x, y, v, 1.0, &dtx, NULL)) { return (NULL); }
odelta = compute_outer_residual(x, y, v, alpha, n);
int iter = 0, rval, nresit = 0, nmult = 1, nresids = 0;
#ifdef BVALGS_VERBOSE
printf(" iogs (outer) : iter = %6i ; odelta = %10e ; dt = %7.1f\n",
iter, odelta, elapsed_time(&start));
#endif
while (odelta > tol && nmult < maxit) {
int iiter=0;
double idelta = odelta;
compute_f(f, y, v, alpha, beta, n);
while (iter+iiter < maxit && idelta > itol) {
gauss_seidel_sweep(g, x, NULL, f,
beta, 1.0, dtx, false, &nx, &idelta, &dtx); nmult++;
if (normed) {
shift_and_scale(x,0.0,1./nx,n); dtx=dtx/nx; nx=1.0;
}
idelta = idelta; iiter++; // adjust for diff and not residual
}
if (dangling_mult(g, x, y, v, 1.0, &dtx, &dtx)) { return (NULL); }
iter++; nmult++;
odelta = compute_outer_residual(x,y,v,alpha,n);
#ifdef BVALGS_VERBOSE
printf(" iogs (outer) : iter = %6i ; odelta = %10e ; dt = %7.1f ; nmult = %9i\n",
iter, odelta, elapsed_time(&start), nmult);
#endif
if (iiter < 2 || odelta < itol) {
break;
}
}
dtx = sum_dtx(g,x); dt = elapsed_time(&start);
simple_time_clock(&start);
while (odelta > tol && nmult-nresids < maxit) {
rval = gauss_seidel_sweep(g, x, NULL, v,
alpha, (1.0-alpha), dtx, false, &nx, &ndiff, &dtx);
nmult++; iter++;
if (normed) {
shift_and_scale(x,0.0,1./nx,n); dtx=dtx/nx; nx=1.0;
}
if (rval) { return (NULL); }
dt += elapsed_time(&start);
/* compute the residual */
if (resid) {
odelta = compute_residual(g,x,y,v,alpha,dtx,nx); nmult++; nresids++;
simple_time_clock(&start);
} else {
simple_time_clock(&start);
if (ndiff < tol && iter>nresit) {
odelta = compute_residual(g,x,y,v,alpha,dtx,nx); nmult++; nresids++;
nresit=iter+(int)((ltol - log(odelta))/(2.0*la));
}
}
#ifdef BVALGS_VERBOSE
printf(" iogs ( gs) : iter = %6i ; delta = %10e ; diff = %10e ; dt = %7.1f sec ; nmult = %6i\n",
iter, odelta, ndiff, dt, nmult );
#endif
}
if (odelta > tol) {
printf("iogs(%6.4f) did not converge to %8e in %6i sweeps\n",
alpha, tol, maxit); fflush(stdout);
} else {
printf("iogs : solved pagerank(a=%6.4f) in %5i its, %5i sweeps, and %5i mults to %8e tol\n",
alpha, iter, nmult-nresids, nmult, tol); fflush(stdout);
}
return y;
}
/* ATS_SOUND *tracker (ANARGS *anargs, char *soundfile)
* partial tracking function
* anargs: pointer to analysis parameters
* soundfile: path to input file
* returns an ATS_SOUND with data issued from analysis
*/
ATS_SOUND *tracker (ANARGS *anargs, char *soundfile, char *resfile)
{
int fd, M_2, first_point, filptr, n_partials = 0;
int frame_n, k, sflen, *win_samps, peaks_size, tracks_size = 0;
int i, frame, i_tmp;
float *window, norm, sfdur, f_tmp;
/* declare structures and buffers */
ATS_SOUND *sound = NULL;
ATS_PEAK *peaks, *tracks = NULL, cpy_peak;
ATS_FRAME *ana_frames = NULL, *unmatched_peaks = NULL;
mus_sample_t **bufs;
ATS_FFT fft;
#ifdef FFTW
fftw_plan plan;
FILE *fftw_wisdom_file;
#endif
/* open input file
we get srate and total_samps in file in anargs */
if ((fd = mus_sound_open_input(soundfile))== -1) {
fprintf(stderr, "%s: %s\n", soundfile, strerror(errno));
return(NULL);
}
/* warn about multi-channel sound files */
if (mus_sound_chans(soundfile) > 1) {
fprintf(stderr, "Error: file has %d channels, must be mono!\n",
mus_sound_chans(soundfile));
return(NULL);
}
fprintf(stderr, "tracking...\n");
/* get sample rate and # of frames from file header */
anargs->srate = mus_sound_srate(soundfile);
sflen = mus_sound_frames(soundfile);
sfdur = (float)sflen/anargs->srate;
/* check analysis parameters */
/* check start time */
if( !(anargs->start >= 0.0 && anargs->start < sfdur) ){
fprintf(stderr, "Warning: start %f out of bounds, corrected to 0.0\n", anargs->start);
anargs->start = (float)0.0;
}
