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subroutine dfftmx(a, b, ntot, n, nspan, isn, m, kt, wt, ck, bt,
* sk, np, nfac)
c
implicit double precision(a-h,o-z)
dimension a(*), b(*), wt(*), ck(*), bt(*), sk(*), np(*), nfac(*)
c
inc = abs(isn)
nt = inc*ntot
ks = inc*nspan
rad = atan(1.0d+0)
s72 = rad/0.6250d+0
c72 = cos(s72)
s72 = sin(s72)
s120 = sqrt(0.750d+0)
if (isn.gt.0) go to 10
s72 = -s72
s120 = -s120
rad = -rad
go to 30
c
c scale by 1/n for isn .gt. 0
c
10 ak = 1.0d+0/dble(n)
do 20 j=1,nt,inc
a(j) = a(j)*ak
b(j) = b(j)*ak
20 continue
c
30 kspan = ks
nn = nt - inc
jc = ks/n
c
c sin, cos values are re-initialized each lim steps
c
lim = 32
klim = lim*jc
i = 0
jf = 0
maxf = m - kt
maxf = nfac(maxf)
if (kt.gt.0) maxf = max(nfac(kt),maxf)
c
c compute fourier transform
c
40 dr = 8.0d+0*dble(jc)/dble(kspan)
cd = 2.0d+0*sin(0.50d+0*dr*rad)**2
sd = sin(dr*rad)
kk = 1
i = i + 1
if (nfac(i).ne.2) go to 110
c
c transform for factor of 2 (including rotation factor)
c
kspan = kspan/2
k1 = kspan + 2
50 k2 = kk + kspan
ak = a(k2)
bk = b(k2)
a(k2) = a(kk) - ak
b(k2) = b(kk) - bk
a(kk) = a(kk) + ak
b(kk) = b(kk) + bk
kk = k2 + kspan
if (kk.le.nn) go to 50
kk = kk - nn
if (kk.le.jc) go to 50
if (kk.gt.kspan) go to 350
60 c1 = 1.0d+0- cd
s1 = sd
mm = min(k1/2,klim)
go to 80
70 ak = c1 - (cd*c1+sd*s1)
s1 = (sd*c1-cd*s1) + s1
c
c the following three statements compensate for truncation
c error. if rounded arithmetic is used, substitute
c c1=ak
c
c1 = 0.50d+0/(ak**2+s1**2) + 0.50d+0
s1 = c1*s1
c1 = c1*ak
80 k2 = kk + kspan
ak = a(kk) - a(k2)
bk = b(kk) - b(k2)
a(kk) = a(kk) + a(k2)
b(kk) = b(kk) + b(k2)
a(k2) = c1*ak - s1*bk
b(k2) = s1*ak + c1*bk
kk = k2 + kspan
if (kk.lt.nt) go to 80
k2 = kk - nt
c1 = -c1
kk = k1 - k2
if (kk.gt.k2) go to 80
kk = kk + jc
if (kk.le.mm) go to 70
if (kk.lt.k2) go to 90
k1 = k1 + inc + inc
kk = (k1-kspan)/2 + jc
if (kk.le.jc+jc) go to 60
go to 40
90 s1 = dble((kk-1)/jc)*dr*rad
c1 = cos(s1)
s1 = sin(s1)
mm = min(k1/2,mm+klim)
go to 80
c
c transform for factor of 3 (optional code)
c
100 k1 = kk + kspan
k2 = k1 + kspan
ak = a(kk)
bk = b(kk)
aj = a(k1) + a(k2)
bj = b(k1) + b(k2)
a(kk) = ak + aj
b(kk) = bk + bj
ak = -0.50d+0*aj + ak
bk = -0.50d+0*bj + bk
aj = (a(k1)-a(k2))*s120
bj = (b(k1)-b(k2))*s120
a(k1) = ak - bj
b(k1) = bk + aj
a(k2) = ak + bj
b(k2) = bk - aj
kk = k2 + kspan
if (kk.lt.nn) go to 100
kk = kk - nn
