Code covered by the BSD License  

Highlights from
slatec

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

[f,a,b,c,epsabs,epsrel,result,abserr,neval,ier,limit,lenw,last,iwork,work]=dqawc(f,a,b,c,epsabs,epsrel,result,abserr,neval,ier,limit,lenw,last,iwork,work);
function [f,a,b,c,epsabs,epsrel,result,abserr,neval,ier,limit,lenw,last,iwork,work]=dqawc(f,a,b,c,epsabs,epsrel,result,abserr,neval,ier,limit,lenw,last,iwork,work);
%***BEGIN PROLOGUE  DQAWC
%***PURPOSE  The routine calculates an approximation result to a
%            Cauchy principal value I = INTEGRAL of F*W over (A,B)
%            (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
%            following claim for accuracy
%            ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).
%***LIBRARY   SLATEC (QUADPACK)
%***CATEGORY  H2A2A1, J4
%***TYPE      doubleprecision (QAWC-S, DQAWC-D)
%***KEYWORDS  AUTOMATIC INTEGRATOR, CAUCHY PRINCIPAL VALUE,
%             CLENSHAW-CURTIS METHOD, GLOBALLY ADAPTIVE, QUADPACK,
%             QUADRATURE, SPECIAL-PURPOSE
%***AUTHOR  Piessens, Robert
%             Applied Mathematics and Programming Division
%             K. U. Leuven
%           de Doncker, Elise
%             Applied Mathematics and Programming Division
%             K. U. Leuven
%***DESCRIPTION
%
%        Computation of a Cauchy principal value
%        Standard fortran subroutine
%        doubleprecision version
%
%
%        PARAMETERS
%         ON ENTRY
%            F      - doubleprecision
%                     function subprogram defining the integrand
%                     function F(X). The actual name for F needs to be
%                     declared E X T E R N A L in the driver program.
%
%            A      - doubleprecision
%                     Under limit of integration
%
%            B      - doubleprecision
%                     Upper limit of integration
%
%            C      - Parameter in the weight function, C.NE.A, C.NE.B.
%                     If C = A or C = B, the routine will end with
%                     IER = 6 .
%
%            EPSABS - doubleprecision
%                     Absolute accuracy requested
%            EPSREL - doubleprecision
%                     Relative accuracy requested
%                     If  EPSABS.LE.0
%                     and EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28),
%                     the routine will end with IER = 6.
%
%         ON RETURN
%            RESULT - doubleprecision
%                     Approximation to the integral
%
%            ABSERR - doubleprecision
%                     Estimate or the modulus of the absolute error,
%                     Which should equal or exceed ABS(I-RESULT)
%
%            NEVAL  - Integer
%                     Number of integrand evaluations
%
%            IER    - Integer
%                     IER = 0 Normal and reliable termination of the
%                             routine. It is assumed that the requested
%                             accuracy has been achieved.
%                     IER.GT.0 Abnormal termination of the routine
%                             the estimates for integral and error are
%                             less reliable. It is assumed that the
%                             requested accuracy has not been achieved.
%            ERROR MESSAGES
%                     IER = 1 Maximum number of subdivisions allowed
%                             has been achieved. One can allow more sub-
%                             divisions by increasing the value of LIMIT
%                             (and taking the according dimension
%                             adjustments into account). However, if
%                             this yields no improvement it is advised
%                             to analyze the integrand in order to
%                             determine the integration difficulties.
%                             If the position of a local difficulty
%                             can be determined (e.g. SINGULARITY,
%                             DISCONTINUITY within the interval) one
%                             will probably gain from splitting up the
%                             interval at this point and calling
%                             appropriate integrators on the subranges.
%                         = 2 The occurrence of roundoff error is detec-
%                             ted, which prevents the requested
%                             tolerance from being achieved.
%                         = 3 Extremely bad integrand behaviour occurs
%                             at some points of the integration
%                             interval.
%                         = 6 The input is invalid, because
%                             C = A or C = B or
%                             (EPSABS.LE.0 and
%                              EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28))
%                             or LIMIT.LT.1 or LENW.LT.LIMIT*4.
%                             RESULT, ABSERR, NEVAL, LAST are set to
%                             zero.  Except when LENW or LIMIT is
%                             invalid, IWORK(1), WORK(LIMIT*2+1) and
%                             WORK(LIMIT*3+1) are set to zero, WORK(1)
%                             is set to A and WORK(LIMIT+1) to B.
%
%         DIMENSIONING PARAMETERS
%            LIMIT - Integer
%                    Dimensioning parameter for IWORK
%                    LIMIT determines the maximum number of subintervals
%                    in the partition of the given integration interval
%                    (A,B), LIMIT.GE.1.
%                    If LIMIT.LT.1, the routine will end with IER = 6.
%
%           LENW   - Integer
%                    Dimensioning parameter for WORK
%                    LENW must be at least LIMIT*4.
%                    If LENW.LT.LIMIT*4, the routine will end with
%                    IER = 6.
%
%            LAST  - Integer
%                    On return, LAST equals the number of subintervals
%                    produced in the subdivision process, which
%                    determines the number of significant elements
%                    actually in the WORK ARRAYS.
%
%         WORK ARRAYS
%            IWORK - Integer
%                    Vector of dimension at least LIMIT, the first K
%                    elements of which contain pointers
%                    to the error estimates over the subintervals,
%                    such that WORK(LIMIT*3+IWORK(1)), ... ,
%                    WORK(LIMIT*3+IWORK(K)) form a decreasing
%                    sequence, with K = LAST if LAST.LE.(LIMIT/2+2),
%                    and K = LIMIT+1-LAST otherwise
%
%            WORK  - doubleprecision
%                    Vector of dimension at least LENW
%                    On return
%                    WORK(1), ..., WORK(LAST) contain the left
%                     end points of the subintervals in the
%                     partition of (A,B),
%                    WORK(LIMIT+1), ..., WORK(LIMIT+LAST) contain
%                     the right end points,
%                    WORK(LIMIT*2+1), ..., WORK(LIMIT*2+LAST) contain
%                     the integral approximations over the subintervals,
%                    WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST)
%                     contain the error estimates.
%
%***REFERENCES  (NONE)
%***ROUTINES CALLED  DQAWCE, XERMSG
%***REVISION HISTORY  (YYMMDD)
%   800101  DATE WRITTEN
%   890831  Modified array declarations.  (WRB)
%   890831  REVISION DATE from Version 3.2
%   891214  Prologue converted to Version 4.0 format.  (BAB)
%   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
%***end PROLOGUE  DQAWC
%
persistent l1 l2 l3 lvl ; 

