1CGERFS(1)                LAPACK routine (version 3.2)                CGERFS(1)
2
3
4

NAME

6       CGERFS - improves the computed solution to a system of linear equations
7       and provides error bounds and backward error estimates for the solution
8

SYNOPSIS

10       SUBROUTINE CGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B,  LDB,  X,
11                          LDX, FERR, BERR, WORK, RWORK, INFO )
12
13           CHARACTER      TRANS
14
15           INTEGER        INFO, LDA, LDAF, LDB, LDX, N, NRHS
16
17           INTEGER        IPIV( * )
18
19           REAL           BERR( * ), FERR( * ), RWORK( * )
20
21           COMPLEX        A(  LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ),
22                          X( LDX, * )
23

PURPOSE

25       CGERFS improves the computed solution to a system of  linear  equations
26       and  provides  error  bounds and backward error estimates for the solu‐
27       tion.
28

ARGUMENTS

30       TRANS   (input) CHARACTER*1
31               Specifies the form of the system of equations:
32               = 'N':  A * X = B     (No transpose)
33               = 'T':  A**T * X = B  (Transpose)
34               = 'C':  A**H * X = B  (Conjugate transpose)
35
36       N       (input) INTEGER
37               The order of the matrix A.  N >= 0.
38
39       NRHS    (input) INTEGER
40               The number of right hand sides, i.e., the number of columns  of
41               the matrices B and X.  NRHS >= 0.
42
43       A       (input) COMPLEX array, dimension (LDA,N)
44               The original N-by-N matrix A.
45
46       LDA     (input) INTEGER
47               The leading dimension of the array A.  LDA >= max(1,N).
48
49       AF      (input) COMPLEX array, dimension (LDAF,N)
50               The  factors  L  and U from the factorization A = P*L*U as com‐
51               puted by CGETRF.
52
53       LDAF    (input) INTEGER
54               The leading dimension of the array AF.  LDAF >= max(1,N).
55
56       IPIV    (input) INTEGER array, dimension (N)
57               The pivot indices from CGETRF; for 1<=i<=N, row i of the matrix
58               was interchanged with row IPIV(i).
59
60       B       (input) COMPLEX array, dimension (LDB,NRHS)
61               The right hand side matrix B.
62
63       LDB     (input) INTEGER
64               The leading dimension of the array B.  LDB >= max(1,N).
65
66       X       (input/output) COMPLEX array, dimension (LDX,NRHS)
67               On  entry,  the  solution  matrix X, as computed by CGETRS.  On
68               exit, the improved solution matrix X.
69
70       LDX     (input) INTEGER
71               The leading dimension of the array X.  LDX >= max(1,N).
72
73       FERR    (output) REAL array, dimension (NRHS)
74               The estimated forward error bound for each solution vector X(j)
75               (the  j-th  column  of the solution matrix X).  If XTRUE is the
76               true solution corresponding to X(j), FERR(j)  is  an  estimated
77               upper bound for the magnitude of the largest element in (X(j) -
78               XTRUE) divided by the magnitude of the largest element in X(j).
79               The  estimate  is as reliable as the estimate for RCOND, and is
80               almost always a slight overestimate of the true error.
81
82       BERR    (output) REAL array, dimension (NRHS)
83               The componentwise relative backward error of each solution vec‐
84               tor  X(j) (i.e., the smallest relative change in any element of
85               A or B that makes X(j) an exact solution).
86
87       WORK    (workspace) COMPLEX array, dimension (2*N)
88
89       RWORK   (workspace) REAL array, dimension (N)
90
91       INFO    (output) INTEGER
92               = 0:  successful exit
93               < 0:  if INFO = -i, the i-th argument had an illegal value
94

PARAMETERS

96       ITMAX is the maximum number of steps of iterative refinement.
97
98
99
100 LAPACK routine (version 3.2)    November 2008                       CGERFS(1)