#:include "common.fypp"
module stdlib_linalg_blas_z
use stdlib_linalg_constants
use stdlib_linalg_blas_aux
use stdlib_linalg_blas_s
use stdlib_linalg_blas_c
use stdlib_linalg_blas_d
implicit none(type,external)
private
public :: sp,dp,qp,lk,ilp,ilp64
#:for ik,it,ii in LINALG_INT_KINDS_TYPES
public :: stdlib${ii}$_zaxpy
public :: stdlib${ii}$_zcopy
public :: stdlib${ii}$_zdotc
public :: stdlib${ii}$_zdotu
public :: stdlib${ii}$_zdrot
public :: stdlib${ii}$_zdscal
public :: stdlib${ii}$_zgbmv
public :: stdlib${ii}$_zgemm
public :: stdlib${ii}$_zgemv
public :: stdlib${ii}$_zgerc
public :: stdlib${ii}$_zgeru
public :: stdlib${ii}$_zhbmv
public :: stdlib${ii}$_zhemm
public :: stdlib${ii}$_zhemv
public :: stdlib${ii}$_zher
public :: stdlib${ii}$_zher2
public :: stdlib${ii}$_zher2k
public :: stdlib${ii}$_zherk
public :: stdlib${ii}$_zhpmv
public :: stdlib${ii}$_zhpr
public :: stdlib${ii}$_zhpr2
public :: stdlib${ii}$_zrotg
public :: stdlib${ii}$_zscal
public :: stdlib${ii}$_zswap
public :: stdlib${ii}$_zsymm
public :: stdlib${ii}$_zsyr2k
public :: stdlib${ii}$_zsyrk
public :: stdlib${ii}$_ztbmv
public :: stdlib${ii}$_ztbsv
public :: stdlib${ii}$_ztpmv
public :: stdlib${ii}$_ztpsv
public :: stdlib${ii}$_ztrmm
public :: stdlib${ii}$_ztrmv
public :: stdlib${ii}$_ztrsm
public :: stdlib${ii}$_ztrsv
#:endfor
! 64-bit real constants
real(dp), parameter, private :: negone = -1.00_dp
real(dp), parameter, private :: zero = 0.00_dp
real(dp), parameter, private :: half = 0.50_dp
real(dp), parameter, private :: one = 1.00_dp
real(dp), parameter, private :: two = 2.00_dp
real(dp), parameter, private :: three = 3.00_dp
real(dp), parameter, private :: four = 4.00_dp
real(dp), parameter, private :: eight = 8.00_dp
real(dp), parameter, private :: ten = 10.00_dp
! 64-bit complex constants
complex(dp), parameter, private :: czero = ( 0.0_dp,0.0_dp)
complex(dp), parameter, private :: chalf = ( 0.5_dp,0.0_dp)
complex(dp), parameter, private :: cone = ( 1.0_dp,0.0_dp)
complex(dp), parameter, private :: cnegone = (-1.0_dp,0.0_dp)
! 64-bit scaling constants
integer, parameter, private :: maxexp = maxexponent(zero)
integer, parameter, private :: minexp = minexponent(zero)
real(dp), parameter, private :: rradix = real(radix(zero),dp)
real(dp), parameter, private :: ulp = epsilon(zero)
real(dp), parameter, private :: eps = ulp*half
real(dp), parameter, private :: safmin = rradix**max(minexp-1,1-maxexp)
real(dp), parameter, private :: safmax = one/safmin
real(dp), parameter, private :: smlnum = safmin/ulp
real(dp), parameter, private :: bignum = safmax*ulp
real(dp), parameter, private :: rtmin = sqrt(smlnum)
real(dp), parameter, private :: rtmax = sqrt(bignum)
! 64-bit Blue's scaling constants
! ssml>=1/s and sbig==1/S with s,S as defined in https://doi.org/10.1145/355769.355771
real(dp), parameter, private :: tsml = rradix**ceiling((minexp-1)*half)
real(dp), parameter, private :: tbig = rradix**floor((maxexp-digits(zero)+1)*half)
real(dp), parameter, private :: ssml = rradix**(-floor((minexp-digits(zero))*half))
real(dp), parameter, private :: sbig = rradix**(-ceiling((maxexp+digits(zero)-1)*half))
contains
#:for ik,it,ii in LINALG_INT_KINDS_TYPES
pure subroutine stdlib${ii}$_zaxpy(n,za,zx,incx,zy,incy)
!! ZAXPY constant times a vector plus a vector.
! -- reference blas level1 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: za
integer(${ik}$), intent(in) :: incx, incy, n
! Array Arguments
complex(dp), intent(in) :: zx(*)
complex(dp), intent(inout) :: zy(*)
! =====================================================================
! Local Scalars
integer(${ik}$) :: i, ix, iy
if (n<=0) return
if (stdlib_cabs1(za)==0.0_dp) return
if (incx==1 .and. incy==1) then
! code for both increments equal to 1
do i = 1,n
zy(i) = zy(i) + za*zx(i)
end do
else
! code for unequal increments or equal increments
! not equal to 1
ix = 1
iy = 1
if (incx<0) ix = (-n+1)*incx + 1
if (incy<0) iy = (-n+1)*incy + 1
do i = 1,n
zy(iy) = zy(iy) + za*zx(ix)
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib${ii}$_zaxpy
pure subroutine stdlib${ii}$_zcopy(n,zx,incx,zy,incy)
!! ZCOPY copies a vector, x, to a vector, y.
! -- reference blas level1 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, incy, n
! Array Arguments
complex(dp), intent(in) :: zx(*)
complex(dp), intent(out) :: zy(*)
! =====================================================================
! Local Scalars
integer(${ik}$) :: i, ix, iy
if (n<=0) return
if (incx==1 .and. incy==1) then
! code for both increments equal to 1
do i = 1,n
zy(i) = zx(i)
end do
else
! code for unequal increments or equal increments
! not equal to 1
ix = 1
iy = 1
if (incx<0) ix = (-n+1)*incx + 1
if (incy<0) iy = (-n+1)*incy + 1
do i = 1,n
zy(iy) = zx(ix)
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib${ii}$_zcopy
pure complex(dp) function stdlib${ii}$_zdotc(n,zx,incx,zy,incy)
!! ZDOTC forms the dot product of two complex vectors
!! ZDOTC = X^H * Y
! -- reference blas level1 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, incy, n
! Array Arguments
complex(dp), intent(in) :: zx(*), zy(*)
! =====================================================================
! Local Scalars
complex(dp) :: ztemp
integer(${ik}$) :: i, ix, iy
! Intrinsic Functions
intrinsic :: conjg
ztemp = (0.0_dp,0.0_dp)
stdlib${ii}$_zdotc = (0.0_dp,0.0_dp)
if (n<=0) return
if (incx==1 .and. incy==1) then
! code for both increments equal to 1
do i = 1,n
ztemp = ztemp + conjg(zx(i))*zy(i)
end do
else
! code for unequal increments or equal increments
! not equal to 1
ix = 1
iy = 1
if (incx<0) ix = (-n+1)*incx + 1
if (incy<0) iy = (-n+1)*incy + 1
do i = 1,n
ztemp = ztemp + conjg(zx(ix))*zy(iy)
ix = ix + incx
iy = iy + incy
end do
end if
stdlib${ii}$_zdotc = ztemp
return
end function stdlib${ii}$_zdotc
pure complex(dp) function stdlib${ii}$_zdotu(n,zx,incx,zy,incy)
!! ZDOTU forms the dot product of two complex vectors
!! ZDOTU = X^T * Y
! -- reference blas level1 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, incy, n
! Array Arguments
complex(dp), intent(in) :: zx(*), zy(*)
! =====================================================================
! Local Scalars
complex(dp) :: ztemp
integer(${ik}$) :: i, ix, iy
ztemp = (0.0_dp,0.0_dp)
stdlib${ii}$_zdotu = (0.0_dp,0.0_dp)
if (n<=0) return
if (incx==1 .and. incy==1) then
! code for both increments equal to 1
do i = 1,n
ztemp = ztemp + zx(i)*zy(i)
end do
else
! code for unequal increments or equal increments
! not equal to 1
ix = 1
iy = 1
if (incx<0) ix = (-n+1)*incx + 1
if (incy<0) iy = (-n+1)*incy + 1
do i = 1,n
ztemp = ztemp + zx(ix)*zy(iy)
ix = ix + incx
iy = iy + incy
end do
end if
stdlib${ii}$_zdotu = ztemp
return
end function stdlib${ii}$_zdotu
pure subroutine stdlib${ii}$_zdrot( n, zx, incx, zy, incy, c, s )
!! Applies a plane rotation, where the cos and sin (c and s) are real
!! and the vectors cx and cy are complex.
!! jack dongarra, linpack, 3/11/78.
! -- reference blas level1 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, incy, n
real(dp), intent(in) :: c, s
! Array Arguments
complex(dp), intent(inout) :: zx(*), zy(*)
! =====================================================================
! Local Scalars
integer(${ik}$) :: i, ix, iy
complex(dp) :: ctemp
! Executable Statements
if( n<=0 )return
if( incx==1 .and. incy==1 ) then
! code for both increments equal to 1
do i = 1, n
ctemp = c*zx( i ) + s*zy( i )
zy( i ) = c*zy( i ) - s*zx( i )
zx( i ) = ctemp
end do
else
! code for unequal increments or equal increments not equal
! to 1
ix = 1
iy = 1
if( incx<0 )ix = ( -n+1 )*incx + 1
if( incy<0 )iy = ( -n+1 )*incy + 1
do i = 1, n
ctemp = c*zx( ix ) + s*zy( iy )
zy( iy ) = c*zy( iy ) - s*zx( ix )
zx( ix ) = ctemp
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib${ii}$_zdrot
pure subroutine stdlib${ii}$_zdscal(n,da,zx,incx)
!! ZDSCAL scales a vector by a constant.
! -- reference blas level1 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
real(dp), intent(in) :: da
integer(${ik}$), intent(in) :: incx, n
! Array Arguments
complex(dp), intent(inout) :: zx(*)
! =====================================================================
! Local Scalars
integer(${ik}$) :: i, nincx
! Intrinsic Functions
intrinsic :: cmplx
if (n<=0 .or. incx<=0) return
if (incx==1) then
! code for increment equal to 1
do i = 1,n
zx(i) = cmplx(da,0.0_dp,KIND=dp)*zx(i)
end do
else
! code for increment not equal to 1
nincx = n*incx
do i = 1,nincx,incx
zx(i) = cmplx(da,0.0_dp,KIND=dp)*zx(i)
end do
end if
return
end subroutine stdlib${ii}$_zdscal
pure subroutine stdlib${ii}$_zgbmv(trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy)
!! 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.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: incx, incy, kl, ku, lda, m, n
character, intent(in) :: trans
! Array Arguments
complex(dp), intent(in) :: a(lda,*), x(*)
complex(dp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, iy, j, jx, jy, k, kup1, kx, ky, lenx, leny
logical(lk) :: noconj
! Intrinsic Functions
intrinsic :: conjg,max,min
! test the input parameters.
info = 0
if (.not.stdlib_lsame(trans,'N') .and. .not.stdlib_lsame(trans,'T') &
.and..not.stdlib_lsame(trans,'C')) then
info = 1
else if (m<0) then
info = 2
else if (n<0) then
info = 3
else if (kl<0) then
info = 4
else if (ku<0) then
info = 5
else if (lda< (kl+ku+1)) then
info = 8
else if (incx==0) then
info = 10
else if (incy==0) then
info = 13
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZGBMV ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or.((alpha==czero).and. (beta==cone))) return
noconj = stdlib_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 (stdlib_lsame(trans,'N')) then
lenx = n
leny = m
else
lenx = m
leny = n
end if
if (incx>0) then
kx = 1
else
kx = 1 - (lenx-1)*incx
end if
if (incy>0) then
ky = 1
else
ky = 1 - (leny-1)*incy
end if
! start the operations. in this version the elements of a are
! accessed sequentially with cone pass through the band part of a.
! first form y := beta*y.
if (beta/=cone) then
if (incy==1) then
if (beta==czero) then
do i = 1,leny
y(i) = czero
end do
else
do i = 1,leny
y(i) = beta*y(i)
end do
end if
else
iy = ky
if (beta==czero) then
do i = 1,leny
y(iy) = czero
iy = iy + incy
end do
else
do i = 1,leny
y(iy) = beta*y(iy)
iy = iy + incy
end do
end if
end if
end if
if (alpha==czero) return
kup1 = ku + 1
if (stdlib_lsame(trans,'N')) then
! form y := alpha*a*x + y.
jx = kx
if (incy==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)
end do
jx = jx + incx
end do
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
end do
jx = jx + incx
if (j>ku) ky = ky + incy
end do
end if
else
! form y := alpha*a**t*x + y or y := alpha*a**h*x + y.
jy = ky
if (incx==1) then
do j = 1,n
temp = czero
k = kup1 - j
if (noconj) then
do i = max(1,j-ku),min(m,j+kl)
temp = temp + a(k+i,j)*x(i)
end do
else
do i = max(1,j-ku),min(m,j+kl)
temp = temp + conjg(a(k+i,j))*x(i)
end do
end if
y(jy) = y(jy) + alpha*temp
jy = jy + incy
end do
else
do j = 1,n
temp = czero
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
end do
else
do i = max(1,j-ku),min(m,j+kl)
temp = temp + conjg(a(k+i,j))*x(ix)
ix = ix + incx
end do
end if
y(jy) = y(jy) + alpha*temp
jy = jy + incy
if (j>ku) kx = kx + incx
end do
end if
end if
return
end subroutine stdlib${ii}$_zgbmv
pure subroutine stdlib${ii}$_zgemm(transa,transb,m,n,k,alpha,a,lda,b,ldb,beta,c,ldc)
!! ZGEMM performs one of the matrix-matrix operations
!! C := alpha*op( A )*op( B ) + beta*C,
!! where op( X ) is one of
!! op( X ) = X or op( X ) = X**T or op( X ) = X**H,
!! alpha and beta are scalars, and A, B and C are matrices, with op( A )
!! an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
! -- reference blas level3 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: k, lda, ldb, ldc, m, n
character, intent(in) :: transa, transb
! Array Arguments
complex(dp), intent(in) :: a(lda,*), b(ldb,*)
complex(dp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: conjg,max
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, j, l, nrowa, nrowb
logical(lk) :: conja, conjb, nota, notb
! set nota and notb as true if a and b respectively are not
! conjugated or transposed, set conja and conjb as true if a and
! b respectively are to be transposed but not conjugated and set
! nrowa and nrowb as the number of rows of a and b respectively.
nota = stdlib_lsame(transa,'N')
notb = stdlib_lsame(transb,'N')
conja = stdlib_lsame(transa,'C')
conjb = stdlib_lsame(transb,'C')
if (nota) then
nrowa = m
else
nrowa = k
end if
if (notb) then
nrowb = k
else
nrowb = n
end if
! test the input parameters.
