Man page - hpr2(3)

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Manual

hpr2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chpr2 (character uplo, integer n, complex alpha, complex,dimension(*) x, integer incx, complex, dimension(*) y, integer incy,complex, dimension(*) ap)
subroutine dspr2 (character uplo, integer n, double precision alpha, doubleprecision, dimension(*) x, integer incx, double precision, dimension(*)y, integer incy, double precision, dimension(*) ap)
subroutine sspr2 (character uplo, integer n, real alpha, real, dimension(*)x, integer incx, real, dimension(*) y, integer incy, real, dimension(*)ap)
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)
Author

NAME

hpr2 - {hp,sp}r2: Hermitian/symmetric rank-2 update

SYNOPSIS

Functions

subroutine chpr2 (uplo, n, alpha, x, incx, y, incy, ap)
CHPR2
subroutine dspr2 (uplo, n, alpha, x, incx, y, incy, ap)
DSPR2
subroutine sspr2 (uplo, n, alpha, x, incx, y, incy, ap)
SSPR2
subroutine zhpr2 (uplo, n, alpha, x, incx, y, incy, ap)
ZHPR2

Detailed Description

Function Documentation

subroutine chpr2 (character uplo, integer n, complex alpha, complex,dimension(*) x, integer incx, complex, dimension(*) y, integer incy,complex, dimension(*) ap)

CHPR2

Purpose:

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.

Parameters

UPLO

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 = ā€™Uā€™ or ā€™uā€™ The upper triangular part of A is
supplied in AP.

UPLO = ā€™Lā€™ or ā€™lā€™ The lower triangular part of A is
supplied in AP.

N

N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.

ALPHA

ALPHA is COMPLEX
On entry, ALPHA specifies the scalar alpha.

X

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.

INCX

INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.

Y

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.

INCY

INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.

AP

AP is COMPLEX array, dimension at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = ā€™Uā€™ or ā€™uā€™, 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 = ā€™Lā€™ or ā€™lā€™, 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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

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.

subroutine dspr2 (character uplo, integer n, double precision alpha, doubleprecision, dimension(*) x, integer incx, double precision, dimension(*)y, integer incy, double precision, dimension(*) ap)

DSPR2

Purpose:

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.

Parameters

UPLO

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 = ā€™Uā€™ or ā€™uā€™ The upper triangular part of A is
supplied in AP.

UPLO = ā€™Lā€™ or ā€™lā€™ The lower triangular part of A is
supplied in AP.

N

N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.

ALPHA

ALPHA is DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.

X

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.

INCX

INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.

Y

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.

INCY

INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.

AP

AP is DOUBLE PRECISION array, dimension at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = ā€™Uā€™ or ā€™uā€™, 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 = ā€™Lā€™ or ā€™lā€™, 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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

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.

subroutine sspr2 (character uplo, integer n, real alpha, real, dimension(*)x, integer incx, real, dimension(*) y, integer incy, real, dimension(*)ap)

SSPR2

Purpose:

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.

Parameters

UPLO

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 = ā€™Uā€™ or ā€™uā€™ The upper triangular part of A is
supplied in AP.

UPLO = ā€™Lā€™ or ā€™lā€™ The lower triangular part of A is
supplied in AP.

N

N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.

ALPHA

ALPHA is REAL
On entry, ALPHA specifies the scalar alpha.

X

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.

INCX

INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.

Y

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.

INCY

INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.

AP

AP is REAL array, dimension at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = ā€™Uā€™ or ā€™uā€™, 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 = ā€™Lā€™ or ā€™lā€™, 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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

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.

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)

ZHPR2

Purpose:

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.

Parameters

UPLO

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 = ā€™Uā€™ or ā€™uā€™ The upper triangular part of A is
supplied in AP.

UPLO = ā€™Lā€™ or ā€™lā€™ The lower triangular part of A is
supplied in AP.

N

N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.

ALPHA

ALPHA is COMPLEX*16
On entry, ALPHA specifies the scalar alpha.

X

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.

INCX

INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.

Y

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.

INCY

INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.

AP

AP is COMPLEX*16 array, dimension at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = ā€™Uā€™ or ā€™uā€™, 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 = ā€™Lā€™ or ā€™lā€™, 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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

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.

Author

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