cosqmb

NAME

SYNOPSIS

 SUBROUTINE COSQMB (LOT, JUMP, N, INC, R, LENR, WSAVE, LENSAV, 
1                   WORK, LENWRK, IER)

 INTEGER    LOT, JUMP, N, INC, LENR, LENSAV, LENWRK, IER
 REAL       R(LENR), WSAVE(LENSAV), WORK(LENWRK)

DESCRIPTION

 FFTPACK 5.0 routine COSQMB computes the one-dimensional Fourier 
 transform of multiple sequences, each of which is a cosine series 
 with odd wave numbers.  This transform is referred to as the 
 backward transform or Fourier synthesis, transforming the sequences 
 from spectral to physical space.
 
 This transform is normalized since a call to COSQMB followed
 by a call to COSQMF (or vice-versa) reproduces the original
 array  within roundoff error.
 
 Input Arguments
 
 LOT     Integer number of sequences to be transformed within
         array R.
 
 JUMP    Integer increment between the locations, in array R,
         of the first elements of two consecutive sequences
         to be transformed.
 
 N       Integer length of each sequence to be transformed.  The 
         transform is most efficient when N is a product of 
         small primes.
 
 INC     Integer increment between the locations, in array R,
         of two consecutive elements within the same sequence.
 
 R       Real array containing LOT sequences, each having length N.
         R can have any number of dimensions, but the total number 
         of locations must be at least LENR.
 
 LENR    Integer dimension of R array.  LENR must be at least
         (LOT-1)*JUMP + INC*(N-1)+ 1.


 WSAVE   Real work array with dimension LENSAV.  WSAVE's contents 
         must be initialized with a call to subroutine COSQMI before 
         the first call to routine COSQMF or COSQMB for a given 
         transform length N.  WSAVE's contents may be re-used for 
         subsequent calls to COSQMF and COSQMB with the same N.


 LENSAV  Integer dimension of WSAVE array.  LENSAV must be at least 
         2*N + INT(LOG (REAL(N))) +4.


 WORK    Real array of dimension LENWRK.
 
 LENWRK  Integer dimension of WORK array.  LENWRK must be at 
         least LOT*N.


 Output Arguments
 
  R      Real output array.  For purposes of exposition, 
         assume R's range of indices is given by 
         R(0:(LOT-1)*JUMP+(N-1)*INC).
 
         The output values of R are written over the input values.
         For I=0,...,LOT-1 and J=0,...,N-1
 
          R(I*JUMP+J*INC) =
 
              N-1
              SUM  R(I*JUMP+N1*INC)*COS(J*(2*N1+1)*PI/(2*N))
              N1=0
 
 WSAVE   Contains values initialized by subroutine COSQMI that
         must not be destroyed between calls to routine COSQMF
         or COSQMB.

 IER     Integer error return
         =  0 successful exit
         =  1 input parameter LENR   not big enough
         =  2 input parameter LENSAV not big enough
         =  3 input parameter LENWRK not big enough
         =  4 input parameters INC,JUMP,N,LOT are not consistent.
         = 20 input error returned by lower level routine

              The parameters integers INC, JUMP, N and LOT are 
              consistent if equality 
              I1*INC + J1*JUMP = I2*INC + J2*JUMP for I1,I2 < N 
              and J1,J2 < LOT implies I1=I2 and J1=J2.

              For multiple FFTs to execute correctly, input variables 
              INC, JUMP, N and LOT must be consistent, otherwise at 
              least one array element mistakenly is transformed more 
              than once.