static inline void ifft8 (complex_t * buf)
{
sample_t tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8;
ifft4 (buf);
ifft2 (buf + 4);
ifft2 (buf + 6);
BUTTERFLY_ZERO (buf[0], buf[2], buf[4], buf[6]);
BUTTERFLY_HALF (buf[1], buf[3], buf[5], buf[7], roots16[1]);
}
static typename std::enable_if<
std::is_same<Border, FullConvolution>::value, void>::type
Convolution(const arma::Mat<eT>& input,
const arma::Mat<eT>& filter,
arma::Mat<eT>& output)
{
// In case of the full convolution outputRows and outputCols doesn't
// represent the true output size when the padLastDim parameter is set,
// instead it's the working size.
const size_t outputRows = input.n_rows + 2 * (filter.n_rows - 1);
size_t outputCols = input.n_cols + 2 * (filter.n_cols - 1);
if (padLastDim)
outputCols++;
// Pad filter and input to the working output shape.
arma::Mat<eT> inputPadded = arma::zeros<arma::Mat<eT> >(outputRows,
outputCols);
inputPadded.submat(filter.n_rows - 1, filter.n_cols - 1,
filter.n_rows - 1 + input.n_rows - 1,
filter.n_cols - 1 + input.n_cols - 1) = input;
arma::Mat<eT> filterPadded = filter;
filterPadded.resize(outputRows, outputCols);
// Perform FFT and IFFT
output = arma::real(ifft2(arma::fft2(inputPadded) % arma::fft2(
filterPadded)));
// Extract the region of interest. We don't need to handle the padLastDim
// parameter in a special way we just cut it out from the output matrix.
output = output.submat(filter.n_rows - 1, filter.n_cols - 1,
2 * (filter.n_rows - 1) + input.n_rows - 1,
2 * (filter.n_cols - 1) + input.n_cols - 1);
}
inline
typename
enable_if2
<
(is_arma_type<T1>::value && is_complex_strict<typename T1::elem_type>::value),
Mat< std::complex<typename T1::pod_type> >
>::result
ifft2(const T1& A, const uword n_rows, const uword n_cols)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
const unwrap<T1> tmp(A);
const Mat<eT>& B = tmp.M;
const bool do_resize = (B.n_rows != n_rows) || (B.n_cols != n_cols);
return ifft2( do_resize ? resize(B,n_rows,n_cols) : B );
}
static typename std::enable_if<
std::is_same<Border, ValidConvolution>::value, void>::type
Convolution(const arma::Mat<eT>& input,
const arma::Mat<eT>& filter,
arma::Mat<eT>& output)
{
arma::Mat<eT> inputPadded = input;
arma::Mat<eT> filterPadded = filter;
if (padLastDim)
inputPadded.resize(inputPadded.n_rows, inputPadded.n_cols + 1);
// Pad filter and input to the output shape.
filterPadded.resize(inputPadded.n_rows, inputPadded.n_cols);
output = arma::real(ifft2(arma::fft2(inputPadded) % arma::fft2(
filterPadded)));
// Extract the region of interest. We don't need to handle the padLastDim in
// a special way we just cut it out from the output matrix.
output = output.submat(filter.n_rows - 1, filter.n_cols - 1,
input.n_rows - 1, input.n_cols - 1);
}
int main(int argc, char* argv[])
{
clock_t tstart, tend;
double duration;
/*Flag*/
bool verb, cmplx;
/*I/O*/
sf_file Fsrc,Fo,Frec; /* I/O files */
sf_file left, right; /*left/right matrix*/
sf_file Fvel, Fden, Ffft; /*Model*/
sf_axis at,az,ax; /* cube axes */
/* I/O arrays*/
float *src; /*point source, distributed source*/
float **lt, **rt;
float **vel, **den, **c11;
/* Grid index variables */
int it,iz,im,ik,ix,i,j;
int nt,nz,nx, m2, nk, nkx, nkz, nzx, nz2, nx2, nzx2, n1, n2, pad1;
float cx, cz;
float kx, kz, dkx, dkz, kx0, kz0;
float dx, dz, dt, d1, d2;
float ox, oz;
sf_complex *cwavex, *cwavez, *cwavemx, *cwavemz;
float **record;
float **wavex, **wavez;
float *curtxx, *pretxx;
float *curvx, *prevx, *curvz, *prevz;
/*source*/
spara sp={0};
int srcrange;
float srctrunc;
bool srcdecay;
float slx, slz;
int spx, spz;
/*options*/
float gdep;
int gp;
tstart = clock();
