pm_quadPack::GK61_type Type Reference

This is the indicator type for generating instances of objects that indicate the use of 30-point Gauss-Legendre quadrature with 61-point Kronrod extension formulae as the drivers in the (Adaptive) Global Gauss-Kronrod Quadrature of getQuadGK. More...

Detailed Description

This is the indicator type for generating instances of objects that indicate the use of 30-point Gauss-Legendre quadrature with 61-point Kronrod extension formulae as the drivers in the (Adaptive) Global Gauss-Kronrod Quadrature of getQuadGK.

This is an empty derived type that exists solely for generating unique objects that are distinguishable as input arguments to procedures under the generic interface getQuadGK.

Possible calling interfaces ⛓

use pm_quadPack, only: GK61_type
type(GK61_type) :: GK61

See also

GK15_type
GK21_type
GK31_type
GK41_type
GK51_type
GK61_type
getQuadGK
getQuadErr

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, RK => RKH ! All other real kinds are also supported.
    use pm_quadpack, only: getQuadErr, GK61
    use pm_quadpack, only: setNodeWeightGK
    use pm_distLogNorm, only: getLogNormCDF
    use pm_distNorm, only: getNormCDF
    use pm_io, only: display_type
    use pm_val2str, only: getStr
 
    implicit none
 
    integer(IK) , parameter     :: NINTMAX = 1000_IK
    real(RK)    , parameter     :: ABSTOL = 0._RK, RELTOL = epsilon(0._RK) * 10000
    real(RK)                    :: lb, ub, truth, integral, abserr, sinfo(4, NINTMAX)
    integer(IK)                 :: err, neval, nint, sindex(NINTMAX)
 
    type(display_type)      :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the Gauss-Kronrod quadrature of the probability density function of the Standard Normal distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("[ABSTOL, RELTOL]")
    call disp%show( [ABSTOL, RELTOL] )
    call disp%show("lb = -100._RK; ub = +100._RK")
                    lb = -100._RK; ub = +100._RK
    call disp%show("err = getQuadErr(getNormPDF, lb, ub, ABSTOL, RELTOL, GK61, integral, abserr, sinfo, sindex, neval, nint)")
                    err = getQuadErr(getNormPDF, lb, ub, ABSTOL, RELTOL, GK61, integral, abserr, sinfo, sindex, neval, nint)
    call disp%show("if (err /= 0_IK) error stop 'integration failed: err = '//getStr(err)")
                    if (err /= 0_IK) error stop 'integration failed: err = '//getStr(err)
    call disp%show("truth = getNormCDF(ub) - getNormCDF(lb)")
                    truth = getNormCDF(ub) - getNormCDF(lb)
    call disp%show("[truth, integral, abserr, abs(integral - truth) / truth]")
    call disp%show( [truth, integral, abserr, abs(integral - truth) / truth] )
    call disp%show("[neval, nint]")
    call disp%show( [neval, nint] )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the Gauss-Kronrod quadrature of the probability density function of the Standard LogNormal distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("[ABSTOL, RELTOL]")
    call disp%show( [ABSTOL, RELTOL] )
    call disp%show("lb = exp(-10._RK); ub = exp(+10._RK)")
                    lb = exp(-10._RK); ub = exp(+10._RK)
    call disp%show("err = getQuadErr(getLogNormPDF, lb, ub, ABSTOL, RELTOL, GK61, integral, abserr, sinfo, sindex, neval, nint)")
                    err = getQuadErr(getLogNormPDF, lb, ub, ABSTOL, RELTOL, GK61, integral, abserr, sinfo, sindex, neval, nint)
    call disp%show("if (err /= 0_IK) error stop 'integration failed: err = '//getStr(err)")
                    if (err /= 0_IK) error stop 'integration failed: err = '//getStr(err)
    call disp%show("truth = getLogNormCDF(ub) - getLogNormCDF(lb)")
                    truth = getLogNormCDF(ub) - getLogNormCDF(lb)
    call disp%show("[truth, integral, abserr, abs(integral - truth) / truth]")
    call disp%show( [truth, integral, abserr, abs(integral - truth) / truth] )
    call disp%show("[neval, nint]")
    call disp%show( [neval, nint] )
    call disp%skip()
 
contains
 
    function getIntSinCos(x) result(integrand)
        real(RK)    , intent(in)    :: x
        real(RK)                    :: integrand
        integrand = cos(100._RK * sin(x))
    end function
 
    function getNormPDF(x) result(pdf)
        use pm_distNorm, only: getNormLogPDF
        real(RK)    , intent(in)    :: x
        real(RK)                    :: pdf
        pdf = exp(getNormLogPDF(x))
    end function
 
    function getLogNormPDF(x) result(pdf)
        use pm_distLogNorm, only: getLogNormLogPDF
        real(RK)    , intent(in)    :: x
        real(RK)                    :: pdf
        pdf = exp(getLogNormLogPDF(x))
    end function
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the Gauss-Kronrod quadrature of the probability density function of the Standard Normal distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
[ABSTOL, RELTOL]
+0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-29
lb = -100._RK; ub = +100._RK
err = getQuadErr(getNormPDF, lb, ub, ABSTOL, RELTOL, GK61, integral, abserr, sinfo, sindex, neval, nint)
if (err /= 0_IK) error stop 'integration failed: err = '//getStr(err)
truth = getNormCDF(ub) - getNormCDF(lb)
[truth, integral, abserr, abs(integral - truth) / truth]
+1.00000000000000000000000000000000000, +1.00000000000000000000000000000000039, +0.946347726268626978289079196639920652E-32, +0.385185988877447170611195588516985464E-33
[neval, nint]
+1159, +10
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the Gauss-Kronrod quadrature of the probability density function of the Standard LogNormal distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
[ABSTOL, RELTOL]
+0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-29
lb = exp(-10._RK); ub = exp(+10._RK)
err = getQuadErr(getLogNormPDF, lb, ub, ABSTOL, RELTOL, GK61, integral, abserr, sinfo, sindex, neval, nint)
if (err /= 0_IK) error stop 'integration failed: err = '//getStr(err)
truth = getLogNormCDF(ub) - getLogNormCDF(lb)
[truth, integral, abserr, abs(integral - truth) / truth]
+0.999999999999999999999984760293951620, +0.999999999999999999999984760293946997, +0.495256829077377151017672632812277594E-31, +0.462223186652936604733441750365875893E-32
[neval, nint]
+2745, +23
 
 

Test:

test_pm_quadPack

Final Remarks ⛓

---

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.
   

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, September 1, 2017, 12:00 AM, Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin

Definition at line 1748 of file pm_quadPack.F90.

---

The documentation for this type was generated from the following file:

• src/fortran/main/pm_quadPack.F90