
NAMEzgbrfs.f SYNOPSISFunctions/Subroutinessubroutine zgbrfs (TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO) Function/Subroutine Documentationsubroutine zgbrfs (characterTRANS, integerN, integerKL, integerKU, integerNRHS, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldafb, * )AFB, integerLDAFB, integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)ZGBRFS Purpose: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. TRANS
Internal Parameters:
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)N N is INTEGER The order of the matrix A. N >= 0.KL KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.KU KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.AB AB is COMPLEX*16 array, dimension (LDAB,N) The original band matrix A, stored in rows 1 to KL+KU+1. The jth column of A is stored in the jth column of the array AB as follows: AB(ku+1+ij,j) = A(i,j) for max(1,jku)<=i<=min(n,j+kl).LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.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.LDAFB LDAFB is INTEGER The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.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).B B is COMPLEX*16 array, dimension (LDB,NRHS) The right hand side matrix B.LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).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.LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).FERR FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bound for each solution vector X(j) (the jth 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 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).WORK WORK is COMPLEX*16 array, dimension (2*N)RWORK RWORK is DOUBLE PRECISION array, dimension (N)INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value ITMAX is the maximum number of steps of iterative refinement. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 205 of file zgbrfs.f.
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