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

Generate and return a random upper and lower Cholesky factorization.
More...

Detailed Description

Generate and return a random upper and lower Cholesky factorization.

See the documentation of pm_distChol for details.
See also setCholRand for generating only the upper or lower subset of the Cholesky factor.

Parameters
[in]mold: The input scalar of,
  1. type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
  2. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
whose type and kind determines the type and kind of the output rand.
The value of mold is ignored entirely within the algorithm.
[in]ndim: The input positive scalar of type integer of default kind IK, representing the rank of the matrix (the number of dimensions) of shape (ndim, ndim).
[in]subset: The input scalar constant that can be any of the following:
  1. the constant uppDia or an object of type uppDia_type implying that the upper-diagonal triangular block of the argument rand must be used while the lower subset is not referenced.
  2. the constant lowDia or an object of type lowDia_type implying that the lower-diagonal triangular block of the argument rand must be used while the upper subset is not referenced.
This argument is merely a convenience to differentiate the different procedure functionalities within this generic interface.
Beware that the oppsite subset will not be set to zero explicitly and it is the user's responsibility to ensure it.
The generic interface getCholRand can be used to generate random Cholesky factors whose complementary subset elements are all set to zero.
Returns
rand : The output matrix of shape (1:ndim, 1:ndim) of the same type and kind as the input argument mold, containing an upper or lower Cholesky factorization as specified by the input subset.


Possible calling interfaces ⛓

use pm_distChol, only: getCholRand
rand(1:ndim, 1:ndim) = getCholRand(mold, ndim, subset)
pm_distChol::getCholRand
Generate and return a random upper and lower Cholesky factorization.
Definition: pm_distChol.F90:115
pm_distChol
This module contains classes and procedures for generating random upper or lower Cholesky factor tria...
Definition: pm_distChol.F90:43
See also
getCovRand
setCovRand
getCholRand
setCholRand


