Return the LU-Pivoted decomposition of the input square matrix mat(ndim,ndim)
.
The LUP factorization takes the form,
\begin{equation}
\text{mat} = P * L * U
\end{equation}
where,
-
\(P\) is the permutation matrix,
-
\(L\) is lower triangular with unit diagonal elements (that are missing in the output
mat
),
-
\(U\) is upper triangular of the decomposition.
The abbreviation LUP stands for the LU factorization with partial Pivoting.
- Parameters
-
[in,out] | mat | : The input contiguous square matrix of shape (ndim, ndim) of,
-
type
complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
-
type
real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the matrix whose LUP factorization must be returned.
On output, mat is completely overwritten by its LU Pivoted decomposition.
|
[out] | rperm | : The output contiguous vector of size ndim of type integer of default kind IK containing the pivot indices (row permutations).
For 1 <= i <= ndim , the i th row of the matrix is interchanged with row rperm(i) .
|
[out] | info | : The output scalar integer of default kind IK that is non-zero if a singular matrix is detected, indicating the LUP decomposition failure.
|
Possible calling interfaces ⛓
call setMatLUP(mat(
1 : ndim,
1 : ndim), rperm(
1 : ndim), info)
Return the LU-Pivoted decomposition of the input square matrix mat(ndim,ndim).
This module contains procedures and generic interfaces relevant to the partially LU Pivoted decomposi...
- Warning
- The condition
size(mat, 1) == size(mat, 2))
must hold for the corresponding input arguments (unless dispatch to LAPACK is enabled).
The condition size(rperm) == shape(mat, 1, IK)
must hold for the corresponding input 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.
- See also
- getMatInv
setMatInv
getMatChol
setMatChol
setMatLUP
- BLAS/LAPACK equivalent:
- The procedures under discussion combine, modernize, and extend the interface and functionalities of Version 3.11 of BLAS/LAPACK routine(s):
SGETRF
, DGETRF
, CGETRF
, and ZGETRF
.
Example usage ⛓
11 integer(IK),
allocatable :: rperm(:), rperm_ref(:)
14 type(display_type) :: disp
18 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
19 call disp%show(
"! Compute the LU-Pivoted decomposition of a real square matrix.")
20 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
25 real(TKG),
allocatable :: mat_lup(:,:), lup_ref(:,:)
26 mat_lup
= reshape( [
1.0_TKG,
+1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG,
2.2_TKG,
2.4_TKG,
2.6_TKG &
27 ,
1.2_TKG,
+1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG,
2.2_TKG,
2.4_TKG &
28 ,
1.4_TKG,
+1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG,
2.2_TKG &
29 ,
1.6_TKG,
+1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG &
30 ,
1.8_TKG,
+1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG &
31 ,
2.0_TKG,
+1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG &
32 ,
2.2_TKG,
+2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG &
33 ,
2.4_TKG,
+2.2_TKG,
2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG &
34 ,
2.6_TKG,
+2.4_TKG,
2.2_TKG,
2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG &
35 ], shape
= [
9,
9], order
= [
2,
1])
36 lup_ref
= reshape( [
2.6_TKG,
2.4_TKG,
2.2_TKG,
2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG &
37 ,
0.4_TKG,
0.3_TKG,
0.6_TKG,
0.8_TKG,
1.1_TKG,
1.4_TKG,
1.7_TKG,
1.9_TKG,
2.2_TKG &
38 ,
0.5_TKG,
-0.4_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG,
2.0_TKG,
2.4_TKG,
2.8_TKG &
39 ,
0.5_TKG,
-0.3_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG,
2.0_TKG,
2.4_TKG &
40 ,
0.6_TKG,
-0.3_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG,
2.0_TKG &
41 ,
0.7_TKG,
-0.2_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG &
42 ,
0.8_TKG,
-0.2_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG &
43 ,
0.8_TKG,
-0.1_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG &
44 ,
0.9_TKG,
-0.1_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG &
45 ], shape
= [
9,
9], order
= [
2,
1])
46 rperm_ref
= [
9,
9,
9,
9,
9,
9,
9,
9,
9]
50 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK))")
52 call disp%show(
"call setMatLUP(mat_lup, rperm, info); if (info /= 0) error stop")
53 call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
56 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK)) ! reconstruct the original matrix.")
