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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 zgtrfs | ( | character | TRANS, |
| integer | N, | ||
| integer | NRHS, | ||
| complex*16, dimension( * ) | DL, | ||
| complex*16, dimension( * ) | D, | ||
| complex*16, dimension( * ) | DU, | ||
| complex*16, dimension( * ) | DLF, | ||
| complex*16, dimension( * ) | DF, | ||
| complex*16, dimension( * ) | DUF, | ||
| complex*16, dimension( * ) | DU2, | ||
| 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 | ||
| ) |
ZGTRFS
Download ZGTRFS + dependencies [TGZ] [ZIP] [TXT]
ZGTRFS improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution.
| [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] | 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] | DL | DL is COMPLEX*16 array, dimension (N-1)
The (n-1) subdiagonal elements of A. |
| [in] | D | D is COMPLEX*16 array, dimension (N)
The diagonal elements of A. |
| [in] | DU | DU is COMPLEX*16 array, dimension (N-1)
The (n-1) superdiagonal elements of A. |
| [in] | DLF | DLF is COMPLEX*16 array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by ZGTTRF. |
| [in] | DF | DF is COMPLEX*16 array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A. |
| [in] | DUF | DUF is COMPLEX*16 array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U. |
| [in] | DU2 | DU2 is COMPLEX*16 array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U. |
| [in] | IPIV | IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i). IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required. |
| [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 ZGTTRS.
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.
1.9.4