.TH "hpr2" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hpr2 \- {hp,sp}r2: Hermitian/symmetric rank-2 update
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBchpr2\fP (uplo, n, alpha, x, incx, y, incy, ap)"
.br
.RI "\fBCHPR2\fP "
.ti -1c
.RI "subroutine \fBdspr2\fP (uplo, n, alpha, x, incx, y, incy, ap)"
.br
.RI "\fBDSPR2\fP "
.ti -1c
.RI "subroutine \fBsspr2\fP (uplo, n, alpha, x, incx, y, incy, ap)"
.br
.RI "\fBSSPR2\fP "
.ti -1c
.RI "subroutine \fBzhpr2\fP (uplo, n, alpha, x, incx, y, incy, ap)"
.br
.RI "\fBZHPR2\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine chpr2 (character uplo, integer n, complex alpha, complex, dimension(*) x, integer incx, complex, dimension(*) y, integer incy, complex, dimension(*) ap)"

.PP
\fBCHPR2\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CHPR2  performs the hermitian rank 2 operation
!>
!>    A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an
!> n by n hermitian matrix, supplied in packed form\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the matrix A is supplied in the packed
!>           array AP as follows:
!>
!>              UPLO = 'U' or 'u'   The upper triangular part of A is
!>                                  supplied in AP\&.
!>
!>              UPLO = 'L' or 'l'   The lower triangular part of A is
!>                                  supplied in AP\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A\&.
!>           N must be at least zero\&.
!> 
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
!>          ALPHA is COMPLEX
!>           On entry, ALPHA specifies the scalar alpha\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is COMPLEX array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) )\&.
!>           Before entry, the incremented array X must contain the n
!>           element vector x\&.
!> 
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X\&. INCX must not be zero\&.
!> 
.fi
.PP
.br
\fIY\fP 
.PP
.nf
!>          Y is COMPLEX array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) )\&.
!>           Before entry, the incremented array Y must contain the n
!>           element vector y\&.
!> 
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y\&. INCY must not be zero\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX array, dimension at least
!>           ( ( n*( n + 1 ) )/2 )\&.
!>           Before entry with  UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular part of the hermitian matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
!>           and a( 2, 2 ) respectively, and so on\&. On exit, the array
!>           AP is overwritten by the upper triangular part of the
!>           updated matrix\&.
!>           Before entry with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular part of the hermitian matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
!>           and a( 3, 1 ) respectively, and so on\&. On exit, the array
!>           AP is overwritten by the lower triangular part of the
!>           updated matrix\&.
!>           Note that the imaginary parts of the diagonal elements need
!>           not be set, they are assumed to be zero, and on exit they
!>           are set to zero\&.
!> 
.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
!>
!>  Level 2 Blas routine\&.
!>
!>  -- Written on 22-October-1986\&.
!>     Jack Dongarra, Argonne National Lab\&.
!>     Jeremy Du Croz, Nag Central Office\&.
!>     Sven Hammarling, Nag Central Office\&.
!>     Richard Hanson, Sandia National Labs\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB144\fP of file \fBchpr2\&.f\fP\&.
.SS "subroutine dspr2 (character uplo, integer n, double precision alpha, double precision, dimension(*) x, integer incx, double precision, dimension(*) y, integer incy, double precision, dimension(*) ap)"

.PP
\fBDSPR2\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DSPR2  performs the symmetric rank 2 operation
!>
!>    A := alpha*x*y**T + alpha*y*x**T + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an
!> n by n symmetric matrix, supplied in packed form\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the matrix A is supplied in the packed
!>           array AP as follows:
!>
!>              UPLO = 'U' or 'u'   The upper triangular part of A is
!>                                  supplied in AP\&.
!>
!>              UPLO = 'L' or 'l'   The lower triangular part of A is
!>                                  supplied in AP\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A\&.
!>           N must be at least zero\&.
!> 
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
!>          ALPHA is DOUBLE PRECISION\&.
!>           On entry, ALPHA specifies the scalar alpha\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is DOUBLE PRECISION array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) )\&.
!>           Before entry, the incremented array X must contain the n
!>           element vector x\&.
!> 
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X\&. INCX must not be zero\&.
!> 
.fi
.PP
.br
\fIY\fP 
.PP
.nf
!>          Y is DOUBLE PRECISION array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) )\&.
!>           Before entry, the incremented array Y must contain the n
!>           element vector y\&.
!> 
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y\&. INCY must not be zero\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is DOUBLE PRECISION array, dimension at least
!>           ( ( n*( n + 1 ) )/2 )\&.
!>           Before entry with  UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular part of the symmetric matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
!>           and a( 2, 2 ) respectively, and so on\&. On exit, the array
!>           AP is overwritten by the upper triangular part of the
!>           updated matrix\&.
!>           Before entry with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular part of the symmetric matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
!>           and a( 3, 1 ) respectively, and so on\&. On exit, the array
!>           AP is overwritten by the lower triangular part of the
!>           updated matrix\&.
!> 
.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
!>
!>  Level 2 Blas routine\&.
!>
!>  -- Written on 22-October-1986\&.
!>     Jack Dongarra, Argonne National Lab\&.
!>     Jeremy Du Croz, Nag Central Office\&.
!>     Sven Hammarling, Nag Central Office\&.
!>     Richard Hanson, Sandia National Labs\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB141\fP of file \fBdspr2\&.f\fP\&.
.SS "subroutine sspr2 (character uplo, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(*) y, integer incy, real, dimension(*) ap)"

