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
|
---
:name: dpbstf
:md5sum: 5a40047148b7bdd37c15d29462a47190
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kd:
:type: integer
:intent: input
- ab:
:type: doublereal
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DPBSTF( UPLO, N, KD, AB, LDAB, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DPBSTF computes a split Cholesky factorization of a real\n\
* symmetric positive definite band matrix A.\n\
*\n\
* This routine is designed to be used in conjunction with DSBGST.\n\
*\n\
* The factorization has the form A = S**T*S where S is a band matrix\n\
* of the same bandwidth as A and the following structure:\n\
*\n\
* S = ( U )\n\
* ( M L )\n\
*\n\
* where U is upper triangular of order m = (n+kd)/2, and L is lower\n\
* triangular of order n-m.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangle of A is stored;\n\
* = 'L': Lower triangle of A is stored.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* KD (input) INTEGER\n\
* The number of superdiagonals of the matrix A if UPLO = 'U',\n\
* or the number of subdiagonals if UPLO = 'L'. KD >= 0.\n\
*\n\
* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)\n\
* On entry, the upper or lower triangle of the symmetric band\n\
* matrix A, stored in the first kd+1 rows of the array. The\n\
* j-th column of A is stored in the j-th column of the array AB\n\
* as follows:\n\
* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;\n\
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).\n\
*\n\
* On exit, if INFO = 0, the factor S from the split Cholesky\n\
* factorization A = S**T*S. See Further Details.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KD+1.\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 factorization could not be completed,\n\
* because the updated element a(i,i) was negative; the\n\
* matrix A is not positive definite.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* The band storage scheme is illustrated by the following example, when\n\
* N = 7, KD = 2:\n\
*\n\
* S = ( s11 s12 s13 )\n\
* ( s22 s23 s24 )\n\
* ( s33 s34 )\n\
* ( s44 )\n\
* ( s53 s54 s55 )\n\
* ( s64 s65 s66 )\n\
* ( s75 s76 s77 )\n\
*\n\
* If UPLO = 'U', the array AB holds:\n\
*\n\
* on entry: on exit:\n\
*\n\
* * * a13 a24 a35 a46 a57 * * s13 s24 s53 s64 s75\n\
* * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54 s65 s76\n\
* a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77\n\
*\n\
* If UPLO = 'L', the array AB holds:\n\
*\n\
* on entry: on exit:\n\
*\n\
* a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77\n\
* a21 a32 a43 a54 a65 a76 * s12 s23 s34 s54 s65 s76 *\n\
* a31 a42 a53 a64 a64 * * s13 s24 s53 s64 s75 * *\n\
*\n\
* Array elements marked * are not used by the routine.\n\
*\n\
* =====================================================================\n\
*\n"
|