if (kk.le.kspan) go to 100
go to 290
c
c transform for factor of 4
c
110 if (nfac(i).ne.4) go to 230
kspnn = kspan
kspan = kspan/4
120 c1 = 1.0d+0
s1 = 0.0d+0
mm = min(kspan,klim)
go to 150
130 c2 = c1 - (cd*c1+sd*s1)
s1 = (sd*c1-cd*s1) + s1
c
c the following three statements compensate for truncation
c error. if rounded arithmetic is used, substitute
c c1=c2
c
c1 = 0.50d+0/(c2**2+s1**2) + 0.50d+0
s1 = c1*s1
c1 = c1*c2
140 c2 = c1**2 - s1**2
s2 = c1*s1*2.0
c3 = c2*c1 - s2*s1
s3 = c2*s1 + s2*c1
150 k1 = kk + kspan
k2 = k1 + kspan
k3 = k2 + kspan
akp = a(kk) + a(k2)
akm = a(kk) - a(k2)
ajp = a(k1) + a(k3)
ajm = a(k1) - a(k3)
a(kk) = akp + ajp
ajp = akp - ajp
bkp = b(kk) + b(k2)
bkm = b(kk) - b(k2)
bjp = b(k1) + b(k3)
bjm = b(k1) - b(k3)
b(kk) = bkp + bjp
bjp = bkp - bjp
if (isn.lt.0) go to 180
akp = akm - bjm
akm = akm + bjm
bkp = bkm + ajm
bkm = bkm - ajm
if (s1.eq.0.0d+0) go to 190
160 a(k1) = akp*c1 - bkp*s1
b(k1) = akp*s1 + bkp*c1
a(k2) = ajp*c2 - bjp*s2
b(k2) = ajp*s2 + bjp*c2
a(k3) = akm*c3 - bkm*s3
b(k3) = akm*s3 + bkm*c3
kk = k3 + kspan
if (kk.le.nt) go to 150
170 kk = kk - nt + jc
if (kk.le.mm) go to 130
c MODIF HERE (WAS .lt.)
if (kk.le.kspan) go to 200
kk = kk - kspan + inc
if (kk.le.jc) go to 120
if (kspan.eq.jc) go to 350
go to 40
180 akp = akm + bjm
akm = akm - bjm
bkp = bkm - ajm
bkm = bkm + ajm
if (s1.ne.0.0d+0) go to 160
190 a(k1) = akp
b(k1) = bkp
a(k2) = ajp
b(k2) = bjp
a(k3) = akm
b(k3) = bkm
kk = k3 + kspan
if (kk.le.nt) go to 150
go to 170
200 s1 = dble((kk-1)/jc)*dr*rad
c1 = cos(s1)
s1 = sin(s1)
mm = min(kspan,mm+klim)
go to 140
c
c transform for factor of 5 (optional code)
c
210 c2 = c72**2 - s72**2
s2 = 2.0d+0*c72*s72
220 k1 = kk + kspan
k2 = k1 + kspan
k3 = k2 + kspan
k4 = k3 + kspan
akp = a(k1) + a(k4)
akm = a(k1) - a(k4)
bkp = b(k1) + b(k4)
bkm = b(k1) - b(k4)
ajp = a(k2) + a(k3)
ajm = a(k2) - a(k3)
bjp = b(k2) + b(k3)
bjm = b(k2) - b(k3)
aa = a(kk)
bb = b(kk)
a(kk) = aa + akp + ajp
b(kk) = bb + bkp + bjp
ak = akp*c72 + ajp*c2 + aa
bk = bkp*c72 + bjp*c2 + bb
aj = akm*s72 + ajm*s2
bj = bkm*s72 + bjm*s2
a(k1) = ak - bj
a(k4) = ak + bj
b(k1) = bk + aj
b(k4) = bk - aj
ak = akp*c2 + ajp*c72 + aa
bk = bkp*c2 + bjp*c72 + bb
aj = akm*s2 - ajm*s72
bj = bkm*s2 - bjm*s72
a(k2) = ak - bj
a(k3) = ak + bj
b(k2) = bk + aj
b(k3) = bk - aj
kk = k4 + kspan
if (kk.lt.nn) go to 220
kk = kk - nn
if (kk.le.kspan) go to 220
go to 290
c
c transform for odd factors
