SGERFS(3F) SGERFS(3F)
SGERFS  improve the computed solution to a system of linear equations
and provides error bounds and backward error estimates for the solution
SUBROUTINE SGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X,
LDX, FERR, BERR, WORK, IWORK, INFO )
CHARACTER TRANS
INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
INTEGER IPIV( * ), IWORK( * )
REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ),
FERR( * ), WORK( * ), X( LDX, * )
SGERFS improves the computed solution to a system of linear equations and
provides error bounds and backward error estimates for the solution.
TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
A (input) REAL array, dimension (LDA,N)
The original NbyN matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
AF (input) REAL array, dimension (LDAF,N)
The factors L and U from the factorization A = P*L*U as computed
by SGETRF.
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indices from SGETRF; for 1<=i<=N, row i of the matrix
was interchanged with row IPIV(i).
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SGERFS(3F) SGERFS(3F)
B (input) REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SGETRS. On exit,
the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector X(j)
(the jth column of the solution matrix X). If XTRUE is the true
solution corresponding to X(j), FERR(j) is an estimated upper
bound for the magnitude of the largest element in (X(j)  XTRUE)
divided by the magnitude of the largest element in X(j). The
estimate is as reliable as the estimate for RCOND, and is almost
always a slight overestimate of the true error.
BERR (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution vector
X(j) (i.e., the smallest relative change in any element of A or B
that makes X(j) an exact solution).
WORK (workspace) REAL array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
ITMAX is the maximum number of steps of iterative refinement.
SGERFS(3F) SGERFS(3F)
SGERFS  improve the computed solution to a system of linear equations
and provides error bounds and backward error estimates for the solution
SUBROUTINE SGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X,
LDX, FERR, BERR, WORK, IWORK, INFO )
CHARACTER TRANS
INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
INTEGER IPIV( * ), IWORK( * )
REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ),
FERR( * ), WORK( * ), X( LDX, * )
SGERFS improves the computed solution to a system of linear equations and
provides error bounds and backward error estimates for the solution.
TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
A (input) REAL array, dimension (LDA,N)
The original NbyN matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
AF (input) REAL array, dimension (LDAF,N)
The factors L and U from the factorization A = P*L*U as computed
by SGETRF.
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indices from SGETRF; for 1<=i<=N, row i of the matrix
was interchanged with row IPIV(i).
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SGERFS(3F) SGERFS(3F)
B (input) REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SGETRS. On exit,
the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector X(j)
(the jth column of the solution matrix X). If XTRUE is the true
solution corresponding to X(j), FERR(j) is an estimated upper
bound for the magnitude of the largest element in (X(j)  XTRUE)
divided by the magnitude of the largest element in X(j). The
estimate is as reliable as the estimate for RCOND, and is almost
always a slight overestimate of the true error.
BERR (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution vector
X(j) (i.e., the smallest relative change in any element of A or B
that makes X(j) an exact solution).
WORK (workspace) REAL array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
ITMAX is the maximum number of steps of iterative refinement.
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