quadpack Module


Uses


Contents

Interfaces

Functions

Subroutines


Interfaces

interface

  • public function scalar_func(x_)

    Arguments

    Type IntentOptional Attributes Name
    real, intent(in) :: x_

    Return Value real


Functions

public function qwgtc(x, c, p2, p3, p4, kp)

QWGTC defines the weight function used by QC25C.

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Arguments

Type IntentOptional Attributes Name
real, intent(in) :: x
real, intent(in) :: c
real, intent(in) :: p2
real, intent(in) :: p3
real, intent(in) :: p4
integer, intent(in) :: kp

Return Value real

public function qwgto(x, omega, p2, p3, p4, integr)

QWGTO defines the weight functions used by QC25O.

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Arguments

Type IntentOptional Attributes Name
real, intent(in) :: x
real, intent(in) :: omega
real, intent(in) :: p2
real, intent(in) :: p3
real, intent(in) :: p4
integer, intent(in) :: integr

Return Value real

public function qwgts(x, a, b, alfa, beta, integr)

QWGTS defines the weight functions used by QC25S.

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Arguments

Type IntentOptional Attributes Name
real, intent(in) :: x
real, intent(in) :: a
real, intent(in) :: b
real, intent(in) :: alfa
real, intent(in) :: beta
integer, intent(in) :: integr

Return Value real

public pure function adjust_abserr(resasc, resabs, abserr)

Adjust estimate of absolute error

Arguments

Type IntentOptional Attributes Name
real, intent(in) :: resasc

Approximation to the integral of abs(f-i/(b-a))
real, intent(in) :: resabs

Approximation to the integral of abs(f)
real, intent(in) :: abserr

Estimate of absolute error

Return Value real


Subroutines

public subroutine aaaa()

AAAA is a dummy subroutine with QUADPACK documentation in its comments.

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Arguments

None

public subroutine qag(f, a, b, epsabs, epsrel, key, result, abserr, neval, ier)

QAG approximates an integral over a finite interval.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: epsabs
real :: epsrel
integer :: key
real :: result
real :: abserr
integer :: neval
integer :: ier

public subroutine qage(f, a, b, epsabs, epsrel, key, limit, result, abserr, neval, ier, alist, blist, rlist, elist, iord, last)

QAGE estimates a definite integral.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: epsabs
real :: epsrel
integer :: key
integer :: limit
real :: result
real :: abserr
integer :: neval
integer :: ier
real :: alist(limit)
real :: blist(limit)
real :: rlist(limit)
real :: elist(limit)
integer :: iord(limit)
integer :: last

public subroutine qagi(f, bound, inf, epsabs, epsrel, result, abserr, neval, ier)

QAGI estimates an integral over a semi-infinite or infinite interval.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: bound
integer :: inf
real :: epsabs
real :: epsrel
real :: result
real :: abserr
integer :: neval
integer :: ier

public subroutine qagp(f, a, b, npts2, points, epsabs, epsrel, result, abserr, neval, ier)

QAGP computes a definite integral.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
integer :: npts2
real :: points(40)
real :: epsabs
real :: epsrel
real :: result
real :: abserr
integer :: neval
integer :: ier

public subroutine qags(f, a, b, epsabs, epsrel, result, abserr, neval, ier)

QAGS estimates the integral of a function.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: epsabs
real :: epsrel
real :: result
real :: abserr
integer :: neval
integer :: ier

public subroutine qawc(f, a, b, c, epsabs, epsrel, result, abserr, neval, ier)

QAWC computes a Cauchy principal value.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: c
real :: epsabs
real :: epsrel
real :: result
real :: abserr
integer :: neval
integer :: ier

public subroutine qawce(f, a, b, c, epsabs, epsrel, limit, result, abserr, neval, ier, alist, blist, rlist, elist, iord, last)

QAWCE computes a Cauchy principal value.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: c
real :: epsabs
real :: epsrel
integer :: limit
real :: result
real :: abserr
integer :: neval
integer :: ier
real :: alist(limit)
real :: blist(limit)
real :: rlist(limit)
real :: elist(limit)
integer :: iord(limit)
integer :: last

public subroutine qawf(f, a, omega, integr, epsabs, result, abserr, neval, ier)

QAWF computes Fourier integrals over the interval [ A, +Infinity ).

