covar test
Oli
4 years ago
parent
44a16ce9b9
commit
e626ff6c93
@ -0,0 +1,645 @@
|
|||||||
|
#include <math.h>
|
||||||
|
#include <stdio.h>
|
||||||
|
#include <time.h>
|
||||||
|
#include "chunk_array.h"
|
||||||
|
|
||||||
|
/*fast fourier transform */
|
||||||
|
/* THE COOLEY-TUKEY FAST FOURIER TRANSFORM */
|
||||||
|
/* EVALUATES COMPLEX FOURIER SERIES FOR COMPLEX OR REAL FUNCTIONS. */
|
||||||
|
/* THAT IS, IT COMPUTES */
|
||||||
|
/* FTRAN(J1,J2,...)=SUM(DATA(I1,I2,...)*W1**(I1-1)*(J1-1) */
|
||||||
|
/* *W2**(I2-1)*(J2-1)*...), */
|
||||||
|
/* WHERE W1=EXP(-2*PI*SQRT(-1)/NN(1)), W2=EXP(-2*PI*SQRT(-1)/NN(2)), */
|
||||||
|
/* ETC. AND I1 AND J1 RUN FROM 1 TO NN(1), I2 AND J2 RUN FROM 1 TO */
|
||||||
|
/* NN(2), ETC. THERE IS NO LIMIT ON THE DIMENSIONALITY (NUMBER OF */
|
||||||
|
/* SUBSCRIPTS) OF THE ARRAY OF DATA. THE PROGRAM WILL PERFORM */
|
||||||
|
/* A THREE-DIMENSIONAL FOURIER TRANSFORM AS EASILY AS A ONE-DIMEN- */
|
||||||
|
/* SIONAL ONE, THO IN A PROPORTIONATELY GREATER TIME. AN INVERSE */
|
||||||
|
/* TRANSFORM CAN BE PERFORMED, IN WHICH THE SIGN IN THE EXPONENTIALS */
|
||||||
|
/* IS +, INSTEAD OF -. IF AN INVERSE TRANSFORM IS PERFORMED UPON */
|
||||||
|
/* AN ARRAY OF TRANSFORMED DATA, THE ORIGINAL DATA WILL REAPPEAR, */
|
||||||
|
/* MULTIPLIED BY NN(1)*NN(2)*... THE ARRAY OF INPUT DATA MAY BE */
|
||||||
|
/* REAL OR COMPLEX, AT THE PROGRAMMERS OPTION, WITH A SAVING OF */
|
||||||
|
/* ABOUT THIRTY PER CENT IN RUNNING TIME FOR REAL OVER COMPLEX. */
|
||||||
|
/* (FOR FASTEST TRANSFORM OF REAL DATA, NN(1) SHOULD BE EVEN.) */
|
||||||
|
/* THE TRANSFORM VALUES ARE ALWAYS COMPLEX, AND ARE RETURNED IN THE */
|
||||||
|
/* ORIGINAL ARRAY OF DATA, REPLACING THE INPUT DATA. THE LENGTH */
|
||||||
|
/* OF EACH DIMENSION OF THE DATA ARRAY MAY BE ANY INTEGER. THE */
|
||||||
|
/* PROGRAM RUNS FASTER ON COMPOSITE INTEGERS THAN ON PRIMES, AND IS */
|
||||||
|
/* PARTICULARLY FAST ON NUMBERS RICH IN FACTORS OF TWO. */
|
||||||
|
/* TIMING IS IN FACT GIVEN BY THE FOLLOWING FORMULA. LET NTOT BE THE */
|
||||||
|
/* TOTAL NUMBER OF POINTS (REAL OR COMPLEX) IN THE DATA ARRAY, THAT */
|
||||||
|
/* IS, NTOT=NN(1)*NN(2)*... DECOMPOSE NTOT INTO ITS PRIME FACTORS, */
|
||||||
|
/* SUCH AS 2**K2 * 3**K3 * 5**K5 * ... LET SUM2 BE THE SUM OF ALL */
|
||||||
|
/* THE FACTORS OF TWO IN NTOT, THAT IS, SUM2 = 2*K2. LET SUMF BE */
|
||||||
|
/* THE SUM OF ALL OTHER FACTORS OF NTOT, THAT IS, SUMF = 3*K3+5*K5+.. */
|
||||||
|
/* THE TIME TAKEN BY A MULTIDIMENSIONAL TRANSFORM ON THESE NTOT DATA */
|
||||||
|
/* IS T = T0 + T1*NTOT + T2*NTOT*SUM2 + T3*NTOT*SUMF. FOR THE PAR- */
|
||||||
|
/* TICULAR IMPLEMENTATION FORTRAN 32 ON THE CDC 3300 (FLOATING POINT */
|
||||||
|
/* ADD TIME = SIX MICROSECONDS), */
|
||||||
|
/* T = 3000 + 600*NTOT + 50*NTOT*SUM2 + 175*NTOT*SUMF MICROSECONDS */
|
||||||
|
/* ON COMPLEX DATA. */
|
||||||
|
/* IMPLEMENTATION OF THE DEFINITION BY SUMMATION WILL RUN IN A TIME */
|
||||||
|