c
230 k = nfac(i)
kspnn = kspan
kspan = kspan/k
if (k.eq.3) go to 100
if (k.eq.5) go to 210
if (k.eq.jf) go to 250
jf = k
s1 = rad/(dble(k)/8.0d+0)
c1 = cos(s1)
s1 = sin(s1)
ck(jf) = 1.0d+0
sk(jf) = 0.0d+0
j = 1
240 ck(j) = ck(k)*c1 + sk(k)*s1
sk(j) = ck(k)*s1 - sk(k)*c1
k = k - 1
ck(k) = ck(j)
sk(k) = -sk(j)
j = j + 1
if (j.lt.k) go to 240
250 k1 = kk
k2 = kk + kspnn
aa = a(kk)
bb = b(kk)
ak = aa
bk = bb
j = 1
k1 = k1 + kspan
260 k2 = k2 - kspan
j = j + 1
wt(j) = a(k1) + a(k2)
ak = wt(j) + ak
bt(j) = b(k1) + b(k2)
bk = bt(j) + bk
j = j + 1
wt(j) = a(k1) - a(k2)
bt(j) = b(k1) - b(k2)
k1 = k1 + kspan
if (k1.lt.k2) go to 260
a(kk) = ak
b(kk) = bk
k1 = kk
k2 = kk + kspnn
j = 1
270 k1 = k1 + kspan
k2 = k2 - kspan
jj = j
ak = aa
bk = bb
aj = 0.0d+0
bj = 0.0d+0
k = 1
280 k = k + 1
ak = wt(k)*ck(jj) + ak
bk = bt(k)*ck(jj) + bk
k = k + 1
aj = wt(k)*sk(jj) + aj
bj = bt(k)*sk(jj) + bj
jj = jj + j
if (jj.gt.jf) jj = jj - jf
if (k.lt.jf) go to 280
k = jf - j
a(k1) = ak - bj
b(k1) = bk + aj
a(k2) = ak + bj
b(k2) = bk - aj
j = j + 1
if (j.lt.k) go to 270
kk = kk + kspnn
if (kk.le.nn) go to 250
kk = kk - nn
if (kk.le.kspan) go to 250
c
c multiply by rotation factor (except for factors of 2 and 4)
c
290 if (i.eq.m) go to 350
kk = jc + 1
300 c2 = 1.0d+0- cd
s1 = sd
mm = min(kspan,klim)
go to 320
310 continue
c2 = c1 - (cd*c1+sd*s1)
s1 = s1 + (sd*c1-cd*s1)
c
c the following three statements compensate for truncation
c error. if rounded arithmetic is used, they may
c be deleted.
c
c1 = 0.50d+0/(c2**2+s1**2) + 0.50d+0
s1 = c1*s1
c2 = c1*c2
320 c1 = c2
s2 = s1
kk = kk + kspan
330 ak = a(kk)
a(kk) = c2*ak - s2*b(kk)
b(kk) = s2*ak + c2*b(kk)
kk = kk + kspnn
if (kk.le.nt) go to 330
ak = s1*s2
s2 = s1*c2 + c1*s2
c2 = c1*c2 - ak
kk = kk - nt + kspan
if (kk.le.kspnn) go to 330
kk = kk - kspnn + jc
if (kk.le.mm) go to 310
c MODIFICATION OF ORIGINAL CODE:
if (kk.le.kspan) go to 340
c SINGLETON's CODE was:
c if (kk.lt.kspan) go to 340
kk = kk - kspan + jc + inc
if (kk.le.jc+jc) go to 300
go to 40
340 s1 = dble((kk-1)/jc)*dr*rad
c2 = cos(s1)
s1 = sin(s1)
mm = min(kspan,mm+klim)
go to 320
c
c permute the results to normal order---done in two stages
c permutation for square factors of n
c
350 np(1) = ks
if (kt.eq.0) go to 440
k = kt + kt + 1
if (m.lt.k) k = k - 1
j = 1
np(k+1) = jc
360 np(j+1) = np(j)/nfac(j)
np(k) = np(k+1)*nfac(j)
j = j + 1
k = k - 1
if (j.lt.k) go to 360