/* check duration */
if(anargs->duration == ATSA_DUR) {
anargs->duration = sfdur - anargs->start;
}
f_tmp = anargs->duration + anargs->start;
if( !(anargs->duration > 0.0 && f_tmp <= sfdur) ){
fprintf(stderr, "Warning: duration %f out of bounds, limited to file duration\n", anargs->duration);
anargs->duration = sfdur - anargs->start;
}
/* print time bounds */
fprintf(stderr, "start: %f duration: %f file dur: %f\n", anargs->start, anargs->duration , sfdur);
/* check lowest frequency */
if( !(anargs->lowest_freq > 0.0 && anargs->lowest_freq < anargs->highest_freq)){
fprintf(stderr, "Warning: lowest freq. %f out of bounds, forced to default: %f\n", anargs->lowest_freq, ATSA_LFREQ);
anargs->lowest_freq = ATSA_LFREQ;
}
/* check highest frequency */
if( !(anargs->highest_freq > anargs->lowest_freq && anargs->highest_freq <= anargs->srate * 0.5 )){
fprintf(stderr, "Warning: highest freq. %f out of bounds, forced to default: %f\n", anargs->highest_freq, ATSA_HFREQ);
anargs->highest_freq = ATSA_HFREQ;
}
/* frequency deviation */
if( !(anargs->freq_dev > 0.0 && anargs->freq_dev < 1.0) ){
fprintf(stderr, "Warning: freq. dev. %f out of bounds, should be > 0.0 and <= 1.0, forced to default: %f\n", anargs->freq_dev, ATSA_FREQDEV);
anargs->freq_dev = ATSA_FREQDEV;
}
/* window cycles */
if( !(anargs->win_cycles >= 1 && anargs->win_cycles <= 8) ){
fprintf(stderr, "Warning: windows cycles %d out of bounds, should be between 1 and 8, forced to default: %d\n", anargs->win_cycles, ATSA_WCYCLES);
anargs->win_cycles = ATSA_WCYCLES;
}
/* window type */
if( !(anargs->win_type >= 0 && anargs->win_type <= 3) ){
fprintf(stderr, "Warning: window type %d out of bounds, should be between 0 and 3, forced to default: %d\n", anargs->win_type, ATSA_WTYPE);
anargs->win_type = ATSA_WTYPE;
}
/* hop size */
if( !(anargs->hop_size > 0.0 && anargs->hop_size <= 1.0) ){
fprintf(stderr, "Warning: hop size %f out of bounds, should be > 0.0 and <= 1.0, forced to default: %f\n", anargs->hop_size, ATSA_HSIZE);
anargs->hop_size = ATSA_HSIZE;
}
/* lowest mag */
if( !(anargs->lowest_mag <= 0.0) ){
fprintf(stderr, "Warning: lowest magnitude %f out of bounds, should be >= 0.0 and <= 1.0, forced to default: %f\n", anargs->lowest_mag, ATSA_LMAG);
anargs->lowest_mag = ATSA_LMAG;
}
/* set some values before checking next set of parameters */
anargs->first_smp = (int)floor(anargs->start * (float)anargs->srate);
anargs->total_samps = (int)floor(anargs->duration * (float)anargs->srate);
/* fundamental cycles */
anargs->cycle_smp = (int)floor((double)anargs->win_cycles * (double)anargs->srate / (double)anargs->lowest_freq);
/* window size */
anargs->win_size = (anargs->cycle_smp % 2 == 0) ? anargs->cycle_smp+1 : anargs->cycle_smp;
/* calculate hop samples */
anargs->hop_smp = floor( (float)anargs->win_size * anargs->hop_size );
/* compute total number of frames */
anargs->frames = compute_frames(anargs);
/* check that we have enough frames for the analysis */
if( !(anargs->frames >= ATSA_MFRAMES) ){
fprintf(stderr, "Error: %d frames are not enough for analysis, nead at least %d\n", anargs->frames , ATSA_MFRAMES);
return(NULL);
}
/* check other user parameters */
/* track length */
if( !(anargs->track_len >= 1 && anargs->track_len < anargs->frames) ){
i_tmp = (ATSA_TRKLEN < anargs->frames) ? ATSA_TRKLEN : anargs->frames-1;
fprintf(stderr, "Warning: track length %d out of bounds, forced to: %d\n", anargs->track_len , i_tmp);
anargs->track_len = i_tmp;
}
/* min. segment length */
if( !(anargs->min_seg_len >= 1 && anargs->min_seg_len < anargs->frames) ){
i_tmp = (ATSA_MSEGLEN < anargs->frames) ? ATSA_MSEGLEN : anargs->frames-1;
