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template<typename T>
void gtrfs(char *trans, integer *n, integer *nrhs, T *dl, T *d, T *du, T *dlf, T *df, T *duf, T *du2, integer *ipiv, T *b, integer *ldb, T *x, integer *ldx, T *ferr, T *berr, T *work, T *iwork, integer *info)# GTRFS improves the computed solution to a system of linear equations.
Purpose:
GTRFS 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.
- Parameters:
TRANS – [in]
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)N – [in]
N is INTEGER
The order of the matrix A. N >= 0.
NRHS – [in]
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
DL – [in]
DL is REAL array, dimension (N-1)
The (n-1) subdiagonal elements of A.
D – [in]
D is REAL array, dimension (N)
The diagonal elements of A.
DU – [in]
DU is REAL array, dimension (N-1)
The (n-1) superdiagonal elements of A.
DLF – [in]
DLF is REAL array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.
DF – [in]
DF is REAL array, dimension (N)
The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUF – [in]
DUF is REAL array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.
DU2 – [in]
DU2 is REAL array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.
IPIV – [in]
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.
B – [in]
B is REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB – [in]
LDB is INTEGER
The leading dimension of the array B. LDB >= fla_max(1,N).
X – [inout]
X is REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SGTTRS. On exit, the improved solution matrix X.
LDX – [in]
LDX is INTEGER
The leading dimension of the array X. LDX >= fla_max(1,N).
FERR – [out]
FERR is REAL 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.
BERR – [out]
BERR is REAL 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).
WORK – [out] WORK is REAL array, dimension (3*N)
IWORK – [out] IWORK is INTEGER array, dimension (N)
INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value