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## man page of LAPACK-3

### LAPACK-3: estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A =

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NAME

LAPACK-3 - estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF## SYNOPSIS

SUBROUTINE ZHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO ) CHARACTER UPLO INTEGER INFO, N DOUBLE PRECISION ANORM, RCOND INTEGER IPIV( * ) COMPLEX*16 AP( * ), WORK( * )## PURPOSE

ZHPCON estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF. 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

UPLO (input) CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**H; = 'L': Lower triangular, form is A = L*D*L**H. N (input) INTEGER The order of the matrix A. N >= 0. AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHPTRF, stored as a packed triangular matrix. IPIV (input) INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHPTRF. ANORM (input) DOUBLE PRECISION The 1-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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