fprintf(stderr, "Warning: min. segment length %d out of bounds, forced to: %d\n", anargs->min_seg_len, i_tmp);
anargs->min_seg_len = i_tmp;
}
/* min. gap length */
if( !(anargs->min_gap_len >= 0 && anargs->min_gap_len < anargs->frames) ){
i_tmp = (ATSA_MGAPLEN < anargs->frames) ? ATSA_MGAPLEN : anargs->frames-1;
fprintf(stderr, "Warning: min. gap length %d out of bounds, forced to: %d\n", anargs->min_gap_len, i_tmp);
anargs->min_gap_len = i_tmp;
}
/* SMR threshold */
if( !(anargs->SMR_thres >= 0.0 && anargs->SMR_thres < ATSA_MAX_DB_SPL) ){
fprintf(stderr, "Warning: SMR threshold %f out of bounds, shoul be >= 0.0 and < %f dB SPL, forced to default: %f\n", anargs->SMR_thres, ATSA_MAX_DB_SPL, ATSA_SMRTHRES);
anargs->SMR_thres = ATSA_SMRTHRES;
}
/* min. seg. SMR */
if( !(anargs->min_seg_SMR >= anargs->SMR_thres && anargs->min_seg_SMR < ATSA_MAX_DB_SPL) ){
fprintf(stderr, "Warning: min. seg. SMR %f out of bounds, shoul be >= %f and < %f dB SPL, forced to default: %f\n", anargs->min_seg_SMR, anargs->SMR_thres, ATSA_MAX_DB_SPL, ATSA_MSEGSMR);
anargs->min_seg_SMR = ATSA_MSEGSMR;
}
/* last peak contibution */
if( !(anargs->last_peak_cont >= 0.0 && anargs->last_peak_cont <= 1.0) ){
fprintf(stderr, "Warning: last peak contibution %f out of bounds, should be >= 0.0 and <= 1.0, forced to default: %f\n", anargs->last_peak_cont, ATSA_LPKCONT);
anargs->last_peak_cont = ATSA_LPKCONT;
}
/* SMR cont. */
if( !(anargs->SMR_cont >= 0.0 && anargs->SMR_cont <= 1.0) ){
fprintf(stderr, "Warning: SMR contibution %f out of bounds, should be >= 0.0 and <= 1.0, forced to default: %f\n", anargs->SMR_cont, ATSA_SMRCONT);
anargs->SMR_cont = ATSA_SMRCONT;
}
/* continue computing parameters */
/* fft size */
anargs->fft_size = ppp2(2*anargs->win_size);
/* allocate memory for sound, we read the whole sound in memory */
bufs = (mus_sample_t **)malloc(sizeof(mus_sample_t*));
bufs[0] = (mus_sample_t *)malloc(sflen * sizeof(mus_sample_t));
/* bufs = malloc(sizeof(mus_sample_t*));
bufs[0] = malloc(sflen * sizeof(mus_sample_t)); */
/* make our window */
window = make_window(anargs->win_type, anargs->win_size);
/* get window norm */
norm = window_norm(window, anargs->win_size);
/* fft mag for computing frequencies */
anargs->fft_mag = (double)anargs->srate / (double)anargs->fft_size;
/* lowest fft bin for analysis */
anargs->lowest_bin = floor( anargs->lowest_freq / anargs->fft_mag );
/* highest fft bin for analisis */
anargs->highest_bin = floor( anargs->highest_freq / anargs->fft_mag );
/* allocate an array analysis frames in memory */
ana_frames = (ATS_FRAME *)malloc(anargs->frames * sizeof(ATS_FRAME));
/* alocate memory to store mid-point window sample numbers */
win_samps = (int *)malloc(anargs->frames * sizeof(int));
/* center point of window */
M_2 = floor((anargs->win_size - 1) / 2);
/* first point in fft buffer to write */
first_point = anargs->fft_size - M_2;
/* half a window from first sample */
filptr = anargs->first_smp - M_2;
/* read sound into memory */
mus_sound_read(fd, 0, sflen-1, 1, bufs);
/* make our fft-struct */
fft.size = anargs->fft_size;
fft.rate = anargs->srate;
#ifdef FFTW
fft.data = fftw_malloc(sizeof(fftw_complex) * fft.size);
if(fftw_import_system_wisdom()) fprintf(stderr, "system wisdom loaded!\n");
else fprintf(stderr, "cannot locate system wisdom!\n");
if((fftw_wisdom_file = fopen("ats-wisdom", "r")) != NULL) {
fftw_import_wisdom_from_file(fftw_wisdom_file);
fprintf(stderr, "ats-wisdom loaded!\n");
fclose(fftw_wisdom_file);
} else fprintf(stderr, "cannot locate ats-wisdom!\n");
plan = fftw_plan_dft_1d(fft.size, fft.data, fft.data, FFTW_FORWARD, FFTW_PATIENT);
#else
fft.fdr = (double *)malloc(anargs->fft_size * sizeof(double));