/* PROPORTIONAL TO NTOT**2. FOR HIGHLY COMPOSITE NTOT, THE SAVINGS */
|
||||||
|
/* OFFERED BY COOLEY-TUKEY CAN BE DRAMATIC. A MATRIX 100 BY 100 WILL */
|
||||||
|
/* BE TRANSFORMED IN TIME PROPORTIONAL TO 10000*(2+2+2+2+5+5+5+5) = */
|
||||||
|
/* 280,000 (ASSUMING T2 AND T3 TO BE ROUGHLY COMPARABLE) VERSUS */
|
||||||
|
/* 10000**2 = 100,000,000 FOR THE STRAIGHTFORWARD TECHNIQUE. */
|
||||||
|
/* THE COOLEY-TUKEY ALGORITHM PLACES TWO RESTRICTIONS UPON THE */
|
||||||
|
/* NATURE OF THE DATA BEYOND THE USUAL RESTRICTION THAT */
|
||||||
|
/* THE DATA FROM ONE CYCLE OF A PERIODIC FUNCTION. THEY ARE-- */
|
||||||
|
/* 1. THE NUMBER OF INPUT DATA AND THE NUMBER OF TRANSFORM VALUES */
|
||||||
|
/* MUST BE THE SAME. */
|
||||||
|
/* 2. CONSIDERING THE DATA TO BE IN THE TIME DOMAIN, */
|
||||||
|
/* THEY MUST BE EQUI-SPACED AT INTERVALS OF DT. FURTHER, THE TRANS- */
|
||||||
|
/* FORM VALUES, CONSIDERED TO BE IN FREQUENCY SPACE, WILL BE EQUI- */
|
||||||
|
/* SPACED FROM 0 TO 2*PI*(NN(I)-1)/(NN(I)*DT) AT INTERVALS OF */
|
||||||
|
/* 2*PI/(NN(I)*DT) FOR EACH DIMENSION OF LENGTH NN(I). OF COURSE, */
|
||||||
|
/* DT NEED NOT BE THE SAME FOR EVERY DIMENSION. */
|
||||||
|
|
||||||
|
/* THE CALLING SEQUENCE IS-- */
|
||||||
|
/* CALL FOURT(DATAR,DATAI,NN,NDIM,IFRWD,ICPLX,WORKR,WORKI) */
|
||||||
|
|
||||||
|
/* DATAR AND DATAI ARE THE ARRAYS USED TO HOLD THE REAL AND IMAGINARY */
|
||||||
|
/* PARTS OF THE INPUT DATA ON INPUT AND THE TRANSFORM VALUES ON */
|
||||||
|
/* OUTPUT. THEY ARE FLOATING POINT ARRAYS, MULTIDIMENSIONAL WITH */
|
||||||
|
/* IDENTICAL DIMENSIONALITY AND EXTENT. THE EXTENT OF EACH DIMENSION */
|
||||||
|
/* IS GIVEN IN THE INTEGER ARRAY NN, OF LENGTH NDIM. THAT IS, */
|
||||||
|
/* NDIM IS THE DIMENSIONALITY OF THE ARRAYS DATAR AND DATAI. */
|
||||||
|
/* IFRWD IS AN INTEGER USED TO INDICATE THE DIRECTION OF THE FOURIER */
|
||||||
|
/* TRANSFORM. IT IS NON-ZERO TO INDICATE A FORWARD TRANSFORM */
|
||||||
|
/* (EXPONENTIAL SIGN IS -) AND ZERO TO INDICATE AN INVERSE TRANSFORM */
|
||||||
|
/* (SIGN IS +). ICPLX IS AN INTEGER TO INDICATE WHETHER THE DATA */
|
||||||
|
/* ARE REAL OR COMPLEX. IT IS NON-ZERO FOR COMPLEX, ZERO FOR REAL. */
|
||||||
|
/* IF IT IS ZERO (REAL) THE CONTENTS OF ARRAY DATAI WILL BE ASSUMED */
|
||||||
|
/* TO BE ZERO, AND NEED NOT BE EXPLICITLY SET TO ZERO. AS EXPLAINED */
|
||||||
|
/* ABOVE, THE TRANSFORM RESULTS ARE ALWAYS COMPLEX AND ARE STORED */
|
||||||
|
/* IN DATAR AND DATAI ON RETURN. WORKR AND WORKI ARE ARRAYS USED */
|
||||||
|
/* FOR WORKING STORAGE. THEY ARE NOT NECESSARY IF ALL THE DIMENSIONS */
|
||||||
|
/* OF THE DATA ARE POWERS OF TWO. IN THIS CASE, THE ARRAYS MAY BE */
|
||||||
|
/* REPLACED BY THE NUMBER 0 IN THE CALLING SEQUENCE. THUS, USE OF */
|
||||||
|
/* POWERS OF TWO CAN FREE A GOOD DEAL OF STORAGE. IF ANY DIMENSION */
|
||||||
|
/* IS NOT A POWER OF TWO, THESE ARRAYS MUST BE SUPPLIED. THEY ARE */
|
||||||
|
/* FLOATING POINT, ONE DIMENSIONAL OF LENGTH EQUAL TO THE LARGEST */
|
||||||
|