58 call disp%show(
"lup_ref ! reference matrix rounded to 1 significant digit.")
60 call disp%show(
"lup_ref - mat_lup, format = SK_'(*(f0.1,:,"", ""))'")
61 call disp%show( lup_ref
- mat_lup,
format = SK_
"(*(f0.1,:,"", ""))")
71 real(TKG),
allocatable :: mat_lup(:,:), lup_ref(:,:)
72 mat_lup
= reshape( [
1.0_TKG,
+1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG,
2.2_TKG,
2.4_TKG,
2.6_TKG &
73 ,
1.2_TKG,
+1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG,
2.2_TKG,
2.4_TKG &
74 ,
1.4_TKG,
+1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG,
2.2_TKG &
75 ,
1.6_TKG,
+1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG &
76 ,
1.8_TKG,
+1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG &
77 ,
2.0_TKG,
+1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG &
78 ,
2.2_TKG,
+2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG &
79 ,
2.4_TKG,
+2.2_TKG,
2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG &
80 ,
2.6_TKG,
+2.4_TKG,
2.2_TKG,
2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG &
81 ], shape
= [
9,
9], order
= [
2,
1])
82 lup_ref
= reshape( [
2.6_TKG,
2.4_TKG,
2.2_TKG,
2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG &
83 ,
0.4_TKG,
0.3_TKG,
0.6_TKG,
0.8_TKG,
1.1_TKG,
1.4_TKG,
1.7_TKG,
1.9_TKG,
2.2_TKG &
84 ,
0.5_TKG,
-0.4_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG,
2.0_TKG,
2.4_TKG,
2.8_TKG &
85 ,
0.5_TKG,
-0.3_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG,
2.0_TKG,
2.4_TKG &
86 ,
0.6_TKG,
-0.3_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG,
2.0_TKG &
87 ,
0.7_TKG,
-0.2_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG &
88 ,
0.8_TKG,
-0.2_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG &
89 ,
0.8_TKG,
-0.1_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG &
90 ,
0.9_TKG,
-0.1_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG &
91 ], shape
= [
9,
9], order
= [
2,
1])
92 rperm_ref
= [
9,
9,
9,
9,
9,
9,
9,
9,
9]
96 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK))")
98 call disp%show(
"call setMatLUP(mat_lup, rperm, info); if (info /= 0) error stop")
99 call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
102 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK)) ! reconstruct the original matrix.")
104 call disp%show(
"lup_ref ! reference matrix rounded to 1 significant digit.")
106 call disp%show(
"lup_ref - mat_lup, format = SK_'(*(f0.1,:,"", ""))'")
107 call disp%show( lup_ref
- mat_lup,
format = SK_
"(*(f0.1,:,"", ""))")
117 real(TKG),
allocatable :: mat_lup(:,:), lup_ref(:,:)
118 mat_lup
= reshape( [
1.0_TKG,
+1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG,
2.2_TKG,
2.4_TKG,
2.6_TKG &
119 ,
1.2_TKG,
+1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG,
2.2_TKG,
2.4_TKG &
120 ,
1.4_TKG,
+1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG,
2.2_TKG &
121 ,
1.6_TKG,
+1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG,
2.0_TKG &
122 ,
1.8_TKG,
+1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG,
1.8_TKG &
123 ,
2.0_TKG,
+1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG,
1.6_TKG &
124 ,
2.2_TKG,
+2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG,
1.4_TKG &
125 ,
2.4_TKG,
+2.2_TKG,
2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG,
1.2_TKG &
126 ,
2.6_TKG,
+2.4_TKG,
2.2_TKG,
2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG &
127 ], shape
= [
9,
9], order
= [
2,
1])
128 lup_ref
= reshape( [
2.6_TKG,
2.4_TKG,
2.2_TKG,
2.0_TKG,
1.8_TKG,
1.6_TKG,
1.4_TKG,
1.2_TKG,
1.0_TKG &
129 ,
0.4_TKG,
0.3_TKG,
0.6_TKG,
0.8_TKG,
1.1_TKG,
1.4_TKG,
1.7_TKG,
1.9_TKG,
2.2_TKG &
130 ,
0.5_TKG,
-0.4_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG,
2.0_TKG,
2.4_TKG,
2.8_TKG &
131 ,
0.5_TKG,
-0.3_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG,
2.0_TKG,
2.4_TKG &
132 ,
0.6_TKG,
-0.3_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG,
2.0_TKG &
133 ,
0.7_TKG,
-0.2_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG,
1.6_TKG &
134 ,
0.8_TKG,
-0.2_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG,
1.2_TKG &
135 ,
0.8_TKG,
-0.1_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG,
0.8_TKG &
136 ,
0.9_TKG,
-0.1_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.0_TKG,
0.4_TKG &
137 ], shape
= [
9,
9], order
= [
2,
1])
138 rperm_ref
= [
9,
9,
9,
9,
9,
9,
9,
9,
9]
142 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK))")
144 call disp%show(
"call setMatLUP(mat_lup, rperm, info); if (info /= 0) error stop")
145 call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
148 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK)) ! reconstruct the original matrix.")
