1ZGERFS(1)                LAPACK routine (version 3.1)                ZGERFS(1)
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NAME

6       ZGERFS - the computed solution to a system of linear equations and pro‐
7       vides 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

31       TRANS   (input) CHARACTER*1
32               Specifies the form of the system of equations:
33               = 'N':  A * X = B     (No transpose)
34               = 'T':  A**T * X = B  (Transpose)
35               = 'C':  A**H * X = B  (Conjugate transpose)
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37       N       (input) INTEGER
38               The order of the matrix A.  N >= 0.
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40       NRHS    (input) INTEGER
41               The number of right hand sides, i.e., the number of columns  of
42               the matrices B and X.  NRHS >= 0.
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44       A       (input) COMPLEX*16 array, dimension (LDA,N)
45               The original N-by-N matrix A.
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47       LDA     (input) INTEGER
48               The leading dimension of the array A.  LDA >= max(1,N).
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50       AF      (input) COMPLEX*16 array, dimension (LDAF,N)
51               The  factors  L  and U from the factorization A = P*L*U as com‐
52               puted by ZGETRF.
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54       LDAF    (input) INTEGER
55               The leading dimension of the array AF.  LDAF >= max(1,N).
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57       IPIV    (input) INTEGER array, dimension (N)
58               The pivot indices from ZGETRF; for 1<=i<=N, row i of the matrix
59               was interchanged with row IPIV(i).
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61       B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
62               The right hand side matrix B.
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64       LDB     (input) INTEGER
65               The leading dimension of the array B.  LDB >= max(1,N).
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67       X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
68               On  entry,  the  solution  matrix X, as computed by ZGETRS.  On
69               exit, the improved solution matrix X.
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71       LDX     (input) INTEGER
72               The leading dimension of the array X.  LDX >= max(1,N).
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74       FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
75               The estimated forward error bound for each solution vector X(j)
76               (the  j-th  column  of the solution matrix X).  If XTRUE is the
77               true solution corresponding to X(j), FERR(j)  is  an  estimated
78               upper bound for the magnitude of the largest element in (X(j) -
79               XTRUE) divided by the magnitude of the largest element in X(j).
80               The  estimate  is as reliable as the estimate for RCOND, and is
81               almost always a slight overestimate of the true error.
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83       BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
84               The componentwise relative backward error of each solution vec‐
85               tor  X(j) (i.e., the smallest relative change in any element of
86               A or B that makes X(j) an exact solution).
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88       WORK    (workspace) COMPLEX*16 array, dimension (2*N)
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90       RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
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92       INFO    (output) INTEGER
93               = 0:  successful exit
94               < 0:  if INFO = -i, the i-th argument had an illegal value
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PARAMETERS

97       ITMAX is the maximum number of steps of iterative refinement.
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101 LAPACK routine (version 3.1)    November 2006                       ZGERFS(1)