FCOSI
Computes parameters needed by FCOST.
Required Arguments
N — Length of the sequence to be transformed. N must be greater than 1. (Input)
WFCOS — Array of length 3N + 15 containing parameters needed by FCOST. (Output)
FORTRAN 90 Interface
Generic: CALL FCOSI (N, WFCOS)
Specific: The specific interface names are S_FCOSI and D_FCOSI.
FORTRAN 77 Interface
Single: CALL FCOSI (N, WFCOS)
Double: The double precision name is DFCOSI.
Description
The routine FCOSI initializes the routine FCOST. An efficient way to make multiple calls for the same N to IMSL routine FCOST is to use routine FCOSI for initialization. (In this case, replace FCOST with F2OST.) The routine FCOSI is based on the routine COSTI in FFTPACK. The package FFTPACK was developed by Paul Swarztrauber at the National Center for Atmospheric Research.
If the IBM Engineering and Scientific Subroutine Library is used, parameters computed by FCOSI are not used. In this case, there is no need to call FCOSI.
Comments
Different WFCOS arrays are needed for different values of N.
Example
In this example, we compute three distinct cosine FFTs by calling FCOSI once and then calling F2OST three times.
USE FCOSI_INT
USE CONST_INT
USE F2OST_INT
USE UMACH_INT
IMPLICIT NONE
INTEGER N
PARAMETER (N=7)
!
INTEGER I, K, NOUT
REAL COEF(N), COS, FLOAT, PI, WFCOS(36), SEQ(N)
INTRINSIC COS, FLOAT
! Get output unit number
CALL UMACH (2, NOUT)
! Initialize the work vector WFCOS
CALL FCOSI (N, WFCOS)
! Different frequencies of the same
! wave will be transformed
PI = CONST('PI')
DO 20 K=1, 3
! Fill the data vector SEQ
! with a pure cosine wave
DO 10 I=1, N
SEQ(I) = COS(FLOAT(K*(I-1))*PI/FLOAT(N-1))
10 CONTINUE
! Compute the transform of SEQ
CALL F2OST (N, SEQ, COEF, WFCOS)
! Print results
WRITE (NOUT,99998)
WRITE (NOUT,99999) (I, SEQ(I), COEF(I), I=1,N)
20 CONTINUE
99998 FORMAT (/, 9X, 'INDEX', 6X, 'SEQ', 7X, 'COEF')
99999 FORMAT (1X, I11, 5X, F6.2, 5X, F6.2)
END
Output
INDEX SEQ COEF
1 1.00 0.00
2 0.87 6.00
3 0.50 0.00
4 0.00 0.00
5 -0.50 0.00
6 -0.87 0.00
7 -1.00 0.00
INDEX SEQ COEF
1 1.00 0.00
2 0.50 0.00
3 -0.50 6.00
4 -1.00 0.00
5 -0.50 0.00
6 0.50 0.00
7 1.00 0.00
INDEX SEQ COEF
1 1.00 0.00
2 0.00 0.00
3 -1.00 0.00
4 0.00 6.00
5 1.00 0.00
6 0.00 0.00
7 -1.00 0.00
