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test.f
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test.f
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PROGRAM TSTFFT
C
C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
C
C VERSION 4 APRIL 1985
C
C A TEST DRIVER FOR
C A PACKAGE OF FORTRAN SUBPROGRAMS FOR THE FAST FOURIER
C TRANSFORM OF PERIODIC AND OTHER SYMMETRIC SEQUENCES
C
C BY
C
C PAUL N SWARZTRAUBER
C
C NATIONAL CENTER FOR ATMOSPHERIC RESEARCH BOULDER,COLORADO 80307
C
C WHICH IS SPONSORED BY THE NATIONAL SCIENCE FOUNDATION
C
C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
C
C
C THIS PROGRAM TESTS THE PACKAGE OF FAST FOURIER
C TRANSFORMS FOR BOTH COMPLEX AND REAL PERIODIC SEQUENCES AND
C CERTIAN OTHER SYMMETRIC SEQUENCES THAT ARE LISTED BELOW.
C
C 1. RFFTI INITIALIZE RFFTF AND RFFTB
C 2. RFFTF FORWARD TRANSFORM OF A REAL PERIODIC SEQUENCE
C 3. RFFTB BACKWARD TRANSFORM OF A REAL COEFFICIENT ARRAY
C
C 4. EZFFTI INITIALIZE EZFFTF AND EZFFTB
C 5. EZFFTF A SIMPLIFIED REAL PERIODIC FORWARD TRANSFORM
C 6. EZFFTB A SIMPLIFIED REAL PERIODIC BACKWARD TRANSFORM
C
C 7. SINTI INITIALIZE SINT
C 8. SINT SINE TRANSFORM OF A REAL ODD SEQUENCE
C
C 9. COSTI INITIALIZE COST
C 10. COST COSINE TRANSFORM OF A REAL EVEN SEQUENCE
C
C 11. SINQI INITIALIZE SINQF AND SINQB
C 12. SINQF FORWARD SINE TRANSFORM WITH ODD WAVE NUMBERS
C 13. SINQB UNNORMALIZED INVERSE OF SINQF
C
C 14. COSQI INITIALIZE COSQF AND COSQB
C 15. COSQF FORWARD COSINE TRANSFORM WITH ODD WAVE NUMBERS
C 16. COSQB UNNORMALIZED INVERSE OF COSQF
C
C 17. CFFTI INITIALIZE CFFTF AND CFFTB
C 18. CFFTF FORWARD TRANSFORM OF A COMPLEX PERIODIC SEQUENCE
C 19. CFFTB UNNORMALIZED INVERSE OF CFFTF
C *** HACKED BY HCP FOR THE DOUBLE PREC. VERSION NOVEMEMBER 1999
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION ND(10) ,X(200) ,Y(200) ,W(2000) ,
1 A(100) ,B(100) ,AH(100) ,BH(100) ,
2 XH(200) ,CX(200) ,CY(200)
DOUBLE COMPLEX CX ,CY
DATA ND(1),ND(2),ND(3),ND(4),ND(5),ND(6),ND(7)/120,54,49,32,4,3,2/
SQRT2 = SQRT(2.0D0)
NNS = 7
DO 157 NZ=1,NNS
N = ND(NZ)
MODN = MOD(N,2)
FN = FLOAT(N)
TFN = FN+FN
NP1 = N+1
NM1 = N-1
DO 101 J=1,NP1
X(J) = SIN(FLOAT(J)*SQRT2)
Y(J) = X(J)
XH(J) = X(J)
