VEC *svd(MAT *A, MAT *U, MAT *V, VEC *d)
#endif
{
STATIC VEC *f=VNULL;
int i, limit;
MAT *A_tmp;
if ( ! A )
error(E_NULL,"svd");
if ( ( U && ( U->m != U->n ) ) || ( V && ( V->m != V->n ) ) )
error(E_SQUARE,"svd");
if ( ( U && U->m != A->m ) || ( V && V->m != A->n ) )
error(E_SIZES,"svd");
A_tmp = m_copy(A,MNULL);
if ( U != MNULL )
m_ident(U);
if ( V != MNULL )
m_ident(V);
limit = min(A_tmp->m,A_tmp->n);
d = v_resize(d,limit);
f = v_resize(f,limit-1);
MEM_STAT_REG(f,TYPE_VEC);
bifactor(A_tmp,U,V);
if ( A_tmp->m >= A_tmp->n )
for ( i = 0; i < limit; i++ )
{
d->ve[i] = A_tmp->me[i][i];
if ( i+1 < limit )
f->ve[i] = A_tmp->me[i][i+1];
}
else
for ( i = 0; i < limit; i++ )
{
d->ve[i] = A_tmp->me[i][i];
if ( i+1 < limit )
f->ve[i] = A_tmp->me[i+1][i];
}
if ( A_tmp->m >= A_tmp->n )
bisvd(d,f,U,V);
else
bisvd(d,f,V,U);
M_FREE(A_tmp);
#ifdef THREADSAFE
V_FREE(f);
#endif
return d;
}
struct fft_plan_3d *fft_3d_create_plan
(MPI_Comm comm, int nfast, int nmid, int nslow,
int in_ilo, int in_ihi, int in_jlo, int in_jhi,
int in_klo, int in_khi,
int out_ilo, int out_ihi, int out_jlo, int out_jhi,
int out_klo, int out_khi,
int scaled, int permute, int *nbuf)
{
struct fft_plan_3d *plan;
int me,nprocs;
int flag,remapflag;
int first_ilo,first_ihi,first_jlo,first_jhi,first_klo,first_khi;
int second_ilo,second_ihi,second_jlo,second_jhi,second_klo,second_khi;
int third_ilo,third_ihi,third_jlo,third_jhi,third_klo,third_khi;
int out_size,first_size,second_size,third_size,copy_size,scratch_size;
int np1=0,np2=0,ip1,ip2;
MPI_Comm_rank(comm, &me);
MPI_Comm_size(comm, &nprocs);
bifactor(nprocs,&np1,&np2);
ip1 = me % np1;
ip2 = me / np1;
/* allocate memory for plan data struct */
plan = (struct fft_plan_3d *) malloc(sizeof(struct fft_plan_3d));
if (plan == NULL) return NULL;
/* remap from initial distribution to layout needed for 1st set of 1d FFTs
not needed if all procs own entire fast axis initially
first indices = distribution after 1st set of FFTs */
if (in_ilo == 0 && in_ihi == nfast-1)
flag = 0;
else
flag = 1;
MPI_Allreduce(&flag,&remapflag,1,MPI_INT,MPI_MAX,comm);
if (remapflag == 0) {
first_ilo = in_ilo;
first_ihi = in_ihi;
first_jlo = in_jlo;
first_jhi = in_jhi;
first_klo = in_klo;
first_khi = in_khi;
plan->pre_plan = NULL;
}
else {
first_ilo = 0;
first_ihi = nfast - 1;
first_jlo = ip1*nmid/np1;
first_jhi = (ip1+1)*nmid/np1 - 1;
first_klo = ip2*nslow/np2;
first_khi = (ip2+1)*nslow/np2 - 1;
plan->pre_plan =
remap_3d_create_plan(comm,in_ilo,in_ihi,in_jlo,in_jhi,in_klo,in_khi,
first_ilo,first_ihi,first_jlo,first_jhi,
first_klo,first_khi,
FFT_PRECISION,0,0,2);
if (plan->pre_plan == NULL) return NULL;
}
/* 1d FFTs along fast axis */
plan->length1 = nfast;
plan->total1 = nfast * (first_jhi-first_jlo+1) * (first_khi-first_klo+1);
/* remap from 1st to 2nd FFT
choose which axis is split over np1 vs np2 to minimize communication
second indices = distribution after 2nd set of FFTs */
second_ilo = ip1*nfast/np1;
second_ihi = (ip1+1)*nfast/np1 - 1;
second_jlo = 0;
second_jhi = nmid - 1;
second_klo = ip2*nslow/np2;
second_khi = (ip2+1)*nslow/np2 - 1;
plan->mid1_plan =
remap_3d_create_plan(comm,
first_ilo,first_ihi,first_jlo,first_jhi,
first_klo,first_khi,
second_ilo,second_ihi,second_jlo,second_jhi,
second_klo,second_khi,
FFT_PRECISION,1,0,2);
if (plan->mid1_plan == NULL) return NULL;
/* 1d FFTs along mid axis */
plan->length2 = nmid;
plan->total2 = (second_ihi-second_ilo+1) * nmid * (second_khi-second_klo+1);
/* remap from 2nd to 3rd FFT
if final distribution is permute=2 with all procs owning entire slow axis
then this remapping goes directly to final distribution
third indices = distribution after 3rd set of FFTs */
if (permute == 2 && out_klo == 0 && out_khi == nslow-1)
flag = 0;
else
flag = 1;
MPI_Allreduce(&flag,&remapflag,1,MPI_INT,MPI_MAX,comm);
if (remapflag == 0) {
third_ilo = out_ilo;
third_ihi = out_ihi;
third_jlo = out_jlo;
third_jhi = out_jhi;
third_klo = out_klo;
third_khi = out_khi;
}
else {
third_ilo = ip1*nfast/np1;
third_ihi = (ip1+1)*nfast/np1 - 1;
third_jlo = ip2*nmid/np2;
third_jhi = (ip2+1)*nmid/np2 - 1;
