| 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 |
– |
} |
