CTRRFS(3F) CTRRFS(3F)
CTRRFS  provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular coefficient
matrix
SUBROUTINE CTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
FERR, BERR, WORK, RWORK, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, LDA, LDB, LDX, N, NRHS
REAL BERR( * ), FERR( * ), RWORK( * )
COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ), X( LDX, * )
CTRRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular coefficient
matrix.
The solution matrix X must be computed by CTRTRS or some other means
before entering this routine. CTRRFS does not do iterative refinement
because doing so cannot improve the backward error.
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
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)
DIAG (input) CHARACTER*1
= 'N': A is nonunit triangular;
= 'U': A is unit triangular.
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) COMPLEX array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading NbyN upper
triangular part of the array A contains the upper triangular
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CTRRFS(3F) CTRRFS(3F)
matrix, and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading NbyN lower triangular
part of the array A contains the lower triangular matrix, and the
strictly upper triangular part of A is not referenced. If DIAG =
'U', the diagonal elements of A are also not referenced and are
assumed to be 1.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
The 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) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
CTRRFS(3F) CTRRFS(3F)
CTRRFS  provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular coefficient
matrix
SUBROUTINE CTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
FERR, BERR, WORK, RWORK, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, LDA, LDB, LDX, N, NRHS
REAL BERR( * ), FERR( * ), RWORK( * )
COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ), X( LDX, * )
CTRRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular coefficient
matrix.
The solution matrix X must be computed by CTRTRS or some other means
before entering this routine. CTRRFS does not do iterative refinement
because doing so cannot improve the backward error.
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
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)
DIAG (input) CHARACTER*1
= 'N': A is nonunit triangular;
= 'U': A is unit triangular.
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) COMPLEX array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading NbyN upper
triangular part of the array A contains the upper triangular
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CTRRFS(3F) CTRRFS(3F)
matrix, and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading NbyN lower triangular
part of the array A contains the lower triangular matrix, and the
strictly upper triangular part of A is not referenced. If DIAG =
'U', the diagonal elements of A are also not referenced and are
assumed to be 1.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
The 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) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
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