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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine zptrfs | ( | character | UPLO, |
| integer | N, | ||
| integer | NRHS, | ||
| double precision, dimension( * ) | D, | ||
| complex*16, dimension( * ) | E, | ||
| double precision, dimension( * ) | DF, | ||
| complex*16, dimension( * ) | EF, | ||
| 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 | ||
| ) |
ZPTRFS
Download ZPTRFS + dependencies [TGZ] [ZIP] [TXT]
ZPTRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution.
| [in] | UPLO | UPLO is CHARACTER*1
Specifies whether the superdiagonal or the subdiagonal of the
tridiagonal matrix A is stored and the form of the
factorization:
= 'U': E is the superdiagonal of A, and A = U**H*D*U;
= 'L': E is the subdiagonal of A, and A = L*D*L**H.
(The two forms are equivalent if A is real.) |
| [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 matrix B. NRHS >= 0. |
| [in] | D | D is DOUBLE PRECISION array, dimension (N)
The n real diagonal elements of the tridiagonal matrix A. |
| [in] | E | E is COMPLEX*16 array, dimension (N-1)
The (n-1) off-diagonal elements of the tridiagonal matrix A
(see UPLO). |
| [in] | DF | DF is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from
the factorization computed by ZPTTRF. |
| [in] | EF | EF is COMPLEX*16 array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal
factor U or L from the factorization computed by ZPTTRF
(see UPLO). |
| [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 ZPTTRS.
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 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). |
| [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 (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.
1.9.4