info = 0
if ((.not.nota) .and. (.not.conja) .and.(.not.stdlib_lsame(transa,'T'))) then
info = 1
else if ((.not.notb) .and. (.not.conjb) .and.(.not.stdlib_lsame(transb,'T'))) &
then
info = 2
else if (m<0) then
info = 3
else if (n<0) then
info = 4
else if (k<0) then
info = 5
else if (lda<max(1,nrowa)) then
info = 8
else if (ldb<max(1,nrowb)) then
info = 10
else if (ldc<max(1,m)) then
info = 13
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZGEMM ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or.(((alpha==czero).or. (k==0)).and. (beta==cone))) &
return
! and when alpha.eq.czero.
if (alpha==czero) then
if (beta==czero) then
do j = 1,n
do i = 1,m
c(i,j) = czero
end do
end do
else
do j = 1,n
do i = 1,m
c(i,j) = beta*c(i,j)
end do
end do
end if
return
end if
! start the operations.
if (notb) then
if (nota) then
! form c := alpha*a*b + beta*c.
do j = 1,n
if (beta==czero) then
do i = 1,m
c(i,j) = czero
end do
else if (beta/=cone) then
do i = 1,m
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
temp = alpha*b(l,j)
do i = 1,m
c(i,j) = c(i,j) + temp*a(i,l)
end do
end do
end do
else if (conja) then
! form c := alpha*a**h*b + beta*c.
do j = 1,n
do i = 1,m
temp = czero
do l = 1,k
temp = temp + conjg(a(l,i))*b(l,j)
end do
if (beta==czero) then
c(i,j) = alpha*temp
else
c(i,j) = alpha*temp + beta*c(i,j)
end if
end do
end do
else
! form c := alpha*a**t*b + beta*c
do j = 1,n
do i = 1,m
temp = czero
do l = 1,k
temp = temp + a(l,i)*b(l,j)
end do
if (beta==czero) then
c(i,j) = alpha*temp
else
c(i,j) = alpha*temp + beta*c(i,j)
end if
end do
end do
end if
else if (nota) then
if (conjb) then
! form c := alpha*a*b**h + beta*c.
do j = 1,n
if (beta==czero) then
do i = 1,m
c(i,j) = czero
end do
else if (beta/=cone) then
do i = 1,m
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
temp = alpha*conjg(b(j,l))
do i = 1,m
c(i,j) = c(i,j) + temp*a(i,l)
end do
end do
end do
else
! form c := alpha*a*b**t + beta*c
do j = 1,n
if (beta==czero) then
do i = 1,m
c(i,j) = czero
end do
else if (beta/=cone) then
do i = 1,m
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
temp = alpha*b(j,l)
do i = 1,m
c(i,j) = c(i,j) + temp*a(i,l)
end do
end do
end do
end if
else if (conja) then
if (conjb) then
! form c := alpha*a**h*b**h + beta*c.
do j = 1,n
do i = 1,m
temp = czero
do l = 1,k
temp = temp + conjg(a(l,i))*conjg(b(j,l))
end do
if (beta==czero) then
c(i,j) = alpha*temp
else
c(i,j) = alpha*temp + beta*c(i,j)
end if
end do
end do
else
! form c := alpha*a**h*b**t + beta*c
do j = 1,n
do i = 1,m
temp = czero
do l = 1,k
temp = temp + conjg(a(l,i))*b(j,l)
end do
if (beta==czero) then
c(i,j) = alpha*temp
else
c(i,j) = alpha*temp + beta*c(i,j)
end if
end do
end do
end if
else
if (conjb) then
! form c := alpha*a**t*b**h + beta*c
do j = 1,n
do i = 1,m
temp = czero
do l = 1,k
temp = temp + a(l,i)*conjg(b(j,l))
end do
if (beta==czero) then
c(i,j) = alpha*temp
else
c(i,j) = alpha*temp + beta*c(i,j)
end if
end do
end do
else
! form c := alpha*a**t*b**t + beta*c
do j = 1,n
do i = 1,m
temp = czero
do l = 1,k
temp = temp + a(l,i)*b(j,l)
end do
if (beta==czero) then
c(i,j) = alpha*temp
else
c(i,j) = alpha*temp + beta*c(i,j)
end if
end do
end do
end if
end if
return
end subroutine stdlib${ii}$_zgemm
pure subroutine stdlib${ii}$_zgemv(trans,m,n,alpha,a,lda,x,incx,beta,y,incy)
!! ZGEMV 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 matrix.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: incx, incy, lda, m, n
character, intent(in) :: trans
! Array Arguments
complex(dp), intent(in) :: a(lda,*), x(*)
complex(dp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, iy, j, jx, jy, kx, ky, lenx, leny
logical(lk) :: noconj
! Intrinsic Functions
intrinsic :: conjg,max
! test the input parameters.
info = 0
if (.not.stdlib_lsame(trans,'N') .and. .not.stdlib_lsame(trans,'T') &
.and..not.stdlib_lsame(trans,'C')) then
info = 1
else if (m<0) then
info = 2
else if (n<0) then
info = 3
else if (lda<max(1,m)) then
info = 6
else if (incx==0) then
info = 8
else if (incy==0) then
info = 11
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZGEMV ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or.((alpha==czero).and. (beta==cone))) return
noconj = stdlib_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 (stdlib_lsame(trans,'N')) then
lenx = n
leny = m
else
lenx = m
leny = n
end if
if (incx>0) then
kx = 1
else
kx = 1 - (lenx-1)*incx
end if
if (incy>0) then
ky = 1
else
ky = 1 - (leny-1)*incy
end if
! start the operations. in this version the elements of a are
! accessed sequentially with cone pass through a.
! first form y := beta*y.
if (beta/=cone) then
if (incy==1) then
if (beta==czero) then
do i = 1,leny
y(i) = czero
end do
else
do i = 1,leny
y(i) = beta*y(i)
end do
end if
else
iy = ky
if (beta==czero) then
do i = 1,leny
y(iy) = czero
iy = iy + incy
end do
else
do i = 1,leny
y(iy) = beta*y(iy)
iy = iy + incy
end do
end if
end if
end if
if (alpha==czero) return
if (stdlib_lsame(trans,'N')) then
! form y := alpha*a*x + y.
jx = kx
if (incy==1) then
do j = 1,n
temp = alpha*x(jx)
do i = 1,m
y(i) = y(i) + temp*a(i,j)
end do
jx = jx + incx
end do
else
do j = 1,n
temp = alpha*x(jx)
iy = ky
do i = 1,m
y(iy) = y(iy) + temp*a(i,j)
iy = iy + incy
end do
jx = jx + incx
end do
end if
else
! form y := alpha*a**t*x + y or y := alpha*a**h*x + y.
jy = ky
if (incx==1) then
do j = 1,n
temp = czero
if (noconj) then
do i = 1,m
temp = temp + a(i,j)*x(i)
end do
else
do i = 1,m
temp = temp + conjg(a(i,j))*x(i)
end do
end if
y(jy) = y(jy) + alpha*temp
jy = jy + incy
end do
else
do j = 1,n
temp = czero
ix = kx
if (noconj) then
do i = 1,m
temp = temp + a(i,j)*x(ix)
ix = ix + incx
end do
else
do i = 1,m
temp = temp + conjg(a(i,j))*x(ix)
ix = ix + incx
end do
end if
y(jy) = y(jy) + alpha*temp
jy = jy + incy
end do
end if
end if
return
end subroutine stdlib${ii}$_zgemv
pure subroutine stdlib${ii}$_zgerc(m,n,alpha,x,incx,y,incy,a,lda)
!! ZGERC performs the rank 1 operation
!! A := alpha*x*y**H + A,
!! where alpha is a scalar, x is an m element vector, y is an n element
!! vector and A is an m by n matrix.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha
integer(${ik}$), intent(in) :: incx, incy, lda, m, n
! Array Arguments
complex(dp), intent(inout) :: a(lda,*)
complex(dp), intent(in) :: x(*), y(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, j, jy, kx
! Intrinsic Functions
intrinsic :: conjg,max
! test the input parameters.
info = 0
if (m<0) then
info = 1
else if (n<0) then
info = 2
else if (incx==0) then
info = 5
else if (incy==0) then
info = 7
else if (lda<max(1,m)) then
info = 9
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZGERC ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or. (alpha==czero)) return
! start the operations. in this version the elements of a are
! accessed sequentially with cone pass through a.
if (incy>0) then
jy = 1
else
jy = 1 - (n-1)*incy
end if
if (incx==1) then
do j = 1,n
if (y(jy)/=czero) then
temp = alpha*conjg(y(jy))
do i = 1,m
a(i,j) = a(i,j) + x(i)*temp
end do
end if
jy = jy + incy
end do
else
if (incx>0) then
kx = 1
else
kx = 1 - (m-1)*incx
end if
do j = 1,n
if (y(jy)/=czero) then
temp = alpha*conjg(y(jy))
ix = kx
do i = 1,m
a(i,j) = a(i,j) + x(ix)*temp
ix = ix + incx
end do
end if
jy = jy + incy
end do
end if
return
end subroutine stdlib${ii}$_zgerc
pure subroutine stdlib${ii}$_zgeru(m,n,alpha,x,incx,y,incy,a,lda)
!! ZGERU performs the rank 1 operation
!! A := alpha*x*y**T + A,
!! where alpha is a scalar, x is an m element vector, y is an n element
!! vector and A is an m by n matrix.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha
integer(${ik}$), intent(in) :: incx, incy, lda, m, n
! Array Arguments
complex(dp), intent(inout) :: a(lda,*)
complex(dp), intent(in) :: x(*), y(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, j, jy, kx
! Intrinsic Functions
intrinsic :: max
! test the input parameters.
info = 0
if (m<0) then
info = 1
else if (n<0) then
info = 2
else if (incx==0) then
info = 5
else if (incy==0) then
info = 7
else if (lda<max(1,m)) then
info = 9
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZGERU ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or. (alpha==czero)) return
! start the operations. in this version the elements of a are
! accessed sequentially with cone pass through a.
if (incy>0) then
jy = 1
else
jy = 1 - (n-1)*incy
end if
if (incx==1) then
do j = 1,n
if (y(jy)/=czero) then
temp = alpha*y(jy)
do i = 1,m
a(i,j) = a(i,j) + x(i)*temp
end do
end if
jy = jy + incy
end do
else
if (incx>0) then
kx = 1
else
kx = 1 - (m-1)*incx
end if
do j = 1,n
if (y(jy)/=czero) then
temp = alpha*y(jy)
ix = kx
do i = 1,m
a(i,j) = a(i,j) + x(ix)*temp
ix = ix + incx
end do
end if
jy = jy + incy
end do
end if
return
end subroutine stdlib${ii}$_zgeru
pure subroutine stdlib${ii}$_zhbmv(uplo,n,k,alpha,a,lda,x,incx,beta,y,incy)
!! ZHBMV 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 band matrix, with k super-diagonals.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: incx, incy, k, lda, n
character, intent(in) :: uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*), x(*)
complex(dp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp1, temp2
integer(${ik}$) :: i, info, ix, iy, j, jx, jy, kplus1, kx, ky, l
! Intrinsic Functions
intrinsic :: real,conjg,max,min
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (n<0) then
info = 2
else if (k<0) then
info = 3
else if (lda< (k+1)) then
info = 6
else if (incx==0) then
info = 8
else if (incy==0) then
info = 11
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZHBMV ',info)
return
end if
! quick return if possible.
if ((n==0) .or. ((alpha==czero).and. (beta==cone))) return
! set up the start points in x and y.
if (incx>0) then
kx = 1
else
kx = 1 - (n-1)*incx
end if
if (incy>0) then
ky = 1
else
ky = 1 - (n-1)*incy
end if
! start the operations. in this version the elements of the array a
! are accessed sequentially with cone pass through a.
! first form y := beta*y.
if (beta/=cone) then
if (incy==1) then
if (beta==czero) then
do i = 1,n
y(i) = czero
end do
else
do i = 1,n
y(i) = beta*y(i)
end do
end if
else
iy = ky
if (beta==czero) then
do i = 1,n
y(iy) = czero
iy = iy + incy
end do
else
do i = 1,n
y(iy) = beta*y(iy)
iy = iy + incy
end do
end if
end if
end if
if (alpha==czero) return
if (stdlib_lsame(uplo,'U')) then
! form y when upper triangle of a is stored.
kplus1 = k + 1
if ((incx==1) .and. (incy==1)) then
do j = 1,n
temp1 = alpha*x(j)
temp2 = czero
l = kplus1 - j
do i = max(1,j-k),j - 1
y(i) = y(i) + temp1*a(l+i,j)
temp2 = temp2 + conjg(a(l+i,j))*x(i)
end do
y(j) = y(j) + temp1*real(a(kplus1,j),KIND=dp) + alpha*temp2
end do
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = czero
ix = kx
iy = ky
l = kplus1 - j
do i = max(1,j-k),j - 1
y(iy) = y(iy) + temp1*a(l+i,j)
temp2 = temp2 + conjg(a(l+i,j))*x(ix)
ix = ix + incx
iy = iy + incy
end do
y(jy) = y(jy) + temp1*real(a(kplus1,j),KIND=dp) + alpha*temp2
jx = jx + incx
jy = jy + incy
if (j>k) then
kx = kx + incx
ky = ky + incy
end if
end do
end if
else
! form y when lower triangle of a is stored.
if ((incx==1) .and. (incy==1)) then
do j = 1,n
temp1 = alpha*x(j)
temp2 = czero
y(j) = y(j) + temp1*real(a(1,j),KIND=dp)
l = 1 - j
do i = j + 1,min(n,j+k)
y(i) = y(i) + temp1*a(l+i,j)
temp2 = temp2 + conjg(a(l+i,j))*x(i)
end do
y(j) = y(j) + alpha*temp2
end do
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = czero
y(jy) = y(jy) + temp1*real(a(1,j),KIND=dp)
l = 1 - j
ix = jx
iy = jy
do i = j + 1,min(n,j+k)
ix = ix + incx
iy = iy + incy
y(iy) = y(iy) + temp1*a(l+i,j)
temp2 = temp2 + conjg(a(l+i,j))*x(ix)
end do
y(jy) = y(jy) + alpha*temp2
jx = jx + incx
jy = jy + incy
end do
end if
end if
return
end subroutine stdlib${ii}$_zhbmv
pure subroutine stdlib${ii}$_zhemm(side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc)
!! ZHEMM performs one of the matrix-matrix operations
!! C := alpha*A*B + beta*C,
!! or
!! C := alpha*B*A + beta*C,
!! where alpha and beta are scalars, A is an hermitian matrix and B and
!! C are m by n matrices.
