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

.in +1c
.ti -1c
.RI "subroutine \fBzpstrf\fP (uplo, n, a, lda, piv, rank, tol, work, info)"
.br
.RI "\fBZPSTRF\fP computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zpstrf (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( n ) piv, integer rank, double precision tol, double precision, dimension( 2*n ) work, integer info)"

.PP
\fBZPSTRF\fP computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZPSTRF computes the Cholesky factorization with complete
 pivoting of a complex Hermitian positive semidefinite matrix A\&.

 The factorization has the form
    P**T * A * P = U**H * U ,  if UPLO = 'U',
    P**T * A * P = L  * L**H,  if UPLO = 'L',
 where U is an upper triangular matrix and L is lower triangular, and
 P is stored as vector PIV\&.

 This algorithm does not attempt to check that A is positive
 semidefinite\&. This version of the algorithm calls level 3 BLAS\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored\&.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
.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 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the symmetric 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, if INFO = 0, the factor U or L from the Cholesky
          factorization as above\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIPIV\fP 
.PP
.nf
          PIV is INTEGER array, dimension (N)
          PIV is such that the nonzero entries are P( PIV(K), K ) = 1\&.
.fi
.PP
.br
\fIRANK\fP 
.PP
.nf
          RANK is INTEGER
          The rank of A given by the number of steps the algorithm
          completed\&.
.fi
.PP
.br
\fITOL\fP 
.PP
.nf
          TOL is DOUBLE PRECISION
          User defined tolerance\&. If TOL < 0, then N*U*MAX( A(K,K) )
          will be used\&. The algorithm terminates at the (K-1)st step
          if the pivot <= TOL\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (2*N)
          Work space\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          < 0: If INFO = -K, the K-th argument had an illegal value,
          = 0: algorithm completed successfully, and
          > 0: the matrix A is either rank deficient with computed rank
               as returned in RANK, or is not positive semidefinite\&. See
               Section 7 of LAPACK Working Note #161 for further
               information\&.
.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

.PP
Definition at line \fB141\fP of file \fBzpstrf\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.