ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_distNorm::getZigNorm Interface Reference

Generate and return the lower right edges of the rectangles of a Ziggurat partitioning of the Normal density function (and the corresponding density function values) to be used for Normal random number generation using the Ziggurat algorithm. More...

Detailed Description

Generate and return the lower right edges of the rectangles of a Ziggurat partitioning of the Normal density function (and the corresponding density function values) to be used for Normal random number generation using the Ziggurat algorithm.

See the documentation of pm_ziggurat for information on the Ziggurat method.
See the documentation of getZig for the meaning of the elements of the output array.

Parameters
[in]nlay: See the documentation of the corresponding argument of getZig.
[in]abserr: See the documentation of the corresponding argument of getZig.
[in]abstol: See the documentation of the corresponding argument of getZig.
Returns
zig : See the documentation of the corresponding output of getZig.


Possible calling interfaces ⛓

use pm_distNorm, only: getZigNorm
zig(1 : 2, 0 : nlay) = getZigNorm(nlay, abserr, abstol = abstol)
pm_distNorm::getZigNorm
Generate and return the lower right edges of the rectangles of a Ziggurat partitioning of the Normal ...
Definition: pm_distNorm.F90:3294
pm_distNorm
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distNorm.F90:179
Warning
All conditions that hold for getZig equally apply to the procedures of this generic interface.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.
Remarks
The procedures under discussion are impure.
See also
getZig
getNormRand
setNormRand


Example usage ⛓

1program example
2
3 use pm_kind, only: SK
4 use pm_kind, only: IK, RK ! all real kinds are supported.
5 use pm_io, only: display_type
6 use pm_distNorm, only: getZigNorm
7 use pm_arrayRebind, only: setRebound
8
9 implicit none
10
11 type(display_type) :: disp
12 disp = display_type(file = "main.out.F90")
13
14 block
15 use pm_kind, only: RKG => RKH
16 real(RKG), allocatable :: zig(:,:)
17 integer(IK) :: nlayer
18 real(RKG) :: abserr
19 call disp%skip()
20 call disp%show("nlayer = 256")
21 nlayer = 256
22 call disp%show("call setRebound(zig, [1_IK, 0_IK], [2_IK, nlayer])")
23 call setRebound(zig, [1_IK, 0_IK], [2_IK, nlayer])
24 call disp%show("zig(:,:) = getZigNorm(nlayer, abserr, abstol = epsilon(0._RKG)) ! rectangle rightmost corners and the corresponding function values.")
25 zig(:,:) = getZigNorm(nlayer, abserr, abstol = epsilon(0._RKG))
26 call disp%show("[nlayer, shape(zig, IK)]")
27 call disp%show( [nlayer, shape(zig, IK)] )
28 call disp%show("abserr")
29 call disp%show( abserr )
30 call disp%show("zig(1, 1) ! The upper rightmost corner of the lowest rectangle (which has a tail) in the ziggurat set.")
31 call disp%show( zig(1, 1) )
32 call disp%show("transpose(zig)")
33 call disp%show( transpose(zig) )!, format = "(sp,*(ES0.37E1,:,', '))")
34 call disp%show("reshape(zig(1, 1 : nlayer - 1) * (zig(2, 2 : nlayer) - zig(2, 1 : nlayer - 1)), [nlayer - 1, 1]) ! area of each partition.")
35 call disp%show( reshape(zig(1, 1 : nlayer - 1) * (zig(2, 2 : nlayer) - zig(2, 1 : nlayer - 1)), [nlayer - 1, 1]) )
36 call disp%skip()
37 end block
38
39 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
40 !Output an example array for illustration.
41 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
42
43 block
44 use pm_io, only: getErrTableWrite, trans
45 use pm_kind, only: RKG => RKH
46 real(RKG) :: abserr
47 if (0 /= getErrTableWrite(SK_"getZigNorm.RK.txt", getZigNorm(64_IK, abserr), trans)) error stop "Failed to write the table to the file."
48 end block
49
50end program example
pm_arrayRebind::setRebound
Resize (shrink or expand) an input allocatable array of rank 1..3 to arbitrary new lower and upper bo...
Definition: pm_arrayRebind.F90:218
pm_io::getErrTableWrite
Generate and return the iostat code resulting from writing the input table of rank 1 or 2 to the spec...
Definition: pm_io.F90:5940
pm_io::show
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726
pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
pm_arrayRebind
This module contains procedures and generic interfaces for resizing allocatable arrays of various typ...
Definition: pm_arrayRebind.F90:64
pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252
pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
pm_kind::RK
integer, parameter RK
The default real kind in the ParaMonte library: real64 in Fortran, c_double in C-Fortran Interoperati...
Definition: pm_kind.F90:543
pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540
pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539
pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858
pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh
2rm main.exe
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh
2rm main.exe
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example output ⛓
1
2nlayer = 256
3call setRebound(zig, [1_IK, 0_IK], [2_IK, nlayer])
4zig(:,:) = getZigNorm(nlayer, abserr, abstol = epsilon(0._RKG)) ! rectangle rightmost corners and the corresponding function values.
5[nlayer, shape(zig, IK)]
6+256, +2, +257
7abserr
8+0.562732655625645475814793555099033451E-33
9zig(1, 1) ! The upper rightmost corner of the lowest rectangle (which has a tail) in the ziggurat set.
10+3.65415288536100877164542972039951567
11transpose(zig)
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Postprocessing of the example output ⛓
1#!/usr/bin/env python
2
3import matplotlib.pyplot as plt
4import pandas as pd
5import numpy as np
6import glob
7import sys
8
9linewidth = 2
10fontsize = 17
11
12for kind in ["RK"]:
13
14 pattern = "*." + kind + ".txt"
15 fileList = glob.glob(pattern)
16
17 for file in fileList:
18
19 df = pd.read_csv(file, delimiter = ",", header = None)
20
21 # start with a square Figure
22 fig = plt.figure(figsize=(8, 8))
23
24 plt.rcParams.update({'font.size': fontsize - 2})
25 ax = plt.subplot()
26
27 ax.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
28 ax.tick_params(axis = "y", which = "minor")
29 ax.tick_params(axis = "x", which = "minor")
30
31 # the scatter plot:
32 ax.plot ( df.values[:, 0]
33 , df.values[:, 1]
34 , linewidth = 2
35 , color = "black"
36 )
37 ax.scatter ( df.values[:, 0]
38 , df.values[:, 1]
39 , s = 8
40 , zorder = 1000
41 , color = "red"
42 )
43
44 ax.set_xlabel("X", fontsize = 17)
45 ax.set_ylabel("Y", fontsize = 17)
46
47 plt.savefig(file.replace(".txt",".png"))

Visualization of the example output ⛓
Test:
test_pm_distNorm


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, April 25, 2015, 2:21 PM, National Institute for Fusion Studies, The University of Texas at Austin

Definition at line 3294 of file pm_distNorm.F90.

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