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
|
---
:name: dsbgst
:md5sum: d2437ea90e45fe4864720cf3787add9d
:category: :subroutine
:arguments:
- vect:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ka:
:type: integer
:intent: input
- kb:
:type: integer
:intent: input
- ab:
:type: doublereal
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- bb:
:type: doublereal
:intent: input
:dims:
- ldbb
- n
- ldbb:
:type: integer
:intent: input
- x:
:type: doublereal
:intent: output
:dims:
- ldx
- n
- ldx:
:type: integer
:intent: input
- work:
:type: doublereal
:intent: workspace
:dims:
- 2*n
- info:
:type: integer
:intent: output
:substitutions:
ldx: "lsame_(&vect,\"V\") ? MAX(1,n) : 1"
:fortran_help: " SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DSBGST reduces a real symmetric-definite banded generalized\n\
* eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,\n\
* such that C has the same bandwidth as A.\n\
*\n\
* B must have been previously factorized as S**T*S by DPBSTF, using a\n\
* split Cholesky factorization. A is overwritten by C = X**T*A*X, where\n\
* X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the\n\
* bandwidth of A.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* VECT (input) CHARACTER*1\n\
* = 'N': do not form the transformation matrix X;\n\
* = 'V': form X.\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 matrices A and B. N >= 0.\n\
*\n\
* KA (input) INTEGER\n\
* The number of superdiagonals of the matrix A if UPLO = 'U',\n\
* or the number of subdiagonals if UPLO = 'L'. KA >= 0.\n\
*\n\
* KB (input) INTEGER\n\
* The number of superdiagonals of the matrix B if UPLO = 'U',\n\
* or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;\n\
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).\n\
*\n\
* On exit, the transformed matrix X**T*A*X, stored in the same\n\
* format as A.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KA+1.\n\
*\n\
* BB (input) DOUBLE PRECISION array, dimension (LDBB,N)\n\
* The banded factor S from the split Cholesky factorization of\n\
* B, as returned by DPBSTF, stored in the first KB+1 rows of\n\
* the array.\n\
*\n\
* LDBB (input) INTEGER\n\
* The leading dimension of the array BB. LDBB >= KB+1.\n\
*\n\
* X (output) DOUBLE PRECISION array, dimension (LDX,N)\n\
* If VECT = 'V', the n-by-n matrix X.\n\
* If VECT = 'N', the array X is not referenced.\n\
*\n\
* LDX (input) INTEGER\n\
* The leading dimension of the array X.\n\
* LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (2*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"
|
