422 |
|
-pow_one * icoeffs[dummy0]; |
423 |
|
} |
424 |
|
} |
425 |
– |
} |
426 |
– |
|
427 |
– |
} |
428 |
– |
|
429 |
– |
/************************************************************************/ |
430 |
– |
/* Inverse spherical harmonic transform. |
431 |
– |
|
432 |
– |
bw -> bandwidth of problem |
433 |
– |
size = 2*bw |
434 |
– |
|
435 |
– |
Inputs rcoeffs and icoeffs are harmonic coefficients stored |
436 |
– |
in (bw * bw) arrays in the order spec'ed above. |
437 |
– |
|
438 |
– |
rdata and idata are (size x size) arrays with the transformed result. |
439 |
– |
|
440 |
– |
transpose_spharmonic_pml_table should be the (double **) |
441 |
– |
result of a call to Transpose_Spharmonic_Pml_Table() |
442 |
– |
|
443 |
– |
workspace is (8 * bw^2) + (10 * bw) |
444 |
– |
|
445 |
– |
*/ |
446 |
– |
|
447 |
– |
/* dataformat =0 -> samples are complex, =1 -> samples real */ |
448 |
– |
|
449 |
– |
void InvFST_semi_memo(double *rcoeffs, double *icoeffs, |
450 |
– |
double *rdata, double *idata, |
451 |
– |
int bw, |
452 |
– |
double **transpose_seminaive_naive_table, |
453 |
– |
double *workspace, |
454 |
– |
int dataformat, |
455 |
– |
int cutoff, |
456 |
– |
fftw_plan *idctPlan, |
457 |
– |
fftw_plan *ifftPlan ) |
458 |
– |
{ |
459 |
– |
int size, m, i, n; |
460 |
– |
double *rdataptr, *idataptr; |
461 |
– |
double *rfourdata, *ifourdata; |
462 |
– |
double *rinvfltres, *iminvfltres, *scratchpad; |
463 |
– |
double *sin_values, *eval_pts; |
464 |
– |
double tmpA ; |
465 |
– |
|
466 |
– |
size = 2*bw ; |
467 |
– |
|
468 |
– |
rfourdata = workspace; /* needs (size * size) */ |
469 |
– |
ifourdata = rfourdata + (size * size); /* needs (size * size) */ |
470 |
– |
rinvfltres = ifourdata + (size * size); /* needs (2 * bw) */ |
471 |
– |
iminvfltres = rinvfltres + (2 * bw); /* needs (2 * bw) */ |
472 |
– |
sin_values = iminvfltres + (2 * bw); /* needs (2 * bw) */ |
473 |
– |
eval_pts = sin_values + (2 * bw); /* needs (2 * bw) */ |
474 |
– |
scratchpad = eval_pts + (2 * bw); /* needs (2 * bw) */ |
475 |
– |
|
476 |
– |
/* total workspace = (8 * bw^2) + (10 * bw) */ |
477 |
– |
|
478 |
– |
/* load up the sin_values array */ |
479 |
– |
n = 2*bw; |
480 |
– |
|
481 |
– |
ArcCosEvalPts(n, eval_pts); |
482 |
– |
for (i=0; i<n; i++) |
483 |
– |
sin_values[i] = sin(eval_pts[i]); |
484 |
– |
|
485 |
– |
|
486 |
– |
/* Now do all of the inverse Legendre transforms */ |
487 |
– |
rdataptr = rcoeffs; |
488 |
– |
idataptr = icoeffs; |
489 |
– |
|
490 |
– |
for (m=0; m<bw; m++) |
491 |
– |
{ |
492 |
– |
/* |
493 |
– |
fprintf(stderr,"m = %d\n",m); |
494 |
– |
*/ |
495 |
– |
|
496 |
– |
if(m < cutoff) |
497 |
– |
{ |
498 |
– |
/* do real part first */ |
499 |
– |
InvSemiNaiveReduced(rdataptr, |
500 |
– |
bw, |
501 |
– |
m, |
502 |
– |
rinvfltres, |
503 |
– |
transpose_seminaive_naive_table[m], |
504 |
– |
sin_values, |
505 |
– |
scratchpad, |
506 |
– |
idctPlan ); |
507 |
– |
|
508 |
– |
/* now do imaginary part */ |
509 |
– |
|
510 |
– |
InvSemiNaiveReduced(idataptr, |
