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ADMB Documentation
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#include <math.h>#include <float.h>Go to the source code of this file.
Functions | |
| template<class Float , class integr_fn > | |
| void | Rdqagi (integr_fn f, void *ex, Float *bound, int *inf, Float *epsabs, Float *epsrel, Float *result, Float *abserr, int *neval, int *ier, int *limit, int *lenw, int *last, int *iwork, Float *work) |
| template<class Float , class integr_fn > | |
| static void | rdqagie (integr_fn f, void *ex, Float *, int *, Float *, Float *, int *, Float *, Float *, int *, int *, Float *, Float *, Float *, Float *, int *, int *) |
| template<class Float , class integr_fn > | |
| void | Rdqags (integr_fn f, void *ex, Float *a, Float *b, Float *epsabs, Float *epsrel, Float *result, Float *abserr, int *neval, int *ier, int *limit, int *lenw, int *last, int *iwork, Float *work) |
| template<class Float , class integr_fn > | |
| static void | rdqagse (integr_fn f, void *ex, Float *, Float *, Float *, Float *, int *, Float *, Float *, int *, int *, Float *, Float *, Float *, Float *, int *, int *) |
| template<class Float > | |
| static void | rdqelg (int *, Float *, Float *, Float *, Float *, int *) |
| template<class Float , class integr_fn > | |
| static void | rdqk15i (integr_fn f, void *ex, Float *, int *, Float *, Float *, Float *, Float *, Float *, Float *) |
| template<class Float , class integr_fn > | |
| static void | rdqk21 (integr_fn f, void *ex, Float *, Float *, Float *, Float *, Float *, Float *) |
| template<class Float > | |
| static void | rdqpsrt (int *, int *, int *, Float *, Float *, int *, int *) |
| void Rdqagi | ( | integr_fn | f, |
| void * | ex, | ||
| Float * | bound, | ||
| int * | inf, | ||
| Float * | epsabs, | ||
| Float * | epsrel, | ||
| Float * | result, | ||
| Float * | abserr, | ||
| int * | neval, | ||
| int * | ier, | ||
| int * | limit, | ||
| int * | lenw, | ||
| int * | last, | ||
| int * | iwork, | ||
| Float * | work | ||
| ) |
Definition at line 71 of file integrate.cpp.
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static |
begin prologue dqagie date written 800101 (yymmdd) revision date 830518 (yymmdd) category no. h2a3a1,h2a4a1 keywords automatic integrator, infinite intervals, general-purpose, transformation, extrapolation, globally adaptive author piessens,robert,appl. math & progr. div - k.u.leuven de doncker,elise,appl. math & progr. div - k.u.leuven 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) <= max(epsabs,epsrel*abs(i)) description
integration over infinite intervals standard fortran subroutine
f - double precision
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 - double precision
finite bound of integration range
(has no meaning if interval is doubly-infinite)
inf - double precision
indicating the kind of integration range involved
inf = 1 corresponds to (bound,+infinity),
inf = -1 to (-infinity,bound),
inf = 2 to (-infinity,+infinity).
epsabs - double precision
absolute accuracy requested
epsrel - double precision
relative accuracy requested
if epsabs <= 0
and epsrel < max(50*rel.mach.acc.,0.5d-28),
the routine will end with ier = 6.
limit - int
gives an upper bound on the number of subintervals
in the partition of (a,b), limit >= 1
on return
result - double precision
approximation to the integral
abserr - double precision
estimate of the modulus of the absolute error,
which should equal or exceed abs(i-result)
neval - int
number of integrand evaluations
ier - int
ier = 0 normal and reliable termination of the
routine. it is assumed that the requested
accuracy has been achieved.
- ier > 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 <= 0 and
epsrel < max(50*rel.mach.acc.,0.5d-28),
result, abserr, neval, last, rlist(1),
elist(1) and iord(1) are set to zero.
alist(1) and blist(1) are set to 0
and 1 respectively.
alist - double precision
vector of dimension at least limit, the first
last elements of which are the left
end points of the subintervals in the partition
of the transformed integration range (0,1).
blist - double precision
vector of dimension at least limit, the first
last elements of which are the right
end points of the subintervals in the partition
of the transformed integration range (0,1).
rlist - double precision
vector of dimension at least limit, the first
last elements of which are the integral
approximations on the subintervals
elist - double precision
vector of dimension at least limit, the first
last elements of which are the moduli of the
absolute error estimates on the subintervals
iord - int
vector of dimension limit, the first k
elements of which are pointers to the
error estimates over the subintervals,
such that elist(iord(1)), ..., elist(iord(k))
form a decreasing sequence, with k = last
if last <= (limit/2+2), and k = limit+1-last
otherwise
last - int
number of subintervals actually produced
in the subdivision process
routines called dqelg,dqk15i,dqpsrt end prologue dqagie
the dimension of rlist2 is determined by the value of
limexp in subroutine dqelg.
list of major variables
-----------------------
alist - list of left end points of all subintervals
considered up to now
blist - list of right end points of all subintervals
considered up to now
rlist(i) - approximation to the integral over
(alist(i),blist(i))
rlist2 - array of dimension at least (limexp+2),
containing the part of the epsilon table
wich is still needed for further computations
elist(i) - error estimate applying to rlist(i)
maxerr - pointer to the interval with largest error
estimate
errmax - elist(maxerr)
erlast - error on the interval currently subdivided
(before that subdivision has taken place)
area - sum of the integrals over the subintervals
errsum - sum of the errors over the subintervals
errbnd - requested accuracy max(epsabs,epsrel*
abs(result))
1 - variable for the left subinterval
2 - variable for the right subinterval
last - index for subdivision
nres - number of calls to the extrapolation routine
numrl2 - number of elements currently in rlist2. if an
appropriate approximation to the compounded
integral has been obtained, it is put in
rlist2(numrl2) after numrl2 has been increased
by one.
small - length of the smallest interval considered up
to now, multiplied by 1.5
erlarg - sum of the errors over the intervals larger
than the smallest interval considered up to now
extrap - logical variable denoting that the routine
is attempting to perform extrapolation. i.e.
before subdividing the smallest interval we
try to decrease the value of erlarg.
noext - logical variable denoting that extrapolation
is no longer allowed (true-value)
machine dependent constants
---------------------------
epmach is the largest relative spacing.
uflow is the smallest positive magnitude.
oflow is the largest positive magnitude.
Definition at line 254 of file integrate.cpp.
Referenced by Rdqagi().
| void Rdqags | ( | integr_fn | f, |
| void * | ex, | ||
| Float * | a, | ||
| Float * | b, | ||
| Float * | epsabs, | ||
| Float * | epsrel, | ||
| Float * | result, | ||
| Float * | abserr, | ||
| int * | neval, | ||
| int * | ier, | ||
| int * | limit, | ||
| int * | lenw, | ||
| int * | last, | ||
| int * | iwork, | ||
| Float * | work | ||
| ) |
Definition at line 805 of file integrate.cpp.
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Definition at line 986 of file integrate.cpp.
Referenced by Rdqags().
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Definition at line 1722 of file integrate.cpp.
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Definition at line 1492 of file integrate.cpp.
Referenced by rdqagie().
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Definition at line 1923 of file integrate.cpp.
Referenced by rdqagse().
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Definition at line 2132 of file integrate.cpp.
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