QCOSI
Computes parameters needed by QCOSF and QCOSB.
Required Arguments
N — Length of the sequence to be transformed. (Input)
WQCOS — Array of length 3N + 15 containing parameters needed by QCOSF and QCOSB. (Output)
FORTRAN 90 Interface
Generic: CALL QCOSI (N, WQCOS)
Specific: The specific interface names are S_QCOSI and D_QCOSI.
FORTRAN 77 Interface
Single: CALL QCOSI (N, WQCOS)
Double: The double precision name is DQCOSI.
Description
The routine QCOSI initializes the routines QCOSF and QCOSB. An efficient way to make multiple calls for the same N to IMSL routine QCOSF or QCOSB is to use routine QCOSI for initialization. (In this case, replace QCOSF or QCOSB with Q2OSF or Q2OSB , respectively.) The routine QCOSI is based on the routine COSQI in FFTPACK, which was developed by Paul Swarztrauber at the National Center for Atmospheric Research.
Comments
Different WQCOS arrays are needed for different values of N.
Example
In this example, we compute three distinct quarter cosine transforms by calling QCOSI once and then calling Q2OSF three times.
USE QCOSI_INT
USE CONST_INT
USE Q2OSF_INT
USE UMACH_INT
IMPLICIT NONE
INTEGER N
PARAMETER (N=7)
!
INTEGER I, K, NOUT
REAL COEF(N), COS, FLOAT, PI, WQCOS(36), SEQ(N)
INTRINSIC COS, FLOAT
! Get output unit number
CALL UMACH (2, NOUT)
! Initialize the work vector WQCOS
CALL QCOSI (N, WQCOS)
! 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((2*K-1)*(I-1))*(PI/2.0)/FLOAT(N))
10 CONTINUE
! Compute the transform of SEQ
CALL Q2OSF (N, SEQ, COEF, WQCOS)
! 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 7.00
2 0.97 0.00
3 0.90 0.00
4 0.78 0.00
5 0.62 0.00
6 0.43 0.00
7 0.22 0.00
INDEX SEQ COEF
1 1.00 0.00
2 0.78 7.00
3 0.22 0.00
4 -0.43 0.00
5 -0.90 0.00
6 -0.97 0.00
7 -0.62 0.00
INDEX SEQ COEF
1 1.00 0.00
2 0.43 0.00
3 -0.62 7.00
4 -0.97 0.00
5 -0.22 0.00
6 0.78 0.00
7 0.90 0.00