third_klo = 0;
third_khi = nslow - 1;
}
plan->mid2_plan =
remap_3d_create_plan(comm,
second_jlo,second_jhi,second_klo,second_khi,
second_ilo,second_ihi,
third_jlo,third_jhi,third_klo,third_khi,
third_ilo,third_ihi,
FFT_PRECISION,1,0,2);
if (plan->mid2_plan == NULL) return NULL;
/* 1d FFTs along slow axis */
plan->length3 = nslow;
plan->total3 = (third_ihi-third_ilo+1) * (third_jhi-third_jlo+1) * nslow;
/* remap from 3rd FFT to final distribution
not needed if permute = 2 and third indices = out indices on all procs */
if (permute == 2 &&
out_ilo == third_ilo && out_ihi == third_ihi &&
out_jlo == third_jlo && out_jhi == third_jhi &&
out_klo == third_klo && out_khi == third_khi)
flag = 0;
else
flag = 1;
MPI_Allreduce(&flag,&remapflag,1,MPI_INT,MPI_MAX,comm);
if (remapflag == 0)
plan->post_plan = NULL;
else {
plan->post_plan =
remap_3d_create_plan(comm,
third_klo,third_khi,third_ilo,third_ihi,
third_jlo,third_jhi,
out_klo,out_khi,out_ilo,out_ihi,
out_jlo,out_jhi,
FFT_PRECISION,(permute+1)%3,0,2);
if (plan->post_plan == NULL) return NULL;
}
/* configure plan memory pointers and allocate work space
out_size = amount of memory given to FFT by user
first/second/third_size = amount of memory needed after pre,mid1,mid2 remaps
copy_size = amount needed internally for extra copy of data
scratch_size = amount needed internally for remap scratch space
for each remap:
use out space for result if big enough, else require copy buffer
accumulate largest required remap scratch space */
out_size = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) * (out_khi-out_klo+1);
first_size = (first_ihi-first_ilo+1) * (first_jhi-first_jlo+1) *
(first_khi-first_klo+1);
second_size = (second_ihi-second_ilo+1) * (second_jhi-second_jlo+1) *
(second_khi-second_klo+1);
third_size = (third_ihi-third_ilo+1) * (third_jhi-third_jlo+1) *
(third_khi-third_klo+1);
copy_size = 0;
scratch_size = 0;
if (plan->pre_plan) {
if (first_size <= out_size)
plan->pre_target = 0;
else {
plan->pre_target = 1;
copy_size = MAX(copy_size,first_size);
}
scratch_size = MAX(scratch_size,first_size);
}
if (plan->mid1_plan) {
if (second_size <= out_size)
plan->mid1_target = 0;
else {
plan->mid1_target = 1;
copy_size = MAX(copy_size,second_size);
}
scratch_size = MAX(scratch_size,second_size);
}
if (plan->mid2_plan) {
if (third_size <= out_size)
plan->mid2_target = 0;
else {
plan->mid2_target = 1;
copy_size = MAX(copy_size,third_size);
}
scratch_size = MAX(scratch_size,third_size);
}
if (plan->post_plan)
scratch_size = MAX(scratch_size,out_size);
*nbuf = copy_size + scratch_size;
if (copy_size) {
plan->copy = (FFT_DATA *) malloc(copy_size*sizeof(FFT_DATA));
if (plan->copy == NULL) return NULL;
}
else plan->copy = NULL;
if (scratch_size) {
plan->scratch = (FFT_DATA *) malloc(scratch_size*sizeof(FFT_DATA));
if (plan->scratch == NULL) return NULL;
}
else plan->scratch = NULL;
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
return plan;
}
struct fft_plan_3d *fft_3d_create_plan(
MPI_Comm comm, int nfast, int nmid, int nslow,
int in_ilo, int in_ihi, int in_jlo, int in_jhi,
int in_klo, int in_khi,
int out_ilo, int out_ihi, int out_jlo, int out_jhi,
int out_klo, int out_khi,
int scaled, int permute, int *nbuf)
{
struct fft_plan_3d *plan;
int me,nprocs;
int i,num,flag,remapflag,fftflag;
int first_ilo,first_ihi,first_jlo,first_jhi,first_klo,first_khi;
int second_ilo,second_ihi,second_jlo,second_jhi,second_klo,second_khi;
int third_ilo,third_ihi,third_jlo,third_jhi,third_klo,third_khi;
int out_size,first_size,second_size,third_size,copy_size,scratch_size;
int np1,np2,ip1,ip2;
int list[50];
// system specific variables
#ifdef FFT_SCSL
FFT_DATA dummy_d[5];
FFT_PREC dummy_p[5];
int isign,isys;
FFT_PREC scalef;
#endif
#ifdef FFT_INTEL
FFT_DATA dummy;
#endif
#ifdef FFT_T3E
FFT_DATA dummy[5];
int isign,isys;
double scalef;
#endif
// query MPI info
MPI_Comm_rank(comm,&me);
MPI_Comm_size(comm,&nprocs);
// compute division of procs in 2 dimensions not on-processor
bifactor(nprocs,&np1,&np2);
ip1 = me % np1;
ip2 = me/np1;
// allocate memory for plan data struct