fft.fdi = (double *)malloc(anargs->fft_size * sizeof(double));
#endif
/* main loop */
for (frame_n=0; frame_n<anargs->frames; frame_n++) {
/* clear fft arrays */
#ifdef FFTW
for(k=0; k<fft.size; k++) fft.data[k][0] = fft.data[k][1] = 0.0f;
#else
for(k=0; k<fft.size; k++) fft.fdr[k] = fft.fdi[k] = 0.0f;
#endif
/* multiply by window */
for (k=0; k<anargs->win_size; k++) {
if ((filptr >= 0) && (filptr < sflen))
#ifdef FFTW
fft.data[(k+first_point)%fft.size][0] = window[k] * MUS_SAMPLE_TO_FLOAT(bufs[0][filptr]);
#else
fft.fdr[(k+first_point)%anargs->fft_size] = window[k] * MUS_SAMPLE_TO_FLOAT(bufs[0][filptr]);
#endif
filptr++;
}
/* we keep sample numbers of window midpoints in win_samps array */
win_samps[frame_n] = filptr - M_2 - 1;
/* move file pointer back */
filptr = filptr - anargs->win_size + anargs->hop_smp;
/* take the fft */
#ifdef FFTW
fftw_execute(plan);
#else
fft_slow(fft.fdr, fft.fdi, fft.size, 1);
#endif
/* peak detection */
peaks_size = 0;
peaks = peak_detection(&fft, anargs->lowest_bin, anargs->highest_bin, anargs->lowest_mag, norm, &peaks_size);
/* peak tracking */
if (peaks != NULL) {
/* evaluate peaks SMR (masking curves) */
evaluate_smr(peaks, peaks_size);
if (frame_n) {
/* initialize or update tracks */
if ((tracks = update_tracks(tracks, &tracks_size, anargs->track_len, frame_n, ana_frames, anargs->last_peak_cont)) != NULL) {
/* do peak matching */
unmatched_peaks = peak_tracking(tracks, &tracks_size, peaks, &peaks_size, anargs->freq_dev, 2.0 * anargs->SMR_cont, &n_partials);
/* kill unmatched peaks from previous frame */
if(unmatched_peaks[0].peaks != NULL) {
for(k=0; k<unmatched_peaks[0].n_peaks; k++) {
cpy_peak = unmatched_peaks[0].peaks[k];
cpy_peak.amp = cpy_peak.smr = 0.0;
peaks = push_peak(&cpy_peak, peaks, &peaks_size);
}
free(unmatched_peaks[0].peaks);
}
/* give birth to peaks from new frame */
if(unmatched_peaks[1].peaks != NULL) {
for(k=0; k<unmatched_peaks[1].n_peaks; k++) {
tracks = push_peak(&unmatched_peaks[1].peaks[k], tracks, &tracks_size);
unmatched_peaks[1].peaks[k].amp = unmatched_peaks[1].peaks[k].smr = 0.0;
ana_frames[frame_n-1].peaks = push_peak(&unmatched_peaks[1].peaks[k], ana_frames[frame_n-1].peaks, &ana_frames[frame_n-1].n_peaks);
}
free(unmatched_peaks[1].peaks);
}
} else {
/* give number to all peaks */
qsort(peaks, peaks_size, sizeof(ATS_PEAK), peak_frq_inc);
for(k=0; k<peaks_size; k++) peaks[k].track = n_partials++;
}
} else {
/* give number to all peaks */
qsort(peaks, peaks_size, sizeof(ATS_PEAK), peak_frq_inc);
for(k=0; k<peaks_size; k++) peaks[k].track = n_partials++;
}
/* attach peaks to ana_frames */
ana_frames[frame_n].peaks = peaks;
ana_frames[frame_n].n_peaks = n_partials;
ana_frames[frame_n].time = (double)(win_samps[frame_n] - anargs->first_smp) / (double)anargs->srate;
/* free memory */
free(unmatched_peaks);
} else {
/* if no peaks found, initialize empty frame */
ana_frames[frame_n].peaks = NULL;
ana_frames[frame_n].n_peaks = 0;
ana_frames[frame_n].time = (double)(win_samps[frame_n] - anargs->first_smp) / (double)anargs->srate;
}
}
/* free up some memory */
free(window);
free(tracks);
#ifdef FFTW
fftw_destroy_plan(plan);
fftw_free(fft.data);
#else
free(fft.fdr);
free(fft.fdi);
#endif
/* init sound */
fprintf(stderr, "Initializing ATS data...");
sound = (ATS_SOUND *)malloc(sizeof(ATS_SOUND));
init_sound(sound, anargs->srate, (int)(anargs->hop_size * anargs->win_size),
anargs->win_size, anargs->frames, anargs->duration, n_partials,
((anargs->type == 3 || anargs->type == 4) ? 1 : 0));
/* store values from frames into the arrays */
for(k=0; k<n_partials; k++) {
for(frame=0; frame<sound->frames; frame++) {
sound->time[k][frame] = ana_frames[frame].time;