sf_init(argc,argv);
if(!sf_getbool("verb",&verb)) verb=false; /* verbosity */
Fvel = sf_input("vel");
Fden = sf_input("den");
/* setup I/O files */
Fsrc = sf_input ("in" );
Fo = sf_output("out");
Frec = sf_output("rec"); /*record*/
/* Read/Write axes */
at = sf_iaxa(Fsrc,1); nt = sf_n(at); dt = sf_d(at);
ax = sf_iaxa(Fvel,2); nx = sf_n(ax); dx = sf_d(ax); ox=sf_o(ax);
az = sf_iaxa(Fvel,1); nz = sf_n(az); dz = sf_d(az); oz=sf_o(az);
sf_oaxa(Fo,az,1);
sf_oaxa(Fo,ax,2);
sf_oaxa(Fo,at,3);
/*set for record*/
sf_oaxa(Frec, at, 1);
sf_oaxa(Frec, ax, 2);
if (!sf_getbool("cmplx",&cmplx)) cmplx=false; /* use complex FFT */
if (!sf_getint("pad1",&pad1)) pad1=1; /* padding factor on the first axis */
nk = fft2_init(cmplx,pad1,nz,nx,&nz2,&nx2);
nzx = nz*nx;
nzx2 = nz2*nx2;
/* propagator matrices */
left = sf_input("left");
right = sf_input("right");
if (!sf_histint(left,"n1",&n2) || n2 != nzx) sf_error("Need n1=%d in left",nzx);
if (!sf_histint(left,"n2",&m2)) sf_error("Need n2= in left");
if (!sf_histint(right,"n1",&n2) || n2 != m2) sf_error("Need n1=%d in right",m2);
if (!sf_histint(right,"n2",&n2) || n2 != nk) sf_error("Need n2=%d in right",nk);
lt = sf_floatalloc2(nzx,m2);
rt = sf_floatalloc2(m2,nk);
sf_floatread(lt[0],nzx*m2,left);
sf_floatread(rt[0],m2*nk,right);
/*model veloctiy & density*/
if (!sf_histint(Fvel,"n1", &n1) || n1 != nz) sf_error("Need n1=%d in vel", nz);
if (!sf_histfloat(Fvel,"d1", &d1) || d1 != dz) sf_error("Need d1=%d in vel", dz);
if (!sf_histint(Fvel,"n2", &n2) || n2 != nx) sf_error("Need n2=%d in vel", nx);
if (!sf_histfloat(Fvel,"d2", &d2) || d2 != dx) sf_error("Need d2=%d in vel", dx);
if (!sf_histint(Fden,"n1", &n1) || n1 != nz) sf_error("Need n1=%d in den", nz);
if (!sf_histfloat(Fden,"d1", &d1) || d1 != dz) sf_error("Need d1=%d in den", dz);
if (!sf_histint(Fden,"n2", &n2) || n2 != nx) sf_error("Need n2=%d in den", nx);
if (!sf_histfloat(Fden,"d2", &d2) || d2 != dx) sf_error("Need d2=%d in den", dx);
vel = sf_floatalloc2(nz, nx);
den = sf_floatalloc2(nz, nx);
c11 = sf_floatalloc2(nz, nx);
sf_floatread(vel[0], nzx, Fvel);
sf_floatread(den[0], nzx, Fden);
for (ix = 0; ix < nx; ix++) {
for (iz = 0; iz < nz; iz++) {
c11[ix][iz] = den[ix][iz]*vel[ix][iz]*vel[ix][iz];
}
}
/*parameters of fft*/
Ffft = sf_input("fft");
if (!sf_histint(Ffft,"n1", &nkz)) sf_error("Need n1 in fft");
if (!sf_histint(Ffft,"n2", &nkx)) sf_error("Need n2 in fft");
if ( nkx*nkz != nk ) sf_error("Need nk=nkx*nkz, nk=%d, nkx=%d, nkz=%d", nk, nkx, nkz);
if (!sf_histfloat(Ffft,"d1", &dkz)) sf_error("Need d1 in fft");
if (!sf_histfloat(Ffft,"d2", &dkx)) sf_error("Need d2 in fft");
if (!sf_histfloat(Ffft,"o1", &kz0)) sf_error("Need o1 in fft");
if (!sf_histfloat(Ffft,"o2", &kx0)) sf_error("Need o2 in fft");
/*parameters of geometry*/
if (!sf_getfloat("gdep", &gdep)) gdep = 0.0;
/*depth of geophone (meter)*/
if (gdep <0.0) sf_error("gdep need to be >=0.0");
/*source and receiver location*/
if (!sf_getfloat("slx", &slx)) slx=-1.0;
/*source location x */
if (!sf_getint("spx", &spx)) spx = -1;
/*source location x (index)*/
if((slx<0 && spx <0) || (slx>=0 && spx >=0 )) sf_error("Need src location");
if (slx >= 0 ) spx = (int)((slx-ox)/dx+0.5);
if (!sf_getfloat("slz", &slz)) slz = -1.0;
/* source location z */
if (!sf_getint("spz", &spz)) spz=-1;
/*source location z (index)*/
if((slz<0 && spz <0) || (slz>=0 && spz >=0 )) sf_error("Need src location");
if (slz >= 0 ) spz = (int)((slz-ox)/dz+0.5);
if (!sf_getfloat("gdep", &gdep)) gdep = -1.0;
/* recorder depth on grid*/
if (!sf_getint("gp", &gp)) gp=0;
/* recorder depth on index*/
if ( gdep>=oz) { gp = (int)((gdep-oz)/dz+0.5);}