101 CONTINUE
C
C TEST SUBROUTINES RFFTI,RFFTF AND RFFTB
C
CALL DFFTI (N,W)
PI = 3.14159265358979323846D0
DT = (PI+PI)/FN
NS2 = (N+1)/2
IF (NS2 .LT. 2) GO TO 104
DO 103 K=2,NS2
SUM1 = 0.0D0
SUM2 = 0.0D0
ARG = FLOAT(K-1)*DT
DO 102 I=1,N
ARG1 = FLOAT(I-1)*ARG
SUM1 = SUM1+X(I)*COS(ARG1)
SUM2 = SUM2+X(I)*SIN(ARG1)
102 CONTINUE
Y(2*K-2) = SUM1
Y(2*K-1) = -SUM2
103 CONTINUE
104 SUM1 = 0.0D0
SUM2 = 0.0D0
DO 105 I=1,NM1,2
SUM1 = SUM1+X(I)
SUM2 = SUM2+X(I+1)
105 CONTINUE
IF (MODN .EQ. 1) SUM1 = SUM1+X(N)
Y(1) = SUM1+SUM2
IF (MODN .EQ. 0) Y(N) = SUM1-SUM2
CALL DFFTF (N,X,W)
RFTF = 0.0D0
DO 106 I=1,N
RFTF = DMAX1(RFTF,ABS(X(I)-Y(I)))
X(I) = XH(I)
106 CONTINUE
RFTF = RFTF/FN
DO 109 I=1,N
SUM = 0.5D0*X(1)
ARG = FLOAT(I-1)*DT
IF (NS2 .LT. 2) GO TO 108
DO 107 K=2,NS2
ARG1 = FLOAT(K-1)*ARG
SUM = SUM+X(2*K-2)*COS(ARG1)-X(2*K-1)*SIN(ARG1)
107 CONTINUE
108 IF (MODN .EQ. 0) SUM = SUM+.5*FLOAT((-1)**(I-1))*X(N)
Y(I) = SUM+SUM
109 CONTINUE
CALL DFFTB (N,X,W)
RFTB = 0.0D0
DO 110 I=1,N
RFTB = DMAX1(RFTB,ABS(X(I)-Y(I)))
X(I) = XH(I)
Y(I) = XH(I)
110 CONTINUE
CALL DFFTB (N,Y,W)
CALL DFFTF (N,Y,W)
CF = 1.0D0/FN
RFTFB = 0.
DO 111 I=1,N
RFTFB = DMAX1(RFTFB,ABS(CF*Y(I)-X(I)))
111 CONTINUE
C
C TEST SUBROUTINES DSINTI AND DSINT
C
DT = PI/FN
DO 112 I=1,NM1
X(I) = XH(I)
112 CONTINUE
DO 114 I=1,NM1
Y(I) = 0.0D0
ARG1 = FLOAT(I)*DT
DO 113 K=1,NM1
Y(I) = Y(I)+X(K)*SIN(FLOAT(K)*ARG1)
113 CONTINUE
Y(I) = Y(I)+Y(I)
114 CONTINUE
CALL DSINTI (NM1,W)
CALL DSINT (NM1,X,W)
CF = 0.5D0/FN
SINTT = 0.0D0
DO 115 I=1,NM1
SINTT = DMAX1(SINTT,ABS(X(I)-Y(I)))
X(I) = XH(I)
Y(I) = X(I)
115 CONTINUE
SINTT = CF*SINTT
CALL DSINT (NM1,X,W)
CALL DSINT (NM1,X,W)
SINTFB = 0.0D0
DO 116 I=1,NM1
SINTFB = DMAX1(SINTFB,ABS(CF*X(I)-Y(I)))
116 CONTINUE
C
C TEST SUBROUTINES COSTI AND COST
C
DO 117 I=1,NP1
X(I) = XH(I)
117 CONTINUE
DO 119 I=1,NP1
Y(I) = 0.5D0*(X(1)+FLOAT((-1)**(I+1))*X(N+1))
ARG = FLOAT(I-1)*DT
DO 118 K=2,N
Y(I) = Y(I)+X(K)*COS(FLOAT(K-1)*ARG)
118 CONTINUE
Y(I) = Y(I)+Y(I)
119 CONTINUE
CALL DCOSTI (NP1,W)
CALL DCOST (NP1,X,W)
COSTT = 0.0D0
DO 120 I=1,NP1
COSTT = DMAX1(COSTT,ABS(X(I)-Y(I)))
X(I) = XH(I)
Y(I) = XH(I)
120 CONTINUE
COSTT = CF*COSTT
CALL DCOST (NP1,X,W)
CALL DCOST (NP1,X,W)
COSTFB = 0.0D0