plan = (struct fft_plan_3d *) malloc(sizeof(struct fft_plan_3d));
if (plan == NULL) return NULL;
// remap from initial distribution to layout needed for 1st set of 1d FFTs
// not needed if all procs own entire fast axis initially
// first indices = distribution after 1st set of FFTs
if (in_ilo == 0 && in_ihi == nfast-1)
flag = 0;
else
flag = 1;
MPI_Allreduce(&flag,&remapflag,1,MPI_INT,MPI_MAX,comm);
if (remapflag == 0) {
first_ilo = in_ilo;
first_ihi = in_ihi;
first_jlo = in_jlo;
first_jhi = in_jhi;
first_klo = in_klo;
first_khi = in_khi;
plan->pre_plan = NULL;
}
else {
first_ilo = 0;
first_ihi = nfast - 1;
first_jlo = ip1*nmid/np1;
first_jhi = (ip1+1)*nmid/np1 - 1;
first_klo = ip2*nslow/np2;
first_khi = (ip2+1)*nslow/np2 - 1;
plan->pre_plan =
remap_3d_create_plan(comm,in_ilo,in_ihi,in_jlo,in_jhi,in_klo,in_khi,
first_ilo,first_ihi,first_jlo,first_jhi,
first_klo,first_khi,2,0,0,FFT_PRECISION);
if (plan->pre_plan == NULL) return NULL;
}
// 1d FFTs along fast axis
plan->length1 = nfast;
plan->total1 = nfast * (first_jhi-first_jlo+1) * (first_khi-first_klo+1);
// remap from 1st to 2nd FFT
// choose which axis is split over np1 vs np2 to minimize communication
// second indices = distribution after 2nd set of FFTs
second_ilo = ip1*nfast/np1;
second_ihi = (ip1+1)*nfast/np1 - 1;
second_jlo = 0;
second_jhi = nmid - 1;
second_klo = ip2*nslow/np2;
second_khi = (ip2+1)*nslow/np2 - 1;
plan->mid1_plan =
remap_3d_create_plan(comm,
first_ilo,first_ihi,first_jlo,first_jhi,
first_klo,first_khi,
second_ilo,second_ihi,second_jlo,second_jhi,
second_klo,second_khi,2,1,0,FFT_PRECISION);
if (plan->mid1_plan == NULL) return NULL;
// 1d FFTs along mid axis
plan->length2 = nmid;
plan->total2 = (second_ihi-second_ilo+1) * nmid * (second_khi-second_klo+1);
// remap from 2nd to 3rd FFT
// if final distribution is permute=2 with all procs owning entire slow axis
// then this remapping goes directly to final distribution
// third indices = distribution after 3rd set of FFTs
if (permute == 2 && out_klo == 0 && out_khi == nslow-1)
flag = 0;
else
flag = 1;
MPI_Allreduce(&flag,&remapflag,1,MPI_INT,MPI_MAX,comm);
if (remapflag == 0) {
third_ilo = out_ilo;
third_ihi = out_ihi;
third_jlo = out_jlo;
third_jhi = out_jhi;
third_klo = out_klo;
third_khi = out_khi;
}
else {
third_ilo = ip1*nfast/np1;
third_ihi = (ip1+1)*nfast/np1 - 1;
third_jlo = ip2*nmid/np2;
third_jhi = (ip2+1)*nmid/np2 - 1;
third_klo = 0;
third_khi = nslow - 1;
}
plan->mid2_plan =
remap_3d_create_plan(comm,
second_jlo,second_jhi,second_klo,second_khi,
second_ilo,second_ihi,
third_jlo,third_jhi,third_klo,third_khi,
third_ilo,third_ihi,2,1,0,FFT_PRECISION);
if (plan->mid2_plan == NULL) return NULL;
// 1d FFTs along slow axis
plan->length3 = nslow;
plan->total3 = (third_ihi-third_ilo+1) * (third_jhi-third_jlo+1) * nslow;
// remap from 3rd FFT to final distribution
// not needed if permute = 2 and third indices = out indices on all procs
if (permute == 2 &&
out_ilo == third_ilo && out_ihi == third_ihi &&
out_jlo == third_jlo && out_jhi == third_jhi &&
out_klo == third_klo && out_khi == third_khi)
flag = 0;
else
flag = 1;
MPI_Allreduce(&flag,&remapflag,1,MPI_INT,MPI_MAX,comm);
if (remapflag == 0)
plan->post_plan = NULL;
else {
plan->post_plan =
remap_3d_create_plan(comm,
third_klo,third_khi,third_ilo,third_ihi,
third_jlo,third_jhi,
out_klo,out_khi,out_ilo,out_ihi,
out_jlo,out_jhi,2,(permute+1)%3,0,FFT_PRECISION);
if (plan->post_plan == NULL) return NULL;
}
// configure plan memory pointers and allocate work space
// out_size = amount of memory given to FFT by user
// first/second/third_size = amount of memory needed after pre,mid1,mid2 remaps
// copy_size = amount needed internally for extra copy of data
// scratch_size = amount needed internally for remap scratch space
// for each remap:
// out space used for result if big enough, else require copy buffer
// accumulate largest required remap scratch space
out_size = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) * (out_khi-out_klo+1);
first_size = (first_ihi-first_ilo+1) * (first_jhi-first_jlo+1) *
