pm_clusTest::mmvue_type Type Reference

This is the derived type for generating objects containing the specifications of a realization of an MMUVE distribution and a collection of randomly sampled points from it.
More...

Public Member Functions
procedure, pass	write => mmvue_type_write

Public Attributes
type(range_type)	range
	The scalar object of type range_type containing the specifications of the MMVUE distribution. More...
integer(IK)	ndim
	The number of dimensions of the domain of the MMVUE distribution. More...
integer(IK)	nell
	The number of ellipsoids in the domain of the MMVUE distribution. More...
integer(IK)	nsam
	The number of random points sampled from the domain of the MMVUE distribution. More...
integer(IK)	nsim = 10000
	The scalar of type integer of default kind IK, representing the number of simulated random vectors from the ellipsoids of the distribution to estimate the effective volumes of the ellipsoids (i.e., the inverse of the PDF of the distribution). More...
real(RKG)	logVolUnitBall
	The natural logarithm of the volume of a unit ball in ndim dimensions. More...
real(RKG)	logDensity
	The scalar of type real containing the natural logarithm of the inverse of the effective volume of a single sampled point from the distribution domain, normalized by the volume of a unit ball. In other words, logDensity = log(mmvue_type%nsam) - mmvue_type%logSumVolNormedEff. More...
real(RKG)	logSumVolNormedEff
	The natural logarithm of the sum of the effective volumes of the distribution ellipsoids, normalized by logVolUnitBall. This measure includes shared volumes between ellipsoids only once from one individual ellipsoid. Because this measure does not have closed expression, it must be approximated using Monte Carlo approach. By definition, this sum is always smaller than or equal to the sum of the individual normalized ellipsoid volumes. The equality happens only when no two ellipsoids overlap. More...
real(RKG), dimension(:,:), allocatable	std
	The matrix of shape (1:ndim, 1:nell) containing the standard deviations of the ellipsoids in the distribution. More...
real(RKG), dimension(:,:), allocatable	sample
	The matrix of shape (1:ndim, 1:nsam) containing the set of uniformly-sampled random points from the distribution domain. More...
real(RKG), dimension(:,:), allocatable	mean
	The matrix of shape (1:ndim, 1:nell) containing the set of nell ellipsoid centers of the distribution domain. More...
real(RKG), dimension(:,:,:), allocatable	invGram
	The matrix of shape (1:ndim, 1:ndim, 1:nell) containing the set of nell ellipsoid inverse-Gramian matrices of the distribution domain. More...
real(RKG), dimension(:,:,:), allocatable	choLowGramUpp
	The matrix of shape (1:ndim, 1:ndim + 1, 1:nell) containing the set of nell ellipsoid Cholesky-Gramian half (triangular) matrices of the distribution domain. More...
real(RKG), dimension(:), allocatable	cumPropVolNormed
	The vector of shape (0:nell) containing the cumulative proportion of volumes of individual ellipsoids in the distribution, used for generating the random sample. More...
real(RKG), dimension(:), allocatable	logVolNormed
	The vector of shape (1:nell) containing the natural logarithm of the set of nell volumes of the Gramian matrices of the distribution domain, normalized by the volume of a unit ball. More...
real(RKG), dimension(:,:), allocatable	mahalSq
	The matrix of shape (1:nell, 1:nsam) containing the square of the Mahalanobis distances the randomly sampled points from each ellipsoid center in the distribution. More...
real(RKG), dimension(:), allocatable	invmul
	The vector of shape (1:nsam) containing the inverse of sample multiplicity, that is, the ellipsoidal membership count of each randomly-sampled point from the distribution. For example, a multiplicity of 3 means that the isam sampled point falls within exactly three ellipsoids in the distribution. More...
integer(IK), dimension(:), allocatable	size
	The vector of shape (1:nell) containing the set of nell counts of randomly-sampled points from within each ellipsoid in the distribution. More...
integer(IK), dimension(:), allocatable	membership
	The vector of shape (1:nsam) containing the ellipsoidal membership of each randomly-sampled point from the distribution. More...
type(err_type)	err

Detailed Description

This is the derived type for generating objects containing the specifications of a realization of an MMUVE distribution and a collection of randomly sampled points from it.

See also the documentation of the type constructor mmvue_typer.

Possible calling interfaces ⛓

use pm_clusTest, only: mmvue_type
type(mmvue_type) :: mmvue
 
mmvue = mmvue_type(rng, range = range_type(), nsim = nsim)

See also

mmvue_typer

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_clusTest, only: mmvue_type, rngf_type
    use pm_io, only: getErrTableWrite, trans
    use pm_io, only: display_type
    use pm_val2str, only: getStr
 
    implicit none
 
    integer(IK) :: itry
    type(mmvue_type) :: mmvue
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    do itry = 0, 9
        call disp%skip()
        call disp%show("mmvue = mmvue_type(rng = rngf_type())")
                        mmvue = mmvue_type(rng = rngf_type())
        call disp%show("[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]")
        call disp%show( [mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim] )
        call disp%show("if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'")
                        if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
        call disp%skip()
    end do
 
