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
|
---
:name: zgbsv
:md5sum: ae5d9df6f8b2826acd8be07569b5c355
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- kl:
:type: integer
:intent: input
- ku:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- ab:
:type: doublecomplex
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- ipiv:
:type: integer
:intent: output
:dims:
- n
- b:
:type: doublecomplex
:intent: input/output
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZGBSV computes the solution to a complex system of linear equations\n\
* A * X = B, where A is a band matrix of order N with KL subdiagonals\n\
* and KU superdiagonals, and X and B are N-by-NRHS matrices.\n\
*\n\
* The LU decomposition with partial pivoting and row interchanges is\n\
* used to factor A as A = L * U, where L is a product of permutation\n\
* and unit lower triangular matrices with KL subdiagonals, and U is\n\
* upper triangular with KL+KU superdiagonals. The factored form of A\n\
* is then used to solve the system of equations A * X = B.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The number of linear equations, i.e., the order of the\n\
* 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\
* NRHS (input) INTEGER\n\
* The number of right hand sides, i.e., the number of columns\n\
* of the matrix B. NRHS >= 0.\n\
*\n\
* AB (input/output) COMPLEX*16 array, dimension (LDAB,N)\n\
* On entry, the matrix A in band storage, in rows KL+1 to\n\
* 2*KL+KU+1; rows 1 to KL of the array need not be set.\n\
* The j-th column of A is stored in the j-th column of the\n\
* array AB as follows:\n\
* AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)\n\
* On exit, details of the factorization: U is stored as an\n\
* upper triangular band matrix with KL+KU superdiagonals in\n\
* rows 1 to KL+KU+1, and the multipliers used during the\n\
* factorization are stored in rows KL+KU+2 to 2*KL+KU+1.\n\
* See below for further details.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= 2*KL+KU+1.\n\
*\n\
* IPIV (output) INTEGER array, dimension (N)\n\
* The pivot indices that define the permutation matrix P;\n\
* row i of the matrix was interchanged with row IPIV(i).\n\
*\n\
* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)\n\
* On entry, the N-by-NRHS right hand side matrix B.\n\
* On exit, if INFO = 0, the N-by-NRHS solution matrix X.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\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, U(i,i) is exactly zero. The factorization\n\
* has been completed, but the factor U is exactly\n\
* singular, and the solution has not been computed.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* The band storage scheme is illustrated by the following example, when\n\
* M = N = 6, KL = 2, KU = 1:\n\
*\n\
* On entry: On exit:\n\
*\n\
* * * * + + + * * * u14 u25 u36\n\
* * * + + + + * * u13 u24 u35 u46\n\
* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56\n\
* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66\n\
* a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *\n\
* a31 a42 a53 a64 * * m31 m42 m53 m64 * *\n\
*\n\
* Array elements marked * are not used by the routine; elements marked\n\
* + need not be set on entry, but are required by the routine to store\n\
* elements of U because of fill-in resulting from the row interchanges.\n\
*\n\
* =====================================================================\n\
*\n\
* .. External Subroutines ..\n EXTERNAL XERBLA, ZGBTRF, ZGBTRS\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX\n\
* ..\n"
|
