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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine dtbrfs | ( | character | uplo, |
| character | trans, | ||
| character | diag, | ||
| integer | n, | ||
| integer | kd, | ||
| integer | nrhs, | ||
| double precision, dimension( ldab, * ) | ab, | ||
| integer | ldab, | ||
| double precision, dimension( ldb, * ) | b, | ||
| integer | ldb, | ||
| double precision, dimension( ldx, * ) | x, | ||
| integer | ldx, | ||
| double precision, dimension( * ) | ferr, | ||
| double precision, dimension( * ) | berr, | ||
| double precision, dimension( * ) | work, | ||
| integer, dimension( * ) | iwork, | ||
| integer | info | ||
| ) |
DTBRFS
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DTBRFS 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 DTBTRS or some other means before entering this routine. DTBRFS 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 = 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (3*N) |
| [out] | IWORK | IWORK is INTEGER 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 186 of file dtbrfs.f.
1.9.7