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
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
|
---
:name: sgtrfs
:md5sum: 07d24cfa02e3c548ded77eb4cde10139
:category: :subroutine
:arguments:
- trans:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- dl:
:type: real
:intent: input
:dims:
- n-1
- d:
:type: real
:intent: input
:dims:
- n
- du:
:type: real
:intent: input
:dims:
- n-1
- dlf:
:type: real
:intent: input
:dims:
- n-1
- df:
:type: real
:intent: input
:dims:
- n
- duf:
:type: real
:intent: input
:dims:
- n-1
- du2:
:type: real
:intent: input
:dims:
- n-2
- ipiv:
:type: integer
:intent: input
:dims:
- n
- b:
:type: real
:intent: input
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- x:
:type: real
:intent: input/output
:dims:
- ldx
- nrhs
- ldx:
:type: integer
:intent: input
- ferr:
:type: real
:intent: output
:dims:
- nrhs
- berr:
:type: real
:intent: output
:dims:
- nrhs
- work:
:type: real
:intent: workspace
:dims:
- 3*n
- iwork:
:type: integer
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SGTRFS improves the computed solution to a system of linear\n\
* equations when the coefficient matrix is tridiagonal, and provides\n\
* error bounds and backward error estimates for the solution.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* TRANS (input) CHARACTER*1\n\
* Specifies the form of the system of equations:\n\
* = 'N': A * X = B (No transpose)\n\
* = 'T': A**T * X = B (Transpose)\n\
* = 'C': A**H * X = B (Conjugate transpose = Transpose)\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 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\
* DL (input) REAL array, dimension (N-1)\n\
* The (n-1) subdiagonal elements of A.\n\
*\n\
* D (input) REAL array, dimension (N)\n\
* The diagonal elements of A.\n\
*\n\
* DU (input) REAL array, dimension (N-1)\n\
* The (n-1) superdiagonal elements of A.\n\
*\n\
* DLF (input) REAL array, dimension (N-1)\n\
* The (n-1) multipliers that define the matrix L from the\n\
* LU factorization of A as computed by SGTTRF.\n\
*\n\
* DF (input) REAL array, dimension (N)\n\
* The n diagonal elements of the upper triangular matrix U from\n\
* the LU factorization of A.\n\
*\n\
* DUF (input) REAL array, dimension (N-1)\n\
* The (n-1) elements of the first superdiagonal of U.\n\
*\n\
* DU2 (input) REAL array, dimension (N-2)\n\
* The (n-2) elements of the second superdiagonal of U.\n\
*\n\
* IPIV (input) INTEGER array, dimension (N)\n\
* The pivot indices; for 1 <= i <= n, row i of the matrix was\n\
* interchanged with row IPIV(i). IPIV(i) will always be either\n\
* i or i+1; IPIV(i) = i indicates a row interchange was not\n\
* required.\n\
*\n\
* B (input) REAL array, dimension (LDB,NRHS)\n\
* The right hand side matrix B.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* X (input/output) REAL array, dimension (LDX,NRHS)\n\
* On entry, the solution matrix X, as computed by SGTTRS.\n\
* On exit, the improved solution matrix X.\n\
*\n\
* LDX (input) INTEGER\n\
* The leading dimension of the array X. LDX >= max(1,N).\n\
*\n\
* FERR (output) REAL array, dimension (NRHS)\n\
* The estimated forward error bound for each solution vector\n\
* X(j) (the j-th column of the solution matrix X).\n\
* If XTRUE is the true solution corresponding to X(j), FERR(j)\n\
* is an estimated upper bound for the magnitude of the largest\n\
* element in (X(j) - XTRUE) divided by the magnitude of the\n\
* largest element in X(j). The estimate is as reliable as\n\
* the estimate for RCOND, and is almost always a slight\n\
* overestimate of the true error.\n\
*\n\
* BERR (output) REAL array, dimension (NRHS)\n\
* The componentwise relative backward error of each solution\n\
* vector X(j) (i.e., the smallest relative change in\n\
* any element of A or B that makes X(j) an exact solution).\n\
*\n\
* WORK (workspace) REAL array, dimension (3*N)\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (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\
* Internal Parameters\n\
* ===================\n\
*\n\
* ITMAX is the maximum number of steps of iterative refinement.\n\
*\n\n\
* =====================================================================\n\
*\n"
|
