cgtrfs-f(3)

cgtrfs.f –

Synopsis

Functions/Subroutines

subroutine cgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
CGTRFS

Function/Subroutine Documentation

subroutine cgtrfs (characterTRANS, integerN, integerNRHS, complex, dimension( * )DL, complex, dimension( * )D, complex, dimension( * )DU, complex, dimension( * )DLF, complex, dimension( * )DF, complex, dimension( * )DUF, complex, dimension( * )DU2, integer, dimension( * )IPIV, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CGTRFS

Purpose:

 CGTRFS 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

 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 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 is COMPLEX array, dimension (N-1)
 The (n-1) subdiagonal elements of A.

 D is COMPLEX array, dimension (N)
 The diagonal elements of A.

 DU is COMPLEX array, dimension (N-1)
 The (n-1) superdiagonal elements of A.

DLF

 DLF is COMPLEX array, dimension (N-1)
 The (n-1) multipliers that define the matrix L from the
 LU factorization of A as computed by CGTTRF.

 DF is COMPLEX array, dimension (N)
 The n diagonal elements of the upper triangular matrix U from
 the LU factorization of A.

DUF

 DUF is COMPLEX array, dimension (N-1)
 The (n-1) elements of the first superdiagonal of U.

DU2

 DU2 is COMPLEX array, dimension (N-2)
 The (n-2) 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 is COMPLEX 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 is COMPLEX array, dimension (LDX,NRHS)
 On entry, the solution matrix X, as computed by CGTTRS.
 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 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

 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

 WORK is COMPLEX array, dimension (2*N)

RWORK

 RWORK is REAL array, dimension (N)

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

 ITMAX is the maximum number of steps of iterative refinement.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 209 of file cgtrfs.f.

Author

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