if (gp < 0.0) sf_error("gdep need to be >=oz");
/*source and receiver location*/
if (!sf_getbool("srcdecay", &srcdecay)) srcdecay=false;
/*source decay*/
if (!sf_getint("srcrange", &srcrange)) srcrange=10;
/*source decay range*/
if (!sf_getfloat("srctrunc", &srctrunc)) srctrunc=100;
/*trunc source after srctrunc time (s)*/
/* read wavelet & reflectivity */
src = sf_floatalloc(nt);
sf_floatread(src,nt,Fsrc);
curtxx = sf_floatalloc(nzx2);
curvx = sf_floatalloc(nzx2);
curvz = sf_floatalloc(nzx2);
pretxx = sf_floatalloc(nzx);
prevx = sf_floatalloc(nzx);
prevz = sf_floatalloc(nzx);
cwavex = sf_complexalloc(nk);
cwavez = sf_complexalloc(nk);
cwavemx = sf_complexalloc(nk);
cwavemz = sf_complexalloc(nk);
wavex = sf_floatalloc2(nzx2,m2);
wavez = sf_floatalloc2(nzx2,m2);
record = sf_floatalloc2(nt,nx);
ifft2_allocate(cwavemx);
ifft2_allocate(cwavemz);
for (iz=0; iz < nzx; iz++) {
pretxx[iz]=0.;
prevx[iz] =0.;
prevz[iz] =0.;
}
for (iz=0; iz < nzx2; iz++) {
curtxx[iz]=0.;
curvx[iz]=0.;
curvz[iz]=0.;
}
/* Check parameters*/
if(verb) {
sf_warning("======================================");
#ifdef SF_HAS_FFTW
sf_warning("FFTW is defined");
#endif
#ifdef SF_HAS_COMPLEX_H
sf_warning("Complex is defined");
#endif
sf_warning("nx=%d nz=%d nzx=%d dx=%f dz=%f", nx, nz, nzx, dx, dz);
sf_warning("nkx=%d nkz=%d dkx=%f dkz=%f nk=%d", nkx, nkz, dkx, dkz, nk);
sf_warning("nx2=%d nz2=%d nzx2=%d", nx2, nz2, nzx2);
sf_warning("======================================");
}
/*set source*/
sp.trunc=srctrunc;
sp.srange=srcrange;
sp.alpha=0.5;
sp.decay=srcdecay?1:0;
/* MAIN LOOP */
for (it=0; it<nt; it++) {
if(verb) sf_warning("it=%d/%d;",it,nt-1);
/*vx, vz--- matrix multiplication */
fft2(curtxx,cwavex); /* P^(k,t) */
for (im = 0; im < m2; im++) {
for (ik = 0; ik < nk; ik++) {
kx = kx0+dkx*(ik/nkz);
kz = kz0+dkz*(ik%nkz);
#ifdef SF_HAS_COMPLEX_H
cwavemz[ik] = cwavex[ik]*rt[ik][im];
cwavemx[ik] = fplus(kx,dx)*cwavemz[ik];
cwavemz[ik] = fplus(kz,dz)*cwavemz[ik];
#else
cwavemz[ik] = sf_crmul(cwavex[ik],rt[ik][im]);
cwavemx[ik] = sf_cmul(fplus(kx,dx), cwavemz[ik]);
cwavemz[ik] = sf_cmul(fplus(kz,dz), cwavemz[ik]);
#endif
}
ifft2(wavex[im], cwavemx); /* dp/dx */
ifft2(wavez[im], cwavemz); /* dp/dz */
}
for (ix = 0; ix < nx; ix++) {
for (iz = 0; iz < nz; iz++) {
i = iz+ix*nz; /* original grid */
j = iz+ix*nz2; /* padded grid */
cx = 0.0;
cz = 0.0;
for (im=0; im<m2; im++) {
cx += lt[im][i]*wavex[im][j];
cz += lt[im][i]*wavez[im][j];
}
curvx[j] = -1*dt/den[ix][iz]*cx + prevx[i];
/*vx(t+dt/2) = -dt/rho*dp/dx(t) + vx(t-dt/2) */
prevx[i] = curvx[j];
curvz[j] = -1*dt/den[ix][iz]*cz + prevz[i];
prevz[i] = curvz[j];
}
}
/*txx--- matrix multiplication */
fft2(curvx, cwavex);
fft2(curvz, cwavez);
for (im = 0; im < m2; im++) {
for (ik = 0; ik < nk; ik++ ) {
kx = kx0 + dkx*(ik/nkz);
kz = kz0 + dkz*(ik%nkz);
#ifdef SF_HAS_COMPLEX_H
cwavemz[ik] = cwavez[ik]*rt[ik][im];
cwavemx[ik] = cwavex[ik]*rt[ik][im];
cwavemx[ik] = fminu(kx,dx)*cwavemx[ik];
cwavemz[ik] = fminu(kz,dz)*cwavemz[ik];
#else
cwavemz[ik] = sf_crmul(cwavez[ik],rt[ik][im]);
cwavemx[ik] = sf_crmul(cwavex[ik],rt[ik][im]);
cwavemx[ik] = sf_cmul(fplus(kx,dx), cwavemx[ik]);
cwavemz[ik] = sf_cmul(fplus(kz,dz), cwavemz[ik]);
#endif
}
ifft2(wavex[im], cwavemx); /* dux/dx */
ifft2(wavez[im], cwavemz); /* duz/dz */
}
for (ix = 0; ix < nx; ix++) {
for (iz = 0; iz < nz; iz++) {
i = iz+ix*nz; /* original grid */
j = iz+ix*nz2; /* padded grid */
cx = 0.0;
cz = 0.0;
for (im=0; im<m2; im++) {
cx += lt[im][i]*wavex[im][j];
cz += lt[im][i]*wavez[im][j];
}
curtxx[j] = -1*dt*c11[ix][iz]*(cx+cz) + pretxx[i];
}
}
if ((it*dt)<=sp.trunc ) {
curtxx[spz+spx*nz2] += src[it]*dt;
}
for (ix = 0; ix < nx; ix++) {