for(i=0; i<ana_frames[frame].n_peaks; i++)
if(ana_frames[frame].peaks[i].track == k) {
sound->amp[k][frame] = ana_frames[frame].peaks[i].amp;
sound->frq[k][frame] = ana_frames[frame].peaks[i].frq;
sound->pha[k][frame] = ana_frames[frame].peaks[i].pha;
sound->smr[k][frame] = ana_frames[frame].peaks[i].smr;
}
}
}
fprintf(stderr, "done!\n");
/* free up ana_frames memory */
/* first, free all peaks in each slot of ana_frames... */
for (k=0; k<anargs->frames; k++) free(ana_frames[k].peaks);
/* ...then free ana_frames */
free(ana_frames);
/* optimize sound */
optimize_sound(anargs, sound);
/* compute residual */
if( anargs->type == 3 || anargs->type == 4 ) {
fprintf(stderr, "Computing residual...");
compute_residual(bufs, sflen, resfile, sound, win_samps, anargs->srate);
fprintf(stderr, "done!\n");
}
/* free the rest of the memory */
free(win_samps);
free(bufs[0]);
free(bufs);
/* analyze residual */
if( anargs->type == 3 || anargs->type == 4 ) {
fprintf(stderr, "Analyzing residual...");
residual_analysis(ATSA_RES_FILE, sound);
fprintf(stderr, "done!\n");
}
#ifdef FFTW
fftw_wisdom_file = fopen("ats-wisdom", "w");
fftw_export_wisdom_to_file(fftw_wisdom_file);
fclose(fftw_wisdom_file);
#endif
fprintf(stderr, "tracking completed.\n");
return(sound);
}
int
main (int argc, char **argv)
{
int mpi_rank, mpi_size;
int n, ln;
double *A, *b, *xA, *xB, *xC, *r, *X, *x;
double lmax, max;
struct timeval before, after;
MPI_Init (&argc, &argv);
MPI_Comm_size (MPI_COMM_WORLD, &mpi_size);
MPI_Comm_rank (MPI_COMM_WORLD, &mpi_rank);
/* Get the argument that indicates the problem size */
n = JACOBI_DEF_SIZE;
if (argc == 2)
n = atoi (argv[1]);
if (mpi_rank == ROOT_NODE)
fprintf (stdout, "n = %d\n", n);
ln = n / mpi_size;
/* Initialize the random seed */
/*srandom((unsigned int) getpid ());*/
/* Allocate memory */
A = (double *) calloc (ln * n, sizeof(double));
if (A == NULL)
{
perror ("calloc");
MPI_Finalize ();
return EXIT_FAILURE;
}
b = (double *) calloc (ln, sizeof(double));
if (b == NULL)
{
perror ("calloc");
MPI_Finalize ();
return EXIT_FAILURE;
}
xA = (double *) calloc (ln, sizeof(double));
if (xA == NULL)
{
perror ("calloc");
MPI_Finalize ();
return EXIT_FAILURE;
}
xB = (double *) calloc (ln, sizeof(double));
if (xB == NULL)
{
perror ("calloc");
MPI_Finalize ();
return EXIT_FAILURE;
}
xC = (double *) calloc (ln, sizeof(double));
if (xC == NULL)
{
perror ("calloc");
MPI_Finalize ();
return EXIT_FAILURE;
}
X = (double *) calloc (n, sizeof(double));
if (X == NULL)
{
perror ("calloc");
MPI_Finalize ();
return EXIT_FAILURE;
}
r = (double *) calloc (ln, sizeof(double));
if (r == NULL)
{
perror ("calloc");
MPI_Finalize ();
return EXIT_FAILURE;
}
generate_matrix (A, ln, n, mpi_rank);
generate_vector (b, ln);
gettimeofday(&before, NULL);
x = jacobi (xA, xB, xC, A, b, ln, n, mpi_rank, mpi_size);
gettimeofday(&after, NULL);
MPI_Allgather (x, ln, MPI_DOUBLE,
X, ln, MPI_DOUBLE, MPI_COMM_WORLD);
/* Compute the residual */
compute_residual (r, A, X, b, ln, n);
/* Compute the maximum absolute value of the residual */
lmax = find_max_abs (r, ln);
MPI_Reduce (&lmax, &max, 1, MPI_DOUBLE, MPI_MAX, ROOT_NODE, MPI_COMM_WORLD);
if (mpi_rank == ROOT_NODE)
display_info (A, x, b, r, n, max, &before, &after);
/* Free the memory */
free (A);
free (b);
free (xA);
free (xB);
free (xC);
free (X);
free (r);
/* Return success */
MPI_Finalize ();
return 0;
}
int main(int argc, char* argv[])
{
// Print help if necessary
bool help = read_bool(argc, argv, "--help", false);
if ((argc < 2) || (help)) {
usage(argv);
return 0;
}
// Use parameters struct for passing parameters to kernels efficiently
parameters prm;
// Parse inputs
