1ZGERFS(1)                LAPACK routine (version 3.2)                ZGERFS(1)
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NAME

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

10       SUBROUTINE ZGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B,  LDB,  X,
11                          LDX, FERR, BERR, WORK, RWORK, INFO )
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13           CHARACTER      TRANS
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15           INTEGER        INFO, LDA, LDAF, LDB, LDX, N, NRHS
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17           INTEGER        IPIV( * )
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19           DOUBLE         PRECISION BERR( * ), FERR( * ), RWORK( * )
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21           COMPLEX*16     A(  LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ),
22                          X( LDX, * )
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PURPOSE

25       ZGERFS improves the computed solution to a system of  linear  equations
26       and  provides  error  bounds and backward error estimates for the solu‐
27       tion.
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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)
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36       N       (input) INTEGER
37               The order of the matrix A.  N >= 0.
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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.
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43       A       (input) COMPLEX*16 array, dimension (LDA,N)
44               The original N-by-N matrix A.
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46       LDA     (input) INTEGER
47               The leading dimension of the array A.  LDA >= max(1,N).
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49       AF      (input) COMPLEX*16 array, dimension (LDAF,N)
50               The  factors  L  and U from the factorization A = P*L*U as com‐
51               puted by ZGETRF.
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53       LDAF    (input) INTEGER
54               The leading dimension of the array AF.  LDAF >= max(1,N).
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56       IPIV    (input) INTEGER array, dimension (N)
57               The pivot indices from ZGETRF; for 1<=i<=N, row i of the matrix
58               was interchanged with row IPIV(i).
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60       B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
61               The right hand side matrix B.
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63       LDB     (input) INTEGER
64               The leading dimension of the array B.  LDB >= max(1,N).
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66       X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
67               On  entry,  the  solution  matrix X, as computed by ZGETRS.  On
68               exit, the improved solution matrix X.
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70       LDX     (input) INTEGER
71               The leading dimension of the array X.  LDX >= max(1,N).
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73       FERR    (output) DOUBLE PRECISION 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.
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82       BERR    (output) DOUBLE PRECISION 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).
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87       WORK    (workspace) COMPLEX*16 array, dimension (2*N)
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89       RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
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91       INFO    (output) INTEGER
92               = 0:  successful exit
93               < 0:  if INFO = -i, the i-th argument had an illegal value
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PARAMETERS

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