/* write wavefield to output */
sf_floatwrite(pretxx+ix*nz,nz,Fo);
}
/*record*/
for (ix = 0; ix < nx; ix++){
record[ix][it] = pretxx[ix*nz+gp];
}
for (ix = 0; ix < nx; ix++) {
for (iz = 0; iz < nz; iz++) {
i = iz+ix*nz; /* original grid */
j = iz+ix*nz2; /* padded grid */
pretxx[i] = curtxx[j];
}
}
}/*End of MAIN LOOP*/
if(verb) sf_warning(".");
for ( ix = 0; ix < nx; ix++) {
sf_floatwrite(record[ix], nt, Frec);
}
tend = clock();
duration=(double)(tend-tstart)/CLOCKS_PER_SEC;
sf_warning(">> The CPU time of sfsglr is: %f seconds << ", duration);
exit (0);
}
void ifftu2(unsigned int D, const long dimensions[D], unsigned long flags, const long ostrides[D], complex float* dst, const long istrides[D], const complex float* src)
{
ifft2(D, dimensions, flags, ostrides, dst, istrides, src);
fftscale2(D, dimensions, flags, ostrides, dst, ostrides, dst);
}
int psp4(float **wvfld, float **wvfld0, float **dat, float **dat_v, float *vel, pspar par)
/*< pseudo-spectral wave extrapolation using wavefield injection >*/
{
/*survey parameters*/
int nx, nz;
float dx, dz;
int n_srcs;
int *spx, *spz;
int gpz, gpx, gpl;
int gpz_v, gpx_v, gpl_v;
int snap;
/*fft related*/
bool cmplx;
int pad1;
/*absorbing boundary*/
bool abc;
int nbt, nbb, nbl, nbr;
float ct,cb,cl,cr;
/*source parameters*/
int src; /*source type*/
int nt;
float dt,*f0,*t0,*A;
/*misc*/
bool verb, ps;
float vref;
int nx1, nz1; /*domain of interest*/
int it,iz,ik,ix,i,j; /* index variables */
int nk,nzx,nz2,nx2,nzx2,nkz,nth;
int it1, it2, its;
float dkx,dkz,kx0,kz0,vref2,kx,kz,k,t;
float c, old;
/*wave prop arrays*/
float *vv;
sf_complex *cwave,*cwavem;
float *wave,*curr,*prev,*lapl;
/*source*/
float **rick;
float freq;
int fft_size;
/*passing the parameters*/
nx = par->nx;
nz = par->nz;
dx = par->dx;
dz = par->dz;
n_srcs= par->n_srcs;
spx = par->spx;
spz = par->spz;
gpz = par->gpz;
gpx = par->gpx;
gpl = par->gpl;
gpz_v = par->gpz_v;
gpx_v = par->gpx_v;
gpl_v = par->gpl_v;
snap = par->snap;
cmplx = par->cmplx;
pad1 = par->pad1;
abc = par->abc;
nbt = par->nbt;
nbb = par->nbb;
nbl = par->nbl;
nbr = par->nbr;
ct = par->ct;
cb = par->cb;
cl = par->cl;
cr = par->cr;
src = par->src;
nt = par->nt;
dt = par->dt;
f0 = par->f0;
t0 = par->t0;
A = par->A;
verb = par->verb;
ps = par->ps;
vref = par->vref;
#ifdef _OPENMP
#pragma omp parallel
{
nth = omp_get_num_threads();
}
#else
nth = 1;
#endif
if (verb) sf_warning(">>>> Using %d threads <<<<<", nth);
nz1 = nz-nbt-nbb;
nx1 = nx-nbl-nbr;
nk = fft2_init(cmplx,pad1,nz,nx,&nz2,&nx2);
nzx = nz*nx;
nzx2 = nz2*nx2;
dkz = 1./(nz2*dz); kz0 = (cmplx)? -0.5/dz:0.;
dkx = 1./(nx2*dx); kx0 = -0.5/dx;
nkz = (cmplx)? nz2:(nz2/2+1);
if(nk!=nx2*nkz) sf_error("wavenumber dimension mismatch!");
sf_warning("dkz=%f,dkx=%f,kz0=%f,kx0=%f",dkz,dkx,kz0,kx0);
sf_warning("nk=%d,nkz=%d,nz2=%d,nx2=%d",nk,nkz,nz2,nx2);
if(abc)
abc_init(nz,nx,nz2,nx2,nbt,nbb,nbl,nbr,ct,cb,cl,cr);
/* allocate and read/initialize arrays */
vv = sf_floatalloc(nzx);
lapl = sf_floatalloc(nk);
wave = sf_floatalloc(nzx2);
curr = sf_floatalloc(nzx2);
prev = sf_floatalloc(nzx2);
cwave = sf_complexalloc(nk);
cwavem = sf_complexalloc(nk);
if (src==0) {
rick = sf_floatalloc2(nt,n_srcs);
for (i=0; i<n_srcs; i++) {
for (it=0; it<nt; it++) {
rick[i][it] = 0.f;
}
rick[i][(int)(t0[i]/dt)] = A[i]; /*time delay*/
freq = f0[i]*dt; /*peak frequency*/
fft_size = 2*kiss_fft_next_fast_size((nt+1)/2);
ricker_init(fft_size, freq, 0);
sf_freqfilt(nt,rick[i]);
ricker_close();
}
} else rick = NULL;
for (iz=0; iz < nzx; iz++) {
vv[iz] = vel[iz]*vel[iz]*dt*dt;
}
vref *= dt;
vref2 = vref*vref;
for (iz=0; iz < nzx2; iz++) {
curr[iz] = 0.;
prev[iz] = 0.;
}