511 |
– |
bw, |
512 |
– |
m, |
513 |
– |
iminvfltres, |
514 |
– |
transpose_seminaive_naive_table[m], |
515 |
– |
sin_values, |
516 |
– |
scratchpad, |
517 |
– |
idctPlan); |
518 |
– |
|
519 |
– |
/* will store normal, then tranpose before doing inverse fft */ |
520 |
– |
memcpy(rfourdata+(m*size), rinvfltres, sizeof(double) * size); |
521 |
– |
memcpy(ifourdata+(m*size), iminvfltres, sizeof(double) * size); |
522 |
– |
|
523 |
– |
/* move to next set of coeffs */ |
524 |
– |
rdataptr += bw-m; |
525 |
– |
idataptr += bw-m; |
526 |
– |
|
527 |
– |
} |
528 |
– |
else |
529 |
– |
{ |
530 |
– |
|
531 |
– |
/* first do the real part */ |
532 |
– |
Naive_SynthesizeX(rdataptr, |
533 |
– |
bw, |
534 |
– |
m, |
535 |
– |
rinvfltres, |
536 |
– |
transpose_seminaive_naive_table[m]); |
537 |
– |
|
538 |
– |
/* now do the imaginary */ |
539 |
– |
Naive_SynthesizeX(idataptr, |
540 |
– |
bw, |
541 |
– |
m, |
542 |
– |
iminvfltres, |
543 |
– |
transpose_seminaive_naive_table[m]); |
544 |
– |
|
545 |
– |
/* will store normal, then tranpose before doing inverse fft */ |
546 |
– |
memcpy(rfourdata+(m*size), rinvfltres, sizeof(double) * size); |
547 |
– |
memcpy(ifourdata+(m*size), iminvfltres, sizeof(double) * size); |
548 |
– |
|
549 |
– |
/* move to next set of coeffs */ |
550 |
– |
|
551 |
– |
rdataptr += bw-m; |
552 |
– |
idataptr += bw-m; |
553 |
– |
|
554 |
– |
} |
555 |
– |
} |
556 |
– |
/* closes m loop */ |
557 |
– |
|
558 |
– |
/* now fill in zero values where m = bw (from problem definition) */ |
559 |
– |
memset(rfourdata + (bw * size), 0, sizeof(double) * size); |
560 |
– |
memset(ifourdata + (bw * size), 0, sizeof(double) * size); |
561 |
– |
|
562 |
– |
/* now if the data is real, we don't have to compute the |
563 |
– |
coefficients whose order is less than 0, i.e. since |
564 |
– |
the data is real, we know that |
565 |
– |
invf-hat(l,-m) = conjugate(invf-hat(l,m)), |
566 |
– |
so use that to get the rest of the real data |
567 |
– |
|
568 |
– |
dataformat =0 -> samples are complex, =1 -> samples real |
569 |
– |
|
570 |
– |
*/ |
571 |
– |
|
572 |
– |
if(dataformat == 0){ |
573 |
– |
|
574 |
– |
/* now do negative m values */ |
575 |
– |
|
576 |
– |
for (m=bw+1; m<size; m++) |
577 |
– |
{ |
578 |
– |
/* |
579 |
– |
fprintf(stderr,"m = %d\n",-(size-m)); |
580 |
– |
*/ |
581 |
– |
|
582 |
– |
if ( (size-m) < cutoff ) |
583 |
– |
{ |
584 |
– |
/* do real part first */ |
585 |
– |
InvSemiNaiveReduced(rdataptr, |
586 |
– |
bw, |
587 |
– |
size - m, |
588 |
– |
rinvfltres, |
589 |
– |
transpose_seminaive_naive_table[size - m], |
590 |
– |
sin_values, |
591 |
– |
scratchpad, |
592 |
– |
idctPlan); |
593 |
– |
|
594 |
– |
/* now do imaginary part */ |
595 |
– |
InvSemiNaiveReduced(idataptr, |
596 |
– |
bw, |
597 |
– |
size - m, |
598 |
– |
iminvfltres, |
599 |
– |
transpose_seminaive_naive_table[size - m], |
600 |
– |
sin_values, |
601 |
– |
scratchpad, |
602 |
– |
idctPlan ); |
603 |
– |
|
604 |
– |
/* will store normal, then tranpose before doing inverse fft */ |
