zgbmv(3f) - [BLAS:COMPLEX_16_BLAS_LEVEL2]
subroutine zgbmv(trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy)
.. Scalar Arguments ..
complex(kind=real64),intent(in) :: alpha,beta
integer,intent(in) :: incx,incy,kl,ku,lda,m,n
character,intent(in) :: trans
..
.. Array Arguments ..
complex(kind=real64),intent(in) :: a(lda,*),x(*)
complex(kind=real64),intent(inout) :: y(*)
..
ZGBMV performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
y := alpha*A**H*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.
TRANS
TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y.
M
M is INTEGER
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
N
N is INTEGER
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
KL
KL is INTEGER
On entry, KL specifies the number of sub-diagonals of the
matrix A. KL must satisfy 0 .le. KL.
KU
KU is INTEGER
On entry, KU specifies the number of super-diagonals of the
matrix A. KU must satisfy 0 .le. KU.
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, the leading ( kl + ku + 1 ) by n part of the
array A must contain the matrix of coefficients, supplied
column by column, with the leading diagonal of the matrix in
row ( ku + 1 ) of the array, the first super-diagonal
starting at position 2 in row ku, the first sub-diagonal
starting at position 1 in row ( ku + 2 ), and so on.
Elements in the array A that do not correspond to elements
in the band matrix (such as the top left ku by ku triangle)
are not referenced.
The following program segment will transfer a band matrix
from conventional full matrix storage to band storage:
DO 20, J = 1, N
K = KU + 1 - J
DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
A( K + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
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
( kl + ku + 1 ).
X
X is complex(kind=real64) array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
Before entry, the incremented array X must contain the
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 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
Before entry, the incremented array Y must contain the
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) | :: | trans | |||
| integer, | intent(in) | :: | m | |||
| integer, | intent(in) | :: | n | |||
| integer, | intent(in) | :: | kl | |||
| integer, | intent(in) | :: | ku | |||
| 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 | :: | k | ||||
| integer, | public | :: | kup1 | ||||
| integer, | public | :: | kx | ||||
| integer, | public | :: | ky | ||||
| integer, | public | :: | lenx | ||||
| integer, | public | :: | leny | ||||
| logical, | public | :: | noconj | ||||
| complex(kind=real64), | public, | parameter | :: | one | = | (1.0d+0,0.0d+0) | |
| complex(kind=real64), | public | :: | temp | ||||
| complex(kind=real64), | public, | parameter | :: | zero | = | (0.0d+0,0.0d+0) |
subroutine zgbmv(trans,m,n,kl,ku,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,kl,ku,lda,m,n
character,intent(in) :: trans
! ..
! .. 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) :: temp
integer i,info,ix,iy,j,jx,jy,k,kup1,kx,ky,lenx,leny
logical noconj
! ..
! .. External Functions ..
! LOGICAL LSAME
! EXTERNAL LSAME
! ..
! .. External Subroutines ..
! EXTERNAL XERBLA
! ..
! .. Intrinsic Functions ..
intrinsic dconjg,max,min
! ..
!
! Test the input parameters.
!
info = 0
if (.not.lsame(trans,'N') .and. .not.lsame(trans,'T') .and. .not.lsame(trans,'C')) then
info = 1
elseif (m.lt.0) then
info = 2
elseif (n.lt.0) then
info = 3
elseif (kl.lt.0) then
info = 4
elseif (ku.lt.0) then
info = 5
elseif (lda.lt. (kl+ku+1)) then
info = 8
elseif (incx.eq.0) then
info = 10
elseif (incy.eq.0) then
info = 13
endif
if (info.ne.0) then
call xerbla('ZGBMV ',info)
return
endif
!
! Quick return if possible.
!
if ((m.eq.0) .or. (n.eq.0) .or. ((alpha.eq.zero).and. (beta.eq.one))) return
!
noconj = lsame(trans,'T')
!
! Set LENX and LENY, the lengths of the vectors x and y, and set
! up the start points in X and Y.
!
if (lsame(trans,'N')) then
lenx = n
leny = m
else
lenx = m
leny = n
endif
if (incx.gt.0) then
kx = 1
else
kx = 1 - (lenx-1)*incx
endif
if (incy.gt.0) then
ky = 1
else
ky = 1 - (leny-1)*incy
endif
!
! Start the operations. In this version the elements of A are
! accessed sequentially with one pass through the band 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:leny) = zero
else
y(1:leny) = beta*y(1:leny)
endif
else
iy = ky
if (beta.eq.zero) then
do i = 1,leny
y(iy) = zero
iy = iy + incy
enddo
else
do i = 1,leny
y(iy) = beta*y(iy)
iy = iy + incy
enddo
endif
endif
endif
if (alpha.eq.zero) return
kup1 = ku + 1
if (lsame(trans,'N')) then
!
! Form y := alpha*A*x + y.
!
jx = kx
if (incy.eq.1) then
do j = 1,n
temp = alpha*x(jx)
k = kup1 - j
do i = max(1,j-ku),min(m,j+kl)
y(i) = y(i) + temp*a(k+i,j)
enddo
jx = jx + incx
enddo
else
do j = 1,n
temp = alpha*x(jx)
iy = ky
k = kup1 - j
do i = max(1,j-ku),min(m,j+kl)
y(iy) = y(iy) + temp*a(k+i,j)
iy = iy + incy
enddo
jx = jx + incx
if (j.gt.ku) ky = ky + incy
enddo
endif
else
!
! Form y := alpha*A**T*x + y or y := alpha*A**H*x + y.
!
jy = ky
if (incx.eq.1) then
do j = 1,n
temp = zero
k = kup1 - j
if (noconj) then
do i = max(1,j-ku),min(m,j+kl)
temp = temp + a(k+i,j)*x(i)
enddo
else
do i = max(1,j-ku),min(m,j+kl)
temp = temp + dconjg(a(k+i,j))*x(i)
enddo
endif
y(jy) = y(jy) + alpha*temp
jy = jy + incy
enddo
else
do j = 1,n
temp = zero
ix = kx
k = kup1 - j
if (noconj) then
do i = max(1,j-ku),min(m,j+kl)
temp = temp + a(k+i,j)*x(ix)
ix = ix + incx
enddo
else
do i = max(1,j-ku),min(m,j+kl)
temp = temp + dconjg(a(k+i,j))*x(ix)
ix = ix + incx
enddo
endif
y(jy) = y(jy) + alpha*temp
jy = jy + incy
if (j.gt.ku) kx = kx + incx
enddo
endif
endif
!
end subroutine zgbmv