cgtcon (l) - Linux Manuals
cgtcon: estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF
Command to display cgtcon
manual in Linux: $ man l cgtcon
NAME
CGTCON - estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF
SYNOPSIS
- SUBROUTINE CGTCON(
-
NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
WORK, INFO )
-
CHARACTER
NORM
-
INTEGER
INFO, N
-
REAL
ANORM, RCOND
-
INTEGER
IPIV( * )
-
COMPLEX
D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
PURPOSE
CGTCON estimates the reciprocal of the condition number of a complex
tridiagonal matrix A using the LU factorization as computed by
CGTTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
ARGUMENTS
- NORM (input) CHARACTER*1
-
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= aq1aq or aqOaq: 1-norm;
= aqIaq: Infinity-norm.
- N (input) INTEGER
-
The order of the matrix A. N >= 0.
- DL (input) COMPLEX array, dimension (N-1)
-
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by CGTTRF.
- D (input) COMPLEX array, dimension (N)
-
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
- DU (input) COMPLEX array, dimension (N-1)
-
The (n-1) elements of the first superdiagonal of U.
- DU2 (input) COMPLEX array, dimension (N-2)
-
The (n-2) elements of the second superdiagonal of U.
- IPIV (input) 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.
- ANORM (input) REAL
-
If NORM = aq1aq or aqOaq, the 1-norm of the original matrix A.
If NORM = aqIaq, the infinity-norm of the original matrix A.
- RCOND (output) REAL
-
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.
- WORK (workspace) COMPLEX array, dimension (2*N)
-
- INFO (output) INTEGER
-
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Pages related to cgtcon
- cgtcon (3)
- cgtrfs (l) - 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
- cgtsv (l) - solves the equation A*X = B,
- cgtsvx (l) - uses the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
- cgttrf (l) - computes an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges
- cgttrs (l) - solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
- cgtts2 (l) - solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
- cgbbrd (l) - reduces a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation