zsycon_3.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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NAME

zsycon_3.f  

SYNOPSIS


 

Functions/Subroutines


subroutine 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 value


 

Author:

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.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
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)
Author