static void test_accuracy(){
rand_t rstat;
int seed=4;
double r0=0.2;
double dx=1./64.;
long N=1+64;
long nx=N;
long ny=N;
seed_rand(&rstat, seed);
map_t *atm=mapnew(nx, ny, dx, dx,NULL);
for(long i=0; i<nx*ny; i++){
atm->p[i]=randn(&rstat);
}
map_t *atm2=mapnew(nx, ny, dx, dx,NULL);
for(long i=0; i<nx*ny; i++){
atm2->p[i]=randn(&rstat);
}
mapwrite(atm, "atm_rand.bin");
mapwrite(atm2, "atm2_rand.bin");
fractal_do((dmat*)atm, dx, r0,L0,ninit);
mapwrite(atm, "atm_frac.bin");
fractal_inv((dmat*)atm, dx, r0,L0,ninit);
mapwrite(atm, "atm_frac_inv.bin");
fractal_trans((dmat*)atm2, dx, r0,L0,ninit);
mapwrite(atm2, "atm2_frac_trans.bin");
fractal_inv_trans((dmat*)atm2, dx, r0,L0,ninit);
mapwrite(atm2, "atm2_frac_inv_trans.bin");
/*
atm2 is u, atm is v, now comparing u'Av against v'A'u. they should be the same.
A^-1Av should be the same as v
A'^-1A'u should be the same as u.
*/
dmat *u=dread("atm2_rand.bin");
dmat *Atu=dread("atm2_frac_trans.bin");
dmat *Av=dread("atm_frac.bin");
dmat *v=dread("atm_rand.bin");
double dot1=dotdbl(u->p, Av->p, NULL, nx*ny);
double dot2=dotdbl(v->p, Atu->p, NULL, nx*ny);
info("dot1=%g, dot2=%g, diff=%g\n", dot1, dot2, dot1-dot2);
dmat *u2=dread("atm2_frac_inv_trans.bin");
dmat *v2=dread("atm_frac_inv.bin");
double d1=ddiff(u, u2);
double d2=ddiff(v, v2);
info("d1=%g, d2=%g\n", d1, d2);
}
static void test_part(){/**Compute the covariance of 4 points with various separation.*/
rand_t rstat;
int seed=4;
double r0=0.2;
double dx=1./64.;
long N=1+2;
long ofx=0;
long ofy=0;
long nx=N;
long ny=N;
long nframe=1000000;
seed_rand(&rstat, seed);
map_t *atm=mapnew(nx, ny, dx,dx, NULL);
dmat *vec=dnew(4,1);
dmat *cov=NULL;
dmat* pp=(dmat*)atm;
for(long i=0; i<nframe; i++){
info("%ld of %ld\n", i, nframe);
for(long j=0; j<nx*ny; j++){
atm->p[j]=randn(&rstat);
}
fractal_do((dmat*)atm, dx, r0,L0,ninit);
vec->p[0]=IND(pp,ofx+0,ofy+0);
vec->p[1]=IND(pp,ofx+1,ofy+0);
vec->p[2]=IND(pp,ofx+0,ofy+1);
vec->p[3]=IND(pp,ofx+1,ofy+1);
dmm(&cov, 1, vec, vec, "nt", 1);
}
dscale(cov, 1./nframe);
writebin(cov,"cov.bin");
}
static void test_cov(){/*not good */
rand_t rstat;
int seed=4;
double r0=0.2;
double dx=1./64;
long N=1+1024;
long nx=N;
long ny=N;
long nframe=1;
seed_rand(&rstat, seed);
map_t *atm=mapnew(nx, ny, dx,dx, NULL);
cmat *atmhat=cnew((N+1)*3,(N+1)*3);
dmat *atmhattot=dnew((N+1)*3,(N+1)*3);
//cfft2plan(atmhat,-1);
//cfft2plan(atmhat, 1);
dset((dmat*)atm,1);
cembedd(atmhat, (dmat*)atm, 0);
cfft2(atmhat, -1);
cabs22d(&atmhattot, 1, atmhat, 1);