! -- reference blas level3 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: lda, ldb, ldc, m, n
character, intent(in) :: side, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*), b(ldb,*)
complex(dp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: real,conjg,max
! Local Scalars
complex(dp) :: temp1, temp2
integer(${ik}$) :: i, info, j, k, nrowa
logical(lk) :: upper
! set nrowa as the number of rows of a.
if (stdlib_lsame(side,'L')) then
nrowa = m
else
nrowa = n
end if
upper = stdlib_lsame(uplo,'U')
! test the input parameters.
info = 0
if ((.not.stdlib_lsame(side,'L')) .and. (.not.stdlib_lsame(side,'R'))) then
info = 1
else if ((.not.upper) .and. (.not.stdlib_lsame(uplo,'L'))) then
info = 2
else if (m<0) then
info = 3
else if (n<0) then
info = 4
else if (lda<max(1,nrowa)) then
info = 7
else if (ldb<max(1,m)) then
info = 9
else if (ldc<max(1,m)) then
info = 12
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZHEMM ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or.((alpha==czero).and. (beta==cone))) return
! and when alpha.eq.czero.
if (alpha==czero) then
if (beta==czero) then
do j = 1,n
do i = 1,m
c(i,j) = czero
end do
end do
else
do j = 1,n
do i = 1,m
c(i,j) = beta*c(i,j)
end do
end do
end if
return
end if
! start the operations.
if (stdlib_lsame(side,'L')) then
! form c := alpha*a*b + beta*c.
if (upper) then
do j = 1,n
do i = 1,m
temp1 = alpha*b(i,j)
temp2 = czero
do k = 1,i - 1
c(k,j) = c(k,j) + temp1*a(k,i)
temp2 = temp2 + b(k,j)*conjg(a(k,i))
end do
if (beta==czero) then
c(i,j) = temp1*real(a(i,i),KIND=dp) + alpha*temp2
else
c(i,j) = beta*c(i,j) + temp1*real(a(i,i),KIND=dp) +&
alpha*temp2
end if
end do
end do
else
do j = 1,n
do i = m,1,-1
temp1 = alpha*b(i,j)
temp2 = czero
do k = i + 1,m
c(k,j) = c(k,j) + temp1*a(k,i)
temp2 = temp2 + b(k,j)*conjg(a(k,i))
end do
if (beta==czero) then
c(i,j) = temp1*real(a(i,i),KIND=dp) + alpha*temp2
else
c(i,j) = beta*c(i,j) + temp1*real(a(i,i),KIND=dp) +&
alpha*temp2
end if
end do
end do
end if
else
! form c := alpha*b*a + beta*c.
loop_170: do j = 1,n
temp1 = alpha*real(a(j,j),KIND=dp)
if (beta==czero) then
do i = 1,m
c(i,j) = temp1*b(i,j)
end do
else
do i = 1,m
c(i,j) = beta*c(i,j) + temp1*b(i,j)
end do
end if
do k = 1,j - 1
if (upper) then
temp1 = alpha*a(k,j)
else
temp1 = alpha*conjg(a(j,k))
end if
do i = 1,m
c(i,j) = c(i,j) + temp1*b(i,k)
end do
end do
do k = j + 1,n
if (upper) then
temp1 = alpha*conjg(a(j,k))
else
temp1 = alpha*a(k,j)
end if
do i = 1,m
c(i,j) = c(i,j) + temp1*b(i,k)
end do
end do
end do loop_170
end if
return
end subroutine stdlib${ii}$_zhemm
pure subroutine stdlib${ii}$_zhemv(uplo,n,alpha,a,lda,x,incx,beta,y,incy)
!! 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.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: incx, incy, lda, n
character, intent(in) :: uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*), x(*)
complex(dp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp1, temp2
integer(${ik}$) :: i, info, ix, iy, j, jx, jy, kx, ky
! Intrinsic Functions
intrinsic :: real,conjg,max
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (n<0) then
info = 2
else if (lda<max(1,n)) then
info = 5
else if (incx==0) then
info = 7
else if (incy==0) then
info = 10
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZHEMV ',info)
return
end if
! quick return if possible.
if ((n==0) .or. ((alpha==czero).and. (beta==cone))) return
! set up the start points in x and y.
if (incx>0) then
kx = 1
else
kx = 1 - (n-1)*incx
end if
if (incy>0) then
ky = 1
else
ky = 1 - (n-1)*incy
end if
! start the operations. in this version the elements of a are
! accessed sequentially with cone pass through the triangular part
! of a.
! first form y := beta*y.
if (beta/=cone) then
if (incy==1) then
if (beta==czero) then
do i = 1,n
y(i) = czero
end do
else
do i = 1,n
y(i) = beta*y(i)
end do
end if
else
iy = ky
if (beta==czero) then
do i = 1,n
y(iy) = czero
iy = iy + incy
end do
else
do i = 1,n
y(iy) = beta*y(iy)
iy = iy + incy
end do
end if
end if
end if
if (alpha==czero) return
if (stdlib_lsame(uplo,'U')) then
! form y when a is stored in upper triangle.
if ((incx==1) .and. (incy==1)) then
do j = 1,n
temp1 = alpha*x(j)
temp2 = czero
do i = 1,j - 1
y(i) = y(i) + temp1*a(i,j)
temp2 = temp2 + conjg(a(i,j))*x(i)
end do
y(j) = y(j) + temp1*real(a(j,j),KIND=dp) + alpha*temp2
end do
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = czero
ix = kx
iy = ky
do i = 1,j - 1
y(iy) = y(iy) + temp1*a(i,j)
temp2 = temp2 + conjg(a(i,j))*x(ix)
ix = ix + incx
iy = iy + incy
end do
y(jy) = y(jy) + temp1*real(a(j,j),KIND=dp) + alpha*temp2
jx = jx + incx
jy = jy + incy
end do
end if
else
! form y when a is stored in lower triangle.
if ((incx==1) .and. (incy==1)) then
do j = 1,n
temp1 = alpha*x(j)
temp2 = czero
y(j) = y(j) + temp1*real(a(j,j),KIND=dp)
do i = j + 1,n
y(i) = y(i) + temp1*a(i,j)
temp2 = temp2 + conjg(a(i,j))*x(i)
end do
y(j) = y(j) + alpha*temp2
end do
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = czero
y(jy) = y(jy) + temp1*real(a(j,j),KIND=dp)
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 + conjg(a(i,j))*x(ix)
end do
y(jy) = y(jy) + alpha*temp2
jx = jx + incx
jy = jy + incy
end do
end if
end if
return
end subroutine stdlib${ii}$_zhemv
pure subroutine stdlib${ii}$_zher(uplo,n,alpha,x,incx,a,lda)
!! ZHER 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.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
real(dp), intent(in) :: alpha
integer(${ik}$), intent(in) :: incx, lda, n
character, intent(in) :: uplo
! Array Arguments
complex(dp), intent(inout) :: a(lda,*)
complex(dp), intent(in) :: x(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, j, jx, kx
! Intrinsic Functions
intrinsic :: real,conjg,max
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (n<0) then
info = 2
else if (incx==0) then
info = 5
else if (lda<max(1,n)) then
info = 7
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZHER ',info)
return
end if
! quick return if possible.
if ((n==0) .or. (alpha==real(czero,KIND=dp))) return
! set the start point in x if the increment is not unity.
if (incx<=0) then
kx = 1 - (n-1)*incx
else if (incx/=1) then
kx = 1
end if
! start the operations. in this version the elements of a are
! accessed sequentially with cone pass through the triangular part
! of a.
if (stdlib_lsame(uplo,'U')) then
! form a when a is stored in upper triangle.
if (incx==1) then
do j = 1,n
if (x(j)/=czero) then
temp = alpha*conjg(x(j))
do i = 1,j - 1
a(i,j) = a(i,j) + x(i)*temp
end do
a(j,j) = real(a(j,j),KIND=dp) + real(x(j)*temp,KIND=dp)
else
a(j,j) = real(a(j,j),KIND=dp)
end if
end do
else
jx = kx
do j = 1,n
if (x(jx)/=czero) then
temp = alpha*conjg(x(jx))
ix = kx
do i = 1,j - 1
a(i,j) = a(i,j) + x(ix)*temp
ix = ix + incx
end do
a(j,j) = real(a(j,j),KIND=dp) + real(x(jx)*temp,KIND=dp)
else
a(j,j) = real(a(j,j),KIND=dp)
end if
jx = jx + incx
end do
end if
else
! form a when a is stored in lower triangle.
if (incx==1) then
do j = 1,n
if (x(j)/=czero) then
temp = alpha*conjg(x(j))
a(j,j) = real(a(j,j),KIND=dp) + real(temp*x(j),KIND=dp)
do i = j + 1,n
a(i,j) = a(i,j) + x(i)*temp
end do
else
a(j,j) = real(a(j,j),KIND=dp)
end if
end do
else
jx = kx
do j = 1,n
if (x(jx)/=czero) then
temp = alpha*conjg(x(jx))
a(j,j) = real(a(j,j),KIND=dp) + real(temp*x(jx),KIND=dp)
ix = jx
do i = j + 1,n
ix = ix + incx
a(i,j) = a(i,j) + x(ix)*temp
end do
else
a(j,j) = real(a(j,j),KIND=dp)
end if
jx = jx + incx
end do
end if
end if
return
end subroutine stdlib${ii}$_zher
pure subroutine stdlib${ii}$_zher2(uplo,n,alpha,x,incx,y,incy,a,lda)
!! ZHER2 performs the hermitian rank 2 operation
!! A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
!! where alpha is a scalar, x and y are n element vectors and A is an n
!! by n hermitian matrix.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha
integer(${ik}$), intent(in) :: incx, incy, lda, n
character, intent(in) :: uplo
! Array Arguments
complex(dp), intent(inout) :: a(lda,*)
complex(dp), intent(in) :: x(*), y(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp1, temp2
integer(${ik}$) :: i, info, ix, iy, j, jx, jy, kx, ky
! Intrinsic Functions
intrinsic :: real,conjg,max
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (n<0) then
info = 2
else if (incx==0) then
info = 5
else if (incy==0) then
info = 7
else if (lda<max(1,n)) then
info = 9
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZHER2 ',info)
return
end if
! quick return if possible.
if ((n==0) .or. (alpha==czero)) return
! set up the start points in x and y if the increments are not both
! unity.
if ((incx/=1) .or. (incy/=1)) then
if (incx>0) then
kx = 1
else
kx = 1 - (n-1)*incx
end if
if (incy>0) then
ky = 1
else
ky = 1 - (n-1)*incy
end if
jx = kx
jy = ky
end if
! start the operations. in this version the elements of a are
! accessed sequentially with cone pass through the triangular part
! of a.
if (stdlib_lsame(uplo,'U')) then
! form a when a is stored in the upper triangle.
if ((incx==1) .and. (incy==1)) then
do j = 1,n
if ((x(j)/=czero) .or. (y(j)/=czero)) then
temp1 = alpha*conjg(y(j))
temp2 = conjg(alpha*x(j))
do i = 1,j - 1
a(i,j) = a(i,j) + x(i)*temp1 + y(i)*temp2
end do
a(j,j) = real(a(j,j),KIND=dp) +real(x(j)*temp1+y(j)*temp2,KIND=dp)
else
a(j,j) = real(a(j,j),KIND=dp)
end if
end do
else
do j = 1,n
if ((x(jx)/=czero) .or. (y(jy)/=czero)) then
temp1 = alpha*conjg(y(jy))
temp2 = conjg(alpha*x(jx))
ix = kx
iy = ky
do i = 1,j - 1
a(i,j) = a(i,j) + x(ix)*temp1 + y(iy)*temp2
ix = ix + incx
iy = iy + incy
end do
a(j,j) = real(a(j,j),KIND=dp) +real(x(jx)*temp1+y(jy)*temp2,KIND=dp)
else
a(j,j) = real(a(j,j),KIND=dp)
end if
jx = jx + incx
jy = jy + incy
end do
end if
else
! form a when a is stored in the lower triangle.
if ((incx==1) .and. (incy==1)) then
do j = 1,n
if ((x(j)/=czero) .or. (y(j)/=czero)) then
temp1 = alpha*conjg(y(j))
temp2 = conjg(alpha*x(j))
a(j,j) = real(a(j,j),KIND=dp) +real(x(j)*temp1+y(j)*temp2,KIND=dp)
do i = j + 1,n
a(i,j) = a(i,j) + x(i)*temp1 + y(i)*temp2
end do
else
a(j,j) = real(a(j,j),KIND=dp)
end if
end do
else
do j = 1,n
if ((x(jx)/=czero) .or. (y(jy)/=czero)) then
temp1 = alpha*conjg(y(jy))
temp2 = conjg(alpha*x(jx))
a(j,j) = real(a(j,j),KIND=dp) +real(x(jx)*temp1+y(jy)*temp2,KIND=dp)
ix = jx
iy = jy
do i = j + 1,n
ix = ix + incx
iy = iy + incy
a(i,j) = a(i,j) + x(ix)*temp1 + y(iy)*temp2
end do
else
a(j,j) = real(a(j,j),KIND=dp)
end if
jx = jx + incx
jy = jy + incy
end do
end if
end if
return
end subroutine stdlib${ii}$_zher2
pure subroutine stdlib${ii}$_zher2k(uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc)
!! ZHER2K performs one of the hermitian rank 2k operations
!! C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,
!! or
!! C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C,
!! where alpha and beta are scalars with beta real, C is an n by n
!! hermitian matrix and A and B are n by k matrices in the first case
!! and k by n matrices in the second case.