/* ARRAY DIMENSION, THAT IS, TO THE LARGEST VALUE OF NN(I). */
|
||||||
|
/* WORKR AND WORKI, IF SUPPLIED, MUST NOT BE THE SAME ARRAYS AS DATAR */
|
||||||
|
/* OR DATAI. ALL SUBSCRIPTS OF ALL ARRAYS BEGIN AT 1. */
|
||||||
|
|
||||||
|
/* THERE ARE NO ERROR MESSAGES OR ERROR HALTS IN THIS PROGRAM. THE */
|
||||||
|
/* PROGRAM RETURNS IMMEDIATELY IF NDIM OR ANY NN(I) IS LESS THAN ONE. */
|
||||||
|
|
||||||
|
/* PROGRAM MODIFIED FROM A SUBROUTINE OF BRENNER */
|
||||||
|
/* 10-06-2000, MLR */
|
||||||
|
|
||||||
|
void fourt_covar(chunk_array_t* datar, double* datai, int nn[3], int ndim, int ifrwd, int icplx, double* workr, double* worki, int cores) {
|
||||||
|
int ifact[21], ntot, idim, np1, n, np2, m, ntwo, iff, idiv, iquot, irem, inon2, non2p, np0, nprev, icase, ifmin, i, j, jmax, np2hf, i2, i1max, i3, j3, i1, ifp1, ifp2, i2max, i1rng, istep, imin, imax, mmax, mmin, mstep, j1, j2max, j2, jmin, j3max, nhalf;
|
||||||
|
double theta, wstpr, wstpi, wminr, wmini, wr, wi, wtemp, thetm, wmstr, wmsti, twowr, sr, si, oldsr, oldsi, stmpr, stmpi, tempr, tempi, difi, difr, sumr, sumi, TWOPI = 6.283185307179586476925286766559;
|
||||||
|
double value1, valuei, valuej, valuei1, valueimin, valuei3, valuej3;
|
||||||
|
|
||||||
|
ntot = 1;
|
||||||
|
for (idim = 0; idim < ndim; idim++) {
|
||||||
|
ntot *= nn[idim];
|
||||||
|
}
|
||||||
|
|
||||||
|
chunk_array_read(datar);
|
||||||
|
|
||||||
|
/*main loop for each dimension*/
|
||||||
|
np1 = 1;
|
||||||
|
for (idim = 1; idim <= ndim; idim++) {
|
||||||
|
n = nn[idim - 1];
|
||||||
|
np2 = np1 * n;
|
||||||
|
|
||||||
|
if (n < 1) {
|
||||||
|
goto L920;
|
||||||
|
} else if (n == 1) {
|
||||||
|
goto L900;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*is n a power of 2 and if not, what are its factors*/
|
||||||
|
m = n;
|
||||||
|
ntwo = np1;
|
||||||
|
iff = 1;
|
||||||
|
idiv = 2;
|
||||||
|
|
||||||
|
L10:
|
||||||
|
iquot = m / idiv;
|
||||||
|
irem = m - idiv * iquot;
|
||||||
|
if (iquot < idiv)
|
||||||
|
goto L50;
|
||||||
|
if (irem == 0) {
|
||||||
|
ntwo *= 2;
|
||||||
|
ifact[iff] = idiv;
|
||||||
|
iff++;
|
||||||
|
m = iquot;
|
||||||
|
goto L10;
|
||||||
|
}
|
||||||
|
idiv = 3;
|
||||||
|
inon2 = iff;
|
||||||
|
|
||||||
|
L30:
|
||||||
|
iquot = m / idiv;
|
||||||
|
irem = m - idiv * iquot;
|
||||||
|
if (iquot < idiv)
|
||||||
|
goto L60;
|
||||||
|
if (irem == 0) {
|
||||||
|
ifact[iff] = idiv;
|
||||||
|
iff++;
|
||||||
|
m = iquot;
|
||||||
|
goto L30;
|
||||||
|
}
|
||||||
|
|
||||||
|
idiv += 2;
|
||||||
|
goto L30;
|
||||||
|
|
||||||
|
L50:
|
||||||
|
inon2 = iff;
|
||||||
|
if (irem != 0)
|
||||||
|
goto L60;
|
||||||
|
ntwo *= 2;
|
||||||
|
goto L70;
|
||||||
|
|
||||||
|
L60:
|
||||||
|
ifact[iff] = m;
|
||||||
|
|
||||||
|
L70:
|
||||||
|
non2p = np2 / ntwo;
|
||||||
|
|
||||||
|
/*SEPARATE FOUR CASES--
|
||||||
|
1. COMPLEX TRANSFORM
|
||||||
|
2. REAL TRANSFORM FOR THE 2ND, 3RD, ETC. DIMENSION. METHOD: TRANSFORM HALF THE DATA, SUPPLYING THE OTHER HALF BY CONJUGATE SYMMETRY.