150 call disp%show(
"lup_ref ! reference matrix rounded to 1 significant digit.")
152 call disp%show(
"lup_ref - mat_lup, format = SK_'(*(f0.1,:,"", ""))'")
153 call disp%show( lup_ref
- mat_lup,
format = SK_
"(*(f0.1,:,"", ""))")
161#if 1 || LAPACK_ENABLED
163 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
164 call disp%show(
"! Compute the LU-Pivoted decomposition of a complex square matrix.")
165 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
170 complex(TKG),
allocatable :: mat_lup(:,:), lup_ref(:,:)
171 mat_lup
= reshape( [ (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0), (
4.4,
-1.0), (
4.8,
-1.0), (
5.2,
-1.0)
&
172 , (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0), (
4.4,
-1.0), (
4.8,
-1.0)
&
173 , (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0), (
4.4,
-1.0)
&
174 , (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0)
&
175 , (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0)
&
176 , (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0)
&
177 , (
4.4,
1.0), (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0)
&
178 , (
4.8,
1.0), (
4.4,
1.0), (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0)
&
179 , (
5.2,
1.0), (
4.8,
1.0), (
4.4,
1.0), (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0)
&
180 ], shape
= [
9,
9], order
= [
2,
1])
181 lup_ref
= reshape( [ (
5.2,
1.0), (
4.8,
1.0), (
4.4,
1.0), (
4.0,
1.0), (
+3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0)
&
182 , (
0.4,
0.1), (
0.6,
-2.0), (
1.1,
-1.9), (
1.7,
-1.9), (
+2.3,
-1.8), (
2.8,
-1.8), (
3.4,
-1.7), (
3.9,
-1.7), (
4.5,
-1.6)
&
183 , (
0.5,
0.1), (
0.0,
-0.1), (
0.6,
-1.9), (
1.2,
-1.8), (
+1.8,
-1.7), (
2.5,
-1.6), (
3.1,
-1.5), (
3.7,
-1.4), (
4.3,
-1.3)
&
184 , (
0.6,
0.1), (
0.0,
-0.1),(
-0.1,
-0.1), (
0.7,
-1.9), (
+1.3,
-1.7), (
2.0,
-1.6), (
2.7,
-1.5), (
3.4,
-1.4), (
4.0,
-1.2)
&
185 , (
0.6,
0.1), (
0.0,
-0.1),(
-0.1,
-0.1),(
-0.1,
0.0), (
+0.7,
-1.9), (
1.5,
-1.7), (
2.2,
-1.6), (
2.9,
-1.5), (
3.7,
-1.3)
&
186 , (
0.7,
0.1), (
0.0,
-0.1), (
0.0,
0.0),(
-0.1,
0.0), (
-0.1,
0.0), (
0.8,
-1.9), (
1.6,
-1.8), (
2.4,
-1.6), (
3.2,
-1.5)
&
187 , (
0.8,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
+0.0,
0.0), (
0.0,
0.0), (
0.8,
-1.9), (
1.7,
-1.8), (
2.5,
-1.8)
&
188 , (
0.9,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
+0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.8,
-2.0), (
1.7,
-1.9)
&
189 , (
0.9,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
+0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.8,
-2.0)
&
190 ], shape
= [
9,
9], order
= [
2,
1])
191 rperm_ref
= [
9,
9,
9,
9,
9,
9,
9,
9,
9]
195 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK))")
197 call disp%show(
"call setMatLUP(mat_lup, rperm, info); if (info /= 0) error stop")
198 call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
201 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK)) ! reconstruct the original matrix.")
