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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 zherfs | ( | character | uplo, |
| integer | n, | ||
| integer | nrhs, | ||
| complex*16, dimension( lda, * ) | a, | ||
| integer | lda, | ||
| complex*16, dimension( ldaf, * ) | af, | ||
| integer | ldaf, | ||
| integer, dimension( * ) | ipiv, | ||
| 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 | ||
| ) |
ZHERFS
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ZHERFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution.
| [in] | UPLO | UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored. |
| [in] | N | N is INTEGER
The order of the matrix A. N >= 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] | A | A is COMPLEX*16 array, dimension (LDA,N)
The Hermitian matrix A. If UPLO = 'U', the leading N-by-N
upper triangular part of A contains the upper triangular part
of the matrix A, and the strictly lower triangular part of A
is not referenced. If UPLO = 'L', the leading N-by-N lower
triangular part of A contains the lower triangular part of
the matrix A, and the strictly upper triangular part of A is
not referenced. |
| [in] | LDA | LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N). |
| [in] | AF | AF is COMPLEX*16 array, dimension (LDAF,N)
The factored form of the matrix A. AF contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**H or
A = L*D*L**H as computed by ZHETRF. |
| [in] | LDAF | LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N). |
| [in] | IPIV | IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHETRF. |
| [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,out] | X | X is COMPLEX*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZHETRS.
On exit, the improved 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 |
ITMAX is the maximum number of steps of iterative refinement.
Definition at line 190 of file zherfs.f.
1.9.7