1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
|
---
:name: spftrf
:md5sum: d1c6046e8099759e3e26aad67c90017d
:category: :subroutine
:arguments:
- transr:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: real
:intent: input/output
:dims:
- n*(n+1)/2
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SPFTRF( TRANSR, UPLO, N, A, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SPFTRF computes the Cholesky factorization of a real symmetric\n\
* positive definite matrix A.\n\
*\n\
* The factorization has the form\n\
* A = U**T * U, if UPLO = 'U', or\n\
* A = L * L**T, if UPLO = 'L',\n\
* where U is an upper triangular matrix and L is lower triangular.\n\
*\n\
* This is the block version of the algorithm, calling Level 3 BLAS.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* TRANSR (input) CHARACTER*1\n\
* = 'N': The Normal TRANSR of RFP A is stored;\n\
* = 'T': The Transpose TRANSR of RFP A is stored.\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangle of RFP A is stored;\n\
* = 'L': Lower triangle of RFP A is stored.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* A (input/output) REAL array, dimension ( N*(N+1)/2 );\n\
* On entry, the symmetric matrix A in RFP format. RFP format is\n\
* described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'\n\
* then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is\n\
* (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is\n\
* the transpose of RFP A as defined when\n\
* TRANSR = 'N'. The contents of RFP A are defined by UPLO as\n\
* follows: If UPLO = 'U' the RFP A contains the NT elements of\n\
* upper packed A. If UPLO = 'L' the RFP A contains the elements\n\
* of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =\n\
* 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N\n\
* is odd. See the Note below for more details.\n\
*\n\
* On exit, if INFO = 0, the factor U or L from the Cholesky\n\
* factorization RFP A = U**T*U or RFP A = L*L**T.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
* > 0: if INFO = i, the leading minor of order i is not\n\
* positive definite, and the factorization could not be\n\
* completed.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* We first consider Rectangular Full Packed (RFP) Format when N is\n\
* even. We give an example where N = 6.\n\
*\n\
* AP is Upper AP is Lower\n\
*\n\
* 00 01 02 03 04 05 00\n\
* 11 12 13 14 15 10 11\n\
* 22 23 24 25 20 21 22\n\
* 33 34 35 30 31 32 33\n\
* 44 45 40 41 42 43 44\n\
* 55 50 51 52 53 54 55\n\
*\n\
*\n\
* Let TRANSR = 'N'. RFP holds AP as follows:\n\
* For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last\n\
* three columns of AP upper. The lower triangle A(4:6,0:2) consists of\n\
* the transpose of the first three columns of AP upper.\n\
* For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first\n\
* three columns of AP lower. The upper triangle A(0:2,0:2) consists of\n\
* the transpose of the last three columns of AP lower.\n\
* This covers the case N even and TRANSR = 'N'.\n\
*\n\
* RFP A RFP A\n\
*\n\
* 03 04 05 33 43 53\n\
* 13 14 15 00 44 54\n\
* 23 24 25 10 11 55\n\
* 33 34 35 20 21 22\n\
* 00 44 45 30 31 32\n\
* 01 11 55 40 41 42\n\
* 02 12 22 50 51 52\n\
*\n\
* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the\n\
* transpose of RFP A above. One therefore gets:\n\
*\n\
*\n\
* RFP A RFP A\n\
*\n\
* 03 13 23 33 00 01 02 33 00 10 20 30 40 50\n\
* 04 14 24 34 44 11 12 43 44 11 21 31 41 51\n\
* 05 15 25 35 45 55 22 53 54 55 22 32 42 52\n\
*\n\
*\n\
* We then consider Rectangular Full Packed (RFP) Format when N is\n\
* odd. We give an example where N = 5.\n\
*\n\
* AP is Upper AP is Lower\n\
*\n\
* 00 01 02 03 04 00\n\
* 11 12 13 14 10 11\n\
* 22 23 24 20 21 22\n\
* 33 34 30 31 32 33\n\
* 44 40 41 42 43 44\n\
*\n\
*\n\
* Let TRANSR = 'N'. RFP holds AP as follows:\n\
* For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last\n\
* three columns of AP upper. The lower triangle A(3:4,0:1) consists of\n\
* the transpose of the first two columns of AP upper.\n\
* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first\n\
* three columns of AP lower. The upper triangle A(0:1,1:2) consists of\n\
* the transpose of the last two columns of AP lower.\n\
* This covers the case N odd and TRANSR = 'N'.\n\
*\n\
* RFP A RFP A\n\
*\n\
* 02 03 04 00 33 43\n\
* 12 13 14 10 11 44\n\
* 22 23 24 20 21 22\n\
* 00 33 34 30 31 32\n\
* 01 11 44 40 41 42\n\
*\n\
* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the\n\
* transpose of RFP A above. One therefore gets:\n\
*\n\
* RFP A RFP A\n\
*\n\
* 02 12 22 00 01 00 10 20 30 40 50\n\
* 03 13 23 33 11 33 11 21 31 41 51\n\
* 04 14 24 34 44 43 44 22 32 42 52\n\
*\n\
* =====================================================================\n\
*\n"
|
