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

6       SGERFS - 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 SGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B,  LDB,  X,
11                          LDX, FERR, BERR, WORK, IWORK, 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( * ), IWORK( * )
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19           REAL           A(  LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ),
20                          FERR( * ), WORK( * ), X( LDX, * )
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PURPOSE

23       SGERFS improves the computed solution to a system of  linear  equations
24       and  provides  error  bounds and backward error estimates for the solu‐
25       tion.
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ARGUMENTS

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

95       ITMAX is the maximum number of steps of iterative refinement.
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99 LAPACK routine (version 3.1)    November 2006                       SGERFS(1)