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: omega
integer :: integr
real :: epsabs
real :: result
real :: abserr
integer :: neval
integer :: ier

public subroutine qawfe(f, a, omega, integr, epsabs, limlst, limit, maxp1, result, abserr, neval, ier, rslst, erlst, ierlst, lst, alist, blist, rlist, elist, iord, nnlog, chebmo)

QAWFE computes Fourier integrals.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: omega
integer :: integr
real :: epsabs
integer :: limlst
integer :: limit
integer :: maxp1
real :: result
real :: abserr
integer :: neval
integer :: ier
real :: rslst(limlst)
real :: erlst(limlst)
integer :: ierlst(limlst)
integer :: lst
real :: alist(limit)
real :: blist(limit)
real :: rlist(limit)
real :: elist(limit)
integer :: iord(limit)
integer :: nnlog(limit)
real :: chebmo(maxp1,25)

public subroutine qawo(f, a, b, omega, integr, epsabs, epsrel, result, abserr, neval, ier)

QAWO computes the integrals of oscillatory integrands.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: omega
integer :: integr
real :: epsabs
real :: epsrel
real :: result
real :: abserr
integer :: neval
integer :: ier

public subroutine qaws(f, a, b, alfa, beta, integr, epsabs, epsrel, result, abserr, neval, ier)

QAWS estimates integrals with algebraico-logarithmic endpoint singularities.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: alfa
real :: beta
integer :: integr
real :: epsabs
real :: epsrel
real :: result
real :: abserr
integer :: neval
integer :: ier

public subroutine qawse(f, a, b, alfa, beta, integr, epsabs, epsrel, limit, result, abserr, neval, ier, alist, blist, rlist, elist, iord, last)

QAWSE estimates integrals with algebraico-logarithmic endpoint singularities.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: alfa
real :: beta
integer :: integr
real :: epsabs
real :: epsrel
integer :: limit
real :: result
real :: abserr
integer :: neval
integer :: ier
real :: alist(limit)
real :: blist(limit)
real :: rlist(limit)
real :: elist(limit)
integer :: iord(limit)
integer :: last

public subroutine qc25c(f, a, b, c, result, abserr, krul, neval)

QC25C returns integration rules for Cauchy Principal Value integrals.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: c
real :: result
real :: abserr
integer :: krul
integer :: neval

public subroutine qc25o(f, a, b, omega, integr, nrmom, maxp1, ksave, result, abserr, neval, resabs, resasc, momcom, chebmo)

QC25O returns integration rules for integrands with a COS or SIN factor.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: omega
integer :: integr
integer :: nrmom
integer :: maxp1
integer :: ksave
real :: result
real :: abserr
integer :: neval
real :: resabs
real :: resasc
integer :: momcom
real :: chebmo(maxp1,25)

public subroutine qc25s(f, a, b, bl, br, alfa, beta, ri, rj, rg, rh, result, abserr, resasc, integr, neval)

QC25S returns rules for algebraico-logarithmic end point singularities.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: bl
real :: br
real :: alfa
real :: beta
real :: ri(25)
real :: rj(25)
real :: rg(25)
real :: rh(25)
real :: result
real :: abserr
real :: resasc
integer :: integr
integer :: neval

public subroutine qcheb(x, fval, cheb12, cheb24)

QCHEB computes the Chebyshev series expansion.

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Arguments

Type IntentOptional Attributes Name
real :: x(11)
real :: fval(25)
real :: cheb12(13)
real :: cheb24(25)

public subroutine qextr(n, epstab, result, abserr, res3la, nres)

QEXTR carries out the Epsilon extrapolation algorithm.