(first_khi-first_klo+1);
second_size = (second_ihi-second_ilo+1) * (second_jhi-second_jlo+1) *
(second_khi-second_klo+1);
third_size = (third_ihi-third_ilo+1) * (third_jhi-third_jlo+1) *
(third_khi-third_klo+1);
copy_size = 0;
scratch_size = 0;
if (plan->pre_plan) {
if (first_size <= out_size)
plan->pre_target = 0;
else {
plan->pre_target = 1;
copy_size = MAX(copy_size,first_size);
}
scratch_size = MAX(scratch_size,first_size);
}
if (plan->mid1_plan) {
if (second_size <= out_size)
plan->mid1_target = 0;
else {
plan->mid1_target = 1;
copy_size = MAX(copy_size,second_size);
}
scratch_size = MAX(scratch_size,second_size);
}
if (plan->mid2_plan) {
if (third_size <= out_size)
plan->mid2_target = 0;
else {
plan->mid2_target = 1;
copy_size = MAX(copy_size,third_size);
}
scratch_size = MAX(scratch_size,third_size);
}
if (plan->post_plan)
scratch_size = MAX(scratch_size,out_size);
*nbuf = copy_size + scratch_size;
if (copy_size) {
plan->copy = (FFT_DATA *) malloc(copy_size*sizeof(FFT_DATA));
if (plan->copy == NULL) return NULL;
}
else plan->copy = NULL;
if (scratch_size) {
plan->scratch = (FFT_DATA *) malloc(scratch_size*sizeof(FFT_DATA));
if (plan->scratch == NULL) return NULL;
}
else plan->scratch = NULL;
// system specific pre-computation of 1d FFT coeffs
// and scaling normalization
#if defined(FFT_SGI)
plan->coeff1 = (FFT_DATA *) malloc((nfast+15)*sizeof(FFT_DATA));
plan->coeff2 = (FFT_DATA *) malloc((nmid+15)*sizeof(FFT_DATA));
plan->coeff3 = (FFT_DATA *) malloc((nslow+15)*sizeof(FFT_DATA));
if (plan->coeff1 == NULL || plan->coeff2 == NULL ||
plan->coeff3 == NULL) return NULL;
FFT_1D_INIT(nfast,plan->coeff1);
FFT_1D_INIT(nmid,plan->coeff2);
FFT_1D_INIT(nslow,plan->coeff3);
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#elif defined(FFT_SCSL)
plan->coeff1 = (FFT_PREC *) malloc((2*nfast+30)*sizeof(FFT_PREC));
plan->coeff2 = (FFT_PREC *) malloc((2*nmid+30)*sizeof(FFT_PREC));
plan->coeff3 = (FFT_PREC *) malloc((2*nslow+30)*sizeof(FFT_PREC));
if (plan->coeff1 == NULL || plan->coeff2 == NULL ||
plan->coeff3 == NULL) return NULL;
plan->work1 = (FFT_PREC *) malloc((2*nfast)*sizeof(FFT_PREC));
plan->work2 = (FFT_PREC *) malloc((2*nmid)*sizeof(FFT_PREC));
plan->work3 = (FFT_PREC *) malloc((2*nslow)*sizeof(FFT_PREC));
if (plan->work1 == NULL || plan->work2 == NULL ||
plan->work3 == NULL) return NULL;
isign = 0;
scalef = 1.0;
isys = 0;
FFT_1D_INIT(isign,nfast,scalef,dummy_d,dummy_d,plan->coeff1,dummy_p,&isys);
FFT_1D_INIT(isign,nmid,scalef,dummy_d,dummy_d,plan->coeff2,dummy_p,&isys);
FFT_1D_INIT(isign,nslow,scalef,dummy_d,dummy_d,plan->coeff3,dummy_p,&isys);
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#elif defined(FFT_ACML)
plan->coeff1 = (FFT_DATA *) malloc((3*nfast+100)*sizeof(FFT_DATA));
plan->coeff2 = (FFT_DATA *) malloc((3*nmid+100)*sizeof(FFT_DATA));
plan->coeff3 = (FFT_DATA *) malloc((3*nslow+100)*sizeof(FFT_DATA));
if (plan->coeff1 == NULL || plan->coeff2 == NULL ||
plan->coeff3 == NULL) return NULL;
int isign = 100;
int isys = 1;
int info = 0;
FFT_DATA *dummy = NULL;
FFT_1D(&isign,&isys,&nfast,dummy,plan->coeff1,&info);
FFT_1D(&isign,&isys,&nmid,dummy,plan->coeff2,&info);
FFT_1D(&isign,&isys,&nslow,dummy,plan->coeff3,&info);
if (scaled == 0) {
plan->scaled = 0;
plan->norm = sqrt(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
} else {
plan->scaled = 1;
plan->norm = sqrt(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#elif defined(FFT_INTEL)
flag = 0;
num = 0;
factor(nfast,&num,list);
for (i = 0; i < num; i++)
if (list[i] != 2 && list[i] != 3 && list[i] != 5) flag = 1;
num = 0;
factor(nmid,&num,list);
for (i = 0; i < num; i++)
if (list[i] != 2 && list[i] != 3 && list[i] != 5) flag = 1;
num = 0;
factor(nslow,&num,list);
for (i = 0; i < num; i++)
if (list[i] != 2 && list[i] != 3 && list[i] != 5) flag = 1;
MPI_Allreduce(&flag,&fftflag,1,MPI_INT,MPI_MAX,comm);
if (fftflag) {
if (me == 0) printf("ERROR: FFTs are not power of 2,3,5\n");
return NULL;
}
plan->coeff1 = (FFT_DATA *) malloc((3*nfast/2+1)*sizeof(FFT_DATA));