|
||||||
|
3. REAL TRANSFORM FOR THE 1ST DIMENSION, N ODD. METHOD: SET THE IMAGINARY PARTS TO ZERO.
|
||||||
|
4. REAL TRANSFORM FOR THE 1ST DIMENSION, N EVEN. METHOD: TRANSFORM A COMPLEX ARRAY OF LENGTH N/2 WHOSE REAL PARTS ARE THE EVEN NUMBERED REAL VALUES AND WHOSE IMAGINARY PARTS ARE THE ODD-NUMBERED REAL VALUES. UNSCRAMBLE AND SUPPLY THE SECOND HALF BY CONJUGATE SYMMETRY. */
|
||||||
|
|
||||||
|
icase = 1;
|
||||||
|
ifmin = 1;
|
||||||
|
if (icplx != 0)
|
||||||
|
goto L100;
|
||||||
|
icase = 2;
|
||||||
|
if (idim > 1)
|
||||||
|
goto L100;
|
||||||
|
icase = 3;
|
||||||
|
if (ntwo <= np1)
|
||||||
|
goto L100;
|
||||||
|
icase = 4;
|
||||||
|
ifmin = 2;
|
||||||
|
ntwo /= 2;
|
||||||
|
n /= 2;
|
||||||
|
np2 /= 2;
|
||||||
|
ntot /= 2;
|
||||||
|
i = 1;
|
||||||
|
for (j = 1; j <= ntot; j++) {
|
||||||
|
chunk_array_get(datar, i, &valuei);
|
||||||
|
chunk_array_get(datar, i, &valuei1);
|
||||||
|
chunk_array_save(datar, j, valuei);
|
||||||
|
|
||||||
|
//datar[j] = datar[i];
|
||||||
|
datai[j] = valuei1;
|
||||||
|
i += 2;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*shuffle data by bit reversal, since n = 2^k. As the shuffling can be done by simple interchange, no working array is needed*/
|
||||||
|
L100:
|
||||||
|
if (non2p > 1)
|
||||||
|
goto L200;
|
||||||
|
np2hf = np2 / 2;
|
||||||
|
j = 1;
|
||||||
|
for (i2 = 1; i2 <= np2; i2 += np1) {
|
||||||
|
if (j >= i2)
|
||||||
|
goto L130;
|
||||||
|
i1max = i2 + np1 - 1;
|
||||||
|
for (i1 = i2; i1 <= i1max; i1++) {
|
||||||
|
for (i3 = i1; i3 <= ntot; i3 += np2) {
|
||||||
|
j3 = j + i3 - i2;
|
||||||
|
//tempr = datar[i3];
|
||||||
|
tempi = datai[i3];
|
||||||
|
//datar[i3] = datar[j3];
|
||||||
|
datai[i3] = datai[j3];
|
||||||
|
//datar[j3] = tempr;
|
||||||
|
datai[j3] = tempi;
|
||||||
|
|
||||||
|
chunk_array_get(datar, i3, &valuei3);
|
||||||
|
chunk_array_get(datar, j3, &valuej3);
|
||||||
|
chunk_array_save(datar, i3, valuej3);
|
||||||
|
chunk_array_save(datar, j3, valuei3);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
L130:
|
||||||
|
m = np2hf;
|
||||||
|
|
||||||
|
L140:
|
||||||
|
if (j <= m) {
|
||||||
|
j += m;
|
||||||
|
} else {
|
||||||
|
j -= m;
|
||||||
|
m /= 2;
|
||||||
|
if (m >= np1)
|
||||||
|
goto L140;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
goto L300;
|
||||||
|
|
||||||
|
/*shuffle data by digit reversal for general n*/
|
||||||
|
L200:
|
||||||
|
for (i1 = 1; i1 <= np1; i1++) {
|
||||||
|
for (i3 = i1; i3 <= ntot; i3 += np2) {
|
||||||
|
j = i3;
|
||||||
|
for (i = 1; i <= n; i++) {
|
||||||
|
if (icase != 3) {
|
||||||
|
//workr[i] = datar[j];
|
||||||
|
chunk_array_get(datar, j, &workr[i]);
|
||||||
|
worki[i] = datai[j];
|
||||||
|
} else {
|
||||||
|
chunk_array_get(datar, j, &workr[i]);
|
||||||
|
//workr[i] = datar[j];
|
||||||
|
worki[i] = 0.;
|
||||||
|
}
|
||||||
|
ifp2 = np2;
|
||||||