! -- reference blas level3 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha
real(dp), intent(in) :: beta
integer(${ik}$), intent(in) :: k, lda, ldb, ldc, n
character, intent(in) :: trans, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*), b(ldb,*)
complex(dp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: real,conjg,max
! Local Scalars
complex(dp) :: temp1, temp2
integer(${ik}$) :: i, info, j, l, nrowa
logical(lk) :: upper
! test the input parameters.
if (stdlib_lsame(trans,'N')) then
nrowa = n
else
nrowa = k
end if
upper = stdlib_lsame(uplo,'U')
info = 0
if ((.not.upper) .and. (.not.stdlib_lsame(uplo,'L'))) then
info = 1
else if ((.not.stdlib_lsame(trans,'N')) .and.(.not.stdlib_lsame(trans,'C'))) &
then
info = 2
else if (n<0) then
info = 3
else if (k<0) then
info = 4
else if (lda<max(1,nrowa)) then
info = 7
else if (ldb<max(1,nrowa)) then
info = 9
else if (ldc<max(1,n)) then
info = 12
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZHER2K',info)
return
end if
! quick return if possible.
if ((n==0) .or. (((alpha==czero).or.(k==0)).and. (beta==one))) return
! and when alpha.eq.czero.
if (alpha==czero) then
if (upper) then
if (beta==real(czero,KIND=dp)) then
do j = 1,n
do i = 1,j
c(i,j) = czero
end do
end do
else
do j = 1,n
do i = 1,j - 1
c(i,j) = beta*c(i,j)
end do
c(j,j) = beta*real(c(j,j),KIND=dp)
end do
end if
else
if (beta==real(czero,KIND=dp)) then
do j = 1,n
do i = j,n
c(i,j) = czero
end do
end do
else
do j = 1,n
c(j,j) = beta*real(c(j,j),KIND=dp)
do i = j + 1,n
c(i,j) = beta*c(i,j)
end do
end do
end if
end if
return
end if
! start the operations.
if (stdlib_lsame(trans,'N')) then
! form c := alpha*a*b**h + conjg( alpha )*b*a**h +
! c.
if (upper) then
do j = 1,n
if (beta==real(czero,KIND=dp)) then
do i = 1,j
c(i,j) = czero
end do
else if (beta/=one) then
do i = 1,j - 1
c(i,j) = beta*c(i,j)
end do
c(j,j) = beta*real(c(j,j),KIND=dp)
else
c(j,j) = real(c(j,j),KIND=dp)
end if
do l = 1,k
if ((a(j,l)/=czero) .or. (b(j,l)/=czero)) then
temp1 = alpha*conjg(b(j,l))
temp2 = conjg(alpha*a(j,l))
do i = 1,j - 1
c(i,j) = c(i,j) + a(i,l)*temp1 +b(i,l)*temp2
end do
c(j,j) = real(c(j,j),KIND=dp) +real(a(j,l)*temp1+b(j,l)*temp2,&
KIND=dp)
end if
end do
end do
else
do j = 1,n
if (beta==real(czero,KIND=dp)) then
do i = j,n
c(i,j) = czero
end do
else if (beta/=one) then
do i = j + 1,n
c(i,j) = beta*c(i,j)
end do
c(j,j) = beta*real(c(j,j),KIND=dp)
else
c(j,j) = real(c(j,j),KIND=dp)
end if
do l = 1,k
if ((a(j,l)/=czero) .or. (b(j,l)/=czero)) then
temp1 = alpha*conjg(b(j,l))
temp2 = conjg(alpha*a(j,l))
do i = j + 1,n
c(i,j) = c(i,j) + a(i,l)*temp1 +b(i,l)*temp2
end do
c(j,j) = real(c(j,j),KIND=dp) +real(a(j,l)*temp1+b(j,l)*temp2,&
KIND=dp)
end if
end do
end do
end if
else
! form c := alpha*a**h*b + conjg( alpha )*b**h*a +
! c.
if (upper) then
do j = 1,n
do i = 1,j
temp1 = czero
temp2 = czero
do l = 1,k
temp1 = temp1 + conjg(a(l,i))*b(l,j)
temp2 = temp2 + conjg(b(l,i))*a(l,j)
end do
if (i==j) then
if (beta==real(czero,KIND=dp)) then
c(j,j) = real(alpha*temp1+conjg(alpha)*temp2,KIND=dp)
else
c(j,j) = beta*real(c(j,j),KIND=dp) +real(alpha*temp1+conjg(&
alpha)*temp2,KIND=dp)
end if
else
if (beta==real(czero,KIND=dp)) then
c(i,j) = alpha*temp1 + conjg(alpha)*temp2
else
c(i,j) = beta*c(i,j) + alpha*temp1 +conjg(alpha)*temp2
end if
end if
end do
end do
else
do j = 1,n
do i = j,n
temp1 = czero
temp2 = czero
do l = 1,k
temp1 = temp1 + conjg(a(l,i))*b(l,j)
temp2 = temp2 + conjg(b(l,i))*a(l,j)
end do
if (i==j) then
if (beta==real(czero,KIND=dp)) then
c(j,j) = real(alpha*temp1+conjg(alpha)*temp2,KIND=dp)
else
c(j,j) = beta*real(c(j,j),KIND=dp) +real(alpha*temp1+conjg(&
alpha)*temp2,KIND=dp)
end if
else
if (beta==real(czero,KIND=dp)) then
c(i,j) = alpha*temp1 + conjg(alpha)*temp2
else
c(i,j) = beta*c(i,j) + alpha*temp1 +conjg(alpha)*temp2
end if
end if
end do
end do
end if
end if
return
end subroutine stdlib${ii}$_zher2k
pure subroutine stdlib${ii}$_zherk(uplo,trans,n,k,alpha,a,lda,beta,c,ldc)
!! ZHERK performs one of the hermitian rank k operations
!! C := alpha*A*A**H + beta*C,
!! or
!! C := alpha*A**H*A + beta*C,
!! where alpha and beta are real scalars, C is an n by n hermitian
!! matrix and A is an n by k matrix in the first case and a k by n
!! matrix in the second case.
! -- reference blas level3 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
real(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: k, lda, ldc, n
character, intent(in) :: trans, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*)
complex(dp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: real,cmplx,conjg,max
! Local Scalars
complex(dp) :: temp
real(dp) :: rtemp
integer(${ik}$) :: i, info, j, l, nrowa
logical(lk) :: upper
! test the input parameters.
if (stdlib_lsame(trans,'N')) then
nrowa = n
else
nrowa = k
end if
upper = stdlib_lsame(uplo,'U')
info = 0
if ((.not.upper) .and. (.not.stdlib_lsame(uplo,'L'))) then
info = 1
else if ((.not.stdlib_lsame(trans,'N')) .and.(.not.stdlib_lsame(trans,'C'))) &
then
info = 2
else if (n<0) then
info = 3
else if (k<0) then
info = 4
else if (lda<max(1,nrowa)) then
info = 7
else if (ldc<max(1,n)) then
info = 10
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZHERK ',info)
return
end if
! quick return if possible.
if ((n==0) .or. (((alpha==zero).or.(k==0)).and. (beta==one))) return
! and when alpha.eq.zero.
if (alpha==zero) then
if (upper) then
if (beta==zero) then
do j = 1,n
do i = 1,j
c(i,j) = zero
end do
end do
else
do j = 1,n
do i = 1,j - 1
c(i,j) = beta*c(i,j)
end do
c(j,j) = beta*real(c(j,j),KIND=dp)
end do
end if
else
if (beta==zero) then
do j = 1,n
do i = j,n
c(i,j) = zero
end do
end do
else
do j = 1,n
c(j,j) = beta*real(c(j,j),KIND=dp)
do i = j + 1,n
c(i,j) = beta*c(i,j)
end do
end do
end if
end if
return
end if
! start the operations.
if (stdlib_lsame(trans,'N')) then
! form c := alpha*a*a**h + beta*c.
if (upper) then
do j = 1,n
if (beta==zero) then
do i = 1,j
c(i,j) = zero
end do
else if (beta/=one) then
do i = 1,j - 1
c(i,j) = beta*c(i,j)
end do
c(j,j) = beta*real(c(j,j),KIND=dp)
else
c(j,j) = real(c(j,j),KIND=dp)
end if
do l = 1,k
if (a(j,l)/=cmplx(zero,KIND=dp)) then
temp = alpha*conjg(a(j,l))
do i = 1,j - 1
c(i,j) = c(i,j) + temp*a(i,l)
end do
c(j,j) = real(c(j,j),KIND=dp) + real(temp*a(i,l),KIND=dp)
end if
end do
end do
else
do j = 1,n
if (beta==zero) then
do i = j,n
c(i,j) = zero
end do
else if (beta/=one) then
c(j,j) = beta*real(c(j,j),KIND=dp)
do i = j + 1,n
c(i,j) = beta*c(i,j)
end do
else
c(j,j) = real(c(j,j),KIND=dp)
end if
do l = 1,k
if (a(j,l)/=cmplx(zero,KIND=dp)) then
temp = alpha*conjg(a(j,l))
c(j,j) = real(c(j,j),KIND=dp) + real(temp*a(j,l),KIND=dp)
do i = j + 1,n
c(i,j) = c(i,j) + temp*a(i,l)
end do
end if
end do
end do
end if
else
! form c := alpha*a**h*a + beta*c.
if (upper) then
do j = 1,n
do i = 1,j - 1
temp = zero
do l = 1,k
temp = temp + conjg(a(l,i))*a(l,j)
end do
if (beta==zero) then
c(i,j) = alpha*temp
else
c(i,j) = alpha*temp + beta*c(i,j)
end if
end do
rtemp = zero
do l = 1,k
rtemp = rtemp + conjg(a(l,j))*a(l,j)
end do
if (beta==zero) then
c(j,j) = alpha*rtemp
else
c(j,j) = alpha*rtemp + beta*real(c(j,j),KIND=dp)
end if
end do
else
do j = 1,n
rtemp = zero
do l = 1,k
rtemp = rtemp + conjg(a(l,j))*a(l,j)
end do
if (beta==zero) then
c(j,j) = alpha*rtemp
else
c(j,j) = alpha*rtemp + beta*real(c(j,j),KIND=dp)
end if
do i = j + 1,n
temp = zero
do l = 1,k
temp = temp + conjg(a(l,i))*a(l,j)
end do
if (beta==zero) then
c(i,j) = alpha*temp
else
c(i,j) = alpha*temp + beta*c(i,j)
end if
end do
end do
end if
end if
return
end subroutine stdlib${ii}$_zherk
pure subroutine stdlib${ii}$_zhpmv(uplo,n,alpha,ap,x,incx,beta,y,incy)
!! 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.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: incx, incy, n
character, intent(in) :: uplo
! Array Arguments
complex(dp), intent(in) :: ap(*), x(*)
complex(dp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp1, temp2
integer(${ik}$) :: i, info, ix, iy, j, jx, jy, k, kk, kx, ky
! Intrinsic Functions
intrinsic :: real,conjg
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (n<0) then
info = 2
else if (incx==0) then
info = 6
else if (incy==0) then
info = 9
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZHPMV ',info)
return
end if
! quick return if possible.
if ((n==0) .or. ((alpha==czero).and. (beta==cone))) return
! set up the start points in x and y.
if (incx>0) then
kx = 1
else
kx = 1 - (n-1)*incx
end if
if (incy>0) then
ky = 1
else
ky = 1 - (n-1)*incy
end if
! start the operations. in this version the elements of the array ap
! are accessed sequentially with cone pass through ap.
! first form y := beta*y.
if (beta/=cone) then
if (incy==1) then
if (beta==czero) then
do i = 1,n
y(i) = czero
end do
else
do i = 1,n
y(i) = beta*y(i)
end do
end if
else
iy = ky
if (beta==czero) then
do i = 1,n
y(iy) = czero
iy = iy + incy
end do
else
do i = 1,n
y(iy) = beta*y(iy)
iy = iy + incy
end do
end if
end if
end if
if (alpha==czero) return
kk = 1
if (stdlib_lsame(uplo,'U')) then
! form y when ap contains the upper triangle.
if ((incx==1) .and. (incy==1)) then
do j = 1,n
temp1 = alpha*x(j)
temp2 = czero
k = kk
do i = 1,j - 1
y(i) = y(i) + temp1*ap(k)
temp2 = temp2 + conjg(ap(k))*x(i)
k = k + 1
end do
y(j) = y(j) + temp1*real(ap(kk+j-1),KIND=dp) + alpha*temp2
kk = kk + j
end do
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = czero
ix = kx
iy = ky
do k = kk,kk + j - 2
y(iy) = y(iy) + temp1*ap(k)
temp2 = temp2 + conjg(ap(k))*x(ix)
ix = ix + incx
iy = iy + incy
end do
y(jy) = y(jy) + temp1*real(ap(kk+j-1),KIND=dp) + alpha*temp2
jx = jx + incx
jy = jy + incy
kk = kk + j
end do
end if
else
! form y when ap contains the lower triangle.
if ((incx==1) .and. (incy==1)) then
do j = 1,n
temp1 = alpha*x(j)
temp2 = czero
y(j) = y(j) + temp1*real(ap(kk),KIND=dp)
k = kk + 1
do i = j + 1,n
y(i) = y(i) + temp1*ap(k)
temp2 = temp2 + conjg(ap(k))*x(i)
k = k + 1
end do
y(j) = y(j) + alpha*temp2
kk = kk + (n-j+1)
end do
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = czero
y(jy) = y(jy) + temp1*real(ap(kk),KIND=dp)
ix = jx
iy = jy
do k = kk + 1,kk + n - j
ix = ix + incx
iy = iy + incy
y(iy) = y(iy) + temp1*ap(k)
temp2 = temp2 + conjg(ap(k))*x(ix)
end do
y(jy) = y(jy) + alpha*temp2
jx = jx + incx
jy = jy + incy
kk = kk + (n-j+1)
end do
end if
end if
return
end subroutine stdlib${ii}$_zhpmv
pure subroutine stdlib${ii}$_zhpr(uplo,n,alpha,x,incx,ap)
!! 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.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
real(dp), intent(in) :: alpha
integer(${ik}$), intent(in) :: incx, n
character, intent(in) :: uplo
! Array Arguments
complex(dp), intent(inout) :: ap(*)
complex(dp), intent(in) :: x(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, j, jx, k, kk, kx
! Intrinsic Functions
intrinsic :: real,conjg
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (n<0) then
info = 2
else if (incx==0) then
info = 5
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZHPR ',info)
return
end if
! quick return if possible.
if ((n==0) .or. (alpha==real(czero,KIND=dp))) return
! set the start point in x if the increment is not unity.
if (incx<=0) then
kx = 1 - (n-1)*incx
else if (incx/=1) then
kx = 1
end if
! start the operations. in this version the elements of the array ap
! are accessed sequentially with cone pass through ap.
kk = 1
if (stdlib_lsame(uplo,'U')) then
! form a when upper triangle is stored in ap.
if (incx==1) then
do j = 1,n
if (x(j)/=czero) then
temp = alpha*conjg(x(j))
k = kk
do i = 1,j - 1
ap(k) = ap(k) + x(i)*temp
k = k + 1
end do
ap(kk+j-1) = real(ap(kk+j-1),KIND=dp) + real(x(j)*temp,KIND=dp)
else
ap(kk+j-1) = real(ap(kk+j-1),KIND=dp)
end if
kk = kk + j
end do
else
jx = kx
do j = 1,n
if (x(jx)/=czero) then
temp = alpha*conjg(x(jx))
ix = kx
do k = kk,kk + j - 2
ap(k) = ap(k) + x(ix)*temp
ix = ix + incx
end do
ap(kk+j-1) = real(ap(kk+j-1),KIND=dp) + real(x(jx)*temp,KIND=dp)
else
ap(kk+j-1) = real(ap(kk+j-1),KIND=dp)
end if
jx = jx + incx
kk = kk + j
end do
end if
else
! form a when lower triangle is stored in ap.
if (incx==1) then
do j = 1,n
if (x(j)/=czero) then
temp = alpha*conjg(x(j))
ap(kk) = real(ap(kk),KIND=dp) + real(temp*x(j),KIND=dp)
k = kk + 1
do i = j + 1,n
ap(k) = ap(k) + x(i)*temp
k = k + 1
end do
else
ap(kk) = real(ap(kk),KIND=dp)
end if
kk = kk + n - j + 1
end do
else
jx = kx
do j = 1,n
if (x(jx)/=czero) then
temp = alpha*conjg(x(jx))
ap(kk) = real(ap(kk),KIND=dp) + real(temp*x(jx),KIND=dp)
ix = jx
do k = kk + 1,kk + n - j
ix = ix + incx
ap(k) = ap(k) + x(ix)*temp
end do
else
ap(kk) = real(ap(kk),KIND=dp)
end if
jx = jx + incx
kk = kk + n - j + 1
end do
end if
end if
return
end subroutine stdlib${ii}$_zhpr
pure subroutine stdlib${ii}$_zhpr2(uplo,n,alpha,x,incx,y,incy,ap)
!! ZHPR2 performs the hermitian rank 2 operation
!! A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
!! where alpha is a scalar, x and y are n element vectors and A is an
!! n by n hermitian matrix, supplied in packed form.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha
integer(${ik}$), intent(in) :: incx, incy, n
character, intent(in) :: uplo
! Array Arguments
complex(dp), intent(inout) :: ap(*)
complex(dp), intent(in) :: x(*), y(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp1, temp2
integer(${ik}$) :: i, info, ix, iy, j, jx, jy, k, kk, kx, ky
! Intrinsic Functions
intrinsic :: real,conjg
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (n<0) then
info = 2
else if (incx==0) then
info = 5
else if (incy==0) then
info = 7
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZHPR2 ',info)
return
end if
! quick return if possible.