ccpd(&atmhat, atmhattot);
cfft2i(atmhat, 1);
cfftshift(atmhat);
dmat *denom=dnew((N+1)*3,(N+1)*3);
dmat *cov=dnew((N+1)*3,(N+1)*3);
creal2d(&denom, 0, atmhat, 1);
writebin(denom, "denom.bin");
dzero(atmhattot);
for(long i=0; i<nframe; i++){
info("%ld of %ld\n", i, nframe);
for(long j=0; j<nx*ny; j++){
atm->p[j]=randn(&rstat);
}
fractal_do((dmat*)atm, dx, r0,L0,ninit);
/*mapwrite(atm, "atm_%ld.bin", i); */
cembedd(atmhat, (dmat*)atm, 0);
cfft2(atmhat, -1);
cabs22d(&atmhattot, 1, atmhat, 1);
if(i==0 || (i+1)%10==0){
dscale(atmhattot, 1./(i+1));
ccpd(&atmhat, atmhattot);
writebin(atmhattot, "atm_psf_%ld.bin",i+1);
cfft2i(atmhat, 1);
cfftshift(atmhat);
creal2d(&cov, 0, atmhat, 1);
for(long k=0; k<cov->nx*cov->ny; k++){
cov->p[k]/=denom->p[k];
}
writebin(cov, "atm_cov_%ld.bin",i+1);
}
}
}
static void test_corner(){/*Compute the covariance of 4 corner points*/
rand_t rstat;
int seed=4;
double r0=0.2;
double dx=32;
long N=1+1;
long nx=N;
long ny=N;
long nframe=1000000;
seed_rand(&rstat, seed);
map_t *atm=mapnew(nx, ny, dx, dx,NULL);
dmat *vec=dref_reshape((dmat*)atm, N*N, 1);
dmat *cov=NULL;
for(long i=0; i<nframe; i++){
info("%ld of %ld\n", i, nframe);
for(long j=0; j<nx*ny; j++){
atm->p[j]=randn(&rstat);
}
fractal_do((dmat*)atm, dx, r0,L0,ninit);
dmm(&cov, 1, vec, vec, "nt", 1);
}
dscale(cov, 1./nframe);
writebin(cov,"cov.bin");
}
/*
Compute cxx on atm to compare against L2, invpsd, fractal.
*/
static void test_cxx(){
rand_t rstat;
int seed=4;
double r0=0.2;
double dx=1./4;
long N=16;
long nx=N;
long ny=N;
long nframe=40960;
seed_rand(&rstat, seed);
{
dmat *cxx=dnew(N*N,N*N);
map_t *atm=mapnew(nx+1, ny+1, dx, dx,NULL);
for(long i=0; i<nframe; i++){
info("%ld of %ld\n", i, nframe);
for(long j=0; j<(nx+1)*(ny+1); j++){
atm->p[j]=randn(&rstat);
}
fractal_do((dmat*)atm, dx, r0, L0, ninit);
dmat *sec=dsub((dmat*)atm, 0, nx, 0, ny);
dmat *atmvec=dref_reshape(sec, nx*ny, 1);
dmm(&cxx,1, atmvec,atmvec,"nt",1);
dfree(atmvec);
dfree(sec);
}
dscale(cxx, 1./nframe);
writebin(cxx, "cxx_fractal");
dfree(cxx);
mapfree(atm);
}
{
dmat *cxx=dnew(N*N,N*N);
dmat *spect=turbpsd(nx, ny, dx, r0, 100, 0, 0.5);
spect->p[0]=spect->p[1];
cmat *atm=cnew(nx, ny);
//cfft2plan(atm, -1);
dmat *atmr=dnew(nx*ny,1);
dmat *atmi=dnew(nx*ny,1);
for(long ii=0; ii<nframe; ii+=2){
info("%ld of %ld\n", ii, nframe);
for(long i=0; i<atm->nx*atm->ny; i++){
atm->p[i]=COMPLEX(randn(&rstat), randn(&rstat))*spect->p[i];
}
cfft2(atm, -1);
for(long i=0; i<atm->nx*atm->ny; i++){
atmr->p[i]=creal(atm->p[i]);