prm.matDims[0] = read_int(argc, argv, "--m", 2);
prm.matDims[1] = read_int(argc, argv, "--k", 2);
prm.matDims[2] = read_int(argc, argv, "--n", 2);
prm.rank = read_int(argc, argv, "--rank", 7);
prm.method = read_string(argc, argv, "--method", (char *)"als");
int maxIters = read_int(argc, argv, "--maxiters", 1000);
int maxSecs = read_int(argc, argv, "--maxsecs", 1000);
double tol = read_double(argc, argv, "--tol", 1e-8);
int printItn = read_int(argc, argv, "--printitn", 0);
double printTol = read_double(argc, argv, "--printtol", 1.0);
int seed = read_int(argc, argv, "--seed", 0);
int numSeeds = read_int(argc, argv, "--numseeds", 1);
bool verbose = read_bool(argc, argv, "--verbose", false);
prm.rnd_maxVal = read_double(argc,argv,"--maxval",1.0);
prm.rnd_pwrOfTwo = read_int(argc,argv,"--pwrof2",0);
bool roundFinal = read_bool(argc, argv, "--rndfin",false);
prm.alpha = read_double(argc,argv, "--alpha", 0.1);
int M = read_int(argc,argv, "--M", 0);
if (M)
{
prm.M[0] = M;
prm.M[1] = M;
prm.M[2] = M;
} else {
prm.M[0] = read_int(argc, argv, "--M0", -1);
prm.M[1] = read_int(argc, argv, "--M1", -1);
prm.M[2] = read_int(argc, argv, "--M2", -1);
}
char * infile = read_string(argc, argv, "--input", NULL);
char * outfile = read_string(argc, argv, "--output", NULL);
if (verbose) {
setbuf(stdout, NULL);
printf("\n\n---------------------------------------------------------\n");
printf("PARAMETERS\n");
printf("dimensions = %d %d %d\n",prm.matDims[0],prm.matDims[1],prm.matDims[2]);
printf("rank = %d\n",prm.rank);
printf("method = %s\n",prm.method);
if (infile)
printf("input = %s\n",infile);
else
{
if (numSeeds == 1)
printf("input = seed %d\n",seed);
else
printf("inputs = seeds %d-%d\n",seed,seed+numSeeds-1);
}
if (outfile)
printf("output = %s\n",outfile);
else
printf("output = none\n");
if (!strcmp(prm.method,"als"))
{
printf("tol = %1.2e\n",tol);
printf("alpha = %1.2e\n",prm.alpha);
printf("maval = %1.2e\n",prm.rnd_maxVal);
printf("M's = (%d,%d,%d)\n",prm.M[0],prm.M[1],prm.M[2]);
printf("maxiters = %d\n",maxIters);
printf("maxsecs = %d\n",maxSecs);
printf("printitn = %d\n",printItn);
printf("printtol = %1.2e\n",printTol);
}
printf("---------------------------------------------------------\n");
}
// Initialize other variables
int i, j, k, numIters, mkn, tidx[3];
double err, errOld, errChange = 0.0, start_als, start_search, elapsed, threshold;
// Compute tensor dimensions
prm.dims[0] = prm.matDims[0]*prm.matDims[1];
prm.dims[1] = prm.matDims[1]*prm.matDims[2];
prm.dims[2] = prm.matDims[0]*prm.matDims[2];
// Compute tensor's nnz, total number of entries, and Frobenius norm
mkn = prm.matDims[0]*prm.matDims[1]*prm.matDims[2];
prm.mkn2 = mkn*mkn;
prm.xNorm = sqrt(mkn);
// Compute number of columns in matricized tensors
for (i = 0; i < 3; i++)
prm.mtCols[i] = prm.mkn2 / prm.dims[i];
// Construct three matricizations of matmul tensor
prm.X = (double**) malloc( 3 * sizeof(double*) );
for (i = 0; i < 3; i++)
prm.X[i] = (double*) calloc( prm.mkn2, sizeof(double) );
for (int mm = 0; mm < prm.matDims[0]; mm++)
for (int kk = 0; kk < prm.matDims[1]; kk++)
for (int nn = 0; nn < prm.matDims[2]; nn++)
{
tidx[0] = mm + kk*prm.matDims[0];
tidx[1] = kk + nn*prm.matDims[1];
tidx[2] = mm + nn*prm.matDims[0];
prm.X[0][tidx[0]+prm.dims[0]*(tidx[1]+prm.dims[1]*tidx[2])] = 1;
prm.X[1][tidx[1]+prm.dims[1]*(tidx[0]+prm.dims[0]*tidx[2])] = 1;
prm.X[2][tidx[2]+prm.dims[2]*(tidx[0]+prm.dims[0]*tidx[1])] = 1;
}
// Allocate factor weights and matrices: working, initial, and model
prm.lambda = (double*) malloc( prm.rank * sizeof(double) );
prm.U = (double**) malloc( 3 * sizeof(double*) );
double** U0 = (double**) malloc( 3 * sizeof(double*) );