if ((n==0) .or. (alpha==czero)) return
! set up the start points in x and y if the increments are not both
! unity.
if ((incx/=1) .or. (incy/=1)) then
if (incx>0) then
kx = 1
else
kx = 1 - (n-1)*incx
end if
if (incy>0) then
ky = 1
else
ky = 1 - (n-1)*incy
end if
jx = kx
jy = ky
end if
! start the operations. in this version the elements of the array ap
! are accessed sequentially with cone pass through ap.
kk = 1
if (stdlib_lsame(uplo,'U')) then
! form a when upper triangle is stored in ap.
if ((incx==1) .and. (incy==1)) then
do j = 1,n
if ((x(j)/=czero) .or. (y(j)/=czero)) then
temp1 = alpha*conjg(y(j))
temp2 = conjg(alpha*x(j))
k = kk
do i = 1,j - 1
ap(k) = ap(k) + x(i)*temp1 + y(i)*temp2
k = k + 1
end do
ap(kk+j-1) = real(ap(kk+j-1),KIND=dp) +real(x(j)*temp1+y(j)*temp2,&
KIND=dp)
else
ap(kk+j-1) = real(ap(kk+j-1),KIND=dp)
end if
kk = kk + j
end do
else
do j = 1,n
if ((x(jx)/=czero) .or. (y(jy)/=czero)) then
temp1 = alpha*conjg(y(jy))
temp2 = conjg(alpha*x(jx))
ix = kx
iy = ky
do k = kk,kk + j - 2
ap(k) = ap(k) + x(ix)*temp1 + y(iy)*temp2
ix = ix + incx
iy = iy + incy
end do
ap(kk+j-1) = real(ap(kk+j-1),KIND=dp) +real(x(jx)*temp1+y(jy)*temp2,&
KIND=dp)
else
ap(kk+j-1) = real(ap(kk+j-1),KIND=dp)
end if
jx = jx + incx
jy = jy + incy
kk = kk + j
end do
end if
else
! form a when lower triangle is stored in ap.
if ((incx==1) .and. (incy==1)) then
do j = 1,n
if ((x(j)/=czero) .or. (y(j)/=czero)) then
temp1 = alpha*conjg(y(j))
temp2 = conjg(alpha*x(j))
ap(kk) = real(ap(kk),KIND=dp) +real(x(j)*temp1+y(j)*temp2,KIND=dp)
k = kk + 1
do i = j + 1,n
ap(k) = ap(k) + x(i)*temp1 + y(i)*temp2
k = k + 1
end do
else
ap(kk) = real(ap(kk),KIND=dp)
end if
kk = kk + n - j + 1
end do
else
do j = 1,n
if ((x(jx)/=czero) .or. (y(jy)/=czero)) then
temp1 = alpha*conjg(y(jy))
temp2 = conjg(alpha*x(jx))
ap(kk) = real(ap(kk),KIND=dp) +real(x(jx)*temp1+y(jy)*temp2,KIND=dp)
ix = jx
iy = jy
do k = kk + 1,kk + n - j
ix = ix + incx
iy = iy + incy
ap(k) = ap(k) + x(ix)*temp1 + y(iy)*temp2
end do
else
ap(kk) = real(ap(kk),KIND=dp)
end if
jx = jx + incx
jy = jy + incy
kk = kk + n - j + 1
end do
end if
end if
return
end subroutine stdlib${ii}$_zhpr2
pure subroutine stdlib${ii}$_zrotg( a, b, c, s )
!! The computation uses the formulas
!! |x| = sqrt( Re(x)**2 + Im(x)**2 )
!! sgn(x) = x / |x| if x /= 0
!! = 1 if x = 0
!! c = |a| / sqrt(|a|**2 + |b|**2)
!! s = sgn(a) * conjg(b) / sqrt(|a|**2 + |b|**2)
!! When a and b are real and r /= 0, the formulas simplify to
!! r = sgn(a)*sqrt(|a|**2 + |b|**2)
!! c = a / r
!! s = b / r
!! the same as in DROTG when |a| > |b|. When |b| >= |a|, the
!! sign of c and s will be different from those computed by DROTG
!! if the signs of a and b are not the same.
! -- reference blas level1 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scaling Constants
! Scalar Arguments
real(dp), intent(out) :: c
complex(dp), intent(inout) :: a
complex(dp), intent(in) :: b
complex(dp), intent(out) :: s
! Local Scalars
real(dp) :: d, f1, f2, g1, g2, h2, p, u, uu, v, vv, w
complex(dp) :: f, fs, g, gs, r, t
! Intrinsic Functions
intrinsic :: abs,aimag,conjg,max,min,real,sqrt
! Statement Functions
real(dp) :: abssq
! Statement Function Definitions
abssq( t ) = real( t,KIND=dp)**2 + aimag( t )**2
! Executable Statements
f = a
g = b
if( g == czero ) then
c = one
s = czero
r = f
else if( f == czero ) then
c = zero
g1 = max( abs(real(g,KIND=dp)), abs(aimag(g)) )
if( g1 > rtmin .and. g1 < rtmax ) then
! use unscaled algorithm
g2 = abssq( g )
d = sqrt( g2 )
s = conjg( g ) / d
r = d
else
! use scaled algorithm
u = min( safmax, max( safmin, g1 ) )
uu = one / u
gs = g*uu
g2 = abssq( gs )
d = sqrt( g2 )
s = conjg( gs ) / d
r = d*u
end if
else
f1 = max( abs(real(f,KIND=dp)), abs(aimag(f)) )
g1 = max( abs(real(g,KIND=dp)), abs(aimag(g)) )
if( f1 > rtmin .and. f1 < rtmax .and. g1 > rtmin .and. g1 < rtmax ) then
! use unscaled algorithm
f2 = abssq( f )
g2 = abssq( g )
h2 = f2 + g2
if( f2 > rtmin .and. h2 < rtmax ) then
d = sqrt( f2*h2 )
else
d = sqrt( f2 )*sqrt( h2 )
end if
p = 1 / d
c = f2*p
s = conjg( g )*( f*p )
r = f*( h2*p )
else
! use scaled algorithm
u = min( safmax, max( safmin, f1, g1 ) )
uu = one / u
gs = g*uu
g2 = abssq( gs )
if( f1*uu < rtmin ) then
! f is not well-scaled when scaled by g1.
! use a different scaling for f.
v = min( safmax, max( safmin, f1 ) )
vv = one / v
w = v * uu
fs = f*vv
f2 = abssq( fs )
h2 = f2*w**2 + g2
else
! otherwise use the same scaling for f and g.
w = one
fs = f*uu
f2 = abssq( fs )
h2 = f2 + g2
end if
if( f2 > rtmin .and. h2 < rtmax ) then
d = sqrt( f2*h2 )
else
d = sqrt( f2 )*sqrt( h2 )
end if
p = 1 / d
c = ( f2*p )*w
s = conjg( gs )*( fs*p )
r = ( fs*( h2*p ) )*u
end if
end if
a = r
return
end subroutine stdlib${ii}$_zrotg
pure subroutine stdlib${ii}$_zscal(n,za,zx,incx)
!! ZSCAL scales a vector by a constant.
! -- reference blas level1 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: za
integer(${ik}$), intent(in) :: incx, n
! Array Arguments
complex(dp), intent(inout) :: zx(*)
! =====================================================================
! Local Scalars
integer(${ik}$) :: i, nincx
if (n<=0 .or. incx<=0) return
if (incx==1) then
! code for increment equal to 1
do i = 1,n
zx(i) = za*zx(i)
end do
else
! code for increment not equal to 1
nincx = n*incx
do i = 1,nincx,incx
zx(i) = za*zx(i)
end do
end if
return
end subroutine stdlib${ii}$_zscal
pure subroutine stdlib${ii}$_zswap(n,zx,incx,zy,incy)
!! ZSWAP interchanges two vectors.
! -- reference blas level1 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, incy, n
! Array Arguments
complex(dp), intent(inout) :: zx(*), zy(*)
! =====================================================================
! Local Scalars
complex(dp) :: ztemp
integer(${ik}$) :: i, ix, iy
if (n<=0) return
if (incx==1 .and. incy==1) then
! code for both increments equal to 1
do i = 1,n
ztemp = zx(i)
zx(i) = zy(i)
zy(i) = ztemp
end do
else
! code for unequal increments or equal increments not equal
! to 1
ix = 1
iy = 1
if (incx<0) ix = (-n+1)*incx + 1
if (incy<0) iy = (-n+1)*incy + 1
do i = 1,n
ztemp = zx(ix)
zx(ix) = zy(iy)
zy(iy) = ztemp
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib${ii}$_zswap
pure subroutine stdlib${ii}$_zsymm(side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc)
!! ZSYMM performs one of the matrix-matrix operations
!! C := alpha*A*B + beta*C,
!! or
!! C := alpha*B*A + beta*C,
!! where alpha and beta are scalars, A is a symmetric matrix and B and
!! C are m by n matrices.
! -- reference blas level3 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: lda, ldb, ldc, m, n
character, intent(in) :: side, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*), b(ldb,*)
complex(dp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: max
! Local Scalars
complex(dp) :: temp1, temp2
integer(${ik}$) :: i, info, j, k, nrowa
logical(lk) :: upper
! set nrowa as the number of rows of a.
if (stdlib_lsame(side,'L')) then
nrowa = m
else
nrowa = n
end if
upper = stdlib_lsame(uplo,'U')
! test the input parameters.
info = 0
if ((.not.stdlib_lsame(side,'L')) .and. (.not.stdlib_lsame(side,'R'))) then
info = 1
else if ((.not.upper) .and. (.not.stdlib_lsame(uplo,'L'))) then
info = 2
else if (m<0) then
info = 3
else if (n<0) then
info = 4
else if (lda<max(1,nrowa)) then
info = 7
else if (ldb<max(1,m)) then
info = 9
else if (ldc<max(1,m)) then
info = 12
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZSYMM ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or.((alpha==czero).and. (beta==cone))) return
! and when alpha.eq.czero.
if (alpha==czero) then
if (beta==czero) then
do j = 1,n
do i = 1,m
c(i,j) = czero
end do
end do
else
do j = 1,n
do i = 1,m
c(i,j) = beta*c(i,j)
end do
end do
end if
return
end if
! start the operations.
if (stdlib_lsame(side,'L')) then
! form c := alpha*a*b + beta*c.
if (upper) then
do j = 1,n
do i = 1,m
temp1 = alpha*b(i,j)
temp2 = czero
do k = 1,i - 1
c(k,j) = c(k,j) + temp1*a(k,i)
temp2 = temp2 + b(k,j)*a(k,i)
end do
if (beta==czero) then
c(i,j) = temp1*a(i,i) + alpha*temp2
else
c(i,j) = beta*c(i,j) + temp1*a(i,i) +alpha*temp2
end if
end do
end do
else
do j = 1,n
do i = m,1,-1
temp1 = alpha*b(i,j)
temp2 = czero
do k = i + 1,m
c(k,j) = c(k,j) + temp1*a(k,i)
temp2 = temp2 + b(k,j)*a(k,i)
end do
if (beta==czero) then
c(i,j) = temp1*a(i,i) + alpha*temp2
else
c(i,j) = beta*c(i,j) + temp1*a(i,i) +alpha*temp2
end if
end do
end do
end if
else
! form c := alpha*b*a + beta*c.
loop_170: do j = 1,n
temp1 = alpha*a(j,j)
if (beta==czero) then
do i = 1,m
c(i,j) = temp1*b(i,j)
end do
else
do i = 1,m
c(i,j) = beta*c(i,j) + temp1*b(i,j)
end do
end if
do k = 1,j - 1
if (upper) then
temp1 = alpha*a(k,j)
else
temp1 = alpha*a(j,k)
end if
do i = 1,m
c(i,j) = c(i,j) + temp1*b(i,k)
end do
end do
do k = j + 1,n
if (upper) then
temp1 = alpha*a(j,k)
else
temp1 = alpha*a(k,j)
end if
do i = 1,m
c(i,j) = c(i,j) + temp1*b(i,k)
end do
end do
end do loop_170
end if
return
end subroutine stdlib${ii}$_zsymm
pure subroutine stdlib${ii}$_zsyr2k(uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc)
!! ZSYR2K performs one of the symmetric rank 2k operations
!! C := alpha*A*B**T + alpha*B*A**T + beta*C,
!! or
!! C := alpha*A**T*B + alpha*B**T*A + beta*C,
!! where alpha and beta are scalars, C is an n by n symmetric matrix
!! and A and B are n by k matrices in the first case and k by n
!! matrices in the second case.