203 call disp%show(
"lup_ref ! reference matrix rounded to 1 significant digit.")
205 call disp%show(
"lup_ref - mat_lup, format = SK_'(*(""("",f0.1,"","",f0.1,"")"",:,"", ""))'")
206 call disp%show( lup_ref
- mat_lup,
format = SK_
"(*(""("",f0.1,"","",f0.1,"")"",:,"", ""))")
216 complex(TKG),
allocatable :: mat_lup(:,:), lup_ref(:,:)
217 mat_lup
= reshape( [ (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0), (
4.4,
-1.0), (
4.8,
-1.0), (
5.2,
-1.0)
&
218 , (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0), (
4.4,
-1.0), (
4.8,
-1.0)
&
219 , (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0), (
4.4,
-1.0)
&
220 , (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0)
&
221 , (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0)
&
222 , (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0)
&
223 , (
4.4,
1.0), (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0)
&
224 , (
4.8,
1.0), (
4.4,
1.0), (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0)
&
225 , (
5.2,
1.0), (
4.8,
1.0), (
4.4,
1.0), (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0)
&
226 ], shape
= [
9,
9], order
= [
2,
1])
227 lup_ref
= reshape( [ (
5.2,
1.0), (
4.8,
1.0), (
4.4,
1.0), (
4.0,
1.0), (
+3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0)
&
228 , (
0.4,
0.1), (
0.6,
-2.0), (
1.1,
-1.9), (
1.7,
-1.9), (
+2.3,
-1.8), (
2.8,
-1.8), (
3.4,
-1.7), (
3.9,
-1.7), (
4.5,
-1.6)
&
229 , (
0.5,
0.1), (
0.0,
-0.1), (
0.6,
-1.9), (
1.2,
-1.8), (
+1.8,
-1.7), (
2.5,
-1.6), (
3.1,
-1.5), (
3.7,
-1.4), (
4.3,
-1.3)
&
230 , (
0.6,
0.1), (
0.0,
-0.1),(
-0.1,
-0.1), (
0.7,
-1.9), (
+1.3,
-1.7), (
2.0,
-1.6), (
2.7,
-1.5), (
3.4,
-1.4), (
4.0,
-1.2)
&
231 , (
0.6,
0.1), (
0.0,
-0.1),(
-0.1,
-0.1),(
-0.1,
0.0), (
+0.7,
-1.9), (
1.5,
-1.7), (
2.2,
-1.6), (
2.9,
-1.5), (
3.7,
-1.3)
&
232 , (
0.7,
0.1), (
0.0,
-0.1), (
0.0,
0.0),(
-0.1,
0.0), (
-0.1,
0.0), (
0.8,
-1.9), (
1.6,
-1.8), (
2.4,
-1.6), (
3.2,
-1.5)
&
233 , (
0.8,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
+0.0,
0.0), (
0.0,
0.0), (
0.8,
-1.9), (
1.7,
-1.8), (
2.5,
-1.8)
&
234 , (
0.9,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
+0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.8,
-2.0), (
1.7,
-1.9)
&
235 , (
0.9,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
+0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.8,
-2.0)
&
236 ], shape
= [
9,
9], order
= [
2,
1])
237 rperm_ref
= [
9,
9,
9,
9,
9,
9,
9,
9,
9]
241 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK))")
243 call disp%show(
"call setMatLUP(mat_lup, rperm, info); if (info /= 0) error stop")
244 call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
247 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK)) ! reconstruct the original matrix.")
249 call disp%show(
"lup_ref ! reference matrix rounded to 1 significant digit.")