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 ⛓

 
mmvue = mmvue_type(rng = rngf_type())
[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]
+2, +11, +5000, +10000
if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
 
 
mmvue = mmvue_type(rng = rngf_type())
[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]
+2, +13, +5000, +10000
if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
 
 
mmvue = mmvue_type(rng = rngf_type())
[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]
+2, +7, +5000, +10000
if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
 
 
mmvue = mmvue_type(rng = rngf_type())
[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]
+2, +4, +5000, +10000
if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
 
 
mmvue = mmvue_type(rng = rngf_type())
[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]
+2, +5, +5000, +10000
if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
 
 
mmvue = mmvue_type(rng = rngf_type())
[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]
+2, +17, +5000, +10000
if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
 
 
mmvue = mmvue_type(rng = rngf_type())
[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]
+2, +13, +5000, +10000
if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
 
 
mmvue = mmvue_type(rng = rngf_type())
[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]
+2, +17, +5000, +10000
if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
 
 
mmvue = mmvue_type(rng = rngf_type())
[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]
+2, +1, +5000, +10000
if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
 
 
mmvue = mmvue_type(rng = rngf_type())
[mmvue%ndim, mmvue%nell, mmvue%nsam, mmvue%nsim]
+2, +1, +5000, +10000
if (0 /= getErrTableWrite(SK_'mmvue_type.'//getStr(itry)//SK_'.txt', reshape([transpose(mmvue%sample), real(mmvue%membership, kind(mmvue%sample))], [mmvue%nsam, mmvue%ndim + 1_IK]))) error stop 'Failed to write the random vectors file.'
 
 

Postprocessing of the example output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import glob
import sys
import os
procname = os.path.basename(os.getcwd())
 
linewidth = 2
fontsize = 17
 
pattern = procname + "*.txt"
fileList = glob.glob(pattern)
 
for file in fileList:
 
    df = pd.read_csv(file, delimiter = ",", header = None)
 
    # definitions for the axes
    left, width = 0.1, 0.65
    bottom, height = 0.1, 0.65
    spacing = 0.015
 
    # start with a square Figure
    fig = plt.figure(figsize = (8, 8), dpi = 200)
 
    
    plt.rcParams.update({'font.size': fontsize - 2})
    ax = plt.subplot()
    #ax = fig.add_axes([left, bottom, width, height]) # scatter plot
    #ax_histx = fig.add_axes([left, bottom + height + spacing, width, 0.2], sharex = ax) # histx
    #ax_histy = fig.add_axes([left + width + spacing, bottom, 0.2, height], sharey = ax) # histy
 
    for axes in [ax]:#, ax_histx, ax_histy]:
        axes.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
        axes.tick_params(axis = "y", which = "minor")
        axes.tick_params(axis = "x", which = "minor")
 
    # no labels
    #ax_histy.tick_params(axis = "y", labelleft = False)
    #ax_histx.tick_params(axis = "x", labelbottom = False)
 
    # the scatter plot:
    ax.scatter  ( df.values[:, 0]
                , df.values[:, 1]
                , c = df.values[:, -1]
                , cmap = "gist_rainbow"
                , zorder = 1000
                , marker = "o"
                , alpha = 1
                , s = 0.7
                )
 
    #ax_histx.hist(df.values[:, 0], bins = 50, zorder = 1000)
    #ax_histy.hist(df.values[:, 1], bins = 50, orientation = "horizontal", zorder = 1000)
 
    ax.set_xlabel("X", fontsize = 17)
    ax.set_ylabel("Y", fontsize = 17)
    #plt.title("file: " + file)
 
    plt.savefig(file.replace(".txt",".svg"))

Visualization of the example output ⛓

Test:

test_pm_clusTest

Todo:

High Priority: This type must be generalized to accept real components of arbitrary kind, once GNU compiler support for PDTs is strong.

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, 2012, 12:00 AM, National Institute for Fusion Studies, The University of Texas Austin

Definition at line 149 of file pm_clusTest.F90.

Member Function/Subroutine Documentation

write()

procedure, pass pm_clusTest::mmvue_type::write

Definition at line 179 of file pm_clusTest.F90.

Member Data Documentation

choLowGramUpp

real(RKG), dimension(:,:,:), allocatable pm_clusTest::mmvue_type::choLowGramUpp

The matrix of shape (1:ndim, 1:ndim + 1, 1:nell) containing the set of nell ellipsoid Cholesky-Gramian half (triangular) matrices of the distribution domain.

Definition at line 169 of file pm_clusTest.F90.

cumPropVolNormed

real(RKG), dimension(:), allocatable pm_clusTest::mmvue_type::cumPropVolNormed

The vector of shape (0:nell) containing the cumulative proportion of volumes of individual ellipsoids in the distribution, used for generating the random sample.

