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## man page of LAPACK-3

### LAPACK-3: estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the

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## NAME

LAPACK-3 - estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF## SYNOPSIS

SUBROUTINE ZGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO ) CHARACTER NORM INTEGER INFO, LDA, N DOUBLE PRECISION ANORM, RCOND DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), WORK( * )## PURPOSE

ZGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * 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. A (input) COMPLEX*16 array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). 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/(norm(A) * norm(inv(A))). WORK (workspace) COMPLEX*16 array, dimension (2*N) RWORK (workspace) DOUBLE PRECISION 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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