251 call disp%show(
"lup_ref - mat_lup, format = SK_'(*(""("",f0.1,"","",f0.1,"")"",:,"", ""))'")
252 call disp%show( lup_ref
- mat_lup,
format = SK_
"(*(""("",f0.1,"","",f0.1,"")"",:,"", ""))")
262 complex(TKG),
allocatable :: mat_lup(:,:), lup_ref(:,:)
263 mat_lup
= reshape( [ (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0), (
4.4,
-1.0), (
4.8,
-1.0), (
5.2,
-1.0)
&
264 , (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0), (
4.4,
-1.0), (
4.8,
-1.0)
&
265 , (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0), (
4.4,
-1.0)
&
266 , (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0), (
4.0,
-1.0)
&
267 , (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0), (
3.6,
-1.0)
&
268 , (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0), (
3.2,
-1.0)
&
269 , (
4.4,
1.0), (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0), (
2.8,
-1.0)
&
270 , (
4.8,
1.0), (
4.4,
1.0), (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0), (
2.4,
-1.0)
&
271 , (
5.2,
1.0), (
4.8,
1.0), (
4.4,
1.0), (
4.0,
1.0), (
3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0)
&
272 ], shape
= [
9,
9], order
= [
2,
1])
273 lup_ref
= reshape( [ (
5.2,
1.0), (
4.8,
1.0), (
4.4,
1.0), (
4.0,
1.0), (
+3.6,
1.0), (
3.2,
1.0), (
2.8,
1.0), (
2.4,
1.0), (
2.0,
1.0)
&
274 , (
0.4,
0.1), (
0.6,
-2.0), (
1.1,
-1.9), (
1.7,
-1.9), (
+2.3,
-1.8), (
2.8,
-1.8), (
3.4,
-1.7), (
3.9,
-1.7), (
4.5,
-1.6)
&
275 , (
0.5,
0.1), (
0.0,
-0.1), (
0.6,
-1.9), (
1.2,
-1.8), (
+1.8,
-1.7), (
2.5,
-1.6), (
3.1,
-1.5), (
3.7,
-1.4), (
4.3,
-1.3)
&
276 , (
0.6,
0.1), (
0.0,
-0.1),(
-0.1,
-0.1), (
0.7,
-1.9), (
+1.3,
-1.7), (
2.0,
-1.6), (
2.7,
-1.5), (
3.4,
-1.4), (
4.0,
-1.2)
&
277 , (
0.6,
0.1), (
0.0,
-0.1),(
-0.1,
-0.1),(
-0.1,
0.0), (
+0.7,
-1.9), (
1.5,
-1.7), (
2.2,
-1.6), (
2.9,
-1.5), (
3.7,
-1.3)
&
278 , (
0.7,
0.1), (
0.0,
-0.1), (
0.0,
0.0),(
-0.1,
0.0), (
-0.1,
0.0), (
0.8,
-1.9), (
1.6,
-1.8), (
2.4,
-1.6), (
3.2,
-1.5)
&
279 , (
0.8,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
+0.0,
0.0), (
0.0,
0.0), (
0.8,
-1.9), (
1.7,
-1.8), (
2.5,
-1.8)
&
280 , (
0.9,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
+0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.8,
-2.0), (
1.7,
-1.9)
&
281 , (
0.9,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
+0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.0,
0.0), (
0.8,
-2.0)
&
282 ], shape
= [
9,
9], order
= [
2,
1])
283 rperm_ref
= [
9,
9,
9,
9,
9,
9,
9,
9,
9]
287 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK))")
289 call disp%show(
"call setMatLUP(mat_lup, rperm, info); if (info /= 0) error stop")
290 call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
293 call disp%show(
"call setResized(rperm, size(mat_lup, 1, IK)) ! reconstruct the original matrix.")
295 call disp%show(
"lup_ref ! reference matrix rounded to 1 significant digit.")
297 call disp%show(
"lup_ref - mat_lup, format = SK_'(*(""("",f0.1,"","",f0.1,"")"",:,"", ""))'")
298 call disp%show( lup_ref
- mat_lup,
format = SK_
"(*(""("",f0.1,"","",f0.1,"")"",:,"", ""))")
Allocate or resize (shrink or expand) an input allocatable scalar string or array of rank 1....
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.
Copy a desired subset of the input source matrix of arbitrary shape (:) or (:,:) to the target subset...
This module contains procedures and generic interfaces for resizing allocatable arrays of various typ...
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 type-parameters frequently used in the ParaMonte librar...
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
integer, parameter CKD
The double precision complex kind in Fortran mode. On most platforms, this is a 64-bit real kind.
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
This module contains procedures and generic interfaces relevant to copying (diagonal or upper/lower t...