Example usage ⛓

1program example
2
3 use pm_kind, only: SK, IK, LK
4 use pm_io, only: display_type
5 use pm_container, only: csp_type
6 use pm_distUnif, only: getUnifRand
7 use pm_matrixClass, only: isMatClass, posdefmat
8 use pm_distChol, only: getCholRand, uppDia, lowDia, subset_type
9
10 implicit none
11
12 integer(IK) :: isub, itry, ndim
13
14 type(csp_type) :: subset(2)
15
16 type(display_type) :: disp
17 disp = display_type(file = "main.out.F90")
18
19 subset = [csp_type(uppDia), csp_type(lowDia)]
20 do isub = 1, size(subset)
21
22 block
23 use pm_kind, only: TKG => RKS ! all real kinds are supported.
24 real(TKG), allocatable :: rand(:,:), cov(:,:)
25 real(TKG) :: mold
26 do itry = 1, 5
27 call disp%skip()
28 call disp%show("ndim = getUnifRand(2, 5)")
29 ndim = getUnifRand(2, 5)
30 call disp%show("[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]")
31 call disp%show( [same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)] )
32 call disp%show("rand = getCholRand(mold, ndim, subset(isub)%val)")
33 rand = getCholRand(mold, ndim, subset(isub)%val)
34 call disp%show("rand")
35 call disp%show( rand )
36 call disp%show("cov = matmul(rand, transpose(rand))")
37 cov = matmul(rand, transpose(rand))
38 call disp%show("isMatClass(cov, posdefmat)")
39 call disp%show( isMatClass(cov, posdefmat) )
40 call disp%skip()
41 end do
42 end block
43
44 block
45 use pm_kind, only: TKG => CKS ! all complex kinds are supported.
46 complex(TKG), allocatable :: rand(:,:), cov(:,:)
47 complex(TKG) :: mold
48 do itry = 1, 5
49 call disp%skip()
50 call disp%show("ndim = getUnifRand(2, 5)")
51 ndim = getUnifRand(2, 5)
52 call disp%show("[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]")
53 call disp%show( [same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)] )
54 call disp%show("rand = getCholRand(mold, ndim, subset(isub)%val)")
55 rand = getCholRand(mold, ndim, subset(isub)%val)
56 call disp%show("rand")
57 call disp%show( rand )
58 call disp%show("cov = matmul(rand, conjg(transpose(rand)))")
59 cov = matmul(rand, conjg(transpose(rand)))
60 call disp%show("isMatClass(cov, posdefmat)")
61 call disp%show( isMatClass(cov, posdefmat) )
62 call disp%skip()
63 end do
64 end block
65
66 end do
67
68end program example
pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4150
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_matrixClass::isMatClass
Generate and return .true. if and only if the input matrix is of the specified input class.
Definition: pm_matrixClass.F90:2115
pm_container
This module contains the derived types for generating allocatable containers of scalar,...
Definition: pm_container.F90:113
pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274
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::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
pm_kind::CKS
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
Definition: pm_kind.F90:570
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::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567
pm_matrixClass
This module contains abstract and concrete derived types that are required for compile-time resolutio...
Definition: pm_matrixClass.F90:82
pm_matrixClass::posdefmat
type(posdefmat_type), parameter posdefmat
This is a scalar parameter object of type hermitian_type that is exclusively used to signify the Herm...
Definition: pm_matrixClass.F90:1030
pm_container::csp_type
This is the csp_type type for generating instances of container of scalar unlimited polymorphic objec...
Definition: pm_container.F90:533
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
2ndim = getUnifRand(2, 5)
3[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
4T, F
5rand = getCholRand(mold, ndim, subset(isub)%val)
6rand
7+1.00000000, +0.431011409, +0.190460011, +0.593082964
8+0.00000000, +0.902346432, -0.702898920, +0.585011184
9+0.00000000, +0.00000000, +0.685316026, +0.224273711
10+0.00000000, +0.00000000, +0.00000000, +0.505683601
11cov = matmul(rand, transpose(rand))
12isMatClass(cov, posdefmat)
13T
14
15
16ndim = getUnifRand(2, 5)
17[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
18T, F
19rand = getCholRand(mold, ndim, subset(isub)%val)
20rand
21+1.00000000, -0.999967039
22+0.00000000, +0.812121667E-2
23cov = matmul(rand, transpose(rand))
24isMatClass(cov, posdefmat)
25T
26
27
28ndim = getUnifRand(2, 5)
29[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
30T, F
31rand = getCholRand(mold, ndim, subset(isub)%val)
32rand
33+1.00000000, +0.344397962, -0.405866913E-1, -0.678654790, +0.440554470
34+0.00000000, +0.938823700, +0.310386062, +0.661256373, -0.128440931
35+0.00000000, +0.00000000, +0.949743807, -0.319285095, +0.135735199
36+0.00000000, +0.00000000, +0.00000000, +0.149888098E-1, -0.221862957
37+0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.849568963
38cov = matmul(rand, transpose(rand))
39isMatClass(cov, posdefmat)
40T
41
42
43ndim = getUnifRand(2, 5)
