QSINI
Computes parameters needed by QSINF and QSINB.
Required Arguments
N — Length of the sequence to be transformed. (Input)
WQSIN — Array of length 3N + 15 containing parameters needed by QSINF and QSINB. (Output)
FORTRAN 90 Interface
Generic: CALL QSINI (N, WQSIN)
Specific: The specific interface names are S_QSINI and D_QSINI.
FORTRAN 77 Interface
Single: CALL QSINI (N, WQSIN)
Double: The double precision name is DQSINI.
Description
The routine QSINI initializes the routines QSINF and QSINB. An efficient way to make multiple calls for the same N to IMSL routine QSINF or QSINB is to use routine QSINI for initialization. (In this case, replace QSINF or QSINB with Q2INF or Q2INB, respectively.) The routine QSINI is based on the routine SINQI in FFTPACK. The package FFTPACK was developed by Paul Swarztrauber at the National Center for Atmospheric Research.
Comments
Different WQSIN arrays are needed for different values of N.
Example
In this example, we compute three distinct quarter sine transforms by calling QSINI once and then calling Q2INF three times.
USE QSINI_INT
USE CONST_INT
USE Q2INF_INT
USE UMACH_INT
IMPLICIT NONE
INTEGER N
PARAMETER (N=7)
!
INTEGER I, K, NOUT
REAL COEF(N), FLOAT, PI, SIN, WQSIN(36), SEQ(N)
INTRINSIC FLOAT, SIN
! Get output unit number
CALL UMACH (2, NOUT)
! Initialize the work vector WQSIN
CALL QSINI (N, WQSIN)
! 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 sine wave
DO 10 I=1, N
SEQ(I) = SIN(FLOAT((2*K-1)*I)*(PI/2.0)/FLOAT(N))
10 CONTINUE
! Compute the transform of SEQ
CALL Q2INF (N, SEQ, COEF, WQSIN)
! 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 0.22 7.00
2 0.43 0.00
3 0.62 0.00
4 0.78 0.00
5 0.90 0.00
6 0.97 0.00
7 1.00 0.00
INDEX SEQ COEF
1 0.62 0.00
2 0.97 7.00
3 0.90 0.00
4 0.43 0.00
5 -0.22 0.00
6 -0.78 0.00
7 -1.00 0.00
INDEX SEQ COEF
1 0.90 0.00
2 0.78 0.00
3 -0.22 7.00
4 -0.97 0.00
5 -0.62 0.00
6 0.43 0.00
7 1.00 0.00
