zhemv(3f) - [BLAS:COMPLEX_16_BLAS_LEVEL2]
subroutine zhemv(uplo,n,alpha,a,lda,x,incx,beta,y,incy)
.. Scalar Arguments ..
complex(kind=real64),intent(in) :: alpha,beta
integer,intent(in) :: incx,incy,lda,n
character,intent(in) :: uplo
..
.. Array Arguments ..
complex(kind=real64),intent(in) :: a(lda,*),x(*)
complex(kind=real64),intent(inout) :: y(*)
..
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.
UPLO
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.
N
N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
ALPHA
ALPHA is complex(kind=real64)
On entry, ALPHA specifies the scalar alpha.
A
A is complex(kind=real64) 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.
LDA
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 ).
X
X is complex(kind=real64) 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(kind=real64)
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(kind=real64) 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.
date:December 2016
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.
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| character(len=1), | intent(in) | :: | uplo | |||
| integer, | intent(in) | :: | n | |||
| complex(kind=real64), | intent(in) | :: | alpha | |||
| complex(kind=real64), | intent(in) | :: | a(lda,*) | |||
| integer, | intent(in) | :: | lda | |||
| complex(kind=real64), | intent(in) | :: | x(*) | |||
| integer, | intent(in) | :: | incx | |||
| complex(kind=real64), | intent(in) | :: | beta | |||
| complex(kind=real64), | intent(inout) | :: | y(*) | |||
| integer, | intent(in) | :: | incy |
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| integer, | public | :: | i | ||||
| integer, | public | :: | info | ||||
| integer, | public | :: | ix | ||||
| integer, | public | :: | iy | ||||
| integer, | public | :: | j | ||||
| integer, | public | :: | jx | ||||
| integer, | public | :: | jy | ||||
| integer, | public | :: | kx | ||||
| integer, | public | :: | ky | ||||
| complex(kind=real64), | public, | parameter | :: | one | = | (1.0d+0,0.0d+0) | |
| complex(kind=real64), | public | :: | temp1 | ||||
| complex(kind=real64), | public | :: | temp2 | ||||
| complex(kind=real64), | public, | parameter | :: | zero | = | (0.0d+0,0.0d+0) |
subroutine zhemv(uplo,n,alpha,a,lda,x,incx,beta,y,incy)
implicit none
!
! -- Reference BLAS level2 routine (version 3.7.0) --
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! December 2016
!
! .. Scalar Arguments ..
complex(kind=real64),intent(in) :: alpha,beta
integer,intent(in) :: incx,incy,lda,n
character,intent(in) :: uplo
! ..
! .. Array Arguments ..
complex(kind=real64),intent(in) :: a(lda,*),x(*)
complex(kind=real64),intent(inout) :: y(*)
! ..
!
! =====================================================================
!
! .. Parameters ..
complex(kind=real64) :: one
parameter (one= (1.0d+0,0.0d+0))
complex(kind=real64) :: zero
parameter (zero= (0.0d+0,0.0d+0))
! ..
! .. Local Scalars ..
complex(kind=real64) :: temp1,temp2
integer i,info,ix,iy,j,jx,jy,kx,ky
! ..
! .. External Functions ..
! logical lsame
! external lsame
! ..
! .. External Subroutines ..
! external xerbla
! ..
! .. Intrinsic Functions ..
intrinsic dble,dconjg,max
! ..
!
! Test the input parameters.
!
info = 0
if (.not.lsame(uplo,'U') .and. .not.lsame(uplo,'L')) then
info = 1
elseif (n.lt.0) then
info = 2
elseif (lda.lt.max(1,n)) then
info = 5
elseif (incx.eq.0) then
info = 7
elseif (incy.eq.0) then
info = 10
endif
if (info.ne.0) then
call xerbla('ZHEMV ',info)
return
endif
!
! Quick return if possible.
!
if ((n.eq.0) .or. ((alpha.eq.zero).and. (beta.eq.one))) return
!
! Set up the start points in X and Y.
!
if (incx.gt.0) then
kx = 1
else
kx = 1 - (n-1)*incx
endif
if (incy.gt.0) then
ky = 1
else
ky = 1 - (n-1)*incy
endif
!
! Start the operations. In this version the elements of A are
! accessed sequentially with one pass through the triangular part
! of A.
!
! First form y := beta*y.
!
if (beta.ne.one) then
if (incy.eq.1) then
if (beta.eq.zero) then
y(1:n) = zero
else
y(1:n) = beta*y(1:n)
endif
else
iy = ky
if (beta.eq.zero) then
do i = 1,n
y(iy) = zero
iy = iy + incy
enddo
else
do i = 1,n
y(iy) = beta*y(iy)
iy = iy + incy
enddo
endif
endif
endif
if (alpha.eq.zero) return
if (lsame(uplo,'U')) then
!
! Form y when A is stored in upper triangle.
!
if ((incx.eq.1) .and. (incy.eq.1)) then
do j = 1,n
temp1 = alpha*x(j)
temp2 = zero
do i = 1,j - 1
y(i) = y(i) + temp1*a(i,j)
temp2 = temp2 + dconjg(a(i,j))*x(i)
enddo
y(j) = y(j) + temp1*dble(a(j,j)) + alpha*temp2
enddo
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = zero
ix = kx
iy = ky
do i = 1,j - 1
y(iy) = y(iy) + temp1*a(i,j)
temp2 = temp2 + dconjg(a(i,j))*x(ix)
ix = ix + incx
iy = iy + incy
enddo
y(jy) = y(jy) + temp1*dble(a(j,j)) + alpha*temp2
jx = jx + incx
jy = jy + incy
enddo
endif
else
!
! Form y when A is stored in lower triangle.
!
if ((incx.eq.1) .and. (incy.eq.1)) then
do j = 1,n
temp1 = alpha*x(j)
temp2 = zero
y(j) = y(j) + temp1*dble(a(j,j))
do i = j + 1,n
y(i) = y(i) + temp1*a(i,j)
temp2 = temp2 + dconjg(a(i,j))*x(i)
enddo
y(j) = y(j) + alpha*temp2
enddo
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = zero
y(jy) = y(jy) + temp1*dble(a(j,j))
ix = jx
iy = jy
do i = j + 1,n
ix = ix + incx
iy = iy + incy
y(iy) = y(iy) + temp1*a(i,j)
temp2 = temp2 + dconjg(a(i,j))*x(ix)
enddo
y(jy) = y(jy) + alpha*temp2
jx = jx + incx
jy = jy + incy
enddo
endif
endif
end subroutine zhemv