/* constructing the pseudo-analytical op */
for (ix=0; ix < nx2; ix++) {
kx = kx0+ix*dkx;
for (iz=0; iz < nkz; iz++) {
kz = kz0+iz*dkz;
k = 2*SF_PI*hypot(kx,kz);
if (ps) lapl[iz+ix*nkz] = -k*k;
else lapl[iz+ix*nkz] = 2.*(cos(vref*k)-1.)/vref2;
}
}
/* modeling */
/* step forward in time */
it1 = 0;
it2 = nt;
its = +1;
/* MAIN LOOP */
for (it=it1; it!=it2; it+=its) {
if(verb) sf_warning("it=%d/%d;",it,nt);
/* matrix multiplication */
fft2(curr,cwave);
for (ik = 0; ik < nk; ik++) {
#ifdef SF_HAS_COMPLEX_H
cwavem[ik] = cwave[ik]*lapl[ik];
#else
cwavem[ik] = sf_cmul(cwave[ik],lapl[ik]);
#endif
}
ifft2(wave,cwavem);
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(ix,iz,i,j,old,c)
#endif
for (ix = 0; ix < nx; ix++) {
for (iz=0; iz < nz; iz++) {
i = iz+ix*nz; /* original grid */
j = iz+ix*nz2; /* padded grid */
old = c = curr[j];
c += c - prev[j];
prev[j] = old;
c += wave[j]*vv[i];
curr[j] = c;
}
}
if (NULL!=wvfld0) { /* wavefield injection */
if (snap > 0 && it%snap==0) {
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(ix,iz,i,j,ik)
#endif
for (ix=0; ix<nx1; ix++) {
for (iz=0; iz<nz1; iz++) {
i = iz + nz1*ix;
j = iz+nbt + (ix+nbl)*nz2; /* padded grid */
ik = iz+nbt + (ix+nbl)*nz; /* padded grid */
curr[j] += vv[ik]*wvfld0[it/snap][i];
}
}
}
} else { /* source injection */
t = it*dt;
for (i=0; i<n_srcs; i++) {
for(ix=-1;ix<=1;ix++) {
for(iz=-1;iz<=1;iz++) {
ik = spz[i]+iz+nz*(spx[i]+ix);
j = spz[i]+iz+nz2*(spx[i]+ix);
if (src==0) {
curr[j] += vv[ik]*rick[i][it]/(abs(ix)+abs(iz)+1);
} else {
curr[j] += vv[ik]*Ricker(t, f0[i], t0[i], A[i])/(abs(ix)+abs(iz)+1);
}
}
}
}
}
/*apply abc*/
if (abc) {
abc_apply(curr);
abc_apply(prev);
}
/* record data */
if (NULL!=dat) {
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(ix)
#endif
for (ix = 0; ix < gpl; ix++) {
dat[ix][it] = curr[gpz+(ix+gpx)*nz2];
}
}
if (NULL!=dat_v) {
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(iz)
#endif
for (iz = 0; iz < gpl_v; iz++) {
dat_v[iz][it] = curr[gpz_v+iz+(gpx_v)*nz2];
}
}
/* save wavefield */
if (snap > 0 && it%snap==0) {
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(ix,iz,i,j)
#endif
for (ix=0; ix<nx1; ix++) {
for (iz=0; iz<nz1; iz++) {
i = iz + nz1*ix;
j = iz+nbt + (ix+nbl)*nz2; /* padded grid */
wvfld[it/snap][i] = curr[j];
}
}
}
}
if(verb) sf_warning(".");
/*free up memory*/
fft2_finalize();
if (abc) abc_close();
free(vv);
free(lapl);
free(wave);
free(curr);
free(prev);
free(cwave);
free(cwavem);
return 0;
}
int psp3(float **wvfld, float **wvfld1, float **dat, float **dat1, float *img, float *vel, pspar par)
/*< pseudo-spectral back propagation of two receiver wavefields >*/
{
/*survey parameters*/
int nx, nz;
float dx, dz;
int n_srcs;
int *spx, *spz;
int gpz, gpx, gpl;
int gpz_v, gpx_v, gpl_v;
int snap;
/*fft related*/
bool cmplx;
int pad1;
/*absorbing boundary*/
bool abc;
int nbt, nbb, nbl, nbr;
float ct,cb,cl,cr;
/*source parameters*/
int src; /*source type*/
int nt;
float dt,*f0,*t0,*A;
/*misc*/
bool verb, ps;
float vref;
int nx1, nz1; /*domain of interest*/
int it,iz,ik,ix,i,j; /* index variables */
int nk,nzx,nz2,nx2,nzx2,nkz,nth;
int it1, it2, its;
float dkx,dkz,kx0,kz0,vref2,kx,kz,k;
float c, old;
/*wave prop arrays*/
float *vv;
sf_complex *cwave,*cwavem;
float *wave,*curr,*curr1,*prev,*prev1,*lapl;
/*passing the parameters*/
nx = par->nx;
nz = par->nz;
dx = par->dx;
dz = par->dz;
n_srcs= par->n_srcs;
spx = par->spx;
spz = par->spz;
gpz = par->gpz;
gpx = par->gpx;
gpl = par->gpl;
gpz_v = par->gpz_v;
gpx_v = par->gpx_v;
gpl_v = par->gpl_v;
snap = par->snap;
cmplx = par->cmplx;
pad1 = par->pad1;
abc = par->abc;
nbt = par->nbt;
nbb = par->nbb;
nbl = par->nbl;
