.TH "SRC/zlahef.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
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.SH NAME
SRC/zlahef.f
.SH SYNOPSIS
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.PP
.SS "Functions/Subroutines"

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.ti -1c
.RI "subroutine \fBzlahef\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)"
.br
.RI "\fBZLAHEF\fP computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlahef (character uplo, integer n, integer nb, integer kb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)"

.PP
\fBZLAHEF\fP computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)\&.  
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\fBPurpose:\fP
.RS 4

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.nf
!>
!> ZLAHEF computes a partial factorization of a complex Hermitian
!> matrix A using the Bunch-Kaufman diagonal pivoting method\&. The
!> partial factorization has the form:
!>
!> A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
!>       ( 0  U22 ) (  0   D  ) ( U12**H U22**H )
!>
!> A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
!>       ( L21  I ) (  0  A22 ) (  0      I     )
!>
!> where the order of D is at most NB\&. The actual order is returned in
!> the argument KB, and is either NB or NB-1, or N if N <= NB\&.
!> Note that U**H denotes the conjugate transpose of U\&.
!>
!> ZLAHEF is an auxiliary routine called by ZHETRF\&. It uses blocked code
!> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
!> A22 (if UPLO = 'L')\&.
!> 
.fi
.PP
 
.RE
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\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          Hermitian matrix A is stored:
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!> 
.fi
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\fIN\fP 
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!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
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\fINB\fP 
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!>          NB is INTEGER
!>          The maximum number of columns of the matrix A that should be
!>          factored\&.  NB should be at least 2 to allow for 2-by-2 pivot
!>          blocks\&.
!> 
.fi
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\fIKB\fP 
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!>          KB is INTEGER
!>          The number of columns of A that were actually factored\&.
!>          KB is either NB-1 or NB, or N if N <= NB\&.
!> 
.fi
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.br
\fIA\fP 
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.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the Hermitian matrix A\&.  If UPLO = 'U', the leading
!>          n-by-n upper triangular part of A contains the upper
!>          triangular part of the matrix A, and the strictly lower
!>          triangular part of A is not referenced\&.  If UPLO = 'L', the
!>          leading n-by-n lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced\&.
!>          On exit, A contains details of the partial factorization\&.
!> 
.fi
.PP
.br
\fILDA\fP 
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.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
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\fIIPIV\fP 
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.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D\&.
!>
!>          If UPLO = 'U':
!>             Only the last KB elements of IPIV are set\&.
!>
!>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
!>             interchanged and D(k,k) is a 1-by-1 diagonal block\&.
!>
!>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
!>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
!>             is a 2-by-2 diagonal block\&.
!>
!>          If UPLO = 'L':
!>             Only the first KB elements of IPIV are set\&.
!>
!>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
!>             interchanged and D(k,k) is a 1-by-1 diagonal block\&.
!>
!>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
!>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
!>             is a 2-by-2 diagonal block\&.
!> 
.fi
.PP
.br
\fIW\fP 
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!>          W is COMPLEX*16 array, dimension (LDW,NB)
!> 
.fi
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\fILDW\fP 
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!>          LDW is INTEGER
!>          The leading dimension of the array W\&.  LDW >= max(1,N)\&.
!> 
.fi
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.br
\fIINFO\fP 
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.nf
!>          INFO is INTEGER
!>          = 0: successful exit
!>          > 0: if INFO = k, D(k,k) is exactly zero\&.  The factorization
!>               has been completed, but the block diagonal matrix D is
!>               exactly singular\&.
!> 
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

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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

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.nf
!>
!>  December 2016,  Igor Kozachenko,
!>                  Computer Science Division,
!>                  University of California, Berkeley
!> 
.fi
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.RE
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Definition at line \fB176\fP of file \fBzlahef\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.