zsycon_3.f - Online Linux Manual Page

Section : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzsycon_3.f
SYNOPSIS
Functions/Subroutinessubroutine zsycon_3 (UPLO, N, A, LDA, E, IPIV, ANORM, RCOND, WORK, INFO)
ZSYCON_3
Function/Subroutine Documentation
subroutine zsycon_3 (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, complex*16, dimension( * ) WORK, integer INFO)ZSYCON_3 Purpose: ZSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK: A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver ZSYTRS_3.Parameters: UPLO UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T).
N N is INTEGER The order of the matrix A. N >= 0.
A A is COMPLEX*16 array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK: a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.
LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
E E is COMPLEX*16 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.
IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSYTRF_RK or ZSYTRF_BK.
ANORM ANORM is DOUBLE PRECISION The 1-norm of the original matrix A.
RCOND RCOND is 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 WORK is COMPLEX*16 array, dimension (2*N)
IWORK IWORK is INTEGER array, dimension (N)
INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal valueAuthor: Univ​. of Tennessee Univ​. of California Berkeley Univ​. of Colorado Denver NAG Ltd​. Date: June 2017 Contributors: June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J​. Higham, Craig Lucas, School of Mathematics, University of Manchester Definition at line 173 of file zsycon_3​.f​.
AuthorGenerated automatically by Doxygen for LAPACK from the source code​. 0
Johanes Gumabo
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