.TH "hemv" 3 "Tue Jan 28 2025 00:54:31" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hemv \- {he,sy}mv: Hermitian/symmetric matrix-vector multiply ([cz]symv in LAPACK)
.SH SYNOPSIS
.br
.PP
.SS "Functions"
.in +1c
.ti -1c
.RI "subroutine \fBchemv\fP (uplo, n, alpha, a, lda, x, incx, beta, y, incy)"
.br
.RI "\fBCHEMV\fP "
.ti -1c
.RI "subroutine \fBdsymv\fP (uplo, n, alpha, a, lda, x, incx, beta, y, incy)"
.br
.RI "\fBDSYMV\fP "
.ti -1c
.RI "subroutine \fBssymv\fP (uplo, n, alpha, a, lda, x, incx, beta, y, incy)"
.br
.RI "\fBSSYMV\fP "
.ti -1c
.RI "subroutine \fBzhemv\fP (uplo, n, alpha, a, lda, x, incx, beta, y, incy)"
.br
.RI "\fBZHEMV\fP "
.ti -1c
.RI "subroutine \fBcsymv\fP (uplo, n, alpha, a, lda, x, incx, beta, y, incy)"
.br
.RI "\fBCSYMV\fP computes a matrix-vector product for a complex symmetric matrix\&. "
.ti -1c
.RI "subroutine \fBzsymv\fP (uplo, n, alpha, a, lda, x, incx, beta, y, incy)"
.br
.RI "\fBZSYMV\fP computes a matrix-vector product for a complex symmetric matrix\&. "
.in -1c
.SH "Detailed Description"
.PP
.SH "Function Documentation"
.PP
.SS "subroutine chemv (character uplo, integer n, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(*) x, integer incx, complex beta, complex, dimension(*) y, integer incy)"
.PP
\fBCHEMV\fP
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
CHEMV 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\&.
.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 array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced\&.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced\&.
.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
\fIA\fP
.PP
.nf
A is COMPLEX array, dimension ( LDA, N )
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the hermitian matrix and the strictly
lower triangular part of A is not referenced\&.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the hermitian matrix and the strictly
upper triangular part of A is not referenced\&.
Note that the imaginary parts of the diagonal elements need
not be set and are assumed to be zero\&.
.fi
.PP
.br
\fILDA\fP
.PP
.nf
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program\&. LDA must be at least
max( 1, n )\&.
.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
\fIBETA\fP
.PP
.nf
BETA is COMPLEX
On entry, BETA specifies the scalar beta\&. When BETA is
supplied as zero then Y need not be set on input\&.
.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\&. On exit, Y is overwritten by the updated
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
.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\&.
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\&.
.fi
.PP
.RE
.PP
.SS "subroutine csymv (character uplo, integer n, complex alpha, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer incx, complex beta, complex, dimension( * ) y, integer incy)"
.PP
\fBCSYMV\fP computes a matrix-vector product for a complex symmetric matrix\&.
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
CSYMV 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\&.
.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 array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced\&.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced\&.
Unchanged on exit\&.
.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\&.
Unchanged on exit\&.
.fi
.PP
.br
\fIALPHA\fP
.PP
.nf
ALPHA is COMPLEX
On entry, ALPHA specifies the scalar alpha\&.
Unchanged on exit\&.
.fi
.PP
.br
\fIA\fP
.PP
.nf
A is COMPLEX array, dimension ( LDA, N )
Before entry, with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced\&.
Before entry, with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced\&.
Unchanged on exit\&.
.fi
.PP
.br
\fILDA\fP
.PP
.nf
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program\&. LDA must be at least
max( 1, N )\&.
Unchanged on exit\&.
.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\&.
Unchanged on exit\&.
.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\&.
Unchanged on exit\&.
.fi
.PP
.br
\fIBETA\fP
.PP
.nf
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\&.
.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\&. On exit, Y is overwritten by the updated
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\&.
Unchanged on exit\&.
.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
.SS "subroutine dsymv (character uplo, integer n, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(*) x, integer incx, double precision beta, double precision, dimension(*) y, integer incy)"
.PP
\fBDSYMV\fP
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
DSYMV 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\&.
.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 array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced\&.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced\&.
.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
\fIA\fP
.PP
.nf
A is DOUBLE PRECISION array, dimension ( LDA, N )
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced\&.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced\&.
.fi
.PP
.br
\fILDA\fP
.PP
.nf
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program\&. LDA must be at least
max( 1, n )\&.
.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
\fIBETA\fP
.PP
.nf
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\&.
.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\&. On exit, Y is overwritten by the updated
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
.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\&.
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\&.
.fi
.PP
.RE
.PP
.SS "subroutine ssymv (character uplo, integer n, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx, real beta, real, dimension(*) y, integer incy)"
.PP
\fBSSYMV\fP
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
SSYMV 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\&.
.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 array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced\&.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced\&.
.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
\fIA\fP
.PP
.nf
A is REAL array, dimension ( LDA, N )
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced\&.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced\&.
.fi
.PP
.br
\fILDA\fP
.PP
.nf
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program\&. LDA must be at least
max( 1, n )\&.
.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
\fIBETA\fP
.PP
.nf
BETA is REAL
On entry, BETA specifies the scalar beta\&. When BETA is
supplied as zero then Y need not be set on input\&.
.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\&. On exit, Y is overwritten by the updated
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
.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\&.
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\&.
.fi
.PP
.RE
.PP
.SS "subroutine zhemv (character uplo, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)"
.PP
\fBZHEMV\fP
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
ZHEMV 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\&.
.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 array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced\&.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced\&.
.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
\fIA\fP
.PP
.nf
A is COMPLEX*16 array, dimension ( LDA, N )
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the hermitian matrix and the strictly
lower triangular part of A is not referenced\&.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the hermitian matrix and the strictly
upper triangular part of A is not referenced\&.
Note that the imaginary parts of the diagonal elements need
not be set and are assumed to be zero\&.
.fi
.PP
.br
\fILDA\fP
.PP
.nf
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program\&. LDA must be at least
max( 1, n )\&.
.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
\fIBETA\fP
.PP
.nf
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\&.
.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\&. On exit, Y is overwritten by the updated
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
.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\&.
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\&.
.fi
.PP
.RE
.PP
.SS "subroutine zsymv (character uplo, integer n, complex*16 alpha, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) x, integer incx, complex*16 beta, complex*16, dimension( * ) y, integer incy)"
.PP
\fBZSYMV\fP computes a matrix-vector product for a complex symmetric matrix\&.
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
ZSYMV 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\&.
.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 array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced\&.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced\&.
Unchanged on exit\&.
.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\&.
Unchanged on exit\&.
.fi
.PP
.br
\fIALPHA\fP
.PP
.nf
ALPHA is COMPLEX*16
On entry, ALPHA specifies the scalar alpha\&.
Unchanged on exit\&.
.fi
.PP
.br
\fIA\fP
.PP
.nf
A is COMPLEX*16 array, dimension ( LDA, N )
Before entry, with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced\&.
Before entry, with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced\&.
Unchanged on exit\&.
.fi
.PP
.br
\fILDA\fP
.PP
.nf
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program\&. LDA must be at least
max( 1, N )\&.
Unchanged on exit\&.
.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\&.
Unchanged on exit\&.
.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\&.
Unchanged on exit\&.
.fi
.PP
.br
\fIBETA\fP
.PP
.nf
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\&.
.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\&. On exit, Y is overwritten by the updated
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\&.
Unchanged on exit\&.
.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
.SH "Author"
.PP
Generated automatically by Doxygen for LAPACK from the source code\&.