atmi->p[i]=cimag(atm->p[i]);
}
dmm(&cxx,1, atmr,atmr,"nt",1);
dmm(&cxx,1, atmi,atmi,"nt",1);
}
dscale(cxx, 1./nframe);
writebin(cxx, "cxx_fft");
dfree(cxx);
dfree(atmr);
dfree(atmi);
cfree(atm);
}
loc_t *loc=mksqloc_auto(16,16,1./4,1./4);
locwrite(loc,"loc");
dmat *B=stfun_kolmogorov(loc, r0);
writebin(B, "B_theory");
}
static void test_psd(){
rand_t rstat;
int seed=4;
double r0=0.2;
double dx=1./64;
long N=1024;
long nx=N;
long ny=N;
long ratio=1;
long xskip=nx*(ratio-1)/2;
long yskip=ny*(ratio-1)/2;
long nframe=512;
seed_rand(&rstat, seed);
if(1){
map_t *atm=mapnew(nx+1, ny+1, dx,dx, NULL);
cmat *hat=cnew(nx*ratio, ny*ratio);
//cfft2plan(hat, -1);
dmat *hattot=dnew(nx*ratio, ny*ratio);
for(long i=0; i<nframe; i++){
info2("%ld of %ld\n", i, nframe);
for(long j=0; j<(nx+1)*(ny+1); j++){
atm->p[j]=randn(&rstat);
}
fractal_do((dmat*)atm, dx, r0,L0,ninit);
czero(hat);
for(long iy=0; iy<ny; iy++){
for(long ix=0; ix<nx; ix++){
IND(hat,ix+xskip,iy+yskip)=IND(atm,ix,iy);
}
}
cfftshift(hat);
cfft2i(hat, -1);
cabs22d(&hattot, 1, hat, 1);
}
dscale(hattot, 1./nframe);
dfftshift(hattot);
writebin(hattot, "PSD_fractal");
}
{
dmat *spect=turbpsd(nx, ny, dx, r0, 100, 0, 0.5);
writebin(spect, "spect");
cmat *hat=cnew(nx*ratio, ny*ratio);
//cfft2plan(hat, -1);
dmat *hattot=dnew(nx*ratio, ny*ratio);
cmat *atm=cnew(nx, ny);
//cfft2plan(atm, -1);
dmat *atmr=dnew(atm->nx, atm->ny);
dmat *atmi=dnew(atm->nx, atm->ny);
cmat* phat=hat;
dmat* patmr=atmr;
dmat* patmi=atmi;
for(long ii=0; ii<nframe; ii+=2){
info2("%ld of %ld\n", ii, nframe);
for(long i=0; i<atm->nx*atm->ny; i++){
atm->p[i]=COMPLEX(randn(&rstat), randn(&rstat))*spect->p[i];
}
cfft2(atm, -1);
for(long i=0; i<atm->nx*atm->ny; i++){
atmr->p[i]=creal(atm->p[i]);
atmi->p[i]=cimag(atm->p[i]);
}
czero(hat);
for(long iy=0; iy<ny; iy++){
for(long ix=0; ix<nx; ix++){
IND(phat,ix+xskip,iy+yskip)=IND(patmr,ix,iy);
}
}
cfftshift(hat);
cfft2i(hat, -1);
cabs22d(&hattot, 1, hat, 1);
czero(hat);
for(long iy=0; iy<ny; iy++){
for(long ix=0; ix<nx; ix++){
IND(phat,ix+xskip,iy+yskip)=IND(patmi,ix,iy);
}
}
cfftshift(hat);
cfft2i(hat, -1);
cabs22d(&hattot, 1, hat, 1);
}
dscale(hattot, 1./nframe);
dfftshift(hattot);
writebin(hattot, "PSD_fft");
}
}
static void test_stfun(){
rand_t rstat;
int seed=4;
double r0=0.2;
double dx=1./16;
long N=32;
long nx=N;
long ny=N;
long nframe=500;
seed_rand(&rstat, seed);
if(L0<9000){
dmat *rr=dlinspace(0, N*dx, N);
dmat *covvk=turbcov(rr, sqrt(2)*N*dx, r0, L0);
writebin(covvk, "cov_vk");