|
iff = ifmin;
|
||||||
|
L250:
|
||||||
|
ifp1 = ifp2 / ifact[iff];
|
||||||
|
j += ifp1;
|
||||||
|
if (j >= i3 + ifp2) {
|
||||||
|
j -= ifp2;
|
||||||
|
ifp2 = ifp1;
|
||||||
|
iff += 1;
|
||||||
|
if (ifp2 > np1)
|
||||||
|
goto L250;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
i2max = i3 + np2 - np1;
|
||||||
|
i = 1;
|
||||||
|
for (i2 = i3; i2 <= i2max; i2 += np1) {
|
||||||
|
chunk_array_save(datar, i2, workr[i]);
|
||||||
|
//datar[i2] = workr[i];
|
||||||
|
datai[i2] = worki[i];
|
||||||
|
i++;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*special case-- W=1*/
|
||||||
|
L300:
|
||||||
|
i1rng = np1;
|
||||||
|
if (icase == 2)
|
||||||
|
i1rng = np0 * (1 + nprev / 2);
|
||||||
|
if (ntwo <= np1)
|
||||||
|
goto L600;
|
||||||
|
for (i1 = 1; i1 <= i1rng; i1++) {
|
||||||
|
imin = np1 + i1;
|
||||||
|
istep = 2 * np1;
|
||||||
|
goto L330;
|
||||||
|
|
||||||
|
L310:
|
||||||
|
j = i1;
|
||||||
|
for (i = imin; i <= ntot; i += istep) {
|
||||||
|
//tempr = datar[i];
|
||||||
|
tempi = datai[i];
|
||||||
|
//datar[i] = datar[j] - tempr;
|
||||||
|
datai[i] = datai[j] - tempi;
|
||||||
|
//datar[j] = datar[j] + tempr;
|
||||||
|
datai[j] = datai[j] + tempi;
|
||||||
|
|
||||||
|
chunk_array_get(datar, i, &valuei);
|
||||||
|
chunk_array_get(datar, j, &valuej);
|
||||||
|
|
||||||
|
chunk_array_save(datar, i, valuej - valuei);
|
||||||
|
chunk_array_save(datar, j, valuej + valuei);
|
||||||
|
|
||||||
|
j += istep;
|
||||||
|
}
|
||||||
|
imin = 2 * imin - i1;
|
||||||
|
istep *= 2;
|
||||||
|
|
||||||
|
L330:
|
||||||
|
if (istep <= ntwo)
|
||||||
|
goto L310;
|
||||||
|
|
||||||
|
/*special case-- W = -sqrt(-1)*/
|
||||||
|
imin = 3 * np1 + i1;
|
||||||
|
istep = 4 * np1;
|
||||||
|
goto L420;
|
||||||
|
|
||||||
|
L400:
|
||||||
|
j = imin - istep / 2;
|
||||||
|
for (i = imin; i <= ntot; i += istep) {
|
||||||
|
if (ifrwd != 0) {
|
||||||
|
tempr = datai[i];
|
||||||
|
//tempi = -datar[i];
|
||||||
|
chunk_array_get(datar, i, &tempi);
|
||||||
|
tempi = -tempi;
|
||||||
|
} else {
|
||||||
|
tempr = -datai[i];
|
||||||
|
//tempi = datar[i];
|
||||||
|
chunk_array_get(datar, i, &tempi);
|
||||||
|
}
|
||||||
|
|
||||||
|
chunk_array_get(datar, j, &valuej);
|
||||||
|
chunk_array_save(datar, i, valuej - tempr);
|
||||||
|
chunk_array_save(datar, j, valuej - tempr);
|
||||||
|
|
||||||
|
//datar[i] = datar[j] - tempr;
|
||||||
|
datai[i] = datai[j] - tempi;
|
||||||
|
//datar[j] += tempr;
|
||||||
|
datai[j] += tempi;
|
||||||
|
j += istep;
|
||||||
|
}
|
||||||
|
|
||||||
|
imin = 2 * imin - i1;
|
||||||
|
istep *= 2;
|
||||||
|
|
||||||
|
L420:
|
||||||
|
if (istep <= ntwo)
|
||||||
|
goto L400;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*main loop for factors of 2. W=EXP(-2*PI*SQRT(-1)*m/mmax) */
|
||||||
|
theta = -TWOPI / 8.;
|
||||||
|
wstpr = 0.;
|
||||||
|
wstpi = -1.;
|
||||||
