.TH "SRC/zhecon_3.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/zhecon_3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzhecon_3\fP (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)"
.br
.RI "\fBZHECON_3\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zhecon_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)"

.PP
\fBZHECON_3\fP  
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\fBPurpose:\fP
.RS 4

.PP
.nf
 ZHECON_3 estimates the reciprocal of the condition number (in the
 1-norm) of a complex Hermitian matrix A using the factorization
 computed by ZHETRF_RK or ZHETRF_BK:

    A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

 where U (or L) is unit upper (or lower) triangular matrix,
 U**H (or L**H) is the conjugate of U (or L), P is a permutation
 matrix, P**T is the transpose of P, and D is Hermitian 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 ZHETRS_3\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          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**H)*(P**T);
          = 'L':  Lower triangular, form is A = P*L*D*(L**H)*(P**T)\&.
.fi
.PP
.br
\fIN\fP 
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.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
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.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          Diagonal of the block diagonal matrix D and factors U or L
          as computed by ZHETRF_RK and ZHETRF_BK:
            a) ONLY diagonal elements of the Hermitian 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\&.
.fi
.PP
.br
\fILDA\fP 
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          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIE\fP 
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.nf
          E is COMPLEX*16 array, dimension (N)
          On entry, contains the superdiagonal (or subdiagonal)
          elements of the Hermitian 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\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by ZHETRF_RK or ZHETRF_BK\&.
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
          ANORM is DOUBLE PRECISION
          The 1-norm of the original matrix A\&.
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
          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\&.
.fi
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\fIWORK\fP 
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          WORK is COMPLEX*16 array, dimension (2*N)
.fi
.PP
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\fIINFO\fP 
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          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
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\fBContributors:\fP
.RS 4

.PP
.nf
  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
.fi
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.RE
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Definition at line \fB164\fP of file \fBzhecon_3\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.