pm_quadTest::intNormPDF_type Type Reference

This is the derived type for generating test integrand objects of the Probability Density Function of the Normal distribution. More...

Inheritance diagram for pm_quadTest::intNormPDF_type:

Collaboration diagram for pm_quadTest::intNormPDF_type:

Public Member Functions
procedure	get => getIntNormPDF
Public Member Functions inherited from pm_quadTest::integrand_type
procedure(get_proc), deferred	get
	The function member returning the value of the unweighted integrand (whether Cauchy/sin/cos/algebraically types of weights) at a specified input point x. More...

Public Attributes
real(RKH)	mu
	The location parameter of the Normal distribution. More...
real(RKH)	sigma
	The scale parameter (standard deviation) of the Normal distribution. More...
real(RKH)	invSigma
	The inverse scale parameter (standard deviation) of the Normal distribution. More...
real(RKH)	logInvSigma
	The natural logarithm of the inverse scale parameter (standard deviation) of the Normal distribution. More...
Public Attributes inherited from pm_quadTest::integrand_type
real(RKH)	lb
	The scalar of type real of the highest kind supported by the library RKH, containing the lower limit of integration. More...
real(RKH)	ub
	The scalar of type real of the highest kind supported by the library RKH, containing the upper limit of integration. More...
real(RKH)	integral
	The scalar of type real of the highest kind supported by the library RKH, containing the true result of integration. More...
real(RKH), dimension(:), allocatable	break
	The scalar of type real of the highest kind supported by the library RKH, containing the points of difficulties of integration. More...
type(wcauchy_type), allocatable	wcauchy
	The scalar of type wcauchy_type, containing the Cauchy singularity of the integrand. More...
character(:, SK), allocatable	desc
	The scalar allocatable character of default kind SK containing a description of the integrand and integration limits and difficulties. More...

Detailed Description

This is the derived type for generating test integrand objects of the Probability Density Function of the Normal distribution.

The full integrand is defined as,

\begin{equation} \pi(x | \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi}}\exp\bigg( -\frac{\big(x - \mu\big)^2}{2\sigma^2} \bigg) ~,~ x \in (-\infty, +\infty) \end{equation}

Parameters

[in]	lb	: The input scalar of type real of kind RKH, containing the lower limit of integration. (optional, default = getInfNeg(real(0,kind(lb)))
[in]	ub	: The input scalar of the same type and kind as lb, containing the upper limit of integration. (optional, default = getInfPos(real(0,kind(ub)))
[in]	mu	: The input scalar of the same type and kind as lb, representing the location parameter of the Normal distribution. (optional, default = 0)
[in]	sigma	: The input scalar of the same type and kind as lb, representing the scale parameter of the Normal distribution. (optional, default = 1.)

Possible calling interfaces ⛓

use pm_quadTest, only: intNormPDF_type
type(intNormPDF_type) :: integrand
 
integrand = intNormPDF_type(lb = lb, ub = ub, mu = mu, sigma = sigma)
print *, "description: ", integrand%desc
print *, "lower limit: ", integrand%lb
print *, "upper limit: ", integrand%ub
print *, "Example integrand value: ", integrand%get(x)

See also

integrand_type

Test:

test_pm_quadPack

Final Remarks ⛓

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For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
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Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Definition at line 1190 of file pm_quadTest.F90.

Member Function/Subroutine Documentation

get()

procedure pm_quadTest::intNormPDF_type::get

Definition at line 1196 of file pm_quadTest.F90.

References pm_kind::RKH.

Member Data Documentation

invSigma

real(RKH) pm_quadTest::intNormPDF_type::invSigma

The inverse scale parameter (standard deviation) of the Normal distribution.

Definition at line 1193 of file pm_quadTest.F90.

logInvSigma

real(RKH) pm_quadTest::intNormPDF_type::logInvSigma

The natural logarithm of the inverse scale parameter (standard deviation) of the Normal distribution.

Definition at line 1194 of file pm_quadTest.F90.

mu

real(RKH) pm_quadTest::intNormPDF_type::mu

The location parameter of the Normal distribution.

Definition at line 1191 of file pm_quadTest.F90.

sigma

real(RKH) pm_quadTest::intNormPDF_type::sigma

The scale parameter (standard deviation) of the Normal distribution.

Definition at line 1192 of file pm_quadTest.F90.

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

• src/fortran/main/pm_quadTest.F90