plan->coeff2 = (FFT_DATA *) malloc((3*nmid/2+1)*sizeof(FFT_DATA));
plan->coeff3 = (FFT_DATA *) malloc((3*nslow/2+1)*sizeof(FFT_DATA));
if (plan->coeff1 == NULL || plan->coeff2 == NULL ||
plan->coeff3 == NULL) return NULL;
flag = 0;
FFT_1D_INIT(&dummy,&nfast,&flag,plan->coeff1);
FFT_1D_INIT(&dummy,&nmid,&flag,plan->coeff2);
FFT_1D_INIT(&dummy,&nslow,&flag,plan->coeff3);
if (scaled == 0) {
plan->scaled = 1;
plan->norm = nfast*nmid*nslow;
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
else
plan->scaled = 0;
#elif defined(FFT_MKL)
DftiCreateDescriptor( &(plan->handle_fast), FFT_MKL_PREC, DFTI_COMPLEX, 1, (MKL_LONG)nfast);
DftiSetValue(plan->handle_fast, DFTI_NUMBER_OF_TRANSFORMS, (MKL_LONG)plan->total1/nfast);
DftiSetValue(plan->handle_fast, DFTI_PLACEMENT,DFTI_INPLACE);
DftiSetValue(plan->handle_fast, DFTI_INPUT_DISTANCE, (MKL_LONG)nfast);
DftiSetValue(plan->handle_fast, DFTI_OUTPUT_DISTANCE, (MKL_LONG)nfast);
DftiCommitDescriptor(plan->handle_fast);
DftiCreateDescriptor( &(plan->handle_mid), FFT_MKL_PREC, DFTI_COMPLEX, 1, (MKL_LONG)nmid);
DftiSetValue(plan->handle_mid, DFTI_NUMBER_OF_TRANSFORMS, (MKL_LONG)plan->total2/nmid);
DftiSetValue(plan->handle_mid, DFTI_PLACEMENT,DFTI_INPLACE);
DftiSetValue(plan->handle_mid, DFTI_INPUT_DISTANCE, (MKL_LONG)nmid);
DftiSetValue(plan->handle_mid, DFTI_OUTPUT_DISTANCE, (MKL_LONG)nmid);
DftiCommitDescriptor(plan->handle_mid);
DftiCreateDescriptor( &(plan->handle_slow), FFT_MKL_PREC, DFTI_COMPLEX, 1, (MKL_LONG)nslow);
DftiSetValue(plan->handle_slow, DFTI_NUMBER_OF_TRANSFORMS, (MKL_LONG)plan->total3/nslow);
DftiSetValue(plan->handle_slow, DFTI_PLACEMENT,DFTI_INPLACE);
DftiSetValue(plan->handle_slow, DFTI_INPUT_DISTANCE, (MKL_LONG)nslow);
DftiSetValue(plan->handle_slow, DFTI_OUTPUT_DISTANCE, (MKL_LONG)nslow);
DftiCommitDescriptor(plan->handle_slow);
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#elif defined(FFT_DEC)
if (scaled == 0) {
plan->scaled = 1;
plan->norm = nfast*nmid*nslow;
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
else
plan->scaled = 0;
#elif defined(FFT_T3E)
plan->coeff1 = (double *) malloc((12*nfast)*sizeof(double));
plan->coeff2 = (double *) malloc((12*nmid)*sizeof(double));
plan->coeff3 = (double *) malloc((12*nslow)*sizeof(double));
if (plan->coeff1 == NULL || plan->coeff2 == NULL ||
plan->coeff3 == NULL) return NULL;
plan->work1 = (double *) malloc((8*nfast)*sizeof(double));
plan->work2 = (double *) malloc((8*nmid)*sizeof(double));
plan->work3 = (double *) malloc((8*nslow)*sizeof(double));
if (plan->work1 == NULL || plan->work2 == NULL ||
plan->work3 == NULL) return NULL;
isign = 0;
scalef = 1.0;
isys = 0;
FFT_1D_INIT(&isign,&nfast,&scalef,dummy,dummy,plan->coeff1,dummy,&isys);
FFT_1D_INIT(&isign,&nmid,&scalef,dummy,dummy,plan->coeff2,dummy,&isys);
FFT_1D_INIT(&isign,&nslow,&scalef,dummy,dummy,plan->coeff3,dummy,&isys);
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#elif defined(FFT_FFTW2)
plan->plan_fast_forward =
fftw_create_plan(nfast,FFTW_FORWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
plan->plan_fast_backward =
fftw_create_plan(nfast,FFTW_BACKWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
if (nmid == nfast) {
plan->plan_mid_forward = plan->plan_fast_forward;
plan->plan_mid_backward = plan->plan_fast_backward;
}
else {
plan->plan_mid_forward =
fftw_create_plan(nmid,FFTW_FORWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
plan->plan_mid_backward =
fftw_create_plan(nmid,FFTW_BACKWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
}
if (nslow == nfast) {
plan->plan_slow_forward = plan->plan_fast_forward;
plan->plan_slow_backward = plan->plan_fast_backward;
}
else if (nslow == nmid) {
plan->plan_slow_forward = plan->plan_mid_forward;
plan->plan_slow_backward = plan->plan_mid_backward;
}
else {
plan->plan_slow_forward =
fftw_create_plan(nslow,FFTW_FORWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
plan->plan_slow_backward =
fftw_create_plan(nslow,FFTW_BACKWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
}
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#elif defined(FFT_FFTW3)
plan->plan_fast_forward =