605 |
– |
if ((m % 2) != 0) |
606 |
– |
for(i=0; i< size; i++){ |
607 |
– |
rinvfltres[i] = -rinvfltres[i]; |
608 |
– |
iminvfltres[i] = -iminvfltres[i]; |
609 |
– |
} |
610 |
– |
|
611 |
– |
memcpy(rfourdata + (m*size), rinvfltres, sizeof(double) * size); |
612 |
– |
memcpy(ifourdata + (m*size), iminvfltres, sizeof(double) * size); |
613 |
– |
|
614 |
– |
/* move to next set of coeffs */ |
615 |
– |
rdataptr += bw-(size-m); |
616 |
– |
idataptr += bw-(size-m); |
617 |
– |
} |
618 |
– |
else |
619 |
– |
{ |
620 |
– |
/* first do the real part */ |
621 |
– |
Naive_SynthesizeX(rdataptr, |
622 |
– |
bw, |
623 |
– |
size-m, |
624 |
– |
rinvfltres, |
625 |
– |
transpose_seminaive_naive_table[size-m]); |
626 |
– |
|
627 |
– |
/* now do the imaginary */ |
628 |
– |
Naive_SynthesizeX(idataptr, |
629 |
– |
bw, |
630 |
– |
size-m, |
631 |
– |
iminvfltres, |
632 |
– |
transpose_seminaive_naive_table[size-m]); |
633 |
– |
|
634 |
– |
/* will store normal, then tranpose before doing inverse fft */ |
635 |
– |
if ((m % 2) != 0) |
636 |
– |
for(i=0; i< size; i++){ |
637 |
– |
rinvfltres[i] = -rinvfltres[i]; |
638 |
– |
iminvfltres[i] = -iminvfltres[i]; |
639 |
– |
} |
640 |
– |
|
641 |
– |
memcpy(rfourdata + (m*size), rinvfltres, sizeof(double) * size); |
642 |
– |
memcpy(ifourdata + (m*size), iminvfltres, sizeof(double) * size); |
643 |
– |
|
644 |
– |
/* move to next set of coeffs */ |
645 |
– |
rdataptr += bw-(size-m); |
646 |
– |
idataptr += bw-(size-m); |
647 |
– |
|
648 |
– |
} |
649 |
– |
|
650 |
– |
} /* closes m loop */ |
651 |
– |
} |
652 |
– |
else { |
653 |
– |
for(m = bw + 1; m < size; m++){ |
654 |
– |
|
655 |
– |
memcpy(rfourdata+(m*size), rfourdata+((size-m)*size), |
656 |
– |
sizeof(double) * size); |
657 |
– |
memcpy(ifourdata+(m*size), ifourdata+((size-m)*size), |
658 |
– |
sizeof(double) * size); |
659 |
– |
for(i = 0; i < size; i++) |
660 |
– |
ifourdata[(m*size)+i] *= -1.0; |
425 |
|
} |
662 |
– |
} |
663 |
– |
|
664 |
– |
/* normalize */ |
665 |
– |
tmpA = 1./(sqrt(2.*M_PI) ); |
666 |
– |
for(i=0;i<4*bw*bw;i++) |
667 |
– |
{ |
668 |
– |
rfourdata[i] *= tmpA ; |
669 |
– |
ifourdata[i] *= tmpA ; |
670 |
– |
} |
671 |
– |
|
672 |
– |
|
673 |
– |
fftw_execute_split_dft( *ifftPlan, |
674 |
– |
ifourdata, rfourdata, |
675 |
– |
idata, rdata ); |
676 |
– |
/* amscray */ |
426 |
|
|
678 |
– |
} |
679 |
– |
|
680 |
– |
/************************************************************************/ |
681 |
– |
/* |
682 |
– |
Zonal Harmonic transform using seminaive algorithm - used in convolutions |
683 |
– |
|
684 |
– |
bw -> bandwidth of problem |
685 |
– |
|
686 |
– |
size = 2 * bw |
687 |
– |
|
688 |
– |
rdata and idata should be pointers to size x size arrays. |
689 |
– |
rres and ires should be pointers to double arrays of size bw. |
690 |
– |
|
691 |
– |
cos_pml_table contains Legendre coefficients of P(0,l) functions |
692 |
– |
and is result of CosPmlTableGen for m = 0; |
693 |
– |