|
if (ifrwd == 0) {
|
||||||
|
theta = -theta;
|
||||||
|
wstpi = 1.;
|
||||||
|
}
|
||||||
|
mmax = 8 * np1;
|
||||||
|
goto L540;
|
||||||
|
|
||||||
|
L500:
|
||||||
|
wminr = cos(theta);
|
||||||
|
wmini = sin(theta);
|
||||||
|
wr = wminr;
|
||||||
|
wi = wmini;
|
||||||
|
mmin = mmax / 2 + np1;
|
||||||
|
mstep = np1 * 2;
|
||||||
|
for (m = mmin; m <= mmax; m += mstep) {
|
||||||
|
for (i1 = 1; i1 <= i1rng; i1++) {
|
||||||
|
istep = mmax;
|
||||||
|
imin = m + i1;
|
||||||
|
L510:
|
||||||
|
j = imin - istep / 2;
|
||||||
|
for (i = imin; i <= ntot; i += istep) {
|
||||||
|
double valuei, valuej;
|
||||||
|
chunk_array_get(datar, i, &valuei);
|
||||||
|
chunk_array_get(datar, j, &valuej);
|
||||||
|
tempr = valuei * wr - datai[i] * wi;
|
||||||
|
tempi = valuei * wi + datai[i] * wr;
|
||||||
|
chunk_array_save(datar, i, valuej - tempr);
|
||||||
|
//datar[i] = valuej - tempr;
|
||||||
|
datai[i] = datai[j] - tempi;
|
||||||
|
chunk_array_save(datar, i, valuej + tempr);
|
||||||
|
//datar[j] += tempr;
|
||||||
|
datai[j] += tempi;
|
||||||
|
j += istep;
|
||||||
|
}
|
||||||
|
imin = 2 * imin - i1;
|
||||||
|
istep *= 2;
|
||||||
|
if (istep <= ntwo)
|
||||||
|
goto L510;
|
||||||
|
}
|
||||||
|
wtemp = wr * wstpi;
|
||||||
|
wr = wr * wstpr - wi * wstpi;
|
||||||
|
wi = wi * wstpr + wtemp;
|
||||||
|
}
|
||||||
|
wstpr = wminr;
|
||||||
|
wstpi = wmini;
|
||||||
|
theta /= 2.;
|
||||||
|
mmax += mmax;
|
||||||
|
L540:
|
||||||
|
if (mmax <= ntwo)
|
||||||
|
goto L500;
|
||||||
|
|
||||||
|
/*main loop for factors not equal to 2-- W=EXP(-2*PI*SQRT(-1)*(j2-i3)/ifp2)*/
|
||||||
|
L600:
|
||||||
|
if (non2p <= 1)
|
||||||
|
goto L700;
|
||||||
|
ifp1 = ntwo;
|
||||||
|
iff = inon2;
|
||||||
|
L610:
|
||||||
|
ifp2 = ifact[iff] * ifp1;
|
||||||
|
theta = -TWOPI / (double)ifact[iff];
|
||||||
|
if (ifrwd == 0)
|
||||||
|
theta = -theta;
|
||||||
|
thetm = theta / (double)(ifp1 / np1);
|
||||||
|
wstpr = cos(theta);
|
||||||
|
wstpi = sin(theta);
|
||||||
|
wmstr = cos(thetm);
|
||||||
|
wmsti = sin(thetm);
|
||||||
|
wminr = 1.;
|
||||||
|
wmini = 0.;
|
||||||
|
|
||||||
|
for (j1 = 1; j1 <= ifp1; j1 += np1) {
|
||||||
|
i1max = j1 + i1rng - 1;
|
||||||
|
for (i1 = j1; i1 <= i1max; i1++) {
|
||||||
|
for (i3 = i1; i3 <= ntot; i3 += np2) {
|
||||||
|
i = 1;
|
||||||
|
wr = wminr;
|
||||||
|
wi = wmini;
|
||||||
|
j2max = i3 + ifp2 - ifp1;
|
||||||
|
for (j2 = i3; j2 <= j2max; j2 += ifp1) {
|
||||||
|
twowr = 2. * wr;
|
||||||
|
jmin = i3;
|
||||||
|
j3max = j2 + np2 - ifp2;
|
||||||
|
for (j3 = j2; j3 <= j3max; j3 += ifp2) {
|
||||||
|
j = jmin + ifp2 - ifp1;
|
||||||
|
//sr = datar[j];
|
||||||
|
chunk_array_get(datar, j, &sr);
|
||||||
|
si = datai[j];
|
||||||
|
oldsr = 0.;
|
||||||
|
oldsi = 0.;
|
||||||
|
j -= ifp1;
|
||||||
|
L620:
|
||||||
|
stmpr = sr;
|
||||||
|
stmpi = si;
|
||||||
|
chunk_array_get(datar, j, &valuej);