FFTW_API(plan_many_dft)(1, &nfast,plan->total1/plan->length1,
NULL,&nfast,1,plan->length1,
NULL,&nfast,1,plan->length1,
FFTW_FORWARD,FFTW_ESTIMATE);
plan->plan_fast_backward =
FFTW_API(plan_many_dft)(1, &nfast,plan->total1/plan->length1,
NULL,&nfast,1,plan->length1,
NULL,&nfast,1,plan->length1,
FFTW_BACKWARD,FFTW_ESTIMATE);
plan->plan_mid_forward =
FFTW_API(plan_many_dft)(1, &nmid,plan->total2/plan->length2,
NULL,&nmid,1,plan->length2,
NULL,&nmid,1,plan->length2,
FFTW_FORWARD,FFTW_ESTIMATE);
plan->plan_mid_backward =
FFTW_API(plan_many_dft)(1, &nmid,plan->total2/plan->length2,
NULL,&nmid,1,plan->length2,
NULL,&nmid,1,plan->length2,
FFTW_BACKWARD,FFTW_ESTIMATE);
plan->plan_slow_forward =
FFTW_API(plan_many_dft)(1, &nslow,plan->total3/plan->length3,
NULL,&nslow,1,plan->length3,
NULL,&nslow,1,plan->length3,
FFTW_FORWARD,FFTW_ESTIMATE);
plan->plan_slow_backward =
FFTW_API(plan_many_dft)(1, &nslow,plan->total3/plan->length3,
NULL,&nslow,1,plan->length3,
NULL,&nslow,1,plan->length3,
FFTW_BACKWARD,FFTW_ESTIMATE);
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#else
plan->cfg_fast_forward = kiss_fft_alloc(nfast,0,NULL,NULL);
plan->cfg_fast_backward = kiss_fft_alloc(nfast,1,NULL,NULL);
if (nmid == nfast) {
plan->cfg_mid_forward = plan->cfg_fast_forward;
plan->cfg_mid_backward = plan->cfg_fast_backward;
}
else {
plan->cfg_mid_forward = kiss_fft_alloc(nmid,0,NULL,NULL);
plan->cfg_mid_backward = kiss_fft_alloc(nmid,1,NULL,NULL);
}
if (nslow == nfast) {
plan->cfg_slow_forward = plan->cfg_fast_forward;
plan->cfg_slow_backward = plan->cfg_fast_backward;
}
else if (nslow == nmid) {
plan->cfg_slow_forward = plan->cfg_mid_forward;
plan->cfg_slow_backward = plan->cfg_mid_backward;
}
else {
plan->cfg_slow_forward = kiss_fft_alloc(nslow,0,NULL,NULL);
plan->cfg_slow_backward = kiss_fft_alloc(nslow,1,NULL,NULL);
}
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#endif
return plan;
}
struct fft_plan_3d *fft_3d_create_plan(
MPI_Comm comm, int nfast, int nmid, int nslow,
int in_ilo, int in_ihi, int in_jlo, int in_jhi,
int in_klo, int in_khi,
int out_ilo, int out_ihi, int out_jlo, int out_jhi,
int out_klo, int out_khi,
int scaled, int permute, int *nbuf)
{
struct fft_plan_3d *plan;
int me,nprocs;
int i,num,flag,remapflag,fftflag;
int first_ilo,first_ihi,first_jlo,first_jhi,first_klo,first_khi;
int second_ilo,second_ihi,second_jlo,second_jhi,second_klo,second_khi;
int third_ilo,third_ihi,third_jlo,third_jhi,third_klo,third_khi;
int out_size,first_size,second_size,third_size,copy_size,scratch_size;
int np1,np2,ip1,ip2;
int list[50];
/* system specific variables */
#ifdef FFT_INTEL
FFT_DATA dummy;
#endif
#ifdef FFT_T3E
FFT_DATA dummy[5];
int isign,isys;
double scalef;
#endif
/* query MPI info */
MPI_Comm_rank(comm,&me);
MPI_Comm_size(comm,&nprocs);
/* compute division of procs in 2 dimensions not on-processor */
bifactor(nprocs,&np1,&np2);
ip1 = me % np1;
ip2 = me/np1;
/* allocate memory for plan data struct */
plan = (struct fft_plan_3d *) malloc(sizeof(struct fft_plan_3d));
if (plan == NULL) return NULL;
/* remap from initial distribution to layout needed for 1st set of 1d FFTs
not needed if all procs own entire fast axis initially
first indices = distribution after 1st set of FFTs */
if (in_ilo == 0 && in_ihi == nfast-1)
flag = 0;
else
flag = 1;
MPI_Allreduce(&flag,&remapflag,1,MPI_INT,MPI_MAX,comm);
if (remapflag == 0) {
first_ilo = in_ilo;
first_ihi = in_ihi;
first_jlo = in_jlo;
first_jhi = in_jhi;
first_klo = in_klo;
first_khi = in_khi;
plan->pre_plan = NULL;
}
else {
first_ilo = 0;
first_ihi = nfast - 1;
first_jlo = ip1*nmid/np1;
first_jhi = (ip1+1)*nmid/np1 - 1;
first_klo = ip2*nslow/np2;
first_khi = (ip2+1)*nslow/np2 - 1;
plan->pre_plan =
remap_3d_create_plan(comm,in_ilo,in_ihi,in_jlo,in_jhi,in_klo,in_khi,
first_ilo,first_ihi,first_jlo,first_jhi,
first_klo,first_khi,
FFT_PRECISION,0,0,2);
if (plan->pre_plan == NULL) return NULL;
}
/* 1d FFTs along fast axis */
plan->length1 = nfast;
plan->total1 = nfast * (first_jhi-first_jlo+1) * (first_khi-first_klo+1);
/* remap from 1st to 2nd FFT