FZT_semi only computes spherical harmonics for m=0. |
694 |
– |
|
695 |
– |
dataformat =0 -> samples are complex, =1 -> samples real |
696 |
– |
|
697 |
– |
workspace needed is (12 * bw) |
698 |
– |
|
699 |
– |
*/ |
700 |
– |
|
701 |
– |
void FZT_semi_memo(double *rdata, double *idata, |
702 |
– |
double *rres, double *ires, |
703 |
– |
int bw, |
704 |
– |
double *cos_pml_table, |
705 |
– |
double *workspace, |
706 |
– |
int dataformat, |
707 |
– |
fftw_plan *dctPlan, |
708 |
– |
double *weights ) |
709 |
– |
{ |
710 |
– |
int i, j, size; |
711 |
– |
double *r0, *i0, dsize; |
712 |
– |
double tmpreal, tmpimag; |
713 |
– |
double tmpA ; |
714 |
– |
double *scratchpad ; |
715 |
– |
|
716 |
– |
size = 2*bw ; |
717 |
– |
|
718 |
– |
/* assign memory */ |
719 |
– |
r0 = workspace; /* needs (2 * bw) */ |
720 |
– |
i0 = r0 + (2 * bw); /* needs (2 * bw) */ |
721 |
– |
scratchpad = i0 + (2 * bw); /* needs (4 * bw) */ |
722 |
– |
|
723 |
– |
/* total workspace = 13*bw */ |
724 |
– |
|
725 |
– |
dsize = 1.0 / ((double) size); |
726 |
– |
tmpA = sqrt( 2.* M_PI ); |
727 |
– |
dsize *= tmpA ; |
728 |
– |
|
729 |
– |
/* compute the m = 0 components */ |
730 |
– |
for (i=0; i<size; i++) { |
731 |
– |
tmpreal = 0.0; |
732 |
– |
tmpimag = 0.0; |
733 |
– |
|
734 |
– |
for(j=0; j<size; j++) { |
735 |
– |
tmpreal += rdata[(i*size)+j]; |
736 |
– |
tmpimag += idata[(i*size)+j]; |
737 |
– |
} |
738 |
– |
/* normalize */ |
739 |
– |
r0[i] = tmpreal*dsize; |
740 |
– |
i0[i] = tmpimag*dsize; |
741 |
– |
} |
742 |
– |
|
743 |
– |
/* do the real part */ |
744 |
– |
SemiNaiveReduced(r0, |
745 |
– |
bw, |
746 |
– |
0, |
747 |
– |
rres, |
748 |
– |
scratchpad, |
749 |
– |
cos_pml_table, |
750 |
– |
weights, |
751 |
– |
dctPlan); |
752 |
– |
|
753 |
– |
if(dataformat == 0) /* do imaginary part */ |
754 |
– |
SemiNaiveReduced(i0, |
755 |
– |
bw, |
756 |
– |
0, |
757 |
– |
ires, |
758 |
– |
scratchpad, |
759 |
– |
cos_pml_table, |
760 |
– |
weights, |
761 |
– |
dctPlan); |
762 |
– |
else /* otherwise set coefficients = 0 */ |
763 |
– |
memset(ires, 0, sizeof(double) * size); |
764 |
– |
|
427 |
|
} |
428 |
|
|
767 |
– |
/************************************************************************/ |
768 |
– |
/* |
769 |
– |
multiplies harmonic coefficients of a function and a filter. |
770 |
– |
See convolution theorem of Driscoll and Healy for details. |
771 |
– |
|
772 |
– |
bw -> bandwidth of problem |
773 |
– |
size = 2*bw |
774 |
– |
|
775 |
– |
datacoeffs should be output of an FST, filtercoeffs the |
776 |
– |
output of an FZT. There should be (bw * bw) datacoeffs, |
777 |
– |
and bw filtercoeffs. |
778 |
– |
rres and ires should point to arrays of dimension bw * bw. |
779 |
– |
|
780 |
– |
*/ |
781 |
– |
|
782 |
– |
void TransMult(double *rdatacoeffs, double *idatacoeffs, |
783 |
– |
double *rfiltercoeffs, double *ifiltercoeffs, |
784 |
– |
double *rres, double *ires, |
785 |
– |
int bw) |
786 |
– |
{ |
787 |
– |
|
788 |
– |
int m, l, size; |
789 |
– |
double *rdptr, *idptr, *rrptr, *irptr; |