nbr = par->nbr;
ct = par->ct;
cb = par->cb;
cl = par->cl;
cr = par->cr;
src = par->src;
nt = par->nt;
dt = par->dt;
f0 = par->f0;
t0 = par->t0;
A = par->A;
verb = par->verb;
ps = par->ps;
vref = par->vref;
#ifdef _OPENMP
#pragma omp parallel
{
nth = omp_get_num_threads();
}
#else
nth = 1;
#endif
if (verb) sf_warning(">>>> Using %d threads <<<<<", nth);
nz1 = nz-nbt-nbb;
nx1 = nx-nbl-nbr;
nk = fft2_init(cmplx,pad1,nz,nx,&nz2,&nx2);
nzx = nz*nx;
nzx2 = nz2*nx2;
dkz = 1./(nz2*dz); kz0 = (cmplx)? -0.5/dz:0.;
dkx = 1./(nx2*dx); kx0 = -0.5/dx;
nkz = (cmplx)? nz2:(nz2/2+1);
if(nk!=nx2*nkz) sf_error("wavenumber dimension mismatch!");
sf_warning("dkz=%f,dkx=%f,kz0=%f,kx0=%f",dkz,dkx,kz0,kx0);
sf_warning("nk=%d,nkz=%d,nz2=%d,nx2=%d",nk,nkz,nz2,nx2);
if(abc)
abc_init(nz,nx,nz2,nx2,nbt,nbb,nbl,nbr,ct,cb,cl,cr);
/* allocate and read/initialize arrays */
vv = sf_floatalloc(nzx);
lapl = sf_floatalloc(nk);
wave = sf_floatalloc(nzx2);
curr = sf_floatalloc(nzx2);
curr1 = sf_floatalloc(nzx2);
prev = sf_floatalloc(nzx2);
prev1 = sf_floatalloc(nzx2);
cwave = sf_complexalloc(nk);
cwavem = sf_complexalloc(nk);
for (iz=0; iz < nzx; iz++) {
vv[iz] = vel[iz]*vel[iz]*dt*dt;
}
vref *= dt;
vref2 = vref*vref;
for (iz=0; iz < nzx2; iz++) {
curr[iz] = 0.;
curr1[iz] = 0.;
prev[iz] = 0.;
prev1[iz] = 0.;
}
for (iz=0; iz < nz1*nx1; iz++) {
img[iz] = 0.;
}
/* constructing the pseudo-analytical op */
for (ix=0; ix < nx2; ix++) {
kx = kx0+ix*dkx;
for (iz=0; iz < nkz; iz++) {
kz = kz0+iz*dkz;
k = 2*SF_PI*hypot(kx,kz);
if (ps) lapl[iz+ix*nkz] = -k*k;
else lapl[iz+ix*nkz] = 2.*(cos(vref*k)-1.)/vref2;
}
}
/* step backward in time */
it1 = nt-1;
it2 = -1;
its = -1;
/* MAIN LOOP */
for (it=it1; it!=it2; it+=its) {
if(verb) sf_warning("it=%d/%d;",it,nt);
/* first receiver wavefield */
/* matrix multiplication */
fft2(curr,cwave);
for (ik = 0; ik < nk; ik++) {
#ifdef SF_HAS_COMPLEX_H
cwavem[ik] = cwave[ik]*lapl[ik];
#else
cwavem[ik] = sf_cmul(cwave[ik],lapl[ik]);
#endif
}
ifft2(wave,cwavem);
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(ix,iz,i,j,old,c)
#endif
for (ix = 0; ix < nx; ix++) {
for (iz=0; iz < nz; iz++) {
i = iz+ix*nz; /* original grid */
j = iz+ix*nz2; /* padded grid */
old = c = curr[j];
c += c - prev[j];
prev[j] = old;
c += wave[j]*vv[i];
curr[j] = c;
}
}
/* inject data */
if (NULL!=dat) {
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(ix)
#endif
for (ix = 0; ix < gpl; ix++) {
curr[gpz+(ix+gpx)*nz2] += vv[gpz+(ix+gpx)*nz]*dat[ix][it];
}
}
/*apply abc*/
if (abc) {
abc_apply(curr);
abc_apply(prev);
}
/* second receiver wavefield */
/* matrix multiplication */
fft2(curr1,cwave);
for (ik = 0; ik < nk; ik++) {
#ifdef SF_HAS_COMPLEX_H
cwavem[ik] = cwave[ik]*lapl[ik];
#else
cwavem[ik] = sf_cmul(cwave[ik],lapl[ik]);
#endif
}
ifft2(wave,cwavem);
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(ix,iz,i,j,old,c)
#endif
for (ix = 0; ix < nx; ix++) {
for (iz=0; iz < nz; iz++) {
i = iz+ix*nz; /* original grid */
j = iz+ix*nz2; /* padded grid */
old = c = curr1[j];
c += c - prev1[j];
prev1[j] = old;
c += wave[j]*vv[i];
curr1[j] = c;
}
}
/* inject data */
if (NULL!=dat1) {
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(ix)
#endif
for (ix = 0; ix < gpl; ix++) {
curr1[gpz+(ix+gpx)*nz2] += vv[gpz+(ix+gpx)*nz]*dat1[ix][it];
}
}
/*apply abc*/
if (abc) {
abc_apply(curr1);
abc_apply(prev1);
}
/* cross-correlation imaging condition */
if (snap > 0 && it%snap==0) {
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(ix,iz,i,j)
#endif
for (ix = 0; ix < nx1; ix++) {
for (iz = 0; iz < nz1; iz++) {
i = iz + nz1*ix;
j = iz+nbt + (ix+nbl)*nz2; /* padded grid */
img[i] += curr[j]*curr1[j]; //!!!IMPORTANT!!!