44[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
45T, F
46rand = getCholRand(mold, ndim, subset(isub)%val)
47rand
48+1.00000000, -0.655208349
49+0.00000000, +0.755448222
50cov = matmul(rand, transpose(rand))
51isMatClass(cov, posdefmat)
52T
53
54
55ndim = getUnifRand(2, 5)
56[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
57T, F
58rand = getCholRand(mold, ndim, subset(isub)%val)
59rand
60+1.00000000, +0.599283457, -0.369215429, -0.103403524, +0.528383136
61+0.00000000, +0.800536871, -0.698699415, -0.337057449E-1, +0.277623609E-1
62+0.00000000, +0.00000000, +0.612779796, -0.702681720, +0.707158506
63+0.00000000, +0.00000000, +0.00000000, +0.703142941, +0.451549232
64+0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.126769796
65cov = matmul(rand, transpose(rand))
66isMatClass(cov, posdefmat)
67T
68
69
70ndim = getUnifRand(2, 5)
71[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
72T, F
73rand = getCholRand(mold, ndim, subset(isub)%val)
74rand
75(+1.00000000, +0.00000000), (+0.501353681, +0.517161131)
76(+0.00000000, +0.00000000), (+0.693677783, +0.00000000)
77cov = matmul(rand, conjg(transpose(rand)))
78isMatClass(cov, posdefmat)
79T
80
81
82ndim = getUnifRand(2, 5)
83[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
84T, F
85rand = getCholRand(mold, ndim, subset(isub)%val)
86rand
87(+1.00000000, +0.00000000), (-0.958445966, -0.268557906)
88(+0.00000000, +0.00000000), (+0.962181538E-1, +0.00000000)
89cov = matmul(rand, conjg(transpose(rand)))
90isMatClass(cov, posdefmat)
91T
92
93
94ndim = getUnifRand(2, 5)
95[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
96T, F
97rand = getCholRand(mold, ndim, subset(isub)%val)
98rand
99(+0.999999940, +0.00000000), (-0.651302457, -0.737995207), (-0.593800768E-1, -0.963791072)
100(+0.00000000, +0.00000000), (+0.176545456, +0.00000000), (-0.373499021E-1, -0.256699622)
101(+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.170607101E-1, +0.00000000)
102cov = matmul(rand, conjg(transpose(rand)))
103isMatClass(cov, posdefmat)
104T
105
106
107ndim = getUnifRand(2, 5)
108[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
109T, F
110rand = getCholRand(mold, ndim, subset(isub)%val)
111rand
112(+0.999999940, +0.00000000), (+0.546174049, -0.463748164E-1), (+0.488137633, +0.404933095)
113(+0.00000000, +0.00000000), (+0.836386979, +0.00000000), (-0.455201685, +0.624451339)
114(+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.245520603E-1, +0.00000000)
115cov = matmul(rand, conjg(transpose(rand)))
116isMatClass(cov, posdefmat)
117T
118
119
120ndim = getUnifRand(2, 5)
121[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
122T, F
123rand = getCholRand(mold, ndim, subset(isub)%val)
124rand
125(+1.00000000, +0.00000000), (+0.585761905, -0.328417152), (-0.393315881, +0.379337490), (-0.372362107, +0.350343198)
126(+0.00000000, +0.00000000), (+0.740962386, +0.00000000), (+0.491754651, -0.555692315), (-0.670220554, +0.108992733)
127(+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.388315916, +0.00000000), (+0.285452873, -0.435228407)
128(+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.813885033E-1, +0.00000000)
129cov = matmul(rand, conjg(transpose(rand)))
130isMatClass(cov, posdefmat)
131T
132
133
134ndim = getUnifRand(2, 5)
135[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
136F, T
137rand = getCholRand(mold, ndim, subset(isub)%val)
138rand
139+1.00000000, +0.00000000
140-0.985380352, +0.170368791
141cov = matmul(rand, transpose(rand))
142isMatClass(cov, posdefmat)
143T
144
145
146ndim = getUnifRand(2, 5)
147[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
148F, T
149rand = getCholRand(mold, ndim, subset(isub)%val)
150rand
151+1.00000000, +0.00000000, +0.00000000, +0.00000000
152+0.143819168, +0.989603937, +0.00000000, +0.00000000
153-0.599744201, +0.669297203E-1, +0.797387779, +0.00000000
154-0.566567898, -0.732030153, -0.627516657E-1, +0.373088300
155cov = matmul(rand, transpose(rand))
156isMatClass(cov, posdefmat)
157T
158
159
160ndim = getUnifRand(2, 5)
161[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
162F, T
163rand = getCholRand(mold, ndim, subset(isub)%val)
164rand
165+0.999999940, +0.00000000, +0.00000000, +0.00000000
166-0.297733128, +0.954649091, +0.00000000, +0.00000000
167-0.875454582E-2, -0.837437689, +0.546462715, +0.00000000
168-0.204685748, -0.729362965, -0.446407348, +0.476291865
169cov = matmul(rand, transpose(rand))
170isMatClass(cov, posdefmat)
171T
172
173
174ndim = getUnifRand(2, 5)
175[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
176F, T
177rand = getCholRand(mold, ndim, subset(isub)%val)
178rand
179+1.00000000, +0.00000000, +0.00000000, +0.00000000
180-0.498659104, +0.866798222, +0.00000000, +0.00000000
181+0.140598938, -0.570691943, +0.809038162, +0.00000000
182-0.345104933, +0.750771224, -0.426404960E-1, +0.561628878
183cov = matmul(rand, transpose(rand))
184isMatClass(cov, posdefmat)
185T
186
187
188ndim = getUnifRand(2, 5)
189[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