dfree(rr);
dfree(covvk);
}
/* return; */
{
map_t *atm=mapnew(nx+1, ny+1, dx, dx,NULL);
stfun_t *data=stfun_init(nx, ny, NULL);
zfarr *save=zfarr_init(nframe, 1, "fractal_atm.bin");
for(long i=0; i<nframe; i++){
for(long j=0; j<(nx+1)*(ny+1); j++){
atm->p[j]=randn(&rstat);
}
fractal_do((dmat*)atm, dx, r0,L0,ninit);
stfun_push(data, (dmat*)atm);
zfarr_dmat(save, i, (dmat*)atm);
if(i%100==0)
info("%ld of %ld\n", i, nframe);
}
zfarr_close(save);
dmat *st=stfun_finalize(data);
writebin(st, "stfun_fractal.bin");
ddraw("fractal", st, NULL,NULL, "Atmosphere","x","y","stfun");
}
/*exit(0); */
{
stfun_t *data=stfun_init(nx, ny, NULL);
dmat *spect=turbpsd(nx, ny, dx, r0, 100, 0, 0.5);
cmat *atm=cnew(nx, ny);
//cfft2plan(atm, -1);
dmat *atmr=dnew(atm->nx, atm->ny);
dmat *atmi=dnew(atm->nx, atm->ny);
spect->p[0]=0;
for(long ii=0; ii<nframe; ii+=2){
for(long i=0; i<atm->nx*atm->ny; i++){
atm->p[i]=COMPLEX(randn(&rstat), randn(&rstat))*spect->p[i];
}
cfft2(atm, -1);
for(long i=0; i<atm->nx*atm->ny; i++){
atmr->p[i]=creal(atm->p[i]);
atmi->p[i]=cimag(atm->p[i]);
}
stfun_push(data, atmr);
stfun_push(data, atmi);
if(ii%100==0)
info("%ld of %ld\n", ii, nframe);
}
dmat *st=stfun_finalize(data);
writebin(st, "stfun_fft.bin");
ddraw("fft", st, NULL,NULL, "Atmosphere","x","y","stfun");
}
}
static void test_accuracy(int argc, char **argv){
double displacex=0.01;
double displacey=0.05;
double scale=1.01;/*.414065; */
int wrap=0;
double D=30;
double D2=32;
int save=1;
if(argc>1){
scale=strtod(argv[1], 0);
}
if(argc>2){
displacex=strtod(argv[2], 0);
}
if(argc>3){
displacey=strtod(argv[3], 0);
}
if(argc>4){
wrap=strtol(argv[4], 0, 10);
}
if(argc>5){
D=strtod(argv[5], 0);
}
if(argc>6){
D2=strtod(argv[6], 0);
}
if(argc>7){
save=strtol(argv[7], 0, 10);
}
double dx=1/64.;
double dsa=0.5;
map_t *screen=mapnew(D2/dx, D2/dx, dx, dx, 0);
dset((dmat*)screen, 1);
for(long iy=0; iy<screen->ny; iy++){
for(long ix=0; ix<screen->nx; ix++){
screen->p[ix+iy*screen->nx]=sin((double)ix/screen->nx*2*M_PI)*sin((double)iy/screen->ny*2*M_PI);
}
}
/*loc for the map */
loc_t *locin=mksqloc(screen->nx,screen->ny,dx,dx,screen->ox,screen->oy);
//pts_t *pts=realloc(mkannloc(D, 0, 1./2.,0), sizeof(pts_t));
pts_t *pts=realloc(mksqloc_auto(D/dsa, D/dsa, dsa, dsa), sizeof(pts_t));
pts->dx=dx;
pts->dy=dx;
pts->nx=dsa/dx;
pts->ny=pts->nx;
loc_t *loc=pts2loc(pts);
loc_create_map(locin);
loc_create_stat(loc);
loc_create_map(loc);
locstat_t *locstat=loc->stat;
map_t *screen2=mapnew2(locin->map);
