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
|
---
:name: sgbequ
:md5sum: e05049ad6bde32cc4308286b8c0a3d8e
:category: :subroutine
:arguments:
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- kl:
:type: integer
:intent: input
- ku:
:type: integer
:intent: input
- ab:
:type: real
:intent: input
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- r:
:type: real
:intent: output
:dims:
- MAX(1,m)
- c:
:type: real
:intent: output
:dims:
- n
- rowcnd:
:type: real
:intent: output
- colcnd:
:type: real
:intent: output
- amax:
:type: real
:intent: output
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SGBEQU computes row and column scalings intended to equilibrate an\n\
* M-by-N band matrix A and reduce its condition number. R returns the\n\
* row scale factors and C the column scale factors, chosen to try to\n\
* make the largest element in each row and column of the matrix B with\n\
* elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.\n\
*\n\
* R(i) and C(j) are restricted to be between SMLNUM = smallest safe\n\
* number and BIGNUM = largest safe number. Use of these scaling\n\
* factors is not guaranteed to reduce the condition number of A but\n\
* works well in practice.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix A. N >= 0.\n\
*\n\
* KL (input) INTEGER\n\
* The number of subdiagonals within the band of A. KL >= 0.\n\
*\n\
* KU (input) INTEGER\n\
* The number of superdiagonals within the band of A. KU >= 0.\n\
*\n\
* AB (input) REAL array, dimension (LDAB,N)\n\
* The band matrix A, stored in rows 1 to KL+KU+1. The j-th\n\
* column of A is stored in the j-th column of the array AB as\n\
* follows:\n\
* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KL+KU+1.\n\
*\n\
* R (output) REAL array, dimension (M)\n\
* If INFO = 0, or INFO > M, R contains the row scale factors\n\
* for A.\n\
*\n\
* C (output) REAL array, dimension (N)\n\
* If INFO = 0, C contains the column scale factors for A.\n\
*\n\
* ROWCND (output) REAL\n\
* If INFO = 0 or INFO > M, ROWCND contains the ratio of the\n\
* smallest R(i) to the largest R(i). If ROWCND >= 0.1 and\n\
* AMAX is neither too large nor too small, it is not worth\n\
* scaling by R.\n\
*\n\
* COLCND (output) REAL\n\
* If INFO = 0, COLCND contains the ratio of the smallest\n\
* C(i) to the largest C(i). If COLCND >= 0.1, it is not\n\
* worth scaling by C.\n\
*\n\
* AMAX (output) REAL\n\
* Absolute value of largest matrix element. If AMAX is very\n\
* close to overflow or very close to underflow, the matrix\n\
* should be scaled.\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, and i is\n\
* <= M: the i-th row of A is exactly zero\n\
* > M: the (i-M)-th column of A is exactly zero\n\
*\n\n\
* =====================================================================\n\
*\n"
|