190F, T
191rand = getCholRand(mold, ndim, subset(isub)%val)
192rand
193+1.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000
194+0.931225538, +0.364443421, +0.00000000, +0.00000000, +0.00000000
195+0.841458321, +0.232422918, +0.487778008, +0.00000000, +0.00000000
196-0.427990258, +0.534431398, -0.359917581, +0.633771837, +0.00000000
197+0.638648152, +0.494456530, -0.337863237, +0.297248363, +0.380963385
198cov = matmul(rand, transpose(rand))
199isMatClass(cov, posdefmat)
200T
201
202
203ndim = getUnifRand(2, 5)
204[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
205F, T
206rand = getCholRand(mold, ndim, subset(isub)%val)
207rand
208(+1.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
209(-0.750156403, -0.486277342), (+0.448106885, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
210(-0.424236029, -0.770430744), (-0.134289891, -0.338273078), (+0.306590587, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
211(+0.422100842, +0.298661411), (+0.346862018, -0.432208240), (+0.219184563, +0.560490787), (+0.251641065, +0.00000000), (+0.00000000, +0.00000000)
212(-0.299449027, +0.505881667), (+0.339169443, +0.460669965), (-0.623089001E-1, -0.572213195E-1), (+0.278725594, -0.212214768), (+0.444164008, +0.00000000)
213cov = matmul(rand, conjg(transpose(rand)))
214isMatClass(cov, posdefmat)
215T
216
217
218ndim = getUnifRand(2, 5)
219[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
220F, T
221rand = getCholRand(mold, ndim, subset(isub)%val)
222rand
223(+1.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
224(-0.164456919, +0.203668982), (+0.965128422, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
225(-0.613006711, +0.344371289), (-0.391044289, +0.552321635E-1), (+0.591324747, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
226(-0.489179611, -0.304220766), (+0.165346071, +0.385288179), (+0.463985950, -0.133975372), (+0.509052515, +0.00000000), (+0.00000000, +0.00000000)
227(-0.308671862, -0.138337892E-1), (-0.178560063, -0.311820507), (-0.140370905, -0.719681561), (-0.210986391, +0.878540277E-1), (+0.430738330, +0.00000000)
228cov = matmul(rand, conjg(transpose(rand)))
229isMatClass(cov, posdefmat)
230T
231
232
233ndim = getUnifRand(2, 5)
234[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
235F, T
236rand = getCholRand(mold, ndim, subset(isub)%val)
237rand
238(+1.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
239(-0.205078840, -0.974743664), (+0.884168744E-1, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
240(+0.437355787, -0.800350130), (-0.251017213, -0.201735243), (+0.253875852, +0.00000000), (+0.00000000, +0.00000000)
241(-0.156143472, -0.120431624), (-0.188329324, +0.491471350), (-0.579425395, +0.499466389), (+0.314488441, +0.00000000)
242cov = matmul(rand, conjg(transpose(rand)))
243isMatClass(cov, posdefmat)
244T
245
246
247ndim = getUnifRand(2, 5)
248[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
249F, T
250rand = getCholRand(mold, ndim, subset(isub)%val)
251rand
252(+1.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
253(-0.778123617, +0.285814285), (+0.559315383, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
254(-0.907061845E-1, +0.508100353E-1), (+0.729050219, +0.665900171), (+0.119387902, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
255(-0.551060140, -0.142469049), (-0.121511482, +0.352817088), (-0.356894732, +0.439488471), (+0.465044498, +0.00000000), (+0.00000000, +0.00000000)
256(-0.363008901E-1, -0.453984082), (-0.228594363, +0.127662629), (-0.549087077E-1, -0.493640333), (-0.452644944, -0.488726407), (+0.183277994, +0.00000000)
257cov = matmul(rand, conjg(transpose(rand)))
258isMatClass(cov, posdefmat)
259T
260
261
262ndim = getUnifRand(2, 5)
263[same_type_as(subset(isub)%val, uppDia), same_type_as(subset(isub)%val, lowDia)]
264F, T
265rand = getCholRand(mold, ndim, subset(isub)%val)
266rand
267(+0.999999940, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
268(+0.691514552, -0.165196881), (+0.703219414, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
269(-0.603671789, +0.432656795), (-0.648069561, +0.478674583E-1), (+0.161564484, +0.00000000), (+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
270(-0.321031511, -0.445555627), (+0.266406685, -0.481722951), (-0.144210504E-1, -0.524895787), (+0.345927477, +0.00000000), (+0.00000000, +0.00000000)
271(+0.826192647E-2, -0.186399132), (-0.459752262, -0.769128203E-1), (+0.502102494, +0.241792127), (-0.516032159, +0.407368273), (+0.713516623E-1, +0.00000000)
272cov = matmul(rand, conjg(transpose(rand)))
273isMatClass(cov, posdefmat)
274T
275
276
Test:
test_pm_distChol


Final Remarks ⛓

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Copyright
Computational Data Science Lab
Author:
Amir Shahmoradi, Monday March 6, 2017, 3:22 pm, Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin.

Definition at line 115 of file pm_distChol.F90.

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