DO 121 I=1,NP1
COSTFB = DMAX1(COSTFB,ABS(CF*X(I)-Y(I)))
121 CONTINUE
C
C TEST SUBROUTINES SINQI,SINQF AND SINQB
C
CF = 0.25D0/FN
DO 122 I=1,N
Y(I) = XH(I)
122 CONTINUE
DT = PI/(FN+FN)
DO 124 I=1,N
X(I) = 0.0D0
ARG = DT*FLOAT(I)
DO 123 K=1,N
X(I) = X(I)+Y(K)*SIN(FLOAT(K+K-1)*ARG)
123 CONTINUE
X(I) = 4.0D0*X(I)
124 CONTINUE
CALL DSINQI (N,W)
CALL DSINQB (N,Y,W)
SINQBT = 0.0D0
DO 125 I=1,N
SINQBT = DMAX1(SINQBT,ABS(Y(I)-X(I)))
X(I) = XH(I)
125 CONTINUE
SINQBT = CF*SINQBT
DO 127 I=1,N
ARG = FLOAT(I+I-1)*DT
Y(I) = 0.5D0*FLOAT((-1)**(I+1))*X(N)
DO 126 K=1,NM1
Y(I) = Y(I)+X(K)*SIN(FLOAT(K)*ARG)
126 CONTINUE
Y(I) = Y(I)+Y(I)
127 CONTINUE
CALL DSINQF (N,X,W)
SINQFT = 0.0D0
DO 128 I=1,N
SINQFT = DMAX1(SINQFT,ABS(X(I)-Y(I)))
Y(I) = XH(I)
X(I) = XH(I)
128 CONTINUE
CALL DSINQF (N,Y,W)
CALL DSINQB (N,Y,W)
SINQFB = 0.0D0
DO 129 I=1,N
SINQFB = DMAX1(SINQFB,ABS(CF*Y(I)-X(I)))
129 CONTINUE
C
C TEST SUBROUTINES COSQI,COSQF AND COSQB
C
DO 130 I=1,N
Y(I) = XH(I)
130 CONTINUE
DO 132 I=1,N
X(I) = 0.0D0
ARG = FLOAT(I-1)*DT
DO 131 K=1,N
X(I) = X(I)+Y(K)*COS(FLOAT(K+K-1)*ARG)
131 CONTINUE
X(I) = 4.0D0*X(I)
132 CONTINUE
CALL DCOSQI (N,W)
CALL DCOSQB (N,Y,W)
COSQBT = 0.0D0
DO 133 I=1,N
COSQBT = DMAX1(COSQBT,ABS(X(I)-Y(I)))
X(I) = XH(I)
133 CONTINUE
COSQBT = CF*COSQBT
DO 135 I=1,N
Y(I) = 0.5D0*X(1)
ARG = FLOAT(I+I-1)*DT
DO 134 K=2,N
Y(I) = Y(I)+X(K)*COS(FLOAT(K-1)*ARG)
134 CONTINUE
Y(I) = Y(I)+Y(I)
135 CONTINUE
CALL DCOSQF (N,X,W)
COSQFT = 0.0D0
DO 136 I=1,N
COSQFT = DMAX1(COSQFT,ABS(Y(I)-X(I)))
X(I) = XH(I)
Y(I) = XH(I)
136 CONTINUE
COSQFT = CF*COSQFT
CALL DCOSQB (N,X,W)
CALL DCOSQF (N,X,W)
COSQFB = 0.0D0
DO 137 I=1,N
COSQFB = DMAX1(COSQFB,ABS(CF*X(I)-Y(I)))
137 CONTINUE
C
C TEST PROGRAMS EZFFTI,EZFFTF,EZFFTB
C
CALL DZFFTI(N,W)
DO 138 I=1,N
X(I) = XH(I)
138 CONTINUE
TPI = 8.0D0*ATAN(1.0D0)
DT = TPI/FLOAT(N)
NS2 = (N+1)/2
CF = 2.0D0/FLOAT(N)
NS2M = NS2-1
IF (NS2M .LE. 0) GO TO 141
DO 140 K=1,NS2M
SUM1 = 0.0D0
SUM2 = 0.0D0
ARG = FLOAT(K)*DT
DO 139 I=1,N
ARG1 = FLOAT(I-1)*ARG
SUM1 = SUM1+X(I)*COS(ARG1)
SUM2 = SUM2+X(I)*SIN(ARG1)
139 CONTINUE
A(K) = CF*SUM1
B(K) = CF*SUM2
140 CONTINUE
141 NM1 = N-1
SUM1 = 0.0D0
SUM2 = 0.0D0
DO 142 I=1,NM1,2
SUM1 = SUM1+X(I)
SUM2 = SUM2+X(I+1)
142 CONTINUE