dset((dmat*)screen2, NAN);
loc_embed(screen2, locin, screen->p);
double *phi_pts, *phi_loc, *phi_stat;
double *phi_loc2loc, *phi_h, *phi_cub, *phi_cub2, *phi_cubh;
double cubic=0.3;
int ii;
info("displacex=%g, displacey=%g, scale=%g, wrap=%d\n",
displacex, displacey,scale,wrap);
double diff1, diff2,diff3,diff14,diff15;
diff1=0;
diff2=0;
diff3=0;
diff14=0;
diff15=0;
phi_pts=calloc(loc->nloc, sizeof(double));
phi_loc=calloc(loc->nloc, sizeof(double));
phi_stat=calloc(loc->nloc, sizeof(double));
phi_loc2loc=calloc(loc->nloc, sizeof(double));
map_t *map1=mapnew2(loc->map);
prop_grid_map(screen, map1, -2, displacex, displacey, scale, wrap, 0,0);
tic;
prop_grid_map(screen, map1, 1, displacex, displacey, scale, wrap, 0,0);
toc("map\t\t");
prop_grid_pts(screen, pts, phi_pts, -2, displacex, displacey, scale, wrap, 0,0);
tic;
prop_grid_pts(screen, pts, phi_pts, 1, displacex, displacey, scale, wrap, 0,0);
toc("pts\t\t");
prop_grid_stat(screen, locstat, phi_stat, -2,displacex, displacey, scale, wrap, 0,0);
tic;
prop_grid_stat(screen, locstat, phi_stat , 1, displacex, displacey, scale, wrap, 0,0);
toc("stat\t");tic;
prop_grid(screen, loc, phi_loc, -2,displacex, displacey, scale, wrap, 0,0);
tic;
prop_grid(screen, loc, phi_loc, 1,displacex, displacey, scale, wrap, 0,0);
toc("loc\t\t");
prop_nongrid(locin, screen->p,loc, phi_loc2loc, -2,displacex, displacey, scale,0,0);
toc("nongrid\t"); tic;
prop_nongrid(locin, screen->p,loc, phi_loc2loc, 1,displacex, displacey, scale,0,0);
toc("nongrid\t");
phi_h=calloc(loc->nloc,sizeof(double));
tic;
dsp *hfor=mkh(locin, loc, displacex, displacey, scale);
toc("mkh\t\t\t");
dspmulvec(phi_h,hfor, screen->p, 'n', -2);
tic;
dspmulvec(phi_h,hfor, screen->p, 'n', 1);
toc("mul h\t\t");
phi_cub=calloc(loc->nloc,sizeof(double));
phi_cub2=calloc(loc->nloc,sizeof(double));
double *phi_cub3=calloc(loc->nloc,sizeof(double));
double *phi_cub4=calloc(loc->nloc,sizeof(double));
phi_cubh=calloc(loc->nloc, sizeof(double));
prop_nongrid_cubic(locin,screen->p,loc,phi_cub,-2, displacex, displacey, scale, cubic,0,0);
tic;
prop_nongrid_cubic(locin,screen->p,loc,phi_cub,1, displacex, displacey, scale, cubic,0,0);
toc("nongrid, cubic\t");
prop_grid_cubic(screen, loc, phi_cub2, -2,displacex, displacey, scale, cubic, 0,0);
tic;
prop_grid_cubic(screen, loc, phi_cub2, 1,displacex, displacey, scale, cubic, 0,0);
toc("grid, cubic\t");
prop_grid_cubic(screen2, loc,phi_cub3, -2,displacex, displacey, scale, cubic, 0,0);
tic;