! -- reference blas level3 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: k, lda, ldb, ldc, n
character, intent(in) :: trans, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*), b(ldb,*)
complex(dp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: max
! Local Scalars
complex(dp) :: temp1, temp2
integer(${ik}$) :: i, info, j, l, nrowa
logical(lk) :: upper
! test the input parameters.
if (stdlib_lsame(trans,'N')) then
nrowa = n
else
nrowa = k
end if
upper = stdlib_lsame(uplo,'U')
info = 0
if ((.not.upper) .and. (.not.stdlib_lsame(uplo,'L'))) then
info = 1
else if ((.not.stdlib_lsame(trans,'N')) .and.(.not.stdlib_lsame(trans,'T'))) &
then
info = 2
else if (n<0) then
info = 3
else if (k<0) then
info = 4
else if (lda<max(1,nrowa)) then
info = 7
else if (ldb<max(1,nrowa)) then
info = 9
else if (ldc<max(1,n)) then
info = 12
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZSYR2K',info)
return
end if
! quick return if possible.
if ((n==0) .or. (((alpha==czero).or.(k==0)).and. (beta==cone))) return
! and when alpha.eq.czero.
if (alpha==czero) then
if (upper) then
if (beta==czero) then
do j = 1,n
do i = 1,j
c(i,j) = czero
end do
end do
else
do j = 1,n
do i = 1,j
c(i,j) = beta*c(i,j)
end do
end do
end if
else
if (beta==czero) then
do j = 1,n
do i = j,n
c(i,j) = czero
end do
end do
else
do j = 1,n
do i = j,n
c(i,j) = beta*c(i,j)
end do
end do
end if
end if
return
end if
! start the operations.
if (stdlib_lsame(trans,'N')) then
! form c := alpha*a*b**t + alpha*b*a**t + c.
if (upper) then
do j = 1,n
if (beta==czero) then
do i = 1,j
c(i,j) = czero
end do
else if (beta/=cone) then
do i = 1,j
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
if ((a(j,l)/=czero) .or. (b(j,l)/=czero)) then
temp1 = alpha*b(j,l)
temp2 = alpha*a(j,l)
do i = 1,j
c(i,j) = c(i,j) + a(i,l)*temp1 +b(i,l)*temp2
end do
end if
end do
end do
else
do j = 1,n
if (beta==czero) then
do i = j,n
c(i,j) = czero
end do
else if (beta/=cone) then
do i = j,n
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
if ((a(j,l)/=czero) .or. (b(j,l)/=czero)) then
temp1 = alpha*b(j,l)
temp2 = alpha*a(j,l)
do i = j,n
c(i,j) = c(i,j) + a(i,l)*temp1 +b(i,l)*temp2
end do
end if
end do
end do
end if
else
! form c := alpha*a**t*b + alpha*b**t*a + c.
if (upper) then
do j = 1,n
do i = 1,j
temp1 = czero
temp2 = czero
do l = 1,k
temp1 = temp1 + a(l,i)*b(l,j)
temp2 = temp2 + b(l,i)*a(l,j)
end do
if (beta==czero) then
c(i,j) = alpha*temp1 + alpha*temp2
else
c(i,j) = beta*c(i,j) + alpha*temp1 +alpha*temp2
end if
end do
end do
else
do j = 1,n
do i = j,n
temp1 = czero
temp2 = czero
do l = 1,k
temp1 = temp1 + a(l,i)*b(l,j)
temp2 = temp2 + b(l,i)*a(l,j)
end do
if (beta==czero) then
c(i,j) = alpha*temp1 + alpha*temp2
else
c(i,j) = beta*c(i,j) + alpha*temp1 +alpha*temp2
end if
end do
end do
end if
end if
return
end subroutine stdlib${ii}$_zsyr2k
pure subroutine stdlib${ii}$_zsyrk(uplo,trans,n,k,alpha,a,lda,beta,c,ldc)
!! ZSYRK performs one of the symmetric rank k operations
!! C := alpha*A*A**T + beta*C,
!! or
!! C := alpha*A**T*A + beta*C,
!! where alpha and beta are scalars, C is an n by n symmetric matrix
!! and A is an n by k matrix in the first case and a k by n matrix
!! in the second case.
! -- reference blas level3 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha, beta
integer(${ik}$), intent(in) :: k, lda, ldc, n
character, intent(in) :: trans, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*)
complex(dp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: max
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, j, l, nrowa
logical(lk) :: upper
! test the input parameters.
if (stdlib_lsame(trans,'N')) then
nrowa = n
else
nrowa = k
end if
upper = stdlib_lsame(uplo,'U')
info = 0
if ((.not.upper) .and. (.not.stdlib_lsame(uplo,'L'))) then
info = 1
else if ((.not.stdlib_lsame(trans,'N')) .and.(.not.stdlib_lsame(trans,'T'))) &
then
info = 2
else if (n<0) then
info = 3
else if (k<0) then
info = 4
else if (lda<max(1,nrowa)) then
info = 7
else if (ldc<max(1,n)) then
info = 10
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZSYRK ',info)
return
end if
! quick return if possible.
if ((n==0) .or. (((alpha==czero).or.(k==0)).and. (beta==cone))) return
! and when alpha.eq.czero.
if (alpha==czero) then
if (upper) then
if (beta==czero) then
do j = 1,n
do i = 1,j
c(i,j) = czero
end do
end do
else
do j = 1,n
do i = 1,j
c(i,j) = beta*c(i,j)
end do
end do
end if
else
if (beta==czero) then
do j = 1,n
do i = j,n
c(i,j) = czero
end do
end do
else
do j = 1,n
do i = j,n
c(i,j) = beta*c(i,j)
end do
end do
end if
end if
return
end if
! start the operations.
if (stdlib_lsame(trans,'N')) then
! form c := alpha*a*a**t + beta*c.
if (upper) then
do j = 1,n
if (beta==czero) then
do i = 1,j
c(i,j) = czero
end do
else if (beta/=cone) then
do i = 1,j
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
if (a(j,l)/=czero) then
temp = alpha*a(j,l)
do i = 1,j
c(i,j) = c(i,j) + temp*a(i,l)
end do
end if
end do
end do
else
do j = 1,n
if (beta==czero) then
do i = j,n
c(i,j) = czero
end do
else if (beta/=cone) then
do i = j,n
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
if (a(j,l)/=czero) then
temp = alpha*a(j,l)
do i = j,n
c(i,j) = c(i,j) + temp*a(i,l)
end do
end if
end do
end do
end if
else
! form c := alpha*a**t*a + beta*c.
if (upper) then
do j = 1,n
do i = 1,j
temp = czero
do l = 1,k
temp = temp + a(l,i)*a(l,j)
end do
if (beta==czero) then
c(i,j) = alpha*temp
else
c(i,j) = alpha*temp + beta*c(i,j)
end if
end do
end do
else
do j = 1,n
do i = j,n
temp = czero
do l = 1,k
temp = temp + a(l,i)*a(l,j)
end do
if (beta==czero) then
c(i,j) = alpha*temp
else
c(i,j) = alpha*temp + beta*c(i,j)
end if
end do
end do
end if
end if
return
end subroutine stdlib${ii}$_zsyrk
pure subroutine stdlib${ii}$_ztbmv(uplo,trans,diag,n,k,a,lda,x,incx)
!! ZTBMV performs one of the matrix-vector operations
!! x := A*x, or x := A**T*x, or x := A**H*x,
!! where x is an n element vector and A is an n by n unit, or non-unit,
!! upper or lower triangular band matrix, with ( k + 1 ) diagonals.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, k, lda, n
character, intent(in) :: diag, trans, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*)
complex(dp), intent(inout) :: x(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, j, jx, kplus1, kx, l
logical(lk) :: noconj, nounit
! Intrinsic Functions
intrinsic :: conjg,max,min
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (.not.stdlib_lsame(trans,'N') .and. .not.stdlib_lsame(trans,'T') &
.and..not.stdlib_lsame(trans,'C')) then
info = 2
else if (.not.stdlib_lsame(diag,'U') .and. .not.stdlib_lsame(diag,'N')) then
info = 3
else if (n<0) then
info = 4
else if (k<0) then
info = 5
else if (lda< (k+1)) then
info = 7
else if (incx==0) then
info = 9
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZTBMV ',info)
return
end if
! quick return if possible.
if (n==0) return
noconj = stdlib_lsame(trans,'T')
nounit = stdlib_lsame(diag,'N')
! set up the start point in x if the increment is not unity. this
! will be ( n - 1 )*incx too small for descending loops.
if (incx<=0) then
kx = 1 - (n-1)*incx
else if (incx/=1) then
kx = 1
end if
! start the operations. in this version the elements of a are
! accessed sequentially with cone pass through a.
if (stdlib_lsame(trans,'N')) then
! form x := a*x.
if (stdlib_lsame(uplo,'U')) then
kplus1 = k + 1
if (incx==1) then
do j = 1,n
if (x(j)/=czero) then
temp = x(j)
l = kplus1 - j
do i = max(1,j-k),j - 1
x(i) = x(i) + temp*a(l+i,j)
end do
if (nounit) x(j) = x(j)*a(kplus1,j)
end if
end do
else
jx = kx
do j = 1,n
if (x(jx)/=czero) then
temp = x(jx)
ix = kx
l = kplus1 - j
do i = max(1,j-k),j - 1
x(ix) = x(ix) + temp*a(l+i,j)
ix = ix + incx
end do
if (nounit) x(jx) = x(jx)*a(kplus1,j)
end if
jx = jx + incx
if (j>k) kx = kx + incx
end do
end if
else
if (incx==1) then
do j = n,1,-1
if (x(j)/=czero) then
temp = x(j)
l = 1 - j
do i = min(n,j+k),j + 1,-1
x(i) = x(i) + temp*a(l+i,j)
end do
if (nounit) x(j) = x(j)*a(1,j)
end if
end do
else
kx = kx + (n-1)*incx
jx = kx
do j = n,1,-1
if (x(jx)/=czero) then
temp = x(jx)
ix = kx
l = 1 - j
do i = min(n,j+k),j + 1,-1
x(ix) = x(ix) + temp*a(l+i,j)
ix = ix - incx
end do
if (nounit) x(jx) = x(jx)*a(1,j)
end if
jx = jx - incx
if ((n-j)>=k) kx = kx - incx
end do
end if
end if
else
! form x := a**t*x or x := a**h*x.
if (stdlib_lsame(uplo,'U')) then
kplus1 = k + 1
if (incx==1) then
do j = n,1,-1
temp = x(j)
l = kplus1 - j
if (noconj) then
if (nounit) temp = temp*a(kplus1,j)
do i = j - 1,max(1,j-k),-1
temp = temp + a(l+i,j)*x(i)
end do
else
if (nounit) temp = temp*conjg(a(kplus1,j))
do i = j - 1,max(1,j-k),-1
temp = temp + conjg(a(l+i,j))*x(i)
end do
end if
x(j) = temp
end do
else
kx = kx + (n-1)*incx
jx = kx
do j = n,1,-1
temp = x(jx)
kx = kx - incx
ix = kx
l = kplus1 - j
if (noconj) then
if (nounit) temp = temp*a(kplus1,j)
do i = j - 1,max(1,j-k),-1
temp = temp + a(l+i,j)*x(ix)
ix = ix - incx
end do
else
if (nounit) temp = temp*conjg(a(kplus1,j))
do i = j - 1,max(1,j-k),-1
temp = temp + conjg(a(l+i,j))*x(ix)
ix = ix - incx
end do
end if
x(jx) = temp
jx = jx - incx
end do
end if
else
if (incx==1) then
do j = 1,n
temp = x(j)
l = 1 - j
if (noconj) then
if (nounit) temp = temp*a(1,j)
do i = j + 1,min(n,j+k)
temp = temp + a(l+i,j)*x(i)
end do
else
if (nounit) temp = temp*conjg(a(1,j))
do i = j + 1,min(n,j+k)
temp = temp + conjg(a(l+i,j))*x(i)
end do
end if
x(j) = temp
end do
else
jx = kx
do j = 1,n
temp = x(jx)
kx = kx + incx
ix = kx
l = 1 - j
if (noconj) then
if (nounit) temp = temp*a(1,j)
do i = j + 1,min(n,j+k)
temp = temp + a(l+i,j)*x(ix)
ix = ix + incx
end do
else
if (nounit) temp = temp*conjg(a(1,j))
do i = j + 1,min(n,j+k)
temp = temp + conjg(a(l+i,j))*x(ix)
ix = ix + incx
end do
end if
x(jx) = temp
jx = jx + incx
end do
end if
end if
end if
return
end subroutine stdlib${ii}$_ztbmv
pure subroutine stdlib${ii}$_ztbsv(uplo,trans,diag,n,k,a,lda,x,incx)
!! ZTBSV solves one of the systems of equations
!! A*x = b, or A**T*x = b, or A**H*x = b,
!! where b and x are n element vectors and A is an n by n unit, or
!! non-unit, upper or lower triangular band matrix, with ( k + 1 )
!! diagonals.
!! No test for singularity or near-singularity is included in this
!! routine. Such tests must be performed before calling this routine.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, k, lda, n
character, intent(in) :: diag, trans, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*)
complex(dp), intent(inout) :: x(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, j, jx, kplus1, kx, l
logical(lk) :: noconj, nounit
! Intrinsic Functions
intrinsic :: conjg,max,min
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (.not.stdlib_lsame(trans,'N') .and. .not.stdlib_lsame(trans,'T') &
.and..not.stdlib_lsame(trans,'C')) then
info = 2
else if (.not.stdlib_lsame(diag,'U') .and. .not.stdlib_lsame(diag,'N')) then
info = 3
else if (n<0) then
info = 4
else if (k<0) then
info = 5
else if (lda< (k+1)) then
info = 7
else if (incx==0) then
info = 9
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZTBSV ',info)
return
end if
! quick return if possible.
if (n==0) return
noconj = stdlib_lsame(trans,'T')
nounit = stdlib_lsame(diag,'N')
! set up the start point in x if the increment is not unity. this
! will be ( n - 1 )*incx too small for descending loops.
if (incx<=0) then
kx = 1 - (n-1)*incx
else if (incx/=1) then
kx = 1
end if
! start the operations. in this version the elements of a are
! accessed by sequentially with cone pass through a.
if (stdlib_lsame(trans,'N')) then
! form x := inv( a )*x.
if (stdlib_lsame(uplo,'U')) then
kplus1 = k + 1
if (incx==1) then
do j = n,1,-1
if (x(j)/=czero) then
l = kplus1 - j
if (nounit) x(j) = x(j)/a(kplus1,j)
temp = x(j)
do i = j - 1,max(1,j-k),-1
x(i) = x(i) - temp*a(l+i,j)
end do
end if
end do
else
kx = kx + (n-1)*incx
jx = kx
do j = n,1,-1
kx = kx - incx
if (x(jx)/=czero) then
ix = kx
l = kplus1 - j
if (nounit) x(jx) = x(jx)/a(kplus1,j)
temp = x(jx)
do i = j - 1,max(1,j-k),-1
x(ix) = x(ix) - temp*a(l+i,j)
ix = ix - incx
end do
end if
jx = jx - incx
end do
end if
else
if (incx==1) then
do j = 1,n
if (x(j)/=czero) then
l = 1 - j
if (nounit) x(j) = x(j)/a(1,j)
temp = x(j)
do i = j + 1,min(n,j+k)
x(i) = x(i) - temp*a(l+i,j)
end do
end if
end do
else
jx = kx
do j = 1,n
kx = kx + incx
if (x(jx)/=czero) then
ix = kx
l = 1 - j
if (nounit) x(jx) = x(jx)/a(1,j)
temp = x(jx)
do i = j + 1,min(n,j+k)
x(ix) = x(ix) - temp*a(l+i,j)
ix = ix + incx
end do
end if
jx = jx + incx
end do
end if
end if
else
! form x := inv( a**t )*x or x := inv( a**h )*x.
