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## man page of LAPACK-3

### LAPACK-3: estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as

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NAME

LAPACK-3 - estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF## SYNOPSIS

SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO ) CHARACTER NORM INTEGER INFO, N DOUBLE PRECISION ANORM, RCOND INTEGER IPIV( * ) COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )## PURPOSE

ZGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF. 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: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N (input) INTEGER The order of the matrix A. N >= 0. DL (input) COMPLEX*16 array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF. D (input) COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU (input) COMPLEX*16 array, dimension (N-1) The (n-1) elements of the first superdiagonal of U. DU2 (input) COMPLEX*16 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) DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND (output) DOUBLE PRECISION 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*16 array, dimension (2*N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value LAPACK routine (version 3.2) March 2011 LAPACK-3(3)

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