Definition at line 170 of file pm_clusTest.F90.

err

type(err_type) pm_clusTest::mmvue_type::err

Definition at line 177 of file pm_clusTest.F90.

invGram

real(RKG), dimension(:,:,:), allocatable pm_clusTest::mmvue_type::invGram

The matrix of shape (1:ndim, 1:ndim, 1:nell) containing the set of nell ellipsoid inverse-Gramian matrices of the distribution domain.

Definition at line 168 of file pm_clusTest.F90.

invmul

real(RKG), dimension(:), allocatable pm_clusTest::mmvue_type::invmul

The vector of shape (1:nsam) containing the inverse of sample multiplicity, that is, the ellipsoidal membership count of each randomly-sampled point from the distribution.
For example, a multiplicity of 3 means that the isam sampled point falls within exactly three ellipsoids in the distribution.

Definition at line 173 of file pm_clusTest.F90.

logDensity

real(RKG) pm_clusTest::mmvue_type::logDensity

The scalar of type real containing the natural logarithm of the inverse of the effective volume of a single sampled point from the distribution domain, normalized by the volume of a unit ball.
In other words, logDensity = log(mmvue_type%nsam) - mmvue_type%logSumVolNormedEff.

Definition at line 157 of file pm_clusTest.F90.

logSumVolNormedEff

real(RKG) pm_clusTest::mmvue_type::logSumVolNormedEff

The natural logarithm of the sum of the effective volumes of the distribution ellipsoids, normalized by logVolUnitBall.
This measure includes shared volumes between ellipsoids only once from one individual ellipsoid.
Because this measure does not have closed expression, it must be approximated using Monte Carlo approach.
By definition, this sum is always smaller than or equal to the sum of the individual normalized ellipsoid volumes.
The equality happens only when no two ellipsoids overlap.

Definition at line 160 of file pm_clusTest.F90.

logVolNormed

real(RKG), dimension(:), allocatable pm_clusTest::mmvue_type::logVolNormed

The vector of shape (1:nell) containing the natural logarithm of the set of nell volumes of the Gramian matrices of the distribution domain, normalized by the volume of a unit ball.

Definition at line 171 of file pm_clusTest.F90.

logVolUnitBall

real(RKG) pm_clusTest::mmvue_type::logVolUnitBall

The natural logarithm of the volume of a unit ball in ndim dimensions.

Definition at line 156 of file pm_clusTest.F90.

mahalSq

real(RKG), dimension(:,:), allocatable pm_clusTest::mmvue_type::mahalSq

The matrix of shape (1:nell, 1:nsam) containing the square of the Mahalanobis distances the randomly sampled points from each ellipsoid center in the distribution.

Definition at line 172 of file pm_clusTest.F90.

mean

real(RKG), dimension(:,:), allocatable pm_clusTest::mmvue_type::mean

The matrix of shape (1:ndim, 1:nell) containing the set of nell ellipsoid centers of the distribution domain.

Definition at line 167 of file pm_clusTest.F90.

membership

integer(IK), dimension(:), allocatable pm_clusTest::mmvue_type::membership

The vector of shape (1:nsam) containing the ellipsoidal membership of each randomly-sampled point from the distribution.

Definition at line 176 of file pm_clusTest.F90.

ndim

integer(IK) pm_clusTest::mmvue_type::ndim

The number of dimensions of the domain of the MMVUE distribution.

Definition at line 151 of file pm_clusTest.F90.

nell

integer(IK) pm_clusTest::mmvue_type::nell

The number of ellipsoids in the domain of the MMVUE distribution.

Definition at line 152 of file pm_clusTest.F90.

nsam

integer(IK) pm_clusTest::mmvue_type::nsam

The number of random points sampled from the domain of the MMVUE distribution.

Definition at line 153 of file pm_clusTest.F90.

nsim

integer(IK) pm_clusTest::mmvue_type::nsim = 10000

The scalar of type integer of default kind IK, representing the number of simulated random vectors from the ellipsoids of the distribution to estimate the effective volumes of the ellipsoids (i.e., the inverse of the PDF of the distribution).

Definition at line 154 of file pm_clusTest.F90.

range

type(range_type) pm_clusTest::mmvue_type::range

The scalar object of type range_type containing the specifications of the MMVUE distribution.

Definition at line 150 of file pm_clusTest.F90.

sample

real(RKG), dimension(:,:), allocatable pm_clusTest::mmvue_type::sample

The matrix of shape (1:ndim, 1:nsam) containing the set of uniformly-sampled random points from the distribution domain.

Definition at line 166 of file pm_clusTest.F90.

size

integer(IK), dimension(:), allocatable pm_clusTest::mmvue_type::size

The vector of shape (1:nell) containing the set of nell counts of randomly-sampled points from within each ellipsoid in the distribution.

Definition at line 175 of file pm_clusTest.F90.

std

real(RKG), dimension(:,:), allocatable pm_clusTest::mmvue_type::std

The matrix of shape (1:ndim, 1:nell) containing the standard deviations of the ellipsoids in the distribution.

Definition at line 165 of file pm_clusTest.F90.

---

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

• src/fortran/main/pm_clusTest.F90