}
}
}
/* save wavefield */
if (snap > 0 && it%snap==0) {
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(ix,iz,i,j)
#endif
for (ix=0; ix<nx1; ix++) {
for (iz=0; iz<nz1; iz++) {
i = iz + nz1*ix;
j = iz+nbt + (ix+nbl)*nz2; /* padded grid */
wvfld[it/snap][i] = curr[j];
wvfld1[it/snap][i] = curr1[j];
}
}
}
}
if(verb) sf_warning(".");
/*free up memory*/
fft2_finalize();
if (abc) abc_close();
free(vv);
free(lapl);
free(wave);
free(curr);
free(curr1);
free(prev);
free(prev1);
free(cwave);
free(cwavem);
return 0;
}
cv::Mat L0Smoothing(cv::Mat Im, double lambda = 0.02, double kappa = 2.0)
{
cv::Mat out(Im.rows, Im.cols, CV_32FC3);
Matrix SR(Im.rows, Im.cols);
Matrix SG(Im.rows, Im.cols);
Matrix SB(Im.rows, Im.cols);
for(int j = 0; j < Im.cols; ++j)
{
for(int i = 0; i < Im.rows; ++i)
{
cv::Vec3f& v1 = Im.at<cv::Vec3f>(i, j);
SR(i, j) = v1[0];
SG(i, j) = v1[1];
SB(i, j) = v1[2];
}
}
double betamax = 1e5;
Matrix fx(1, 2);
fx(0, 0) = 1;
fx(0, 1) = -1;
Matrix fy(2, 1);
fy(0, 0) = 1;
fy(1, 0) = -1;
Matrix sizeI2D(1, 2);
sizeI2D(0, 0) = Im.rows;
sizeI2D(0, 1) = Im.cols;
Matrix2 otfFx = psf2otf(fx, sizeI2D);
Matrix2 otfFy = psf2otf(fy, sizeI2D);
Matrix otfFx2 = MatAbsPow2(otfFx);
Matrix otfFy2 = MatAbsPow2(otfFy);
Matrix2 Normin1R = fft2(SR);
Matrix2 Normin1G = fft2(SG);
Matrix2 Normin1B = fft2(SB);
Matrix Denormin2 = otfFx2 + otfFy2;
float beta = 2 * lambda;
int count = 1;
while(beta < betamax)
{
float lb = lambda / beta;
Matrix Denormin = beta * Denormin2;
MatAdd(Denormin, 1);
Matrix hR = Matdiff(SR, 2);
Matrix vR = Matdiff(SR, 1);
Matrix hG = Matdiff(SG, 2);
Matrix vG = Matdiff(SG, 1);
Matrix hB = Matdiff(SB, 2);
Matrix vB = Matdiff(SB, 1);
Matrix Pos2Sum = MatPow2(hR) + MatPow2(vR) +
MatPow2(hG) + MatPow2(vG) +
MatPow2(hB) + MatPow2(vB);
for(int j = 0; j < Im.cols; ++j)
{
for(int i = 0; i < Im.rows; ++i)
{
if(Pos2Sum(i, j) < lb)
{
hR(i, j) = 0;
vR(i, j) = 0;
hG(i, j) = 0;
vG(i, j) = 0;
hB(i, j) = 0;
vB(i, j) = 0;
}
}
}
Matrix Normin2R = Matdiffinv(hR, 2) + Matdiffinv(vR, 1);
Matrix Normin2G = Matdiffinv(hG, 2) + Matdiffinv(vG, 1);
Matrix Normin2B = Matdiffinv(hB, 2) + Matdiffinv(vB, 1);
Matrix2 FSR = (Normin1R + fft2(Normin2R) * beta) / Denormin;
Matrix2 FSG = (Normin1G + fft2(Normin2G) * beta) / Denormin;
Matrix2 FSB = (Normin1B + fft2(Normin2B) * beta) / Denormin;
SR = ifft2(FSR);
SG = ifft2(FSG);
SB = ifft2(FSB);
beta = beta * kappa;
printf(".");
for(uint i = 0; i < out.rows; ++i)
{
for(uint j = 0; j < out.cols; ++j)
{
cv::Vec3f& v1 = out.at<cv::Vec3f>(i, j);
v1[0] = SR(i, j);
v1[1] = SG(i, j);
v1[2] = SB(i, j);
}
}
cv::imshow("out", out);
char filename[100];
sprintf(filename, "o%02d.png", count++);
cv::Mat theout;
out.convertTo(theout, CV_8UC3, 255);
cv::imwrite(filename, theout);
cv::waitKey(1);
}
for(uint j = 0; j < out.cols; ++j)
{
for(uint i = 0; i < out.rows; ++i)
{
cv::Vec3f& v1 = out.at<cv::Vec3f>(i, j);
v1[0] = SR(i, j);
v1[1] = SG(i, j);
v1[2] = SB(i, j);
}
}
return out;
}
int main(int argc, char* argv[])
{
int iz,im,ik,ix,i,j; /* index variables */
int nz,nx, m2, nk, nzx, nz2, nx2, nzx2, n2;
float c;
sf_complex *cwavem;
float **wave, *curr;
sf_complex **lt, **rt;
sf_file left, right, inp, mig;
sf_init(argc,argv);
inp = sf_input("in");
mig = sf_output("out");
if (SF_FLOAT != sf_gettype(inp)) sf_error("Need float input");
if (!sf_histint(inp,"n1",&nz)) sf_error("No n1= in input");
if (!sf_histint(inp,"n2",&nx)) sf_error("No n2= in input");
nk = fft2_init(false,1,nz,nx,&nz2,&nx2);
nzx = nz*nx;
nzx2 = nz2*nx2;
/* propagator matrices */
left = sf_input("left");
right = sf_input("right");
if (!sf_histint(left,"n1",&n2) || n2 != nzx) sf_error("Need n1=%d in left",nzx);
if (!sf_histint(left,"n2",&m2)) sf_error("Need n2= in left");
if (!sf_histint(right,"n1",&n2) || n2 != m2) sf_error("Need n1=%d in right",m2);
if (!sf_histint(right,"n2",&n2) || n2 != nk) sf_error("Need n2=%d in right",nk);
lt = sf_complexalloc2(nzx,m2);
rt = sf_complexalloc2(m2,nk);
sf_complexread(lt[0],nzx*m2,left);
sf_complexread(rt[0],m2*nk,right);
wave = sf_floatalloc2(nzx2,m2);
cwavem = sf_complexalloc(nk);
curr = sf_floatalloc(nz);
ifft2_allocate(cwavem);
for (im = 0; im < m2; im++) {
#ifdef _OPENMP
#pragma omp parallel for private(ik)
#endif
for (ik = 0; ik < nk; ik++) {
cwavem[ik] = rt[ik][im];
}
ifft2(wave[im],cwavem);
}
for (ix = 0; ix < nx; ix++) {
#ifdef _OPENMP
#pragma omp parallel for private(iz,i,j,c,im)
#endif
for (iz=0; iz < nz; iz++) {
i = iz+ix*nz; /* original grid */
j = iz+ix*nz2; /* padded grid */
for (im = 0; im < m2; im++) {
c += crealf(lt[im][i])*wave[im][j];
}
curr[iz] = c;
}
sf_floatwrite(curr,nz,mig);
}
exit (0);
}
void main() {
//* Initialize parameters (system size, grid spacing, etc.)