790 |
– |
|
791 |
– |
size = 2*bw ; |
792 |
– |
|
793 |
– |
rdptr = rdatacoeffs; |
794 |
– |
idptr = idatacoeffs; |
795 |
– |
rrptr = rres; |
796 |
– |
irptr = ires; |
797 |
– |
|
798 |
– |
for (m=0; m<bw; m++) { |
799 |
– |
for (l=m; l<bw; l++) { |
800 |
– |
compmult(rfiltercoeffs[l], ifiltercoeffs[l], |
801 |
– |
rdptr[l-m], idptr[l-m], |
802 |
– |
rrptr[l-m], irptr[l-m]); |
803 |
– |
|
804 |
– |
rrptr[l-m] *= sqrt(4*M_PI/(2*l+1)); |
805 |
– |
irptr[l-m] *= sqrt(4*M_PI/(2*l+1)); |
806 |
– |
|
807 |
– |
} |
808 |
– |
rdptr += bw-m; idptr += bw-m; |
809 |
– |
rrptr += bw-m; irptr += bw-m; |
810 |
– |
} |
811 |
– |
for (m=bw+1; m<size; m++) { |
812 |
– |
for (l=size-m; l<bw; l++){ |
813 |
– |
compmult(rfiltercoeffs[l], ifiltercoeffs[l], |
814 |
– |
rdptr[l-size+m], idptr[l-size+m], |
815 |
– |
rrptr[l-size+m], irptr[l-size+m]); |
816 |
– |
|
817 |
– |
rrptr[l-size+m] *= sqrt(4*M_PI/(2*l+1)); |
818 |
– |
irptr[l-size+m] *= sqrt(4*M_PI/(2*l+1)); |
819 |
– |
|
820 |
– |
} |
821 |
– |
rdptr += m-bw; idptr += m-bw; |
822 |
– |
rrptr += m-bw; irptr += m-bw; |
823 |
– |
} |
824 |
– |
|
825 |
– |
} |
826 |
– |
|
827 |
– |
/************************************************************************/ |
828 |
– |
/* Here's the big banana |
829 |
– |
Convolves two functions defined on the 2-sphere. |
830 |
– |
Uses seminaive algorithms for spherical harmonic transforms |
831 |
– |
|
832 |
– |
size = 2*bw |
833 |
– |
|
834 |
– |
Inputs: |
835 |
– |
|
836 |
– |
rdata, idata - (size * size) arrays containing real and |
837 |
– |
imaginary parts of sampled function. |
838 |
– |
rfilter, ifilter - (size * size) arrays containing real and |
839 |
– |
imaginary parts of sampled filter function. |
840 |
– |
rres, ires - (size * size) arrays containing real and |
841 |
– |
imaginary parts of result function. |
842 |
– |
|
843 |
– |
|
844 |
– |
Suggestion - if you want to do multiple convolutions, |
845 |
– |
don't keep allocating and freeing space with every call, |
846 |
– |
or keep recomputing the spharmonic_pml tables. |
847 |
– |
Allocate workspace once before you call this function, then |
848 |
– |
just set up pointers as first step of this procedure rather |
849 |
– |
than mallocing. And do the same with the FST, FZT, and InvFST functions. |
850 |
– |
|
851 |
– |
ASSUMPTIONS: |
852 |
– |
1. data is strictly REAL |
853 |
– |
2. will do semi-naive algorithm for ALL orders -> change the cutoff |
854 |
– |
value if you want it to be different |
855 |
– |
|
856 |
– |
Memory requirements for Conv2Sphere |
857 |
– |
|
858 |
– |
Need space for spharmonic tables and local workspace and |
859 |
– |
scratchpad space for FST_semi |
860 |
– |
|
861 |
– |
Let legendreSize = Reduced_Naive_TableSize(bw,cutoff) + |
862 |
– |
Reduced_SpharmonicTableSize(bw,cutoff) |
863 |
– |
|
864 |
– |
Then the workspace needs to be this large: |
865 |
– |
|
866 |
– |
2 * legendreSize + |
867 |
– |
8 * (bw*bw) + 10*bw + |
868 |
– |
4 * (bw*bw) + 2*bw |
869 |
– |
|
870 |
– |
for a total of |
