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
|
---
:name: cla_gbamv
:md5sum: 6fdc0ec1e9d677c211aaed9e1e36bb0c
:category: :subroutine
:arguments:
- trans:
:type: integer
:intent: input
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- kl:
:type: integer
:intent: input
- ku:
:type: integer
:intent: input
- alpha:
:type: real
:intent: input
- ab:
:type: real
:intent: input
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- x:
:type: real
:intent: input
:dims:
- "trans == ilatrans_(\"N\") ? 1 + ( n - 1 )*abs( incx ) : 1 + ( m - 1 )*abs( incx )"
- incx:
:type: integer
:intent: input
- beta:
:type: real
:intent: input
- y:
:type: real
:intent: input/output
:dims:
- "trans == ilatrans_(\"N\") ? 1 + ( m - 1 )*abs( incy ) : 1 + ( n - 1 )*abs( incy )"
- incy:
:type: integer
:intent: input
:substitutions:
ldab: MAX(1,m)
:fortran_help: " SUBROUTINE CLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SLA_GBAMV performs one of the matrix-vector operations\n\
*\n\
* y := alpha*abs(A)*abs(x) + beta*abs(y),\n\
* or y := alpha*abs(A)'*abs(x) + beta*abs(y),\n\
*\n\
* where alpha and beta are scalars, x and y are vectors and A is an\n\
* m by n matrix.\n\
*\n\
* This function is primarily used in calculating error bounds.\n\
* To protect against underflow during evaluation, components in\n\
* the resulting vector are perturbed away from zero by (N+1)\n\
* times the underflow threshold. To prevent unnecessarily large\n\
* errors for block-structure embedded in general matrices,\n\
* \"symbolically\" zero components are not perturbed. A zero\n\
* entry is considered \"symbolic\" if all multiplications involved\n\
* in computing that entry have at least one zero multiplicand.\n\
*\n\n\
* Arguments\n\
* ==========\n\
*\n\
* TRANS (input) INTEGER\n\
* On entry, TRANS specifies the operation to be performed as\n\
* follows:\n\
*\n\
* BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y)\n\
* BLAS_TRANS y := alpha*abs(A')*abs(x) + beta*abs(y)\n\
* BLAS_CONJ_TRANS y := alpha*abs(A')*abs(x) + beta*abs(y)\n\
*\n\
* Unchanged on exit.\n\
*\n\
* M (input) INTEGER\n\
* On entry, M specifies the number of rows of the matrix A.\n\
* M must be at least zero.\n\
* Unchanged on exit.\n\
*\n\
* N (input) INTEGER\n\
* On entry, N specifies the number of columns of the matrix A.\n\
* N must be at least zero.\n\
* Unchanged on exit.\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\
* ALPHA (input) REAL\n\
* On entry, ALPHA specifies the scalar alpha.\n\
* Unchanged on exit.\n\
*\n\
* A (input) REAL array, dimension (LDA,n)\n\
* Before entry, the leading m by n part of the array A must\n\
* contain the matrix of coefficients.\n\
* Unchanged on exit.\n\
*\n\
* LDA (input) INTEGER\n\
* On entry, LDA specifies the first dimension of A as declared\n\
* in the calling (sub) program. LDA must be at least\n\
* max( 1, m ).\n\
* Unchanged on exit.\n\
*\n\
* X (input) REAL array, dimension at least\n\
* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'\n\
* and at least\n\
* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.\n\
* Before entry, the incremented array X must contain the\n\
* vector x.\n\
* Unchanged on exit.\n\
*\n\
* INCX (input) INTEGER\n\
* On entry, INCX specifies the increment for the elements of\n\
* X. INCX must not be zero.\n\
* Unchanged on exit.\n\
*\n\
* BETA (input) REAL\n\
* On entry, BETA specifies the scalar beta. When BETA is\n\
* supplied as zero then Y need not be set on input.\n\
* Unchanged on exit.\n\
*\n\
* Y (input/output) REAL array, dimension at least\n\
* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'\n\
* and at least\n\
* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.\n\
* Before entry with BETA non-zero, the incremented array Y\n\
* must contain the vector y. On exit, Y is overwritten by the\n\
* updated vector y.\n\
*\n\
* INCY (input) INTEGER\n\
* On entry, INCY specifies the increment for the elements of\n\
* Y. INCY must not be zero.\n\
* Unchanged on exit.\n\
*\n\
*\n\
* Level 2 Blas routine.\n\
*\n\n\
* =====================================================================\n\
*\n"
|