IF (MODN .EQ. 1) SUM1 = SUM1+X(N)
AZERO = 0.5D0*CF*(SUM1+SUM2)
IF (MODN .EQ. 0) A(NS2) = 0.5D0*CF*(SUM1-SUM2)
CALL DZFFTF (N,X,AZEROH,AH,BH,W)
DEZF1 = ABS(AZEROH-AZERO)
IF (MODN .EQ. 0) DEZF1 = DMAX1(DEZF1,ABS(A(NS2)-AH(NS2)))
IF (NS2M .LE. 0) GO TO 144
DO 143 I=1,NS2M
DEZF1 = DMAX1(DEZF1,ABS(AH(I)-A(I)),ABS(BH(I)-B(I)))
143 CONTINUE
144 NS2 = N/2
IF (MODN .EQ. 0) B(NS2) = 0.0D0
DO 146 I=1,N
SUM = AZERO
ARG1 = FLOAT(I-1)*DT
DO 145 K=1,NS2
ARG2 = FLOAT(K)*ARG1
SUM = SUM+A(K)*COS(ARG2)+B(K)*SIN(ARG2)
145 CONTINUE
X(I) = SUM
146 CONTINUE
CALL DZFFTB (N,Y,AZERO,A,B,W)
DEZB1 = 0.0D0
DO 147 I=1,N
DEZB1 = DMAX1(DEZB1,ABS(X(I)-Y(I)))
X(I) = XH(I)
147 CONTINUE
CALL DZFFTF (N,X,AZERO,A,B,W)
CALL DZFFTB (N,Y,AZERO,A,B,W)
DEZFB = 0.0D0
DO 148 I=1,N
DEZFB = DMAX1(DEZFB,ABS(X(I)-Y(I)))
148 CONTINUE
C
C TEST CFFTI,CFFTF,CFFTB
C
DO 149 I=1,N
CX(I) = DCMPLX(COS(SQRT2*FLOAT(I)),SIN(SQRT2*FLOAT(I*I)))
149 CONTINUE
DT = (PI+PI)/FN
DO 151 I=1,N
ARG1 = -FLOAT(I-1)*DT
CY(I) = (0.0D0,0.0D0)
DO 150 K=1,N
ARG2 = FLOAT(K-1)*ARG1
CY(I) = CY(I)+DCMPLX(COS(ARG2),SIN(ARG2))*CX(K)
150 CONTINUE
151 CONTINUE
CALL ZFFTI (N,W)
CALL ZFFTF (N,CX,W)
DCFFTF = 0.0D0
DO 152 I=1,N
DCFFTF = DMAX1(DCFFTF,ABS(CX(I)-CY(I)))
CX(I) = CX(I)/FN
152 CONTINUE
DCFFTF = DCFFTF/FN
DO 154 I=1,N
ARG1 = FLOAT(I-1)*DT
CY(I) = (0.0D0,0.0D0)
DO 153 K=1,N
ARG2 = FLOAT(K-1)*ARG1
CY(I) = CY(I)+DCMPLX(COS(ARG2),SIN(ARG2))*CX(K)
153 CONTINUE
154 CONTINUE
CALL ZFFTB (N,CX,W)
DCFFTB = 0.0D0
DO 155 I=1,N
DCFFTB = DMAX1(DCFFTB,ABS(CX(I)-CY(I)))
CX(I) = CY(I)
155 CONTINUE
CF = 1.0D0/FN
CALL ZFFTF (N,CX,W)
CALL ZFFTB (N,CX,W)
DCFB = 0.0D0
DO 156 I=1,N
DCFB = DMAX1(DCFB,ABS(CF*CX(I)-CY(I)))
156 CONTINUE
WRITE (6,1001) N,RFTF,RFTB,RFTFB,SINTT,SINTFB,COSTT,COSTFB,
1 SINQFT,SINQBT,SINQFB,COSQFT,COSQBT,COSQFB,DEZF1,
2 DEZB1,DEZFB,DCFFTF,DCFFTB,DCFB
157 CONTINUE
C
C
C
1001 FORMAT (2H0N,I5,8H RFFTF ,E10.3,8H RFFTB ,E10.3,8H RFFTFB ,
1 E10.3,8H SINT ,E10.3,8H SINTFB ,E10.3,8H COST ,E10.3/
2 7X,8H COSTFB ,E10.3,8H SINQF ,E10.3,8H SINQB ,E10.3,
3 8H SINQFB ,E10.3,8H COSQF ,E10.3,8H COSQB ,E10.3/7X,
4 8H COSQFB ,E10.3,8H DEZF ,E10.3,8H DEZB ,E10.3,
5 8H DEZFB ,E10.3,8H CFFTF ,E10.3,8H CFFTB ,E10.3/
6 7X,8H CFFTFB ,E10.3)
C
END