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
|
---
:name: dtprfs
:md5sum: 6ebdcf9618f401dd3cc557634f2c0b07
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- trans:
:type: char
:intent: input
- diag:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- ap:
:type: doublereal
:intent: input
:dims:
- n*(n+1)/2
- b:
:type: doublereal
:intent: input
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- x:
:type: doublereal
:intent: input
:dims:
- ldx
- nrhs
- ldx:
:type: integer
:intent: input
- ferr:
:type: doublereal
:intent: output
:dims:
- nrhs
- berr:
:type: doublereal
:intent: output
:dims:
- nrhs
- work:
:type: doublereal
:intent: workspace
:dims:
- 3*n
- iwork:
:type: integer
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions:
n: ldb
:fortran_help: " SUBROUTINE DTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DTPRFS provides error bounds and backward error estimates for the\n\
* solution to a system of linear equations with a triangular packed\n\
* coefficient matrix.\n\
*\n\
* The solution matrix X must be computed by DTPTRS or some other\n\
* means before entering this routine. DTPRFS does not do iterative\n\
* refinement because doing so cannot improve the backward error.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': A is upper triangular;\n\
* = 'L': A is lower triangular.\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\
* DIAG (input) CHARACTER*1\n\
* = 'N': A is non-unit triangular;\n\
* = 'U': A is unit triangular.\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 matrices B and X. NRHS >= 0.\n\
*\n\
* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)\n\
* The upper or lower triangular matrix A, packed columnwise in\n\
* a linear array. The j-th column of A is stored in the array\n\
* AP as follows:\n\
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;\n\
* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.\n\
* If DIAG = 'U', the diagonal elements of A are not referenced\n\
* and are assumed to be 1.\n\
*\n\
* B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)\n\
* The solution matrix X.\n\
*\n\
* LDX (input) INTEGER\n\
* The leading dimension of the array X. LDX >= max(1,N).\n\
*\n\
* FERR (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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\n\
* =====================================================================\n\
*\n"
|