prm.model = (double**) malloc( 3 * sizeof(double*) );
for (i = 0; i < 3; i++)
{
prm.U[i] = (double*) calloc( prm.mkn2, sizeof(double) );
U0[i] = (double*) calloc( prm.dims[i]*prm.rank, sizeof(double) );
prm.model[i] = (double*) calloc( prm.dims[i]*prm.rank, sizeof(double) );
}
// Allocate coefficient matrix within ALS (Khatri-Rao product)
int maxMatDim = prm.matDims[0];
if (maxMatDim < prm.matDims[1]) maxMatDim = prm.matDims[1];
if (maxMatDim < prm.matDims[2]) maxMatDim = prm.matDims[2];
prm.A = (double*) malloc( maxMatDim*mkn*prm.rank * sizeof(double) );
// Allocate workspaces
prm.tau = (double*) malloc( mkn * sizeof(double) );
prm.lwork = maxMatDim*mkn*prm.rank;
prm.work = (double*) malloc( prm.lwork * sizeof(double) );
prm.iwork = (int*) malloc( prm.mkn2 * sizeof(int) );
// Allocate matrices for normal equations
int maxDim = prm.dims[0];
if (maxDim < prm.dims[1]) maxDim = prm.dims[1];
if (maxDim < prm.dims[2]) maxDim = prm.dims[2];
prm.NE_coeff = (double*) malloc( prm.rank*prm.rank * sizeof(double) );
prm.NE_rhs = (double*) malloc( maxDim*prm.rank * sizeof(double) );
prm.residual = (double*) malloc( prm.mkn2 * sizeof(double) );
//--------------------------------------------------
// Search Loop
//--------------------------------------------------
int mySeed = seed, numGoodSeeds = 0, statusCnt = 0, status = 1;
start_search = wall_time();
for (int seed_cnt = 0; seed_cnt < numSeeds; ++seed_cnt)
{
// Set starting point from random seed (match Matlab Tensor Toolbox)
RandomMT cRMT(mySeed);
for (i = 0; i < 3; i++)
for (j = 0; j < prm.dims[i]; j++)
for (k = 0; k < prm.rank; k++)
U0[i][j+k*prm.dims[i]] = cRMT.genMatlabMT();
for (i = 0; i < prm.rank; i++)
prm.lambda[i] = 1.0;
// Copy starting point
for (i = 0; i < 3; i++)
cblas_dcopy(prm.dims[i]*prm.rank,U0[i],1,prm.U[i],1);
// read from file if input is given
if( infile )
read_input( infile, prm );
if (verbose)
{
printf("\nSTARTING POINT...\n");
for (i = 0; i < 3; i++)
{
printf("Factor matrix %d:\n",i);
print_matrix(prm.U[i],prm.dims[i],prm.rank,prm.dims[i]);
}
printf("\n");
}
//--------------------------------------------------
// Main ALS Loop
//--------------------------------------------------
start_als = wall_time();
err = 1.0;
threshold = 1e-4;
for (numIters = 0; numIters < maxIters && (wall_time()-start_als) < maxSecs; numIters++)
{
errOld = err;
if (!strcmp(prm.method,"als"))
{
// Perform an iteration of ALS using NE with Smirnov's penalty term
err = als( prm );
}
else if (!strcmp(prm.method,"sparsify"))
{
// print stats before sparsifying
printf("Old residual: %1.2e\n",compute_residual(prm,2,true));
printf("Old nnz (larger than %1.1e): %d %d %d\n", threshold, nnz(prm.U[0],prm.dims[0]*prm.rank,threshold), nnz(prm.U[1],prm.dims[1]*prm.rank,threshold), nnz(prm.U[2],prm.dims[2]*prm.rank,threshold) );
// sparsify and return
printf("\nSparsifying...\n\n");
sparsify( prm );
numIters = maxIters;
// print stats after sparsifying
printf("New residual: %1.2e\n",compute_residual(prm,2,true));
printf("New nnz (larger than %1.1e): %d %d %d\n", threshold, nnz(prm.U[0],prm.dims[0]*prm.rank,threshold), nnz(prm.U[1],prm.dims[1]*prm.rank,threshold), nnz(prm.U[2],prm.dims[2]*prm.rank,threshold) );
}
else if (!strcmp(prm.method,"round"))
{
// print stats before rounding
printf("Old residual: %1.2e\n",compute_residual(prm,2,true));
printf("Old nnz (larger than %1.1e): %d %d %d\n", threshold, nnz(prm.U[0],prm.dims[0]*prm.rank,threshold), nnz(prm.U[1],prm.dims[1]*prm.rank,threshold), nnz(prm.U[2],prm.dims[2]*prm.rank,threshold) );
// round and return
for (i = 0; i < 3; i++)
{
capping(prm.U[i],prm.dims[i]*prm.rank,prm.rnd_maxVal);
rounding(prm.U[i],prm.dims[i]*prm.rank,prm.rnd_pwrOfTwo);