choose which axis is split over np1 vs np2 to minimize communication
second indices = distribution after 2nd set of FFTs */
second_ilo = ip1*nfast/np1;
second_ihi = (ip1+1)*nfast/np1 - 1;
second_jlo = 0;
second_jhi = nmid - 1;
second_klo = ip2*nslow/np2;
second_khi = (ip2+1)*nslow/np2 - 1;
plan->mid1_plan =
remap_3d_create_plan(comm,
first_ilo,first_ihi,first_jlo,first_jhi,
first_klo,first_khi,
second_ilo,second_ihi,second_jlo,second_jhi,
second_klo,second_khi,
FFT_PRECISION,1,0,2);
if (plan->mid1_plan == NULL) return NULL;
/* 1d FFTs along mid axis */
plan->length2 = nmid;
plan->total2 = (second_ihi-second_ilo+1) * nmid * (second_khi-second_klo+1);
/* remap from 2nd to 3rd FFT
if final distribution is permute=2 with all procs owning entire slow axis
then this remapping goes directly to final distribution
third indices = distribution after 3rd set of FFTs */
if (permute == 2 && out_klo == 0 && out_khi == nslow-1)
flag = 0;
else
flag = 1;
MPI_Allreduce(&flag,&remapflag,1,MPI_INT,MPI_MAX,comm);
if (remapflag == 0) {
third_ilo = out_ilo;
third_ihi = out_ihi;
third_jlo = out_jlo;
third_jhi = out_jhi;
third_klo = out_klo;
third_khi = out_khi;
}
else {
third_ilo = ip1*nfast/np1;
third_ihi = (ip1+1)*nfast/np1 - 1;
third_jlo = ip2*nmid/np2;
third_jhi = (ip2+1)*nmid/np2 - 1;
third_klo = 0;
third_khi = nslow - 1;
}
plan->mid2_plan =
remap_3d_create_plan(comm,
second_jlo,second_jhi,second_klo,second_khi,
second_ilo,second_ihi,
third_jlo,third_jhi,third_klo,third_khi,
third_ilo,third_ihi,
FFT_PRECISION,1,0,2);
if (plan->mid2_plan == NULL) return NULL;
/* 1d FFTs along slow axis */
plan->length3 = nslow;
plan->total3 = (third_ihi-third_ilo+1) * (third_jhi-third_jlo+1) * nslow;
/* remap from 3rd FFT to final distribution
not needed if permute = 2 and third indices = out indices on all procs */
if (permute == 2 &&
out_ilo == third_ilo && out_ihi == third_ihi &&
out_jlo == third_jlo && out_jhi == third_jhi &&
out_klo == third_klo && out_khi == third_khi)
flag = 0;
else
flag = 1;
MPI_Allreduce(&flag,&remapflag,1,MPI_INT,MPI_MAX,comm);
if (remapflag == 0)
plan->post_plan = NULL;
else {
plan->post_plan =
remap_3d_create_plan(comm,
third_klo,third_khi,third_ilo,third_ihi,
third_jlo,third_jhi,
out_klo,out_khi,out_ilo,out_ihi,
out_jlo,out_jhi,
FFT_PRECISION,(permute+1)%3,0,2);
if (plan->post_plan == NULL) return NULL;
}
/* configure plan memory pointers and allocate work space
out_size = amount of memory given to FFT by user
first/second/third_size = amount of memory needed after pre,mid1,mid2 remaps
copy_size = amount needed internally for extra copy of data
scratch_size = amount needed internally for remap scratch space
for each remap:
use out space for result if big enough, else require copy buffer
accumulate largest required remap scratch space */
out_size = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) * (out_khi-out_klo+1);
first_size = (first_ihi-first_ilo+1) * (first_jhi-first_jlo+1) *
(first_khi-first_klo+1);
second_size = (second_ihi-second_ilo+1) * (second_jhi-second_jlo+1) *
(second_khi-second_klo+1);
third_size = (third_ihi-third_ilo+1) * (third_jhi-third_jlo+1) *
(third_khi-third_klo+1);
copy_size = 0;
scratch_size = 0;
if (plan->pre_plan) {
if (first_size <= out_size)
plan->pre_target = 0;
else {
plan->pre_target = 1;
copy_size = MAX(copy_size,first_size);
}
scratch_size = MAX(scratch_size,first_size);
}
if (plan->mid1_plan) {
if (second_size <= out_size)
plan->mid1_target = 0;
else {
plan->mid1_target = 1;
copy_size = MAX(copy_size,second_size);
}
scratch_size = MAX(scratch_size,second_size);
}
if (plan->mid2_plan) {
if (third_size <= out_size)
plan->mid2_target = 0;
else {
plan->mid2_target = 1;
copy_size = MAX(copy_size,third_size);
}
scratch_size = MAX(scratch_size,third_size);
}
if (plan->post_plan)
scratch_size = MAX(scratch_size,out_size);
*nbuf = copy_size + scratch_size;
if (copy_size) {
plan->copy = (FFT_DATA *) malloc(copy_size*sizeof(FFT_DATA));
if (plan->copy == NULL) return NULL;
}
else plan->copy = NULL;
if (scratch_size) {
plan->scratch = (FFT_DATA *) malloc(scratch_size*sizeof(FFT_DATA));