871 |
– |
|
872 |
– |
2 * legendreSize + |
873 |
– |
12 * (bw*bw) + 12*bw ; |
874 |
– |
|
875 |
– |
|
876 |
– |
|
877 |
– |
*/ |
878 |
– |
void Conv2Sphere_semi_memo(double *rdata, double *idata, |
879 |
– |
double *rfilter, double *ifilter, |
880 |
– |
double *rres, double *ires, |
881 |
– |
int bw, |
882 |
– |
double *workspace) |
883 |
– |
{ |
884 |
– |
int size, spharmonic_bound ; |
885 |
– |
int legendreSize, cutoff ; |
886 |
– |
double *frres, *fires, *filtrres, *filtires, *trres, *tires; |
887 |
– |
double **spharmonic_pml_table, **transpose_spharmonic_pml_table; |
888 |
– |
double *spharmonic_result_space, *transpose_spharmonic_result_space; |
889 |
– |
double *scratchpad; |
890 |
– |
|
891 |
– |
/* fftw */ |
892 |
– |
int rank, howmany_rank ; |
893 |
– |
fftw_iodim dims[1], howmany_dims[1]; |
894 |
– |
|
895 |
– |
/* forward transform stuff */ |
896 |
– |
fftw_plan dctPlan, fftPlan ; |
897 |
– |
double *weights ; |
898 |
– |
|
899 |
– |
/* inverse transform stuff */ |
900 |
– |
fftw_plan idctPlan, ifftPlan ; |
901 |
– |
|
902 |
– |
size =2*bw ; |
903 |
– |
cutoff = bw ; |
904 |
– |
legendreSize = Reduced_Naive_TableSize(bw,cutoff) + |
905 |
– |
Reduced_SpharmonicTableSize(bw,cutoff) ; |
906 |
– |
|
907 |
– |
/* assign space */ |
908 |
– |
|
909 |
– |
spharmonic_bound = legendreSize ; |
910 |
– |
|
911 |
– |
spharmonic_result_space = workspace; /* needs legendreSize */ |
912 |
– |
|
913 |
– |
transpose_spharmonic_result_space = |
914 |
– |
spharmonic_result_space + legendreSize ; /* needs legendreSize */ |
915 |
– |
|
916 |
– |
frres = transpose_spharmonic_result_space + |
917 |
– |
legendreSize ; /* needs (bw*bw) */ |
918 |
– |
fires = frres + (bw*bw); /* needs (bw*bw) */ |
919 |
– |
trres = fires + (bw*bw); /* needs (bw*bw) */ |
920 |
– |
tires = trres + (bw*bw); /* needs (bw*bw) */ |
921 |
– |
filtrres = tires + (bw*bw); /* needs bw */ |
922 |
– |
filtires = filtrres + bw; /* needs bw */ |
923 |
– |
scratchpad = filtires + bw; /* needs (8*bw^2)+(10*bw) */ |
924 |
– |
|
925 |
– |
/* allocate space, and compute, the weights for this bandwidth */ |
926 |
– |
weights = (double *) malloc(sizeof(double) * 4 * bw); |
927 |
– |
makeweights( bw, weights ); |
928 |
– |
|
929 |
– |
/* make the fftw plans */ |
930 |
– |
|
931 |
– |
/* make DCT plans -> note that I will be using the GURU |
932 |
– |
interface to execute these plans within the routines*/ |
933 |
– |
|
934 |
– |
/* forward DCT */ |
935 |
– |
dctPlan = fftw_plan_r2r_1d( 2*bw, weights, rdata, |
936 |
– |
FFTW_REDFT10, FFTW_ESTIMATE ) ; |
937 |
– |
|
938 |
– |
/* inverse DCT */ |
939 |
– |
idctPlan = fftw_plan_r2r_1d( 2*bw, weights, rdata, |
940 |
– |
FFTW_REDFT01, FFTW_ESTIMATE ); |
941 |
– |
|
942 |
– |
/* |
943 |
– |
fft "preamble" ; |
944 |
– |
note that this plan places the output in a transposed array |
945 |
– |
*/ |
946 |
– |
rank = 1 ; |
947 |
– |
dims[0].n = 2*bw ; |
948 |
– |
dims[0].is = 1 ; |
949 |
– |
dims[0].os = 2*bw ; |
950 |
– |
howmany_rank = 1 ; |
951 |
– |
