Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF

**SYNOPSIS**

SUBROUTINE SGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, IWORK, INFO ) CHARACTER NORM INTEGER INFO, N REAL ANORM, RCOND INTEGER IPIV( * ), IWORK( * ) REAL D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )

**PURPOSE**

SGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF. 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) REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF. D (input) REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU (input) REAL array, dimension (N-1) The (n-1) elements of the first superdiagonal of U. DU2 (input) REAL 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 = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', 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) REAL array, dimension (2*N) IWORK (workspace) INTEGER array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value LAPACK routine (version 3.3.1) April 2011 SGTCON(3lapack)