if (stdlib_lsame(uplo,'U')) then
kplus1 = k + 1
if (incx==1) then
do j = 1,n
temp = x(j)
l = kplus1 - j
if (noconj) then
do i = max(1,j-k),j - 1
temp = temp - a(l+i,j)*x(i)
end do
if (nounit) temp = temp/a(kplus1,j)
else
do i = max(1,j-k),j - 1
temp = temp - conjg(a(l+i,j))*x(i)
end do
if (nounit) temp = temp/conjg(a(kplus1,j))
end if
x(j) = temp
end do
else
jx = kx
do j = 1,n
temp = x(jx)
ix = kx
l = kplus1 - j
if (noconj) then
do i = max(1,j-k),j - 1
temp = temp - a(l+i,j)*x(ix)
ix = ix + incx
end do
if (nounit) temp = temp/a(kplus1,j)
else
do i = max(1,j-k),j - 1
temp = temp - conjg(a(l+i,j))*x(ix)
ix = ix + incx
end do
if (nounit) temp = temp/conjg(a(kplus1,j))
end if
x(jx) = temp
jx = jx + incx
if (j>k) kx = kx + incx
end do
end if
else
if (incx==1) then
do j = n,1,-1
temp = x(j)
l = 1 - j
if (noconj) then
do i = min(n,j+k),j + 1,-1
temp = temp - a(l+i,j)*x(i)
end do
if (nounit) temp = temp/a(1,j)
else
do i = min(n,j+k),j + 1,-1
temp = temp - conjg(a(l+i,j))*x(i)
end do
if (nounit) temp = temp/conjg(a(1,j))
end if
x(j) = temp
end do
else
kx = kx + (n-1)*incx
jx = kx
do j = n,1,-1
temp = x(jx)
ix = kx
l = 1 - j
if (noconj) then
do i = min(n,j+k),j + 1,-1
temp = temp - a(l+i,j)*x(ix)
ix = ix - incx
end do
if (nounit) temp = temp/a(1,j)
else
do i = min(n,j+k),j + 1,-1
temp = temp - conjg(a(l+i,j))*x(ix)
ix = ix - incx
end do
if (nounit) temp = temp/conjg(a(1,j))
end if
x(jx) = temp
jx = jx - incx
if ((n-j)>=k) kx = kx - incx
end do
end if
end if
end if
return
end subroutine stdlib${ii}$_ztbsv
pure subroutine stdlib${ii}$_ztpmv(uplo,trans,diag,n,ap,x,incx)
!! ZTPMV performs one of the matrix-vector operations
!! x := A*x, or x := A**T*x, or x := A**H*x,
!! where x is an n element vector and A is an n by n unit, or non-unit,
!! upper or lower triangular matrix, supplied in packed form.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, n
character, intent(in) :: diag, trans, uplo
! Array Arguments
complex(dp), intent(in) :: ap(*)
complex(dp), intent(inout) :: x(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, j, jx, k, kk, kx
logical(lk) :: noconj, nounit
! Intrinsic Functions
intrinsic :: conjg
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (.not.stdlib_lsame(trans,'N') .and. .not.stdlib_lsame(trans,'T') &
.and..not.stdlib_lsame(trans,'C')) then
info = 2
else if (.not.stdlib_lsame(diag,'U') .and. .not.stdlib_lsame(diag,'N')) then
info = 3
else if (n<0) then
info = 4
else if (incx==0) then
info = 7
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZTPMV ',info)
return
end if
! quick return if possible.
if (n==0) return
noconj = stdlib_lsame(trans,'T')
nounit = stdlib_lsame(diag,'N')
! set up the start point in x if the increment is not unity. this
! will be ( n - 1 )*incx too small for descending loops.
if (incx<=0) then
kx = 1 - (n-1)*incx
else if (incx/=1) then
kx = 1
end if
! start the operations. in this version the elements of ap are
! accessed sequentially with cone pass through ap.
if (stdlib_lsame(trans,'N')) then
! form x:= a*x.
if (stdlib_lsame(uplo,'U')) then
kk = 1
if (incx==1) then
do j = 1,n
if (x(j)/=czero) then
temp = x(j)
k = kk
do i = 1,j - 1
x(i) = x(i) + temp*ap(k)
k = k + 1
end do
if (nounit) x(j) = x(j)*ap(kk+j-1)
end if
kk = kk + j
end do
else
jx = kx
do j = 1,n
if (x(jx)/=czero) then
temp = x(jx)
ix = kx
do k = kk,kk + j - 2
x(ix) = x(ix) + temp*ap(k)
ix = ix + incx
end do
if (nounit) x(jx) = x(jx)*ap(kk+j-1)
end if
jx = jx + incx
kk = kk + j
end do
end if
else
kk = (n* (n+1))/2
if (incx==1) then
do j = n,1,-1
if (x(j)/=czero) then
temp = x(j)
k = kk
do i = n,j + 1,-1
x(i) = x(i) + temp*ap(k)
k = k - 1
end do
if (nounit) x(j) = x(j)*ap(kk-n+j)
end if
kk = kk - (n-j+1)
end do
else
kx = kx + (n-1)*incx
jx = kx
do j = n,1,-1
if (x(jx)/=czero) then
temp = x(jx)
ix = kx
do k = kk,kk - (n- (j+1)),-1
x(ix) = x(ix) + temp*ap(k)
ix = ix - incx
end do
if (nounit) x(jx) = x(jx)*ap(kk-n+j)
end if
jx = jx - incx
kk = kk - (n-j+1)
end do
end if
end if
else
! form x := a**t*x or x := a**h*x.
if (stdlib_lsame(uplo,'U')) then
kk = (n* (n+1))/2
if (incx==1) then
do j = n,1,-1
temp = x(j)
k = kk - 1
if (noconj) then
if (nounit) temp = temp*ap(kk)
do i = j - 1,1,-1
temp = temp + ap(k)*x(i)
k = k - 1
end do
else
if (nounit) temp = temp*conjg(ap(kk))
do i = j - 1,1,-1
temp = temp + conjg(ap(k))*x(i)
k = k - 1
end do
end if
x(j) = temp
kk = kk - j
end do
else
jx = kx + (n-1)*incx
do j = n,1,-1
temp = x(jx)
ix = jx
if (noconj) then
if (nounit) temp = temp*ap(kk)
do k = kk - 1,kk - j + 1,-1
ix = ix - incx
temp = temp + ap(k)*x(ix)
end do
else
if (nounit) temp = temp*conjg(ap(kk))
do k = kk - 1,kk - j + 1,-1
ix = ix - incx
temp = temp + conjg(ap(k))*x(ix)
end do
end if
x(jx) = temp
jx = jx - incx
kk = kk - j
end do
end if
else
kk = 1
if (incx==1) then
do j = 1,n
temp = x(j)
k = kk + 1
if (noconj) then
if (nounit) temp = temp*ap(kk)
do i = j + 1,n
temp = temp + ap(k)*x(i)
k = k + 1
end do
else
if (nounit) temp = temp*conjg(ap(kk))
do i = j + 1,n
temp = temp + conjg(ap(k))*x(i)
k = k + 1
end do
end if
x(j) = temp
kk = kk + (n-j+1)
end do
else
jx = kx
do j = 1,n
temp = x(jx)
ix = jx
if (noconj) then
if (nounit) temp = temp*ap(kk)
do k = kk + 1,kk + n - j
ix = ix + incx
temp = temp + ap(k)*x(ix)
end do
else
if (nounit) temp = temp*conjg(ap(kk))
do k = kk + 1,kk + n - j
ix = ix + incx
temp = temp + conjg(ap(k))*x(ix)
end do
end if
x(jx) = temp
jx = jx + incx
kk = kk + (n-j+1)
end do
end if
end if
end if
return
end subroutine stdlib${ii}$_ztpmv
pure subroutine stdlib${ii}$_ztpsv(uplo,trans,diag,n,ap,x,incx)
!! ZTPSV solves one of the systems of equations
!! A*x = b, or A**T*x = b, or A**H*x = b,
!! where b and x are n element vectors and A is an n by n unit, or
!! non-unit, upper or lower triangular matrix, supplied in packed form.
!! No test for singularity or near-singularity is included in this
!! routine. Such tests must be performed before calling this routine.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, n
character, intent(in) :: diag, trans, uplo
! Array Arguments
complex(dp), intent(in) :: ap(*)
complex(dp), intent(inout) :: x(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, j, jx, k, kk, kx
logical(lk) :: noconj, nounit
! Intrinsic Functions
intrinsic :: conjg
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (.not.stdlib_lsame(trans,'N') .and. .not.stdlib_lsame(trans,'T') &
.and..not.stdlib_lsame(trans,'C')) then
info = 2
else if (.not.stdlib_lsame(diag,'U') .and. .not.stdlib_lsame(diag,'N')) then
info = 3
else if (n<0) then
info = 4
else if (incx==0) then
info = 7
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZTPSV ',info)
return
end if
! quick return if possible.
if (n==0) return
noconj = stdlib_lsame(trans,'T')
nounit = stdlib_lsame(diag,'N')
! set up the start point in x if the increment is not unity. this
! will be ( n - 1 )*incx too small for descending loops.
if (incx<=0) then
kx = 1 - (n-1)*incx
else if (incx/=1) then
kx = 1
end if
! start the operations. in this version the elements of ap are
! accessed sequentially with cone pass through ap.
if (stdlib_lsame(trans,'N')) then
! form x := inv( a )*x.
if (stdlib_lsame(uplo,'U')) then
kk = (n* (n+1))/2
if (incx==1) then
do j = n,1,-1
if (x(j)/=czero) then
if (nounit) x(j) = x(j)/ap(kk)
temp = x(j)
k = kk - 1
do i = j - 1,1,-1
x(i) = x(i) - temp*ap(k)
k = k - 1
end do
end if
kk = kk - j
end do
else
jx = kx + (n-1)*incx
do j = n,1,-1
if (x(jx)/=czero) then
if (nounit) x(jx) = x(jx)/ap(kk)
temp = x(jx)
ix = jx
do k = kk - 1,kk - j + 1,-1
ix = ix - incx
x(ix) = x(ix) - temp*ap(k)
end do
end if
jx = jx - incx
kk = kk - j
end do
end if
else
kk = 1
if (incx==1) then
do j = 1,n
if (x(j)/=czero) then
if (nounit) x(j) = x(j)/ap(kk)
temp = x(j)
k = kk + 1
do i = j + 1,n
x(i) = x(i) - temp*ap(k)
k = k + 1
end do
end if
kk = kk + (n-j+1)
end do
else
jx = kx
do j = 1,n
if (x(jx)/=czero) then
if (nounit) x(jx) = x(jx)/ap(kk)
temp = x(jx)
ix = jx
do k = kk + 1,kk + n - j
ix = ix + incx
x(ix) = x(ix) - temp*ap(k)
end do
end if
jx = jx + incx
kk = kk + (n-j+1)
end do
end if
end if
else
! form x := inv( a**t )*x or x := inv( a**h )*x.
if (stdlib_lsame(uplo,'U')) then
kk = 1
if (incx==1) then
do j = 1,n
temp = x(j)
k = kk
if (noconj) then
do i = 1,j - 1
temp = temp - ap(k)*x(i)
k = k + 1
end do
if (nounit) temp = temp/ap(kk+j-1)
else
do i = 1,j - 1
temp = temp - conjg(ap(k))*x(i)
k = k + 1
end do
if (nounit) temp = temp/conjg(ap(kk+j-1))
end if
x(j) = temp
kk = kk + j
end do
else
jx = kx
do j = 1,n
temp = x(jx)
ix = kx
if (noconj) then
do k = kk,kk + j - 2
temp = temp - ap(k)*x(ix)
ix = ix + incx
end do
if (nounit) temp = temp/ap(kk+j-1)
else
do k = kk,kk + j - 2
temp = temp - conjg(ap(k))*x(ix)
ix = ix + incx
end do
if (nounit) temp = temp/conjg(ap(kk+j-1))
end if
x(jx) = temp
jx = jx + incx
kk = kk + j
end do
end if
else
kk = (n* (n+1))/2
if (incx==1) then
do j = n,1,-1
temp = x(j)
k = kk
if (noconj) then
do i = n,j + 1,-1
temp = temp - ap(k)*x(i)
k = k - 1
end do
if (nounit) temp = temp/ap(kk-n+j)
else
do i = n,j + 1,-1
temp = temp - conjg(ap(k))*x(i)
k = k - 1
end do
if (nounit) temp = temp/conjg(ap(kk-n+j))
end if
x(j) = temp
kk = kk - (n-j+1)
end do
else
kx = kx + (n-1)*incx
jx = kx
do j = n,1,-1
temp = x(jx)
ix = kx
if (noconj) then
do k = kk,kk - (n- (j+1)),-1
temp = temp - ap(k)*x(ix)
ix = ix - incx
end do
if (nounit) temp = temp/ap(kk-n+j)
else
do k = kk,kk - (n- (j+1)),-1
temp = temp - conjg(ap(k))*x(ix)
ix = ix - incx
end do
if (nounit) temp = temp/conjg(ap(kk-n+j))
end if
x(jx) = temp
jx = jx - incx
kk = kk - (n-j+1)
end do
end if
end if
end if
return
end subroutine stdlib${ii}$_ztpsv
pure subroutine stdlib${ii}$_ztrmm(side,uplo,transa,diag,m,n,alpha,a,lda,b,ldb)
!! ZTRMM performs one of the matrix-matrix operations
!! B := alpha*op( A )*B, or B := alpha*B*op( A )
!! where alpha is a scalar, B is an m by n matrix, A is a unit, or
!! non-unit, upper or lower triangular matrix and op( A ) is one of
!! op( A ) = A or op( A ) = A**T or op( A ) = A**H.