.PP
\fBSSPR2\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SSPR2  performs the symmetric rank 2 operation
!>
!>    A := alpha*x*y**T + alpha*y*x**T + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an
!> n by n symmetric matrix, supplied in packed form\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the matrix A is supplied in the packed
!>           array AP as follows:
!>
!>              UPLO = 'U' or 'u'   The upper triangular part of A is
!>                                  supplied in AP\&.
!>
!>              UPLO = 'L' or 'l'   The lower triangular part of A is
!>                                  supplied in AP\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A\&.
!>           N must be at least zero\&.
!> 
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
!>          ALPHA is REAL
!>           On entry, ALPHA specifies the scalar alpha\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is REAL array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) )\&.
!>           Before entry, the incremented array X must contain the n
!>           element vector x\&.
!> 
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X\&. INCX must not be zero\&.
!> 
.fi
.PP
.br
\fIY\fP 
.PP
.nf
!>          Y is REAL array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) )\&.
!>           Before entry, the incremented array Y must contain the n
!>           element vector y\&.
!> 
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y\&. INCY must not be zero\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is REAL array, dimension at least
!>           ( ( n*( n + 1 ) )/2 )\&.
!>           Before entry with  UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular part of the symmetric matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
!>           and a( 2, 2 ) respectively, and so on\&. On exit, the array
!>           AP is overwritten by the upper triangular part of the
!>           updated matrix\&.
!>           Before entry with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular part of the symmetric matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
!>           and a( 3, 1 ) respectively, and so on\&. On exit, the array
!>           AP is overwritten by the lower triangular part of the
!>           updated matrix\&.
!> 
.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
!>
!>  Level 2 Blas routine\&.
!>
!>  -- Written on 22-October-1986\&.
!>     Jack Dongarra, Argonne National Lab\&.
!>     Jeremy Du Croz, Nag Central Office\&.
!>     Sven Hammarling, Nag Central Office\&.
!>     Richard Hanson, Sandia National Labs\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB141\fP of file \fBsspr2\&.f\fP\&.
.SS "subroutine zhpr2 (character uplo, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(*) ap)"

.PP
\fBZHPR2\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZHPR2  performs the hermitian rank 2 operation
!>
!>    A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an
!> n by n hermitian matrix, supplied in packed form\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the matrix A is supplied in the packed
!>           array AP as follows:
!>
!>              UPLO = 'U' or 'u'   The upper triangular part of A is
!>                                  supplied in AP\&.
!>
!>              UPLO = 'L' or 'l'   The lower triangular part of A is
!>                                  supplied in AP\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A\&.
!>           N must be at least zero\&.
!> 
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
!>          ALPHA is COMPLEX*16
!>           On entry, ALPHA specifies the scalar alpha\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is COMPLEX*16 array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) )\&.
!>           Before entry, the incremented array X must contain the n
!>           element vector x\&.
!> 
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X\&. INCX must not be zero\&.
!> 
.fi
.PP
.br
\fIY\fP 
.PP
.nf
!>          Y is COMPLEX*16 array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) )\&.
!>           Before entry, the incremented array Y must contain the n
!>           element vector y\&.
!> 
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y\&. INCY must not be zero\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX*16 array, dimension at least
!>           ( ( n*( n + 1 ) )/2 )\&.
!>           Before entry with  UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular part of the hermitian matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
!>           and a( 2, 2 ) respectively, and so on\&. On exit, the array
!>           AP is overwritten by the upper triangular part of the
!>           updated matrix\&.
!>           Before entry with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular part of the hermitian matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
!>           and a( 3, 1 ) respectively, and so on\&. On exit, the array
!>           AP is overwritten by the lower triangular part of the
!>           updated matrix\&.
!>           Note that the imaginary parts of the diagonal elements need
!>           not be set, they are assumed to be zero, and on exit they
!>           are set to zero\&.
!> 
.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
!>
!>  Level 2 Blas routine\&.
!>
!>  -- Written on 22-October-1986\&.
!>     Jack Dongarra, Argonne National Lab\&.
!>     Jeremy Du Croz, Nag Central Office\&.
!>     Sven Hammarling, Nag Central Office\&.
!>     Richard Hanson, Sandia National Labs\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB144\fP of file \fBzhpr2\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.