double eps0 = 8.8542e-12; // Permittivity (C^2/(N m^2))
int N = 64; // Number of grid points on a side (square grid)
double L = 1; // System size
double h = L/N; // Grid spacing for periodic boundary conditions
Matrix x(N), y(N);
int i,j;
for( i=1; i<=N; i++ )
x(i) = (i-0.5)*h; // Coordinates of grid points
y = x; // Square grid
cout << "System is a square of length " << L << endl;
//* Set up charge density rho(i,j)
Matrix rho(N,N);
rho.set(0.0); // Initialize charge density to zero
cout << "Enter number of line charges: "; int M; cin >> M;
for( i=1; i<=M; i++ ) {
cout << "For charge #" << i << endl;
cout << "Enter x coordinate: "; double xc; cin >> xc;
cout << "Enter y coordinate: "; double yc; cin >> yc;
int ii = (int)(xc/h) + 1; // Place charge at nearest
int jj = (int)(yc/h) + 1; // grid point
cout << "Enter charge density: "; double q; cin >> q;
rho(ii,jj) += q/(h*h);
}
//* Compute matrix P
const double pi = 3.141592654;
Matrix cx(N), cy(N);
for( i=1; i<=N; i++ )
cx(i) = cos((2*pi/N)*(i-1));
cy = cx;
Matrix RealP(N,N), ImagP(N,N);
double numerator = -h*h/(2*eps0);
double tinyNumber = 1e-20; // Avoids division by zero
for( i=1; i<=N; i++ )
for( j=1; j<=N; j++ )
RealP(i,j) = numerator/(cx(i)+cy(j)-2+tinyNumber);
ImagP.set(0.0);
//* Compute potential using MFT method
Matrix RealR(N,N), ImagR(N,N), RealF(N,N), ImagF(N,N);
for( i=1; i<=N; i++ )
for( j=1; j<=N; j++ ) {
RealR(i,j) = rho(i,j);
ImagR(i,j) = 0.0; // Copy rho into R for input to fft2
}
fft2(RealR,ImagR); // Transform rho into wavenumber domain
// Compute phi in the wavenumber domain
for( i=1; i<=N; i++ )
for( j=1; j<=N; j++ ) {
RealF(i,j) = RealR(i,j)*RealP(i,j) - ImagR(i,j)*ImagP(i,j);
ImagF(i,j) = RealR(i,j)*ImagP(i,j) + ImagR(i,j)*RealP(i,j);
}
Matrix phi(N,N);
ifft2(RealF,ImagF); // Inv. transf. phi into the coord. domain
for( i=1; i<=N; i++ )
for( j=1; j<=N; j++ )
phi(i,j) = RealF(i,j);
//* Print out the plotting variables: x, y, phi
ofstream xOut("x.txt"), yOut("y.txt"), phiOut("phi.txt");
for( i=1; i<=N; i++ ) {
xOut << x(i) << endl;
yOut << y(i) << endl;
for( j=1; j<N; j++ )
phiOut << phi(i,j) << ", ";
phiOut << phi(i,N) << endl;
}
}
void compute_imgcov(const long cov_dims[4], complex float* imgcov, const long nskerns_dims[5], const complex float* nskerns)
{
debug_printf(DP_DEBUG1, "Zeropad...\n");
long xh = cov_dims[0];
long yh = cov_dims[1];
long zh = cov_dims[2];
long kx = nskerns_dims[0];
long ky = nskerns_dims[1];
long kz = nskerns_dims[2];
long channels = nskerns_dims[3];
long nr_kernels = nskerns_dims[4];
long imgkern_dims[5] = { xh, yh, zh, channels, nr_kernels };
complex float* imgkern1 = md_alloc(5, imgkern_dims, CFL_SIZE);
complex float* imgkern2 = md_alloc(5, imgkern_dims, CFL_SIZE);
md_resize_center(5, imgkern_dims, imgkern1, nskerns_dims, nskerns, CFL_SIZE);
// resort array
debug_printf(DP_DEBUG1, "FFT (juggling)...\n");
long istr[5];
long mstr[5];
long idim[5] = { xh, yh, zh, channels, nr_kernels };
long mdim[5] = { nr_kernels, channels, xh, yh, zh };
md_calc_strides(5, istr, idim, CFL_SIZE);
md_calc_strides(5, mstr, mdim, CFL_SIZE);
long m2str[5] = { mstr[2], mstr[3], mstr[4], mstr[1], mstr[0] };
ifftmod(5, imgkern_dims, FFT_FLAGS, imgkern1, imgkern1);
ifft2(5, imgkern_dims, FFT_FLAGS, m2str, imgkern2, istr, imgkern1);
float scalesq = (kx * ky * kz) * (xh * yh * zh); // second part for FFT scaling
md_free(imgkern1);
debug_printf(DP_DEBUG1, "Calculate Gram matrix...\n");
int cosize = channels * (channels + 1) / 2;
assert(cov_dims[3] == cosize);
#pragma omp parallel for collapse(3)
for (int k = 0; k < zh; k++) {
for (int j = 0; j < yh; j++) {
for (int i = 0; i < xh; i++) {
complex float gram[cosize];
gram_matrix2(channels, gram, nr_kernels, (const complex float (*)[nr_kernels])(imgkern2 + ((k * yh + j) * xh + i) * (channels * nr_kernels)));
#ifdef FLIP
// add (scaled) identity matrix
for (int i = 0, l = 0; i < channels; i++)
for (int j = 0; j <= i; j++, l++)
gram[l] = ((i == j) ? (kx * ky * kz) : 0.) - gram[l];
#endif
for (int l = 0; l < cosize; l++)
imgcov[(((l * zh) + k) * yh + j) * xh + i] = gram[l] / scalesq;
}
}
}
md_free(imgkern2);
}
