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
162
163
164
165
166
167
|
---
:name: sgbbrd
:md5sum: a63bfd9042ac59ad25fe20ca4dea72f6
:category: :subroutine
:arguments:
- vect:
:type: char
:intent: input
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- ncc:
:type: integer
:intent: input
- kl:
:type: integer
:intent: input
- ku:
:type: integer
:intent: input
- ab:
:type: real
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- d:
:type: real
:intent: output
:dims:
- MIN(m,n)
- e:
:type: real
:intent: output
:dims:
- MIN(m,n)-1
- q:
:type: real
:intent: output
:dims:
- ldq
- m
- ldq:
:type: integer
:intent: input
- pt:
:type: real
:intent: output
:dims:
- ldpt
- n
- ldpt:
:type: integer
:intent: input
- c:
:type: real
:intent: input/output
:dims:
- ldc
- ncc
- ldc:
:type: integer
:intent: input
- work:
:type: real
:intent: workspace
:dims:
- 2*MAX(m,n)
- info:
:type: integer
:intent: output
:substitutions:
m: ldab
ldq: "((lsame_(&vect,\"Q\")) || (lsame_(&vect,\"B\"))) ? MAX(1,m) : 1"
ldpt: "((lsame_(&vect,\"P\")) || (lsame_(&vect,\"B\"))) ? MAX(1,n) : 1"
:fortran_help: " SUBROUTINE SGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT, LDPT, C, LDC, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SGBBRD reduces a real general m-by-n band matrix A to upper\n\
* bidiagonal form B by an orthogonal transformation: Q' * A * P = B.\n\
*\n\
* The routine computes B, and optionally forms Q or P', or computes\n\
* Q'*C for a given matrix C.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* VECT (input) CHARACTER*1\n\
* Specifies whether or not the matrices Q and P' are to be\n\
* formed.\n\
* = 'N': do not form Q or P';\n\
* = 'Q': form Q only;\n\
* = 'P': form P' only;\n\
* = 'B': form both.\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\
* NCC (input) INTEGER\n\
* The number of columns of the matrix C. NCC >= 0.\n\
*\n\
* KL (input) INTEGER\n\
* The number of subdiagonals of the matrix A. KL >= 0.\n\
*\n\
* KU (input) INTEGER\n\
* The number of superdiagonals of the matrix A. KU >= 0.\n\
*\n\
* AB (input/output) REAL array, dimension (LDAB,N)\n\
* On entry, the m-by-n band matrix A, stored in rows 1 to\n\
* KL+KU+1. The j-th column of A is stored in the j-th column of\n\
* the array AB as follows:\n\
* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).\n\
* On exit, A is overwritten by values generated during the\n\
* reduction.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array A. LDAB >= KL+KU+1.\n\
*\n\
* D (output) REAL array, dimension (min(M,N))\n\
* The diagonal elements of the bidiagonal matrix B.\n\
*\n\
* E (output) REAL array, dimension (min(M,N)-1)\n\
* The superdiagonal elements of the bidiagonal matrix B.\n\
*\n\
* Q (output) REAL array, dimension (LDQ,M)\n\
* If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q.\n\
* If VECT = 'N' or 'P', the array Q is not referenced.\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q.\n\
* LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.\n\
*\n\
* PT (output) REAL array, dimension (LDPT,N)\n\
* If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'.\n\
* If VECT = 'N' or 'Q', the array PT is not referenced.\n\
*\n\
* LDPT (input) INTEGER\n\
* The leading dimension of the array PT.\n\
* LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.\n\
*\n\
* C (input/output) REAL array, dimension (LDC,NCC)\n\
* On entry, an m-by-ncc matrix C.\n\
* On exit, C is overwritten by Q'*C.\n\
* C is not referenced if NCC = 0.\n\
*\n\
* LDC (input) INTEGER\n\
* The leading dimension of the array C.\n\
* LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.\n\
*\n\
* WORK (workspace) REAL array, dimension (2*max(M,N))\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit.\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
*\n\n\
* =====================================================================\n\
*\n"
|
