LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine ztbrfs | ( | character | UPLO, |
character | TRANS, | ||
character | DIAG, | ||
integer | N, | ||
integer | KD, | ||
integer | NRHS, | ||
complex*16, dimension( ldab, * ) | AB, | ||
integer | LDAB, | ||
complex*16, dimension( ldb, * ) | B, | ||
integer | LDB, | ||
complex*16, dimension( ldx, * ) | X, | ||
integer | LDX, | ||
double precision, dimension( * ) | FERR, | ||
double precision, dimension( * ) | BERR, | ||
complex*16, dimension( * ) | WORK, | ||
double precision, dimension( * ) | RWORK, | ||
integer | INFO | ||
) |
ZTBRFS
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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.
[in] | UPLO | UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. |
[in] | TRANS | TRANS is 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) |
[in] | DIAG | DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[in] | KD | KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. |
[in] | NRHS | NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. |
[in] | AB | AB is 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 j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,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. |
[in] | LDAB | LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. |
[in] | B | B is COMPLEX*16 array, dimension (LDB,NRHS) The right hand side matrix B. |
[in] | LDB | LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). |
[in] | X | X is COMPLEX*16 array, dimension (LDX,NRHS) The solution matrix X. |
[in] | LDX | LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N). |
[out] | FERR | FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bound for each solution vector X(j) (the j-th 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. |
[out] | BERR | BERR is 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). |
[out] | WORK | WORK is COMPLEX*16 array, dimension (2*N) |
[out] | RWORK | RWORK is DOUBLE PRECISION array, dimension (N) |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value |
Definition at line 190 of file ztbrfs.f.