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

.in +1c
.ti -1c
.RI "subroutine \fBzhetrf\fP (uplo, n, a, lda, ipiv, work, lwork, info)"
.br
.RI "\fBZHETRF\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zhetrf (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
!>
!> ZHETRF computes the factorization of a complex Hermitian matrix A
!> using the Bunch-Kaufman diagonal pivoting method\&.  The form of the
!> factorization is
!>
!>    A = U*D*U**H  or  A = L*D*L**H
!>
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and D is Hermitian and block diagonal with
!> 1-by-1 and 2-by-2 diagonal blocks\&.
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.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, the block diagonal matrix D and the multipliers used
!>          to obtain the factor U or L (see below for further details)\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D\&.
!>          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 UPLO = 'U' and 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' and 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
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The length of WORK\&. LWORK >= 1\&. For best performance
!>          LWORK >= N*NB, where NB is the block size returned by ILAENV\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, D(i,i) is exactly zero\&.  The factorization
!>                has been completed, but the block diagonal matrix D is
!>                exactly singular, and division by zero will occur if it
!>                is used to solve a system of equations\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
!>
!>  If UPLO = 'U', then A = U*D*U**H, where
!>     U = P(n)*U(n)* \&.\&.\&. *P(k)U(k)* \&.\&.\&.,
!>  i\&.e\&., U is a product of terms P(k)*U(k), where k decreases from n to
!>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
!>  and 2-by-2 diagonal blocks D(k)\&.  P(k) is a permutation matrix as
!>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
!>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
!>
!>             (   I    v    0   )   k-s
!>     U(k) =  (   0    I    0   )   s
!>             (   0    0    I   )   n-k
!>                k-s   s   n-k
!>
!>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k)\&.
!>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
!>  and A(k,k), and v overwrites A(1:k-2,k-1:k)\&.
!>
!>  If UPLO = 'L', then A = L*D*L**H, where
!>     L = P(1)*L(1)* \&.\&.\&. *P(k)*L(k)* \&.\&.\&.,
!>  i\&.e\&., L is a product of terms P(k)*L(k), where k increases from 1 to
!>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
!>  and 2-by-2 diagonal blocks D(k)\&.  P(k) is a permutation matrix as
!>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
!>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
!>
!>             (   I    0     0   )  k-1
!>     L(k) =  (   0    I     0   )  s
!>             (   0    v     I   )  n-k-s+1
!>                k-1   s  n-k-s+1
!>
!>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k)\&.
!>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
!>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1)\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB176\fP of file \fBzhetrf\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.