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LAPACK
3.4.2
LAPACK: Linear Algebra PACKage
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Go to the source code of this file.
Functions/Subroutines | |
| subroutine | ztbrfs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO) |
| ZTBRFS | |
| 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
Download ZTBRFS + dependencies [TGZ] [ZIP] [TXT]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 188 of file ztbrfs.f.
1.8.1.1 
