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

Generate and return the quantile of the univariate Normal distribution at the specified input CDF. More...

Detailed Description

Generate and return the quantile of the univariate Normal distribution at the specified input CDF.

Parameters
[out]quantile: The output scalar or array of the same shape as the input array-like arguments, of,
  1. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the quantile of the distribution at the specified input cdf.
[in]cdf: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as the output quantile, representing the point(s) (probabilities) at which the quantile must be computed.
The cdf must be in the range \([0, 1]\).
[in]mu: The input scalar or array of the same shape as other array-like arguments of the same type and kind as the output quantile representing the location parameter of the distribution.
(optional, default = 0)
[in]sigma: The input scalar of the same type and kind as the output quantile, representing the scale parameter of the distribution.
(optional, default = 1.)


Possible calling interfaces

call setNormQuan(quantile, cdf)
call setNormQuan(quantile, cdf, mu)
call setNormQuan(quantile, cdf, mu, sigma)
Generate and return the quantile of the univariate Normal distribution at the specified input CDF.
This module contains classes and procedures for computing various statistical quantities related to t...
Warning
The condition 0. < sigma must hold for the corresponding procedure argument.
The condition 0. <= cdf .and. cdf <= 1. must hold for the corresponding procedure arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.
The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.
Remarks
The procedures under discussion are elemental.
Note
The procedures of this generic interface are merely wrappers around the procedures of setErfInv.
See the documentation of setErfInv about the accuracy of the computed quantile.
See also
getNormQuan


Example usage

1program example
2
3 use pm_kind, only: SK, IK, LK
5 use pm_distNorm, only: setNormQuan
7 use pm_io, only: display_type
8
9 implicit none
10
11 real, allocatable :: cdf(:), quantile(:), mu(:), sigma(:) ! all real kinds are supported.
12
13 type(display_type) :: disp
14 disp = display_type(file = "main.out.F90")
15
16 call disp%skip()
17 call disp%show("cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]")
18 cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
19 call disp%show("call setResized(quantile, size(cdf, 1, IK))")
20 call setResized(quantile, size(cdf, 1, IK))
21 call disp%show("call setNormQuan(quantile, cdf)")
22 call setNormQuan(quantile, cdf)
23 call disp%show("quantile")
24 call disp%show( quantile )
25 call disp%skip()
26
27 call disp%skip()
28 call disp%show("cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]")
29 cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
30 call disp%show("call setResized(quantile, size(cdf, 1, IK))")
31 call setResized(quantile, size(cdf, 1, IK))
32 call disp%show("call setNormQuan(quantile, cdf, mu = 1.)")
33 call setNormQuan(quantile, cdf, mu = 1.)
34 call disp%show("quantile")
35 call disp%show( quantile )
36 call disp%skip()
37
38 call disp%skip()
39 call disp%show("cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]")
40 cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
41 call disp%show("call setResized(quantile, size(cdf, 1, IK))")
42 call setResized(quantile, size(cdf, 1, IK))
43 call disp%show("call setNormQuan(quantile, cdf, mu = 1., sigma = 10.)")
44 call setNormQuan(quantile, cdf, mu = 1., sigma = 10.)
45 call disp%show("quantile")
46 call disp%show( quantile )
47 call disp%skip()
48
49 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
50 ! Output an example quantile array for visualization.
51 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
52
53 block
54 integer(IK) :: fileUnit, i
55 open(newunit = fileUnit, file = "setNormQuan.RK.txt")
56 cdf = getLinSpace(0., 1., count = 1000_IK, lopen = .true._LK, fopen = .true._LK)
57 call setResized(quantile, 4_IK)
58 do i = 1, size(cdf)
59 call setNormQuan(quantile, cdf(i), [0., 0., 0., -2.], sigma = [3., 1., 0.3, 1.])
60 write(fileUnit, "(5(g0,:,','))") cdf(i), quantile
61 end do
62 close(fileUnit)
63 end block
64
65end program example
Allocate or resize (shrink or expand) an input allocatable scalar string or array of rank 1....
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
This module contains procedures and generic interfaces for resizing allocatable arrays of various typ...
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
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
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
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
2cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
3call setResized(quantile, size(cdf, 1, IK))
4call setNormQuan(quantile, cdf)
5quantile
6-0.340282347E+39, -1.64485335, -1.00000107, +0.00000000, +0.408795118, +1.64485335, +0.340282347E+39
7
8
9cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
10call setResized(quantile, size(cdf, 1, IK))
11call setNormQuan(quantile, cdf, mu = 1.)
12quantile
13-0.340282347E+39, -0.644853354, -0.107288361E-5, +1.00000000, +1.40879512, +2.64485335, +0.340282347E+39
14
15
16cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
17call setResized(quantile, size(cdf, 1, IK))
18call setNormQuan(quantile, cdf, mu = 1., sigma = 10.)
19quantile
20-0.340282347E+39, -15.4485340, -9.00001049, +1.00000000, +5.08795118, +17.4485340, +0.340282347E+39
21
22

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
12marker ={ "CK" : "-"
13 , "IK" : "."
14 , "RK" : "-"
15 }
16xlab = { "CK" : "CDF ( real/imaginary components )"
17 , "IK" : "CDF ( integer-valued )"
18 , "RK" : "CDF ( real-valued )"
19 }
20legends = [ r"$\mu = 0.0,~\sigma = 3.0$"
21 , r"$\mu = 0.0,~\sigma = 1.0$"
22 , r"$\mu = 0.0,~\sigma = 0.3$"
23 , r"$\mu = -2.,~\sigma = 1.0$"
24 ]
25
26for kind in ["IK", "CK", "RK"]:
27
28 pattern = "*." + kind + ".txt"
29 fileList = glob.glob(pattern)
30 if len(fileList) == 1:
31
32 df = pd.read_csv(fileList[0], delimiter = ",")
33
34 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
35 ax = plt.subplot()
36
37 if kind == "CK":
38 plt.plot( df.values[:, 0]
39 , df.values[:,1:5]
40 , marker[kind]
41 , linewidth = linewidth
42 #, color = "r"
43 )
44 plt.plot( df.values[:, 1]
45 , df.values[:,1:5]
46 , marker[kind]
47 , linewidth = linewidth
48 #, color = "blue"
49 )
50 else:
51 plt.plot( df.values[:, 0]
52 , df.values[:,1:5]
53 , marker[kind]
54 , linewidth = linewidth
55 #, color = "r"
56 )
57 ax.legend ( legends
58 , fontsize = fontsize
59 )
60
61 plt.xticks(fontsize = fontsize - 2)
62 plt.yticks(fontsize = fontsize - 2)
63 ax.set_xlabel(xlab[kind], fontsize = 17)
64 ax.set_ylabel("Quantile Function (ICDF)", fontsize = 17)
65
66 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
67 ax.tick_params(axis = "y", which = "minor")
68 ax.tick_params(axis = "x", which = "minor")
69
70 plt.savefig(fileList[0].replace(".txt",".png"))
71
72 elif len(fileList) > 1:
73
74 sys.exit("Ambiguous file list exists.")

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.

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Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

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

Definition at line 1276 of file pm_distNorm.F90.


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