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Manual

hpr

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chpr (character uplo, integer n, real alpha, complex,dimension(*) x, integer incx, complex, dimension(*) ap)
subroutine cspr (character uplo, integer n, complex alpha, complex,dimension( * ) x, integer incx, complex, dimension( * ) ap)
subroutine dspr (character uplo, integer n, double precision alpha, doubleprecision, dimension(*) x, integer incx, double precision, dimension(*)ap)
subroutine sspr (character uplo, integer n, real alpha, real, dimension(*)x, integer incx, real, dimension(*) ap)
subroutine zhpr (character uplo, integer n, double precision alpha,complex*16, dimension(*) x, integer incx, complex*16, dimension(*) ap)
subroutine zspr (character uplo, integer n, complex*16 alpha, complex*16,dimension( * ) x, integer incx, complex*16, dimension( * ) ap)
Author

NAME

hpr - {hp,sp}r: Hermitian/symmetric rank-1 update

SYNOPSIS

Functions

subroutine chpr (uplo, n, alpha, x, incx, ap)
CHPR
subroutine dspr (uplo, n, alpha, x, incx, ap)
DSPR
subroutine sspr (uplo, n, alpha, x, incx, ap)
SSPR
subroutine zhpr (uplo, n, alpha, x, incx, ap)
ZHPR
subroutine cspr (uplo, n, alpha, x, incx, ap)
CSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.
subroutine zspr (uplo, n, alpha, x, incx, ap)
ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

Detailed Description

Function Documentation

subroutine chpr (character uplo, integer n, real alpha, complex,dimension() x, integer incx, complex, dimension() ap)

CHPR

Purpose:

CHPR performs the hermitian rank 1 operation

A := alpha*x*x**H + A,

where alpha is a real scalar, x is an n element vector 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 = ’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.

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 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.

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.

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 cspr (character uplo, integer n, complex alpha, complex,dimension( * ) x, integer incx, complex, dimension( * ) ap)

CSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

Purpose:

CSPR performs the symmetric rank 1 operation

A := alpha*x*x**H + A,

where alpha is a complex scalar, x is an n element vector 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 = ’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.

Unchanged on exit.

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

ALPHA

ALPHA is COMPLEX
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.

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.
Unchanged on exit.

INCX

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

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 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.
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.

subroutine dspr (character uplo, integer n, double precision alpha, doubleprecision, dimension() x, integer incx, double precision, dimension()ap)

DSPR

Purpose:

DSPR performs the symmetric rank 1 operation

A := alpha*x*x**T + A,

where alpha is a real scalar, x is an n element vector 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 = ’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.

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 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.

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.

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 sspr (character uplo, integer n, real alpha, real, dimension()x, integer incx, real, dimension() ap)

SSPR

Purpose:

SSPR performs the symmetric rank 1 operation

A := alpha*x*x**T + A,

where alpha is a real scalar, x is an n element vector 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 = ’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.

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 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.

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.

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 zhpr (character uplo, integer n, double precision alpha,complex16, dimension() x, integer incx, complex16, dimension() ap)

ZHPR

Purpose:

ZHPR performs the hermitian rank 1 operation

A := alpha*x*x**H + A,

where alpha is a real scalar, x is an n element vector 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 = ’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.

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 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.

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.

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 zspr (character uplo, integer n, complex16 alpha, complex16,dimension( * ) x, integer incx, complex16, dimension( ) ap)

ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

Purpose:

ZSPR performs the symmetric rank 1 operation

A := alpha*x*x**H + A,

where alpha is a complex scalar, x is an n element vector 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 = ’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.

Unchanged on exit.

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

ALPHA

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

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.
Unchanged on exit.

INCX

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

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 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.
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.

Author

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