}
numIters = maxIters;
// print stats after rounding
printf("New residual: %1.2e\n",compute_residual(prm,2,true));
printf("New nnz (larger than %1.1e): %d %d %d\n", threshold, nnz(prm.U[0],prm.dims[0]*prm.rank,threshold), nnz(prm.U[1],prm.dims[1]*prm.rank,threshold), nnz(prm.U[2],prm.dims[2]*prm.rank,threshold) );
}
else
die("Invalid method\n");
// Compute change in relative residual norm
errChange = fabs(err - errOld);
// Print info at current iteration
if ((printItn > 0) && (((numIters + 1) % printItn) == 0))
{
// print info
printf ("Iter %d: residual = %1.5e change = %1.5e\n", numIters + 1, err, errChange);
}
// Check for convergence
if ( numIters > 0 && errChange < tol )
break;
}
// If rounding, round final solution and re-compute residual
if(roundFinal)
{
// normalize columns in A and B factors, put arbitrary weights into C
normalize_model( prm, 2 );
// cap large values and round to nearest power of 2
for (i = 0; i < 3; i++)
{
capping(prm.U[i],prm.dims[i]*prm.rank,prm.rnd_maxVal);
rounding(prm.U[i],prm.dims[i]*prm.rank,prm.rnd_pwrOfTwo);
}
err = compute_residual(prm,0,true);
}
// Print status if searching over many seeds
statusCnt++;
if (numSeeds > 1000 && statusCnt == numSeeds/10)
{
printf("...%d%% complete...\n",10*status);
status++;
statusCnt = 0;
}
// Print final info
elapsed = wall_time() - start_als;
if ((printItn > 0 || verbose) && !strcmp(prm.method,"als"))
{
if (infile)
printf("\nInput %s ",infile);
else
printf("\nInitial seed %d ",mySeed);
printf("achieved residual %1.3e in %d iterations and %1.3e seconds\n \t final residual change: %1.3e\n \t average time per iteration: %1.3e s\n", err, numIters, elapsed, errChange, elapsed/numIters);
}
if (verbose)
{
printf("\nSOLUTION...\n");
for (i = 0; i < 3; i++)
{
printf("Factor matrix %d:\n",i);
if (roundFinal || !strcmp(prm.method,"round"))
print_int_matrix(prm.U[i], prm.dims[i], prm.rank, prm.dims[i], prm.rnd_pwrOfTwo);
else
print_matrix(prm.U[i],prm.dims[i],prm.rank,prm.dims[i]);
}
if (err < printTol)
numGoodSeeds++;
}
else if (err < printTol)
{
numGoodSeeds++;
printf("\n\n***************************************\n");
if (infile)
printf("Input %s: ",infile);
else
printf("Initial seed %d: ",mySeed);
printf("after %d iterations, achieved residual %1.3e with final residual change of %1.3e\n", numIters, err, errChange);
if (roundFinal)
{
for (i = 0; i < 3; i++)
{
printf("Factor matrix %d:\n",i);
print_int_matrix(prm.U[i], prm.dims[i], prm.rank, prm.dims[i], prm.rnd_pwrOfTwo);
}
int count = 0;
for (i = 0; i < 3; i++)
count += nnz(prm.U[i],prm.dims[i]*prm.rank);
printf("\ttotal nnz in solution: %d\n",count);
printf("\tnaive adds/subs: %d\n",count - prm.dims[2] - 2*prm.rank);
}
printf("***************************************\n\n\n");
}
// write to output
if( outfile )
write_output( outfile, prm );
mySeed++;
}
// Final report of processor statistics
elapsed = wall_time()-start_search;
// Print stats
if (!strcmp(prm.method,"als"))
{
printf("\n\n------------------------------------------------------------\n");
printf("Time elapsed: \t%1.1e\tseconds\n",elapsed);
printf("Total number of seeds tried: \t%d\n",numSeeds);
printf("Total number of good seeds: \t%d",numGoodSeeds);
printf("\t(residual < %2.1e)\n",printTol);
printf("------------------------------------------------------------\n");
}
// free allocated memory
for (i = 0; i < 3; i++)
{
free( prm.X[i] );
free( prm.U[i] );
free( U0[i] );
free( prm.model[i] );
}
free( prm.X );
free( prm.U );
free( U0 );
free( prm.model );
free( prm.lambda );
free( prm.A );
free( prm.NE_coeff );
free( prm.NE_rhs );
free( prm.residual );
free( prm.tau );
free( prm.work );
free( prm.iwork );
return 0;
}
