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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine zgbrfs | ( | character | TRANS, |
integer | N, | ||
integer | KL, | ||
integer | KU, | ||
integer | NRHS, | ||
complex*16, dimension( ldab, * ) | AB, | ||
integer | LDAB, | ||
complex*16, dimension( ldafb, * ) | AFB, | ||
integer | LDAFB, | ||
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 | ||
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ZGBRFS
Download ZGBRFS + dependencies [TGZ] [ZIP] [TXT]
ZGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, 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] | KL | KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. |
[in] | KU | KU is INTEGER The number of superdiagonals within the band of A. KU >= 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 COMPLEX*16 array, dimension (LDAB,N) The original band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). |
[in] | LDAB | LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. |
[in] | AFB | AFB is COMPLEX*16 array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as computed by ZGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. |
[in] | LDAFB | LDAFB is INTEGER The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1. |
[in] | IPIV | IPIV is INTEGER array, dimension (N) The pivot indices from ZGBTRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i). |
[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 ZGBTRS. 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 208 of file zgbrfs.f.