ZTBRFS(3F) ZTBRFS(3F)
ZTBRFS  provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix
SUBROUTINE ZTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
LDX, FERR, BERR, WORK, RWORK, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, KD, LDAB, LDB, LDX, N, NRHS
DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
COMPLEX*16 AB( LDAB, * ), B( LDB, * ), WORK( * ), X( LDX, * )
ZTBRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix.
The solution matrix X must be computed by ZTBTRS or some other means
before entering this routine. ZTBRFS 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.
KD (input) INTEGER
The number of superdiagonals or subdiagonals of the triangular
band matrix A. KD >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
Page 1
ZTBRFS(3F) ZTBRFS(3F)
AB (input) COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the first
kd+1 rows of the array. The jth column of A is stored in the jth
column of the array AB as follows: if UPLO = 'U', AB(kd+1+ij,j)
= A(i,j) for max(1,jkd)<=i<=j; if UPLO = 'L', AB(1+ij,j)
= A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal
elements of A are not referenced and are assumed to be 1.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS)
The solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
ZTBRFS(3F) ZTBRFS(3F)
ZTBRFS  provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix
SUBROUTINE ZTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
LDX, FERR, BERR, WORK, RWORK, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, KD, LDAB, LDB, LDX, N, NRHS
DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
COMPLEX*16 AB( LDAB, * ), B( LDB, * ), WORK( * ), X( LDX, * )
ZTBRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix.
The solution matrix X must be computed by ZTBTRS or some other means
before entering this routine. ZTBRFS 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.
KD (input) INTEGER
The number of superdiagonals or subdiagonals of the triangular
band matrix A. KD >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
Page 1
ZTBRFS(3F) ZTBRFS(3F)
AB (input) COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the first
kd+1 rows of the array. The jth column of A is stored in the jth
column of the array AB as follows: if UPLO = 'U', AB(kd+1+ij,j)
= A(i,j) for max(1,jkd)<=i<=j; if UPLO = 'L', AB(1+ij,j)
= A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal
elements of A are not referenced and are assumed to be 1.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS)
The solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
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