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort -fpp -standard-semantics -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 /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example output ⛓
8+1.00000000,
+1.20000005,
+1.39999998,
+1.60000002,
+1.79999995,
+2.00000000,
+2.20000005,
+2.40000010,
+2.59999990
9+1.20000005,
+1.00000000,
+1.20000005,
+1.39999998,
+1.60000002,
+1.79999995,
+2.00000000,
+2.20000005,
+2.40000010
10+1.39999998,
+1.20000005,
+1.00000000,
+1.20000005,
+1.39999998,
+1.60000002,
+1.79999995,
+2.00000000,
+2.20000005
11+1.60000002,
+1.39999998,
+1.20000005,
+1.00000000,
+1.20000005,
+1.39999998,
+1.60000002,
+1.79999995,
+2.00000000
12+1.79999995,
+1.60000002,
+1.39999998,
+1.20000005,
+1.00000000,
+1.20000005,
+1.39999998,
+1.60000002,
+1.79999995
13+2.00000000,
+1.79999995,
+1.60000002,
+1.39999998,
+1.20000005,
+1.00000000,
+1.20000005,
+1.39999998,
+1.60000002
14+2.20000005,
+2.00000000,
+1.79999995,
+1.60000002,
+1.39999998,
+1.20000005,
+1.00000000,
+1.20000005,
+1.39999998
15+2.40000010,
+2.20000005,
+2.00000000,
+1.79999995,
+1.60000002,
+1.39999998,
+1.20000005,
+1.00000000,
+1.20000005
16+2.59999990,
+2.40000010,
+2.20000005,
+2.00000000,
+1.79999995,
+1.60000002,
+1.39999998,
+1.20000005,
+1.00000000
18call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
20+2.59999990,
+2.40000010,
+2.20000005,
+2.00000000,
+1.79999995,
+1.60000002,
+1.39999998,
+1.20000005,
+1.00000000
21+0.384615391,
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+1.93846154,
+2.21538448
22+0.461538494,
-0.388889551,
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23+0.538461566,
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24+0.615384638,
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25+0.692307711,
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27+0.846153855,
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31+2.59999990,
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32+0.400000006,
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33+0.500000000,
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35+0.600000024,
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36+0.699999988,
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37+0.800000012,
-0.200000003,
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39+0.899999976,
-0.100000001,
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+0.00000000,
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+0.00000000,
+0.00000000,
+0.400000006
40lup_ref
- mat_lup,
format = SK_
'(*(f0.1,:,", "))'
41.
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+2.2000000000000002,
+2.0000000000000000,
+1.8000000000000000,
+1.6000000000000001,
+1.3999999999999999,
+1.2000000000000000,
+1.0000000000000000
67call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
69+2.6000000000000001,
+2.3999999999999999,
+2.2000000000000002,
+2.0000000000000000,
+1.8000000000000000,
+1.6000000000000001,
+1.3999999999999999,
+1.2000000000000000,
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+1.3846153846153846,
+1.6615384615384619,
+1.9384615384615385,
+2.2153846153846155
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-0.38888888888888812,
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+0.79999999999999949,
+1.1999999999999995,
+1.5999999999999992,
+1.9999999999999989,
+2.3999999999999990,
+2.7999999999999985
72+0.53846153846153832,
-0.33333333333333198,
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84+0.59999999999999998,
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89lup_ref
- mat_lup,
format = SK_
'(*(f0.1,:,", "))'
90.
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111+2.00000000000000000000000000000000000,
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112+2.20000000000000000000000000000000015,
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113+2.39999999999999999999999999999999992,
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116call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
118+2.60000000000000000000000000000000008,
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137+0.900000000000000000000000000000000019,
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138lup_ref
- mat_lup,
format = SK_
'(*(f0.1,:,", "))'
139.
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166(
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167(
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170call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
172(
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173(
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174(
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175(
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176(
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177(
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178(
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179(
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180(
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183(
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184(
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186(
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187(
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188(
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189(
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190(
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191(
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192lup_ref
- mat_lup,
format = SK_
'(*("(",f0.1,",",f0.1,")",:,", "))'
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219call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
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241lup_ref
- mat_lup,
format = SK_
'(*("(",f0.1,",",f0.1,")",:,", "))'
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268call setMatLUP(mat_lup, rperm, info);
if (info
/= 0)
error stop
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290lup_ref
- mat_lup,
format = SK_
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- Test:
- test_pm_matrixLUP
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, 1:43 PM, Institute for Computational Engineering and Sciences (ICES), The University of Texas Austin
Definition at line 191 of file pm_matrixLUP.F90.