howmany_dims[0].n = 2*bw ; |
952 |
– |
howmany_dims[0].is = 2*bw ; |
953 |
– |
howmany_dims[0].os = 1 ; |
954 |
– |
|
955 |
– |
/* forward fft */ |
956 |
– |
fftPlan = fftw_plan_guru_split_dft( rank, dims, |
957 |
– |
howmany_rank, howmany_dims, |
958 |
– |
rdata, idata, |
959 |
– |
workspace, workspace+(4*bw*bw), |
960 |
– |
FFTW_ESTIMATE ); |
961 |
– |
|
962 |
– |
/* |
963 |
– |
now plan for inverse fft - note that this plans assumes |
964 |
– |
that I'm working with a transposed array, e.g. the inputs |
965 |
– |
for a length 2*bw transform are placed every 2*bw apart, |
966 |
– |
the output will be consecutive entries in the array |
967 |
– |
*/ |
968 |
– |
rank = 1 ; |
969 |
– |
dims[0].n = 2*bw ; |
970 |
– |
dims[0].is = 2*bw ; |
971 |
– |
dims[0].os = 1 ; |
972 |
– |
howmany_rank = 1 ; |
973 |
– |
howmany_dims[0].n = 2*bw ; |
974 |
– |
howmany_dims[0].is = 1 ; |
975 |
– |
howmany_dims[0].os = 2*bw ; |
976 |
– |
|
977 |
– |
/* inverse fft */ |
978 |
– |
ifftPlan = fftw_plan_guru_split_dft( rank, dims, |
979 |
– |
howmany_rank, howmany_dims, |
980 |
– |
rdata, idata, |
981 |
– |
workspace, workspace+(4*bw*bw), |
982 |
– |
FFTW_ESTIMATE ); |
983 |
– |
|
984 |
– |
|
985 |
– |
/* precompute the associated Legendre fcts */ |
986 |
– |
spharmonic_pml_table = |
987 |
– |
Spharmonic_Pml_Table(bw, |
988 |
– |
spharmonic_result_space, |
989 |
– |
scratchpad); |
990 |
– |
|
991 |
– |
transpose_spharmonic_pml_table = |
992 |
– |
Transpose_Spharmonic_Pml_Table(spharmonic_pml_table, |
993 |
– |
bw, |
994 |
– |
transpose_spharmonic_result_space, |
995 |
– |
scratchpad); |
996 |
– |
FST_semi_memo(rdata, idata, |
997 |
– |
frres, fires, |
998 |
– |
bw, |
999 |
– |
spharmonic_pml_table, |
1000 |
– |
scratchpad, |
1001 |
– |
1, |
1002 |
– |
bw, |
1003 |
– |
&dctPlan, |
1004 |
– |
&fftPlan, |
1005 |
– |
weights ); |
1006 |
– |
|
1007 |
– |
FZT_semi_memo(rfilter, ifilter, |
1008 |
– |
filtrres, filtires, |
1009 |
– |
bw, |
1010 |
– |
spharmonic_pml_table[0], |
1011 |
– |
scratchpad, |
1012 |
– |
1, |
1013 |
– |
&dctPlan, |
1014 |
– |
weights ); |
1015 |
– |
|
1016 |
– |
TransMult(frres, fires, filtrres, filtires, trres, tires, bw); |
1017 |
– |
|
1018 |
– |
InvFST_semi_memo(trres, tires, |
1019 |
– |
rres, ires, |
1020 |
– |
bw, |
1021 |
– |
transpose_spharmonic_pml_table, |
1022 |
– |
scratchpad, |
1023 |
– |
1, |
1024 |
– |
bw, |
1025 |
– |
&idctPlan, |
1026 |
– |
&ifftPlan ); |
1027 |
– |
|
1028 |
– |
free( weights ) ; |
1029 |
– |
|
1030 |
– |
/*** |
1031 |
– |
have to free the memory that was allocated in |
1032 |
– |
Spharmonic_Pml_Table() and |
1033 |
– |
Transpose_Spharmonic_Pml_Table() |
1034 |
– |
***/ |
1035 |
– |
|
1036 |
– |
free(spharmonic_pml_table); |
1037 |
– |
free(transpose_spharmonic_pml_table); |
1038 |
– |
|
1039 |
– |
/* destroy plans */ |
1040 |
– |
fftw_destroy_plan( ifftPlan ) ; |
1041 |
– |
fftw_destroy_plan( fftPlan ) ; |
1042 |
– |
fftw_destroy_plan( idctPlan ) ; |
1043 |
– |
fftw_destroy_plan( dctPlan ) ; |
1044 |
– |
} |