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Arguments

Type IntentOptional Attributes Name
integer :: n
real :: epstab(52)
real :: result
real :: abserr
real :: res3la(3)
integer :: nres

public subroutine qfour(f, a, b, omega, integr, epsabs, epsrel, limit, icall, maxp1, result, abserr, neval, ier, alist, blist, rlist, elist, iord, nnlog, momcom, chebmo)

QFOUR estimates the integrals of oscillatory functions.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: omega
integer :: integr
real :: epsabs
real :: epsrel
integer :: limit
integer :: icall
integer :: maxp1
real :: result
real :: abserr
integer :: neval
integer :: ier
real :: alist(limit)
real :: blist(limit)
real :: rlist(limit)
real :: elist(limit)
integer :: iord(limit)
integer :: nnlog(limit)
integer :: momcom
real :: chebmo(maxp1,25)

public subroutine qk15(f, a, b, result, abserr, resabs, resasc)

QK15 carries out a 15 point Gauss-Kronrod quadrature rule.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: result
real :: abserr
real :: resabs
real :: resasc

public subroutine qk15i(f, boun, inf, a, b, result, abserr, resabs, resasc)

QK15I applies a 15 point Gauss-Kronrod quadrature on an infinite interval.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: boun
integer :: inf
real :: a
real :: b
real :: result
real :: abserr
real :: resabs
real :: resasc

public subroutine qk15w(f, w, p1, p2, p3, p4, kp, a, b, result, abserr, resabs, resasc)

QK15W applies a 15 point Gauss-Kronrod rule for a weighted integrand.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
public function w(absc_, p1_, p2_, p3_, p4_, kp_)
Arguments
Type IntentOptional Attributes Name
real, intent(in) :: absc_
real, intent(in) :: p1_
real, intent(in) :: p2_
real, intent(in) :: p3_
real, intent(in) :: p4_
integer, intent(in) :: kp_
Return Value real
real :: p1
real :: p2
real :: p3
real :: p4
integer :: kp
real :: a
real :: b
real :: result
real :: abserr
real :: resabs
real :: resasc

public subroutine qk21(f, a, b, result, abserr, resabs, resasc)

QK21 carries out a 21 point Gauss-Kronrod quadrature rule.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: result
real :: abserr
real :: resabs
real :: resasc

public subroutine qk31(f, a, b, result, abserr, resabs, resasc)

QK31 carries out a 31 point Gauss-Kronrod quadrature rule.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: result
real :: abserr
real :: resabs
real :: resasc

public subroutine qk41(f, a, b, result, abserr, resabs, resasc)

QK41 carries out a 41 point Gauss-Kronrod quadrature rule.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: result
real :: abserr
real :: resabs
real :: resasc

public subroutine qk51(f, a, b, result, abserr, resabs, resasc)

QK51 carries out a 51 point Gauss-Kronrod quadrature rule.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: result
real :: abserr
real :: resabs
real :: resasc

public subroutine qk61(f, a, b, result, abserr, resabs, resasc)

QK61 carries out a 61 point Gauss-Kronrod quadrature rule.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: result
real :: abserr
real :: resabs
real :: resasc

public subroutine qmomo(alfa, beta, ri, rj, rg, rh, integr)

QMOMO computes modified Chebyshev moments.

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Arguments

Type IntentOptional Attributes Name
real :: alfa
real :: beta
real :: ri(25)
real :: rj(25)
real :: rg(25)
real :: rh(25)
integer :: integr

public subroutine qng(f, a, b, epsabs, epsrel, result, abserr, neval, ier)

QNG estimates an integral, using non-adaptive integration.

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Arguments

Type IntentOptional Attributes Name
procedure(scalar_func) :: f
real :: a
real :: b
real :: epsabs
real :: epsrel
real :: result
real :: abserr
integer :: neval
integer :: ier

public subroutine qsort(limit, last, maxerr, ermax, elist, iord, nrmax)

QSORT maintains the order of a list of local error estimates.

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Arguments

Type IntentOptional Attributes Name
integer :: limit
integer :: last
integer :: maxerr
real :: ermax
real :: elist(last)
integer :: iord(last)
integer :: nrmax

public subroutine timestamp()

TIMESTAMP prints the current YMDHMS date as a time stamp.

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Arguments

None