cosq1b

NAME

SYNOPSIS

 SUBROUTINE COSQ1B (N, INC, R, LENR, WSAVE, LENSAV, WORK, LENWRK, IER)

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

DESCRIPTION

 FFTPACK 5.0 routine COSQ1B computes the one-dimensional Fourier 
 transform of a sequence which is a cosine series with odd wave 
 numbers.  This transform is referred to as the backward transform 
 or Fourier synthesis, transforming the sequence from spectral to 
 physical space.
 
 This transform is normalized since a call to COSQ1B followed
 by a call to COSQ1F (or vice-versa) reproduces the original
 array  within roundoff error.
 
 Input Arguments
 
 N       Integer number of elements to be transformed in the 
         sequence. 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 sequence.
 
 R       Real array of length LENR containing the sequence to be 
         transformed.
 
 LENR    Integer dimension of R array.  LENR must be at least
         INC*(N-1)+ 1.


 WSAVE   Real work array of length LENSAV.  WSAVE's contents must 
         be initialized with a call to subroutine COSQ1I before the 
         first call to routine COSQ1F or COSQ1B for a given transform
         length N.  WSAVE's contents may be re-used for subsequent 
         calls to COSQ1F and COSQ1B 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 N.


 Output Arguments
 
  R      Real output array.  For purposes of exposition, 
         assume R's range of indices is given by 
         R(0:(N-1)*INC).
 
         The output values of R are written over the input values.
         For J=0,...,N-1
 
          R(J*INC) =
 
              N-1
              SUM  R(N1*INC)*COS(J*(2*N1+1)*PI/(2*N))
              N1=0
 
 WSAVE   Contains values initialized by subroutine COSQ1I that
         must not be destroyed between calls to routine COSQ1F
         or COSQ1B.


 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
         = 20 input error returned by lower level routine