Code covered by the BSD License

Highlights fromslatec

from slatec by Ben Barrowes
The slatec library converted into matlab functions.

[n,x,wsave]=cosqb(n,x,wsave);
```function [n,x,wsave]=cosqb(n,x,wsave);
persistent tsqrt2 x1 ;

if isempty(tsqrt2), tsqrt2=0; end;
if isempty(x1), x1=0; end;
%***BEGIN PROLOGUE  COSQB
%***PURPOSE  Compute the unnormalized inverse cosine transform.
%***LIBRARY   SLATEC (FFTPACK)
%***CATEGORY  J1A3
%***TYPE      SINGLE PRECISION (COSQB-S)
%***KEYWORDS  FFTPACK, INVERSE COSINE FOURIER TRANSFORM
%***AUTHOR  Swarztrauber, P. N., (NCAR)
%***DESCRIPTION
%
%  subroutine COSQB computes the fast Fourier transform of quarter
%  wave data. That is, COSQB computes a sequence from its
%  representation in terms of a cosine series with odd wave numbers.
%  The transform is defined below at output parameter X.
%
%  COSQB is the unnormalized inverse of COSQF since a call of COSQB
%  followed by a call of COSQF will multiply the input sequence X
%  by 4*N.
%
%  The array WSAVE which is used by subroutine COSQB must be
%  initialized by calling subroutine COSQI(N,WSAVE).
%
%
%  Input Parameters
%
%  N       the length of the array X to be transformed.  The method
%          is most efficient when N is a product of small primes.
%
%  X       an array which contains the sequence to be transformed
%
%  WSAVE   a work array which must be dimensioned at least 3*N+15
%          in the program that calls COSQB.  The WSAVE array must be
%          initialized by calling subroutine COSQI(N,WSAVE), and a
%          different WSAVE array must be used for each different
%          value of N.  This initialization does not have to be
%          repeated so long as N remains unchanged.  Thus subsequent
%          transforms can be obtained faster than the first.
%
%  Output Parameters
%
%  X       For I=1,...,N
%
%               X(I)= the sum from K=1 to K=N of
%
%                  2*X(K)*COS((2*K-1)*(I-1)*PI/(2*N))
%
%               A call of COSQB followed by a call of
%               COSQF will multiply the sequence X by 4*N.
%               Therefore COSQF is the unnormalized inverse
%               of COSQB.
%
%  WSAVE   contains initialization calculations which must not
%          be destroyed between calls of COSQB or COSQF.
%
%***REFERENCES  P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
%                 Computations (G. Rodrigue, ed.), Academic Press,
%                 1982, pp. 51-83.
%***ROUTINES CALLED  COSQB1
%***REVISION HISTORY  (YYMMDD)
%   790601  DATE WRITTEN
%   830401  Modified to use SLATEC library source file format.
%   860115  Modified by Ron Boisvert to adhere to Fortran 77 by
%           (a) changing dummy array size declarations (1) to (*),
%           (b) changing definition of variable TSQRT2 by using
%               FORTRAN intrinsic function SQRT instead of a DATA
%               statement.
%   861211  REVISION DATE from Version 3.2
%   881128  Modified by Dick Valent to meet prologue standards.
%   891214  Prologue converted to Version 4.0 format.  (BAB)
%   920501  Reformatted the REFERENCES section.  (WRB)
%***end PROLOGUE  COSQB
x_shape=size(x);x=reshape(x,1,[]);
wsave_shape=size(wsave);wsave=reshape(wsave,1,[]);
%***FIRST EXECUTABLE STATEMENT  COSQB
tsqrt2 = 2..*sqrt(2.);
if( n<2 )
x(1) = 4..*x(1);
x_shape=zeros(x_shape);x_shape(:)=x(1:numel(x_shape));x=x_shape;
wsave_shape=zeros(wsave_shape);wsave_shape(:)=wsave(1:numel(wsave_shape));wsave=wsave_shape;
return;
elseif( n==2 ) ;
x1 = 4..*(x(1)+x(2));
x(2) = tsqrt2.*(x(1)-x(2));
x(1) = x1;
x_shape=zeros(x_shape);x_shape(:)=x(1:numel(x_shape));x=x_shape;
wsave_shape=zeros(wsave_shape);wsave_shape(:)=wsave(1:numel(wsave_shape));wsave=wsave_shape;
return;
else;
[n,x,wsave,dumvar4]=cosqb1(n,x,wsave,wsave(sub2ind(size(wsave),max(n+1,1)):end));   dumvar4i=find((wsave(sub2ind(size(wsave),max(n+1,1)):end))~=(dumvar4));   wsave(n+1-1+dumvar4i)=dumvar4(dumvar4i);
end;
x_shape=zeros(x_shape);x_shape(:)=x(1:numel(x_shape));x=x_shape;
wsave_shape=zeros(wsave_shape);wsave_shape(:)=wsave(1:numel(wsave_shape));wsave=wsave_shape;
end
%DECK COSQF1
```