|
||||||
|
sr = twowr * sr - oldsr + valuej;
|
||||||
|
si = twowr * si - oldsi + datai[j];
|
||||||
|
oldsr = stmpr;
|
||||||
|
oldsi = stmpi;
|
||||||
|
j -= ifp1;
|
||||||
|
if (j > jmin)
|
||||||
|
goto L620;
|
||||||
|
workr[i] = wr * sr - wi * si - oldsr + valuej;
|
||||||
|
worki[i] = wi * sr + wr * si - oldsi + datai[j];
|
||||||
|
jmin += ifp2;
|
||||||
|
i++;
|
||||||
|
}
|
||||||
|
wtemp = wr * wstpi;
|
||||||
|
wr = wr * wstpr - wi * wstpi;
|
||||||
|
wi = wi * wstpr + wtemp;
|
||||||
|
}
|
||||||
|
i = 1;
|
||||||
|
for (j2 = i3; j2 <= j2max; j2 += ifp1) {
|
||||||
|
j3max = j2 + np2 - ifp2;
|
||||||
|
for (j3 = j2; j3 <= j3max; j3 += ifp2) {
|
||||||
|
//datar[j3] = workr[i];
|
||||||
|
chunk_array_save(datar, j3, workr[i]);
|
||||||
|
datai[j3] = worki[i];
|
||||||
|
i++;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
wtemp = wminr * wmsti;
|
||||||
|
wminr = wminr * wmstr - wmini * wmsti;
|
||||||
|
wmini = wmini * wmstr + wtemp;
|
||||||
|
}
|
||||||
|
iff++;
|
||||||
|
ifp1 = ifp2;
|
||||||
|
if (ifp1 < np2)
|
||||||
|
goto L610;
|
||||||
|
|
||||||
|
/*complete a real transform in the 1st dimension, n even, by conjugate symmetries*/
|
||||||
|
L700:
|
||||||
|
switch (icase) {
|
||||||
|
case 1:
|
||||||
|
goto L900;
|
||||||
|
break;
|
||||||
|
case 2:
|
||||||
|
goto L800;
|
||||||
|
break;
|
||||||
|
case 3:
|
||||||
|
goto L900;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
|
||||||
|
nhalf = n;
|
||||||
|
n += n;
|
||||||
|
theta = -TWOPI / (double)n;
|
||||||
|
if (ifrwd == 0)
|
||||||
|
theta = -theta;
|
||||||
|
wstpr = cos(theta);
|
||||||
|
wstpi = sin(theta);
|
||||||
|
wr = wstpr;
|
||||||
|
wi = wstpi;
|
||||||
|
imin = 2;
|
||||||
|
jmin = nhalf;
|
||||||
|
goto L725;
|
||||||
|
L710:
|
||||||
|
j = jmin;
|
||||||
|
for (i = imin; i <= ntot; i += np2) {
|
||||||
|
double valuei, valuej;
|
||||||
|
chunk_array_get(datar, i, &valuei);
|
||||||
|
chunk_array_get(datar, j, &valuej);
|
||||||
|
sumr = (valuei + valuej) / 2.;
|
||||||
|
sumi = (datai[i] + datai[j]) / 2.;
|
||||||
|
difr = (valuei - valuej) / 2.;
|
||||||
|
difi = (datai[i] - datai[j]) / 2.;
|
||||||
|
tempr = wr * sumi + wi * difr;
|
||||||
|
tempi = wi * sumi - wr * difr;
|
||||||
|
chunk_array_save(datar, i, sumr + tempr);
|
||||||
|
//datar[i] = sumr + tempr;
|
||||||
|
datai[i] = difi + tempi;
|
||||||
|
chunk_array_save(datar, j, sumr - tempr);
|
||||||
|
//datar[j] = sumr - tempr;
|
||||||
|
datai[j] = tempi - difi;
|
||||||
|
j += np2;
|
||||||
|
}
|
||||||
|
imin++;
|
||||||
|
jmin--;
|
||||||
|
wtemp = wr * wstpi;
|
||||||
|
wr = wr * wstpr - wi * wstpi;
|
||||||
|
wi = wi * wstpr + wtemp;
|
||||||
|
L725:
|
||||||
|
if (imin < jmin) {
|
||||||
|
goto L710;
|
||||||
|
} else if (imin > jmin) {
|
||||||
|
goto L740;
|
||||||
|
}
|
||||||
|
if (ifrwd == 0)
|
||||||
|
goto L740;
|
||||||
|
