[f,bound,inf,epsabs,epsrel,result,abserr,neval,ier,limit,lenw,last,iwork,work]=qagi(f,bound,inf,epsabs,epsrel,result,abserr,neval,ier,limit,lenw,last,iwork,work);

function [f,bound,inf,epsabs,epsrel,result,abserr,neval,ier,limit,lenw,last,iwork,work]=qagi(f,bound,inf,epsabs,epsrel,result,abserr,neval,ier,limit,lenw,last,iwork,work);
%***BEGIN PROLOGUE  QAGI
%***PURPOSE  The routine calculates an approximation result to a given
%            INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
%                    OR I = Integral of F over (-INFINITY,BOUND)
%                    OR I = Integral of F over (-INFINITY,+INFINITY)
%            Hopefully satisfying following claim for accuracy
%            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
%***LIBRARY   SLATEC (QUADPACK)
%***CATEGORY  H2A3A1, H2A4A1
%***TYPE      SINGLE PRECISION (QAGI-S, DQAGI-D)
%***KEYWORDS  AUTOMATIC INTEGRATOR, EXTRAPOLATION, GENERAL-PURPOSE,
%             GLOBALLY ADAPTIVE, INFINITE INTERVALS, QUADPACK,
%             QUADRATURE, TRANSFORMATION
%***AUTHOR  Piessens, Robert
%             Applied Mathematics and Programming Division
%             K. U. Leuven
%           de Doncker, Elise
%             Applied Mathematics and Programming Division
%             K. U. Leuven
%***DESCRIPTION
%
%        Integration over infinite intervals
%        Standard fortran subroutine
%
%        PARAMETERS
%         ON ENTRY
%            F      - Real
%                     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.
%
%            BOUND  - Real
%                     Finite bound of integration range
%                     (has no meaning if interval is doubly-infinite)
%
%            INF    - Integer
%                     indicating the kind of integration range involved
%                     INF = 1 corresponds to  (BOUND,+INFINITY),
%                     INF = -1            to  (-INFINITY,BOUND),
%                     INF = 2             to (-INFINITY,+INFINITY).
%
%            EPSABS - Real
%                     Absolute accuracy requested
%            EPSREL - Real
%                     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 - Real
%                     Approximation to the integral
%
%            ABSERR - Real
%                     Estimate of 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 result 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
%                             subdivisions 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 the
%                             integrator on the subranges. If possible,
%                             an appropriate special-purpose integrator
%                             should be used, which is designed for
%                             handling the type of difficulty involved.
%                         = 2 The occurrence of roundoff error is
%                             detected, which prevents the requested
%                             tolerance from being achieved.
%                             The error may be under-estimated.
%                         = 3 Extremely bad integrand behaviour occurs
%                             at some points of the integration
%                             interval.
%                         = 4 The algorithm does not converge.
%                             Roundoff error is detected in the
%                             extrapolation table.
%                             It is assumed that the requested tolerance
%                             cannot be achieved, and that the returned
%                             RESULT is the best which can be obtained.
%                         = 5 The integral is probably divergent, or
%                             slowly convergent. It must be noted that
%                             divergence can occur with any other value
%                             of IER.
%                         = 6 The input is invalid, because
%                             (EPSABS.LE.0 and
%                              EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28))
%                              or LIMIT.LT.1 or LENIW.LT.LIMIT*4.
%                             RESULT, ABSERR, NEVAL, LAST are set to
%                             zero.  Except when LIMIT or LENIW 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  - Real
%                    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)
%                     contain the error estimates.
%
%***REFERENCES  (NONE)
%***ROUTINES CALLED  QAGIE, 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  QAGI
%
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  QAGI
ier = 6;
neval = 0;
last = 0;
result = 0.0e+00;
abserr = 0.0e+00;
if( limit>=1 && lenw>=limit.*4 )
%
%         PREPARE CALL FOR QAGIE.
%
l1 = fix(limit + 1);
l2 = fix(limit + l1);
l3 = fix(limit + l2);
%
[f,bound,inf,epsabs,epsrel,limit,result,abserr,neval,ier,dumvar11,dumvar12,dumvar13,dumvar14,iwork,last]=qagie(f,bound,inf,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);   dumvar11i=find((work(sub2ind(size(work),max(1,1)):end))~=(dumvar11));dumvar12i=find((work(sub2ind(size(work),max(l1,1)):end))~=(dumvar12));dumvar13i=find((work(sub2ind(size(work),max(l2,1)):end))~=(dumvar13));dumvar14i=find((work(sub2ind(size(work),max(l3,1)):end))~=(dumvar14));   work(1-1+dumvar11i)=dumvar11(dumvar11i); work(l1-1+dumvar12i)=dumvar12(dumvar12i); work(l2-1+dumvar13i)=dumvar13(dumvar13i); work(l3-1+dumvar14i)=dumvar14(dumvar14i); 
%
%         CALL ERROR HANDLER IF NECESSARY.
%
lvl = 0;
end;
if( ier==6 )
lvl = 1;
end;
if( ier~=0 )
[dumvar1,dumvar2,dumvar3,ier,lvl]=xermsg('SLATEC','QAGI','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 QAGPE