k3 = np(k+1)
kspan = np(2)
kk = jc + 1
k2 = kspan + 1
j = 1
if (n.ne.ntot) go to 400
c
c permutation for single-variate transform (optional code)
c
370 ak = a(kk)
a(kk) = a(k2)
a(k2) = ak
bk = b(kk)
b(kk) = b(k2)
b(k2) = bk
kk = kk + inc
k2 = kspan + k2
if (k2.lt.ks) go to 370
380 k2 = k2 - np(j)
j = j + 1
k2 = np(j+1) + k2
if (k2.gt.np(j)) go to 380
j = 1
390 if (kk.lt.k2) go to 370
kk = kk + inc
k2 = kspan + k2
if (k2.lt.ks) go to 390
if (kk.lt.ks) go to 380
jc = k3
go to 440
c
c permutation for multivariate transform
c
400 k = kk + jc
410 ak = a(kk)
a(kk) = a(k2)
a(k2) = ak
bk = b(kk)
b(kk) = b(k2)
b(k2) = bk
kk = kk + inc
k2 = k2 + inc
if (kk.lt.k) go to 410
kk = kk + ks - jc
k2 = k2 + ks - jc
if (kk.lt.nt) go to 400
k2 = k2 - nt + kspan
kk = kk - nt + jc
if (k2.lt.ks) go to 400
420 k2 = k2 - np(j)
j = j + 1
k2 = np(j+1) + k2
if (k2.gt.np(j)) go to 420
j = 1
430 if (kk.lt.k2) go to 400
kk = kk + jc
k2 = kspan + k2
if (k2.lt.ks) go to 430
if (kk.lt.ks) go to 420
jc = k3
440 if (2*kt+1.ge.m) return
kspnn = np(kt+1)
c
c permutation for square-free factors of n
c
j = m - kt
nfac(j+1) = 1
450 nfac(j) = nfac(j)*nfac(j+1)
j = j - 1
if (j.ne.kt) go to 450
kt = kt + 1
nn = nfac(kt) - 1
jj = 0
j = 0
go to 480
460 jj = jj - k2
k2 = kk
k = k + 1
kk = nfac(k)
470 jj = kk + jj
if (jj.ge.k2) go to 460
np(j) = jj
480 k2 = nfac(kt)
k = kt + 1
kk = nfac(k)
j = j + 1
if (j.le.nn) go to 470
c
c determine the permutation cycles of length greater than 1
c
j = 0
go to 500
490 k = kk
kk = np(k)
np(k) = -kk
if (kk.ne.j) go to 490
k3 = kk
500 j = j + 1
kk = np(j)
if (kk.lt.0) go to 500
if (kk.ne.j) go to 490
np(j) = -j
if (j.ne.nn) go to 500
maxf = inc*maxf
c
c reorder a and b, following the permutation cycles
c
go to 570
510 j = j - 1
if (np(j).lt.0) go to 510
jj = jc
520 kspan = jj
if (jj.gt.maxf) kspan = maxf
jj = jj - kspan
k = np(j)
kk = jc*k + i + jj
k1 = kk + kspan
k2 = 0
530 k2 = k2 + 1
wt(k2) = a(k1)
bt(k2) = b(k1)
k1 = k1 - inc
if (k1.ne.kk) go to 530
540 k1 = kk + kspan
k2 = k1 - jc*(k+np(k))
k = -np(k)
550 a(k1) = a(k2)
b(k1) = b(k2)
k1 = k1 - inc
k2 = k2 - inc
if (k1.ne.kk) go to 550
kk = k2
if (k.ne.j) go to 540
k1 = kk + kspan
k2 = 0
560 k2 = k2 + 1
a(k1) = wt(k2)
b(k1) = bt(k2)
k1 = k1 - inc
if (k1.ne.kk) go to 560
if (jj.ne.0) go to 520
if (j.ne.1) go to 510
570 j = k3 + 1
nt = nt - kspnn
i = nt - inc + 1
if (nt.ge.0) go to 510
return
end
|