prop_grid_cubic(screen2, loc,phi_cub3, 1,displacex, displacey, scale, cubic, 0,0);
toc("grid2, cubic\t");
prop_grid_stat_cubic(screen, locstat,phi_cub4, -2,displacex, displacey, scale, cubic, 0,0);
tic;
prop_grid_stat_cubic(screen, locstat,phi_cub4, 1,displacex, displacey, scale, cubic, 0,0);
toc("grid 2stat, cubic\t");
dsp *hforcubic;
tic;
hforcubic=mkh_cubic(locin, loc, displacex, displacey, scale, cubic);
toc("mkh cubic \t\t");
dspmulvec(phi_cubh, hforcubic,screen->p,'n',-2);
tic;
dspmulvec(phi_cubh, hforcubic,screen->p,'n',1);
toc("cubic mul h\t\t");
double diffc12=0,diff45=0,diff46=0,diff47=0;
for(ii=0; ii<loc->nloc; ii++){
diff1+=fabs(phi_loc[ii]-phi_pts[ii]);
diff2+=fabs(phi_stat[ii]-phi_loc[ii]);
diff3+=fabs(phi_stat[ii]-phi_pts[ii]);
diff14+=fabs(phi_loc2loc[ii]-phi_pts[ii]);
diff15+=fabs(phi_h[ii]-phi_pts[ii]);
diff45+=fabs(phi_loc2loc[ii]-phi_h[ii]);
diffc12+=fabs(phi_cub[ii]-phi_cubh[ii]);
diff46+=fabs(phi_cub[ii]-phi_cub2[ii]);
diff47+=fabs(phi_cub[ii]-phi_cub3[ii]);
}
info2("(pts-loc)=\t%g\n(loc-stat)=\t%g\n(stat-pts)=\t%g\n"
"(loc2loc-pts)=\t%g\n(h-pts)=\t%g\n"
"(loc2loc-h)=\t%g\n"
"(cub:h-loc2loc)=\t%g\n"
"(cub:map2loc-loc2loc)=\t%g\n"
"(cub:locmap2loc-loc2loc=\t%g\n"
,diff1, diff2,diff3,diff14,diff15,diff45,diffc12,
diff46, diff47);
// exit(0);
if(!save) return;
mapwrite(screen2,"accphi_screen2");
mapwrite(screen,"accphi_screen");
locwrite((loc_t*)pts,"accphi_pts");
locwrite(loc,"accphi_loc");
locwrite(locin, "accphi_locin");
loc_create_map_npad(locin, 0, 0, 0);
mapwrite(locin->map, "accphi_locin_map");
mapwrite(loc->map, "accphi_loc_map");
mapwrite(map1, "accphi_map2map.bin");
writedbl(phi_pts,loc->nloc,1,"accphi_pts1.bin");
writedbl(phi_loc,loc->nloc,1,"accphi_loc0.bin");
writedbl(phi_stat,loc->nloc,1,"accphi_stat.bin");
writedbl(phi_loc2loc,loc->nloc,1,"accphi_loc2loc.bin");
writedbl(phi_h,loc->nloc,1,"accphi_loc2h.bin");
writedbl(phi_cub,loc->nloc,1,"accphi_cub_loc2loc.bin");
writedbl(phi_cub2,loc->nloc,1,"accphi_cub_map2loc.bin");
writedbl(phi_cub3,loc->nloc,1,"accphi_cub_locmap2loc.bin");
writedbl(phi_cub4,loc->nloc,1,"accphi_cub_locmap2stat.bin");
writedbl(phi_cubh,loc->nloc,1,"accphi_cub_loc2h.bin");
info("saved\n");
writedbl(phi_pts,loc->nloc,1,"accphi_pts.bin");
writedbl(phi_cub,loc->nloc,1,"accphi_cub.bin");
writebin(hfor, "accphi_hfor");
writebin(hforcubic, "accphi_cub_hfor");
dspfree(hfor);
dspfree(hforcubic);
free(phi_loc); free(phi_stat);
free(phi_loc2loc);
free(phi_pts);
free(phi_h);
free(phi_cub);
free(phi_cubh);
cellfree(screen);
locfree(locin);
}