for (i = imin; i <= ntot; i += np2) {
|
||||||
|
datai[i] = -datai[i];
|
||||||
|
}
|
||||||
|
L740:
|
||||||
|
np2 *= 2;
|
||||||
|
ntot *= 2;
|
||||||
|
j = ntot + 1;
|
||||||
|
imax = ntot / 2 + 1;
|
||||||
|
L745:
|
||||||
|
imin = imax - nhalf;
|
||||||
|
i = imin;
|
||||||
|
goto L755;
|
||||||
|
L750:
|
||||||
|
//datar[j] = datar[i];
|
||||||
|
chunk_array_get(datar, i, &valuei);
|
||||||
|
chunk_array_save(datar, j, valuei);
|
||||||
|
datai[j] = -datai[i];
|
||||||
|
L755:
|
||||||
|
i++;
|
||||||
|
j--;
|
||||||
|
if (i < imax)
|
||||||
|
goto L750;
|
||||||
|
|
||||||
|
chunk_array_get(datar, imin, &valueimin);
|
||||||
|
chunk_array_save(datar, j, valueimin - datai[imin]);
|
||||||
|
//datar[j] = datar[imin] - datai[imin];
|
||||||
|
datai[j] = 0.;
|
||||||
|
if (i >= j) {
|
||||||
|
goto L780;
|
||||||
|
} else {
|
||||||
|
goto L770;
|
||||||
|
}
|
||||||
|
L765:
|
||||||
|
//datar[j] = datar[i];
|
||||||
|
chunk_array_get(datar, i, &valuei);
|
||||||
|
chunk_array_save(datar, j, valuei);
|
||||||
|
datai[j] = datai[i];
|
||||||
|
L770:
|
||||||
|
i--;
|
||||||
|
j--;
|
||||||
|
if (i > imin)
|
||||||
|
goto L765;
|
||||||
|
//datar[j] = datar[imin] + datai[imin];
|
||||||
|
chunk_array_get(datar, imin, &valueimin);
|
||||||
|
chunk_array_save(datar, j, valueimin - datai[imin]);
|
||||||
|
datai[j] = 0.;
|
||||||
|
imax = imin;
|
||||||
|
goto L745;
|
||||||
|
L780:
|
||||||
|
chunk_array_get(datar, 1, &value1);
|
||||||
|
chunk_array_save(datar, 1, value1 + datai[1]);
|
||||||
|
//datar[1] += datai[1];
|
||||||
|
datai[1] = 0.;
|
||||||
|
goto L900;
|
||||||
|
|
||||||
|
/*complete a real transform for the 2nd, 3rd, ... dimension by conjugate symmetries*/
|
||||||
|
L800:
|
||||||
|
if (nprev <= 2)
|
||||||
|
goto L900;
|
||||||
|
for (i3 = 1; i3 <= ntot; i3 += np2) {
|
||||||
|
i2max = i3 + np2 - np1;
|
||||||
|
for (i2 = i3; i2 <= i2max; i2 += np1) {
|
||||||
|
imax = i2 + np1 - 1;
|
||||||
|
imin = i2 + i1rng;
|
||||||
|
jmax = 2 * i3 + np1 - imin;
|
||||||
|
if (i2 > i3)
|
||||||
|
jmax += np2;
|
||||||
|
if (idim > 2) {
|
||||||
|
j = jmax + np0;
|
||||||
|
for (i = imin; i <= imax; i++) {
|
||||||
|
//datar[i] = datar[j];
|
||||||
|
chunk_array_get(datar, j, &valuej);
|
||||||
|
chunk_array_save(datar, i, valuej);
|
||||||
|
datai[i] = -datai[j];
|
||||||
|
j--;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
j = jmax;
|
||||||
|
for (i = imin; i <= imax; i += np0) {
|
||||||
|
//datar[i] = datar[j];
|
||||||
|
chunk_array_get(datar, j, &valuej);
|
||||||
|
chunk_array_save(datar, i, valuej);
|
||||||
|
datai[i] = -datai[j];
|
||||||
|
j -= np0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*end of loop on each dimension*/
|
||||||
|
L900:
|
||||||
|
np0 = np1;
|
||||||
|
np1 = np2;
|
||||||
|
nprev = n;
|
||||||
|
}
|
||||||
|
L920: return;
|
||||||
|
}
|
||||||
Loading…
Reference in New Issue