Man page - hpmv(3)

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Manual

hpmv

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chpmv (character uplo, integer n, complex alpha, complex,dimension(*) ap, complex, dimension(*) x, integer incx, complex beta,complex, dimension(*) y, integer incy)
subroutine cspmv (character uplo, integer n, complex alpha, complex,dimension( * ) ap, complex, dimension( * ) x, integer incx, complexbeta, complex, dimension( * ) y, integer incy)
subroutine dspmv (character uplo, integer n, double precision alpha, doubleprecision, dimension(*) ap, double precision, dimension(*) x, integerincx, double precision beta, double precision, dimension(*) y, integerincy)
subroutine sspmv (character uplo, integer n, real alpha, real, dimension(*)ap, real, dimension(*) x, integer incx, real beta, real, dimension(*)y, integer incy)
subroutine zhpmv (character uplo, integer n, complex*16 alpha, complex*16,dimension(*) ap, complex*16, dimension(*) x, integer incx, complex*16beta, complex*16, dimension(*) y, integer incy)
subroutine zspmv (character uplo, integer n, complex*16 alpha, complex*16,dimension( * ) ap, complex*16, dimension( * ) x, integer incx,complex*16 beta, complex*16, dimension( * ) y, integer incy)
Author

NAME

hpmv - {hp,sp}mv: Hermitian/symmetric matrix-vector multiply

SYNOPSIS

Functions

subroutine chpmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
CHPMV
subroutine dspmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
DSPMV
subroutine sspmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
SSPMV
subroutine zhpmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
ZHPMV
subroutine cspmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
CSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix
subroutine zspmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix

Detailed Description

Function Documentation

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

CHPMV

Purpose:

CHPMV performs the matrix-vector operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, 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.

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.
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.
Note that the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.

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.

BETA

BETA is COMPLEX
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.

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. On exit, Y is overwritten by the updated
vector y.

INCY

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- 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 cspmv (character uplo, integer n, complex alpha, complex,dimension( * ) ap, complex, dimension( * ) x, integer incx, complexbeta, complex, dimension( * ) y, integer incy)

CSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix

Purpose:

CSPMV performs the matrix-vector operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, 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.

Unchanged on exit.

N

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.

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 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.
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.
Unchanged on exit.

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.
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.

BETA

BETA is COMPLEX
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.

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. On exit, Y is overwritten by the updated
vector y.

INCY

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dspmv (character uplo, integer n, double precision alpha, doubleprecision, dimension(*) ap, double precision, dimension(*) x, integerincx, double precision beta, double precision, dimension(*) y, integerincy)

DSPMV

Purpose:

DSPMV performs the matrix-vector operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, 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.

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.
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.

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.

BETA

BETA is DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.

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. On exit, Y is overwritten by the updated
vector y.

INCY

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- 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 sspmv (character uplo, integer n, real alpha, real, dimension(*)ap, real, dimension(*) x, integer incx, real beta, real, dimension(*)y, integer incy)

SSPMV

Purpose:

SSPMV performs the matrix-vector operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, 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.

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.
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.

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.

BETA

BETA is REAL
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.

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. On exit, Y is overwritten by the updated
vector y.

INCY

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- 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 zhpmv (character uplo, integer n, complex*16 alpha, complex*16,dimension(*) ap, complex*16, dimension(*) x, integer incx, complex*16beta, complex*16, dimension(*) y, integer incy)

ZHPMV

Purpose:

ZHPMV performs the matrix-vector operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, 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.

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.
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.
Note that the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.

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.

BETA

BETA is COMPLEX*16
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.

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. On exit, Y is overwritten by the updated
vector y.

INCY

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- 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 zspmv (character uplo, integer n, complex*16 alpha, complex*16,dimension( * ) ap, complex*16, dimension( * ) x, integer incx,complex*16 beta, complex*16, dimension( * ) y, integer incy)

ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix

Purpose:

ZSPMV performs the matrix-vector operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, 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.

Unchanged on exit.

N

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.

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 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.
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.
Unchanged on exit.

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.
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.

BETA

BETA is COMPLEX*16
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.

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. On exit, Y is overwritten by the updated
vector y.

INCY

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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