[LEGACY code]
Return the lowertriangle of the Cholesky factorization \(L\) of the symmetric positivedefinite realvalued matrix represented by the uppertriangle of the input argument \(\ms{mat} = L.L^T\).
On input, the upper triangle and diagonal of mat
must be specified, which remains intact on output.
 Parameters

[in,out]  mat  : The input array of shape (ndim, ndim) of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128).

On input, the upper triangle and diagonals of
mat contain the square symmetric positivedefinite (covariance) matrix whose Cholesky factorization is to be computed.

On output, the lower triangle of
mat contains the lower triangle of the Cholesky factorization of the matrix, while the upper triangle and diagonals remain intact.

[out]  dia  : The output vector of the same type and kind as mat containing the diagonal elements of the lower triangle of the Cholesky factorization.
If the Cholesky factorization fails, dia(1) = idim will be set, where idim is the column index causing the singularity.

[in]  ndim  : The input integer of default kind IK representing the rank of the input square matrix (ndim,ndim) .

Possible calling interfaces ⛓
call setChoLow(mat, dia, ndim) ! Explicit
shape dummy argument unsafe interface(for benchmarking purposes)
[LEGACY code] Return the lowertriangle of the Cholesky factorization of the symmetric positivedef...
This module contains procedures and generic interfaces for computing the Cholesky factorization of po...
 Warning
 This generic interface with explicitshape dummy arguments is not recommended for general usage.
It exists merely for benchmarking purposes against the alternative modern interface setMatChol.
However, if used, and the Cholesky factorization fails, dia(1)
will be set to idim
where idim
is the index of the column causing the singularity.

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.
 See also
 getMatChol
setMatChol
Example usage ⛓
10 real(RKH),
allocatable :: matrix_RKH(:,:), chodia_RKH(:)
11 real(RKD),
allocatable :: matrix_RKD(:,:), chodia_RKD(:)
12 real(RKS),
allocatable :: matrix_RKS(:,:), chodia_RKS(:)
15 type(display_type) :: disp
23 matrix_RKH
= reshape( [
1._RKH,
0._RKH,
0._RKH &
24 ,
0._RKH,
4._RKH,
0._RKH &
25 ,
2._RKH,
0._RKH,
8._RKH ], shape
= [
3,
3])
27 call disp%show(
"matrix Upper Triangle")
30 allocate(chodia_RKH(
size(matrix_RKH,
dim = 1)))
31 call setChoLow(matrix_RKH, chodia_RKH,
size(chodia_RKH,
1,
IK))
32 if (chodia_RKH(
1)
<= 0)
error stop
34 call disp%show(
"matrix Upper Triangle / Cholesky Lower Triangle")
44 matrix_RKD
= real(matrix_RKH,
kind = RKD)
47 call disp%show(
"matrix Upper Triangle")
50 allocate(chodia_RKD(
size(matrix_RKD,
dim = 1)))
51 call setChoLow(matrix_RKD, chodia_RKD,
size(chodia_RKD,
1,
IK))
52 if (chodia_RKD(
1)
<= 0)
error stop
54 call disp%show(
"matrix Upper Triangle / Cholesky Lower Triangle")
64 matrix_RKS
= real(matrix_RKH,
kind = RKS)
67 call disp%show(
"matrix Upper Triangle")
70 allocate(chodia_RKS(
size(matrix_RKS,
dim = 1)))
71 call setChoLow(matrix_RKS, chodia_RKS,
size(chodia_RKS,
1,
IK))
72 if (chodia_RKS(
1)
<= 0)
error stop
74 call disp%show(
"matrix Upper Triangle / Cholesky Lower Triangle")
This is a generic method of the derived type display_type with pass attribute.
This is a generic method of the derived type display_type with pass attribute.
This module contains classes and procedures for input/output (IO) or generic display operations on st...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind typeparameters frequently used in the ParaMonte librar...
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in CFortran Interoper...
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64bit real kind.
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in CFortran Intero...
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highestprecision real kind t...
integer, parameter RKS
The singleprecision real kind in Fortran mode. On most platforms, this is an 32bit real kind.
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort fpp standardsemantics O3 Wl,rpath,../../../lib I../../../inc main.F90 ../../../lib/libparamonte* o main.exe
Example Windows Batch compile command via Intel ifort
compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standardsemantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran cpp ffreelinelengthnone O3 Wl,rpath,../../../lib I../../../inc main.F90 ../../../lib/libparamonte* o main.exe
Example output ⛓
2+1.00000000000000000000000000000000000,
+0.00000000000000000000000000000000000,
+2.00000000000000000000000000000000000
3+0.00000000000000000000000000000000000,
+4.00000000000000000000000000000000000,
+0.00000000000000000000000000000000000
4+0.00000000000000000000000000000000000,
+0.00000000000000000000000000000000000,
+8.00000000000000000000000000000000000
5matrix Upper Triangle
/ Cholesky Lower Triangle
6+1.00000000000000000000000000000000000,
+0.00000000000000000000000000000000000,
+2.00000000000000000000000000000000000
7+0.00000000000000000000000000000000000,
+4.00000000000000000000000000000000000,
+0.00000000000000000000000000000000000
8+2.00000000000000000000000000000000000,
+0.00000000000000000000000000000000000,
+8.00000000000000000000000000000000000
10+1.00000000000000000000000000000000000,
+2.00000000000000000000000000000000000,
+2.00000000000000000000000000000000000
13+1.0000000000000000,
+0.0000000000000000,
+2.0000000000000000
14+0.0000000000000000,
+4.0000000000000000,
+0.0000000000000000
15+2.0000000000000000,
+0.0000000000000000,
+8.0000000000000000
16matrix Upper Triangle
/ Cholesky Lower Triangle
17+1.0000000000000000,
+0.0000000000000000,
+2.0000000000000000
18+0.0000000000000000,
+4.0000000000000000,
+0.0000000000000000
19+2.0000000000000000,
+0.0000000000000000,
+8.0000000000000000
21+1.0000000000000000,
+2.0000000000000000,
+2.0000000000000000
24+1.00000000,
+0.00000000,
+2.00000000
25+0.00000000,
+4.00000000,
+0.00000000
26+2.00000000,
+0.00000000,
+8.00000000
27matrix Upper Triangle
/ Cholesky Lower Triangle
28+1.00000000,
+0.00000000,
+2.00000000
29+0.00000000,
+4.00000000,
+0.00000000
30+2.00000000,
+0.00000000,
+8.00000000
32+1.00000000,
+2.00000000,
+2.00000000
 Test:
 test_pm_matrixChol
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.

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.

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, Apr 21, 2017, 1:54 AM, Institute for Computational Engineering and Sciences (ICES), The University of Texas Austin
Definition at line 209 of file pm_matrixChol.F90.