
NAMEzgtrfs.f SYNOPSISFunctions/Subroutinessubroutine zgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO) Function/Subroutine Documentationsubroutine zgtrfs (characterTRANS, integerN, integerNRHS, 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, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)ZGTRFS Purpose: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. 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.NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.DL DL is COMPLEX*16 array, dimension (N1) The (n1) subdiagonal elements of A.D D is COMPLEX*16 array, dimension (N) The diagonal elements of A.DU DU is COMPLEX*16 array, dimension (N1) The (n1) superdiagonal elements of A.DLF DLF is COMPLEX*16 array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF.DF DF is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.DUF DUF is COMPLEX*16 array, dimension (N1) The (n1) elements of the first superdiagonal of U.DU2 DU2 is COMPLEX*16 array, dimension (N2) The (n2) elements of the second superdiagonal of U.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.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 ZGTTRS. 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:
September 2012
Definition at line 209 of file zgtrfs.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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