1DGERFS(1) LAPACK routine (version 3.2) DGERFS(1)
2
6 DGERFS - improves the computed solution to a system of linear equations
7 and provides error bounds and backward error estimates for the solution
8
10 SUBROUTINE DGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X,
11 LDX, FERR, BERR, WORK, IWORK, INFO )
12 CHARACTER TRANS
14 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
16 INTEGER IPIV( * ), IWORK( * )
18 DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
20 BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
21
23 DGERFS improves the computed solution to a system of linear equations
24 and provides error bounds and backward error estimates for the solu‐
25 tion.
26
28 TRANS (input) CHARACTER*1
29 Specifies the form of the system of equations:
30 = 'N': A * X = B (No transpose)
31 = 'T': A**T * X = B (Transpose)
32 = 'C': A**H * X = B (Conjugate transpose = Transpose)
33 N (input) INTEGER
35 The order of the matrix A. N >= 0.
36 NRHS (input) INTEGER
38 The number of right hand sides, i.e., the number of columns of
39 the matrices B and X. NRHS >= 0.
40 A (input) DOUBLE PRECISION array, dimension (LDA,N)
42 The original N-by-N matrix A.
43 LDA (input) INTEGER
45 The leading dimension of the array A. LDA >= max(1,N).
46 AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
48 The factors L and U from the factorization A = P*L*U as com‐
49 puted by DGETRF.
50 LDAF (input) INTEGER
52 The leading dimension of the array AF. LDAF >= max(1,N).
53 IPIV (input) INTEGER array, dimension (N)
55 The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix
56 was interchanged with row IPIV(i).
57 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
59 The right hand side matrix B.
60 LDB (input) INTEGER
62 The leading dimension of the array B. LDB >= max(1,N).
63 X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
65 On entry, the solution matrix X, as computed by DGETRS. On
66 exit, the improved solution matrix X.
67 LDX (input) INTEGER
69 The leading dimension of the array X. LDX >= max(1,N).
70 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
72 The estimated forward error bound for each solution vector X(j)
73 (the j-th column of the solution matrix X). If XTRUE is the
74 true solution corresponding to X(j), FERR(j) is an estimated
75 upper bound for the magnitude of the largest element in (X(j) -
76 XTRUE) divided by the magnitude of the largest element in X(j).
77 The estimate is as reliable as the estimate for RCOND, and is
78 almost always a slight overestimate of the true error.
79 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
81 The componentwise relative backward error of each solution vec‐
82 tor X(j) (i.e., the smallest relative change in any element of
83 A or B that makes X(j) an exact solution).
84 WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
86 IWORK (workspace) INTEGER array, dimension (N)
88 INFO (output) INTEGER
90 = 0: successful exit
91 < 0: if INFO = -i, the i-th argument had an illegal value
92
94 ITMAX is the maximum number of steps of iterative refinement.
95 LAPACK routine (version 3.2) November 2008 DGERFS(1)