if (plan->scratch == NULL) return NULL;
}
else plan->scratch = NULL;
/* system specific pre-computation of 1d FFT coeffs
and scaling normalization */
#ifdef FFT_SGI
plan->coeff1 = (FFT_DATA *) malloc((nfast+15)*sizeof(FFT_DATA));
plan->coeff2 = (FFT_DATA *) malloc((nmid+15)*sizeof(FFT_DATA));
plan->coeff3 = (FFT_DATA *) malloc((nslow+15)*sizeof(FFT_DATA));
if (plan->coeff1 == NULL || plan->coeff2 == NULL ||
plan->coeff3 == NULL) return NULL;
FFT_1D_INIT(nfast,plan->coeff1);
FFT_1D_INIT(nmid,plan->coeff2);
FFT_1D_INIT(nslow,plan->coeff3);
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#endif
#ifdef FFT_INTEL
flag = 0;
num = 0;
factor(nfast,&num,list);
for (i = 0; i < num; i++)
if (list[i] != 2 && list[i] != 3 && list[i] != 5) flag = 1;
num = 0;
factor(nmid,&num,list);
for (i = 0; i < num; i++)
if (list[i] != 2 && list[i] != 3 && list[i] != 5) flag = 1;
num = 0;
factor(nslow,&num,list);
for (i = 0; i < num; i++)
if (list[i] != 2 && list[i] != 3 && list[i] != 5) flag = 1;
MPI_Allreduce(&flag,&fftflag,1,MPI_INT,MPI_MAX,comm);
if (fftflag) {
if (me == 0) printf("ERROR: FFTs are not power of 2,3,5\n");
return NULL;
}
plan->coeff1 = (FFT_DATA *) malloc((3*nfast/2+1)*sizeof(FFT_DATA));
plan->coeff2 = (FFT_DATA *) malloc((3*nmid/2+1)*sizeof(FFT_DATA));
plan->coeff3 = (FFT_DATA *) malloc((3*nslow/2+1)*sizeof(FFT_DATA));
if (plan->coeff1 == NULL || plan->coeff2 == NULL ||
plan->coeff3 == NULL) return NULL;
flag = 0;
FFT_1D_INIT(&dummy,&nfast,&flag,plan->coeff1);
FFT_1D_INIT(&dummy,&nmid,&flag,plan->coeff2);
FFT_1D_INIT(&dummy,&nslow,&flag,plan->coeff3);
if (scaled == 0) {
plan->scaled = 1;
plan->norm = nfast*nmid*nslow;
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
else
plan->scaled = 0;
#endif
#ifdef FFT_DEC
if (scaled == 0) {
plan->scaled = 1;
plan->norm = nfast*nmid*nslow;
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
else
plan->scaled = 0;
#endif
#ifdef FFT_T3E
plan->coeff1 = (double *) malloc((12*nfast)*sizeof(double));
plan->coeff2 = (double *) malloc((12*nmid)*sizeof(double));
plan->coeff3 = (double *) malloc((12*nslow)*sizeof(double));
if (plan->coeff1 == NULL || plan->coeff2 == NULL ||
plan->coeff3 == NULL) return NULL;
plan->work1 = (double *) malloc((8*nfast)*sizeof(double));
plan->work2 = (double *) malloc((8*nmid)*sizeof(double));
plan->work3 = (double *) malloc((8*nslow)*sizeof(double));
if (plan->work1 == NULL || plan->work2 == NULL ||
plan->work3 == NULL) return NULL;
isign = 0;
scalef = 1.0;
isys = 0;
FFT_1D_INIT(&isign,&nfast,&scalef,dummy,dummy,plan->coeff1,dummy,&isys);
FFT_1D_INIT(&isign,&nmid,&scalef,dummy,dummy,plan->coeff2,dummy,&isys);
FFT_1D_INIT(&isign,&nslow,&scalef,dummy,dummy,plan->coeff3,dummy,&isys);
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#endif
#ifdef FFT_FFTW
plan->plan_fast_forward =
fftw_create_plan(nfast,FFTW_FORWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
plan->plan_fast_backward =
fftw_create_plan(nfast,FFTW_BACKWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
if (nmid == nfast) {
plan->plan_mid_forward = plan->plan_fast_forward;
plan->plan_mid_backward = plan->plan_fast_backward;
}
else {
plan->plan_mid_forward =
fftw_create_plan(nmid,FFTW_FORWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
plan->plan_mid_backward =
fftw_create_plan(nmid,FFTW_BACKWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
}
if (nslow == nfast) {
plan->plan_slow_forward = plan->plan_fast_forward;
plan->plan_slow_backward = plan->plan_fast_backward;
}
else if (nslow == nmid) {
plan->plan_slow_forward = plan->plan_mid_forward;
plan->plan_slow_backward = plan->plan_mid_backward;
}
else {
plan->plan_slow_forward =
fftw_create_plan(nslow,FFTW_FORWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
plan->plan_slow_backward =
fftw_create_plan(nslow,FFTW_BACKWARD,FFTW_ESTIMATE | FFTW_IN_PLACE);
}
if (scaled == 0)
plan->scaled = 0;
else {
plan->scaled = 1;
plan->norm = 1.0/(nfast*nmid*nslow);
plan->normnum = (out_ihi-out_ilo+1) * (out_jhi-out_jlo+1) *
(out_khi-out_klo+1);
}
#endif
return plan;
}