if isempty(lvl), lvl=0; end;
if isempty(l1), l1=0; end;
if isempty(l2), l2=0; end;
if isempty(l3), l3=0; end;
%
iwork_shape=size(iwork);iwork=reshape(iwork,1,[]);
work_shape=size(work);work=reshape(work,1,[]);
%
%
%         CHECK VALIDITY OF LIMIT AND LENW.
%
%***FIRST EXECUTABLE STATEMENT  DQAWC
ier = 6;
neval = 0;
last = 0;
result = 0.0d+00;
abserr = 0.0d+00;
if( limit>=1 && lenw>=limit.*4 )
%
%         PREPARE CALL FOR DQAWCE.
%
l1 = fix(limit + 1);
l2 = fix(limit + l1);
l3 = fix(limit + l2);
[f,a,b,c,epsabs,epsrel,limit,result,abserr,neval,ier,dumvar12,dumvar13,dumvar14,dumvar15,iwork,last]=dqawce(f,a,b,c,epsabs,epsrel,limit,result,abserr,neval,ier,work(sub2ind(size(work),max(1,1)):end),work(sub2ind(size(work),max(l1,1)):end),work(sub2ind(size(work),max(l2,1)):end),work(sub2ind(size(work),max(l3,1)):end),iwork,last);   dumvar12i=find((work(sub2ind(size(work),max(1,1)):end))~=(dumvar12));dumvar13i=find((work(sub2ind(size(work),max(l1,1)):end))~=(dumvar13));dumvar14i=find((work(sub2ind(size(work),max(l2,1)):end))~=(dumvar14));dumvar15i=find((work(sub2ind(size(work),max(l3,1)):end))~=(dumvar15));   work(1-1+dumvar12i)=dumvar12(dumvar12i); work(l1-1+dumvar13i)=dumvar13(dumvar13i); work(l2-1+dumvar14i)=dumvar14(dumvar14i); work(l3-1+dumvar15i)=dumvar15(dumvar15i); 
%
%         CALL ERROR HANDLER IF NECESSARY.
%
lvl = 0;
end;
if( ier==6 )
lvl = 1;
end;
if( ier~=0 )
[dumvar1,dumvar2,dumvar3,ier,lvl]=xermsg('SLATEC','DQAWC','ABNORMAL RETURN',ier,lvl);
end;
iwork_shape=zeros(iwork_shape);iwork_shape(:)=iwork(1:numel(iwork_shape));iwork=iwork_shape;
work_shape=zeros(work_shape);work_shape(:)=work(1:numel(work_shape));work=work_shape;
end
%DECK DQAWFE

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