! -- reference blas level3 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha
integer(${ik}$), intent(in) :: lda, ldb, m, n
character, intent(in) :: diag, side, transa, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*)
complex(dp), intent(inout) :: b(ldb,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: conjg,max
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, j, k, nrowa
logical(lk) :: lside, noconj, nounit, upper
! test the input parameters.
lside = stdlib_lsame(side,'L')
if (lside) then
nrowa = m
else
nrowa = n
end if
noconj = stdlib_lsame(transa,'T')
nounit = stdlib_lsame(diag,'N')
upper = stdlib_lsame(uplo,'U')
info = 0
if ((.not.lside) .and. (.not.stdlib_lsame(side,'R'))) then
info = 1
else if ((.not.upper) .and. (.not.stdlib_lsame(uplo,'L'))) then
info = 2
else if ((.not.stdlib_lsame(transa,'N')) .and.(.not.stdlib_lsame(transa,'T')) .and.(&
.not.stdlib_lsame(transa,'C'))) then
info = 3
else if ((.not.stdlib_lsame(diag,'U')) .and. (.not.stdlib_lsame(diag,'N'))) &
then
info = 4
else if (m<0) then
info = 5
else if (n<0) then
info = 6
else if (lda<max(1,nrowa)) then
info = 9
else if (ldb<max(1,m)) then
info = 11
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZTRMM ',info)
return
end if
! quick return if possible.
if (m==0 .or. n==0) return
! and when alpha.eq.czero.
if (alpha==czero) then
do j = 1,n
do i = 1,m
b(i,j) = czero
end do
end do
return
end if
! start the operations.
if (lside) then
if (stdlib_lsame(transa,'N')) then
! form b := alpha*a*b.
if (upper) then
do j = 1,n
do k = 1,m
if (b(k,j)/=czero) then
temp = alpha*b(k,j)
do i = 1,k - 1
b(i,j) = b(i,j) + temp*a(i,k)
end do
if (nounit) temp = temp*a(k,k)
b(k,j) = temp
end if
end do
end do
else
do j = 1,n
do k = m,1,-1
if (b(k,j)/=czero) then
temp = alpha*b(k,j)
b(k,j) = temp
if (nounit) b(k,j) = b(k,j)*a(k,k)
do i = k + 1,m
b(i,j) = b(i,j) + temp*a(i,k)
end do
end if
end do
end do
end if
else
! form b := alpha*a**t*b or b := alpha*a**h*b.
if (upper) then
do j = 1,n
do i = m,1,-1
temp = b(i,j)
if (noconj) then
if (nounit) temp = temp*a(i,i)
do k = 1,i - 1
temp = temp + a(k,i)*b(k,j)
end do
else
if (nounit) temp = temp*conjg(a(i,i))
do k = 1,i - 1
temp = temp + conjg(a(k,i))*b(k,j)
end do
end if
b(i,j) = alpha*temp
end do
end do
else
do j = 1,n
do i = 1,m
temp = b(i,j)
if (noconj) then
if (nounit) temp = temp*a(i,i)
do k = i + 1,m
temp = temp + a(k,i)*b(k,j)
end do
else
if (nounit) temp = temp*conjg(a(i,i))
do k = i + 1,m
temp = temp + conjg(a(k,i))*b(k,j)
end do
end if
b(i,j) = alpha*temp
end do
end do
end if
end if
else
if (stdlib_lsame(transa,'N')) then
! form b := alpha*b*a.
if (upper) then
do j = n,1,-1
temp = alpha
if (nounit) temp = temp*a(j,j)
do i = 1,m
b(i,j) = temp*b(i,j)
end do
do k = 1,j - 1
if (a(k,j)/=czero) then
temp = alpha*a(k,j)
do i = 1,m
b(i,j) = b(i,j) + temp*b(i,k)
end do
end if
end do
end do
else
do j = 1,n
temp = alpha
if (nounit) temp = temp*a(j,j)
do i = 1,m
b(i,j) = temp*b(i,j)
end do
do k = j + 1,n
if (a(k,j)/=czero) then
temp = alpha*a(k,j)
do i = 1,m
b(i,j) = b(i,j) + temp*b(i,k)
end do
end if
end do
end do
end if
else
! form b := alpha*b*a**t or b := alpha*b*a**h.
if (upper) then
loop_280: do k = 1,n
do j = 1,k - 1
if (a(j,k)/=czero) then
if (noconj) then
temp = alpha*a(j,k)
else
temp = alpha*conjg(a(j,k))
end if
do i = 1,m
b(i,j) = b(i,j) + temp*b(i,k)
end do
end if
end do
temp = alpha
if (nounit) then
if (noconj) then
temp = temp*a(k,k)
else
temp = temp*conjg(a(k,k))
end if
end if
if (temp/=cone) then
do i = 1,m
b(i,k) = temp*b(i,k)
end do
end if
end do loop_280
else
loop_320: do k = n,1,-1
do j = k + 1,n
if (a(j,k)/=czero) then
if (noconj) then
temp = alpha*a(j,k)
else
temp = alpha*conjg(a(j,k))
end if
do i = 1,m
b(i,j) = b(i,j) + temp*b(i,k)
end do
end if
end do
temp = alpha
if (nounit) then
if (noconj) then
temp = temp*a(k,k)
else
temp = temp*conjg(a(k,k))
end if
end if
if (temp/=cone) then
do i = 1,m
b(i,k) = temp*b(i,k)
end do
end if
end do loop_320
end if
end if
end if
return
end subroutine stdlib${ii}$_ztrmm
pure subroutine stdlib${ii}$_ztrmv(uplo,trans,diag,n,a,lda,x,incx)
!! ZTRMV performs one of the matrix-vector operations
!! x := A*x, or x := A**T*x, or x := A**H*x,
!! where x is an n element vector and A is an n by n unit, or non-unit,
!! upper or lower triangular matrix.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, lda, n
character, intent(in) :: diag, trans, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*)
complex(dp), intent(inout) :: x(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, j, jx, kx
logical(lk) :: noconj, nounit
! Intrinsic Functions
intrinsic :: conjg,max
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (.not.stdlib_lsame(trans,'N') .and. .not.stdlib_lsame(trans,'T') &
.and..not.stdlib_lsame(trans,'C')) then
info = 2
else if (.not.stdlib_lsame(diag,'U') .and. .not.stdlib_lsame(diag,'N')) then
info = 3
else if (n<0) then
info = 4
else if (lda<max(1,n)) then
info = 6
else if (incx==0) then
info = 8
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZTRMV ',info)
return
end if
! quick return if possible.
if (n==0) return
noconj = stdlib_lsame(trans,'T')
nounit = stdlib_lsame(diag,'N')
! set up the start point in x if the increment is not unity. this
! will be ( n - 1 )*incx too small for descending loops.
if (incx<=0) then
kx = 1 - (n-1)*incx
else if (incx/=1) then
kx = 1
end if
! start the operations. in this version the elements of a are
! accessed sequentially with cone pass through a.
if (stdlib_lsame(trans,'N')) then
! form x := a*x.
if (stdlib_lsame(uplo,'U')) then
if (incx==1) then
do j = 1,n
if (x(j)/=czero) then
temp = x(j)
do i = 1,j - 1
x(i) = x(i) + temp*a(i,j)
end do
if (nounit) x(j) = x(j)*a(j,j)
end if
end do
else
jx = kx
do j = 1,n
if (x(jx)/=czero) then
temp = x(jx)
ix = kx
do i = 1,j - 1
x(ix) = x(ix) + temp*a(i,j)
ix = ix + incx
end do
if (nounit) x(jx) = x(jx)*a(j,j)
end if
jx = jx + incx
end do
end if
else
if (incx==1) then
do j = n,1,-1
if (x(j)/=czero) then
temp = x(j)
do i = n,j + 1,-1
x(i) = x(i) + temp*a(i,j)
end do
if (nounit) x(j) = x(j)*a(j,j)
end if
end do
else
kx = kx + (n-1)*incx
jx = kx
do j = n,1,-1
if (x(jx)/=czero) then
temp = x(jx)
ix = kx
do i = n,j + 1,-1
x(ix) = x(ix) + temp*a(i,j)
ix = ix - incx
end do
if (nounit) x(jx) = x(jx)*a(j,j)
end if
jx = jx - incx
end do
end if
end if
else
! form x := a**t*x or x := a**h*x.
if (stdlib_lsame(uplo,'U')) then
if (incx==1) then
do j = n,1,-1
temp = x(j)
if (noconj) then
if (nounit) temp = temp*a(j,j)
do i = j - 1,1,-1
temp = temp + a(i,j)*x(i)
end do
else
if (nounit) temp = temp*conjg(a(j,j))
do i = j - 1,1,-1
temp = temp + conjg(a(i,j))*x(i)
end do
end if
x(j) = temp
end do
else
jx = kx + (n-1)*incx
do j = n,1,-1
temp = x(jx)
ix = jx
if (noconj) then
if (nounit) temp = temp*a(j,j)
do i = j - 1,1,-1
ix = ix - incx
temp = temp + a(i,j)*x(ix)
end do
else
if (nounit) temp = temp*conjg(a(j,j))
do i = j - 1,1,-1
ix = ix - incx
temp = temp + conjg(a(i,j))*x(ix)
end do
end if
x(jx) = temp
jx = jx - incx
end do
end if
else
if (incx==1) then
do j = 1,n
temp = x(j)
if (noconj) then
if (nounit) temp = temp*a(j,j)
do i = j + 1,n
temp = temp + a(i,j)*x(i)
end do
else
if (nounit) temp = temp*conjg(a(j,j))
do i = j + 1,n
temp = temp + conjg(a(i,j))*x(i)
end do
end if
x(j) = temp
end do
else
jx = kx
do j = 1,n
temp = x(jx)
ix = jx
if (noconj) then
if (nounit) temp = temp*a(j,j)
do i = j + 1,n
ix = ix + incx
temp = temp + a(i,j)*x(ix)
end do
else
if (nounit) temp = temp*conjg(a(j,j))
do i = j + 1,n
ix = ix + incx
temp = temp + conjg(a(i,j))*x(ix)
end do
end if
x(jx) = temp
jx = jx + incx
end do
end if
end if
end if
return
end subroutine stdlib${ii}$_ztrmv
pure subroutine stdlib${ii}$_ztrsm(side,uplo,transa,diag,m,n,alpha,a,lda,b,ldb)
!! ZTRSM solves one of the matrix equations
!! op( A )*X = alpha*B, or X*op( A ) = alpha*B,
!! where alpha is a scalar, X and B are m by n matrices, A is a unit, or
!! non-unit, upper or lower triangular matrix and op( A ) is one of
!! op( A ) = A or op( A ) = A**T or op( A ) = A**H.
!! The matrix X is overwritten on B.
! -- reference blas level3 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
complex(dp), intent(in) :: alpha
integer(${ik}$), intent(in) :: lda, ldb, m, n
character, intent(in) :: diag, side, transa, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*)
complex(dp), intent(inout) :: b(ldb,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: conjg,max
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, j, k, nrowa
logical(lk) :: lside, noconj, nounit, upper
! test the input parameters.
lside = stdlib_lsame(side,'L')
if (lside) then
nrowa = m
else
nrowa = n
end if
noconj = stdlib_lsame(transa,'T')
nounit = stdlib_lsame(diag,'N')
upper = stdlib_lsame(uplo,'U')
info = 0
if ((.not.lside) .and. (.not.stdlib_lsame(side,'R'))) then
info = 1
else if ((.not.upper) .and. (.not.stdlib_lsame(uplo,'L'))) then
info = 2
else if ((.not.stdlib_lsame(transa,'N')) .and.(.not.stdlib_lsame(transa,'T')) .and.(&
.not.stdlib_lsame(transa,'C'))) then
info = 3
else if ((.not.stdlib_lsame(diag,'U')) .and. (.not.stdlib_lsame(diag,'N'))) &
then
info = 4
else if (m<0) then
info = 5
else if (n<0) then
info = 6
else if (lda<max(1,nrowa)) then
info = 9
else if (ldb<max(1,m)) then
info = 11
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZTRSM ',info)
return
end if
! quick return if possible.
if (m==0 .or. n==0) return
! and when alpha.eq.czero.
if (alpha==czero) then
do j = 1,n
do i = 1,m
b(i,j) = czero
end do
end do
return
end if
! start the operations.
if (lside) then
if (stdlib_lsame(transa,'N')) then
! form b := alpha*inv( a )*b.
if (upper) then
do j = 1,n
if (alpha/=cone) then
do i = 1,m
b(i,j) = alpha*b(i,j)
end do
end if
do k = m,1,-1
if (b(k,j)/=czero) then
if (nounit) b(k,j) = b(k,j)/a(k,k)
do i = 1,k - 1
b(i,j) = b(i,j) - b(k,j)*a(i,k)
end do
end if
end do
end do
else
do j = 1,n
if (alpha/=cone) then
do i = 1,m
b(i,j) = alpha*b(i,j)
end do
end if
do k = 1,m
if (b(k,j)/=czero) then
if (nounit) b(k,j) = b(k,j)/a(k,k)
do i = k + 1,m
b(i,j) = b(i,j) - b(k,j)*a(i,k)
end do
end if
end do
end do
end if
else
! form b := alpha*inv( a**t )*b
! or b := alpha*inv( a**h )*b.
if (upper) then
do j = 1,n
do i = 1,m
temp = alpha*b(i,j)
if (noconj) then
do k = 1,i - 1
temp = temp - a(k,i)*b(k,j)
end do
if (nounit) temp = temp/a(i,i)
else
do k = 1,i - 1
temp = temp - conjg(a(k,i))*b(k,j)
end do
if (nounit) temp = temp/conjg(a(i,i))
end if
b(i,j) = temp
end do
end do
else
do j = 1,n
do i = m,1,-1
temp = alpha*b(i,j)
if (noconj) then
do k = i + 1,m
temp = temp - a(k,i)*b(k,j)
end do
if (nounit) temp = temp/a(i,i)
else
do k = i + 1,m
temp = temp - conjg(a(k,i))*b(k,j)
end do
if (nounit) temp = temp/conjg(a(i,i))
end if
b(i,j) = temp
end do
end do
end if
end if
else
if (stdlib_lsame(transa,'N')) then
! form b := alpha*b*inv( a ).
if (upper) then
do j = 1,n
if (alpha/=cone) then
do i = 1,m
b(i,j) = alpha*b(i,j)
end do
end if
do k = 1,j - 1
if (a(k,j)/=czero) then
do i = 1,m
b(i,j) = b(i,j) - a(k,j)*b(i,k)
end do
end if
end do
if (nounit) then
temp = cone/a(j,j)
do i = 1,m
b(i,j) = temp*b(i,j)
end do
end if
end do
else
do j = n,1,-1
if (alpha/=cone) then
do i = 1,m
b(i,j) = alpha*b(i,j)
end do
end if
do k = j + 1,n
if (a(k,j)/=czero) then
do i = 1,m
b(i,j) = b(i,j) - a(k,j)*b(i,k)
end do
end if
end do
if (nounit) then
temp = cone/a(j,j)
do i = 1,m
b(i,j) = temp*b(i,j)
end do
end if
end do
end if
else
! form b := alpha*b*inv( a**t )
! or b := alpha*b*inv( a**h ).
if (upper) then
loop_330: do k = n,1,-1
if (nounit) then
if (noconj) then
temp = cone/a(k,k)
else
temp = cone/conjg(a(k,k))
end if
do i = 1,m
b(i,k) = temp*b(i,k)
end do
end if
do j = 1,k - 1
if (a(j,k)/=czero) then
if (noconj) then
temp = a(j,k)
else
temp = conjg(a(j,k))
end if
do i = 1,m
b(i,j) = b(i,j) - temp*b(i,k)
end do
end if
end do
if (alpha/=cone) then
do i = 1,m
b(i,k) = alpha*b(i,k)
end do
end if
end do loop_330
else
loop_380: do k = 1,n
if (nounit) then
if (noconj) then
temp = cone/a(k,k)
else
temp = cone/conjg(a(k,k))
end if
do i = 1,m
b(i,k) = temp*b(i,k)
end do
end if
do j = k + 1,n
if (a(j,k)/=czero) then
if (noconj) then
temp = a(j,k)
else
temp = conjg(a(j,k))
end if
do i = 1,m
b(i,j) = b(i,j) - temp*b(i,k)
end do
end if
end do
if (alpha/=cone) then
do i = 1,m
b(i,k) = alpha*b(i,k)
end do
end if
end do loop_380
end if
end if
end if
return
end subroutine stdlib${ii}$_ztrsm
pure subroutine stdlib${ii}$_ztrsv(uplo,trans,diag,n,a,lda,x,incx)
!! ZTRSV solves one of the systems of equations
!! A*x = b, or A**T*x = b, or A**H*x = b,
!! where b and x are n element vectors and A is an n by n unit, or
!! non-unit, upper or lower triangular matrix.
!! No test for singularity or near-singularity is included in this
!! routine. Such tests must be performed before calling this routine.
! -- reference blas level2 routine --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! Scalar Arguments
integer(${ik}$), intent(in) :: incx, lda, n
character, intent(in) :: diag, trans, uplo
! Array Arguments
complex(dp), intent(in) :: a(lda,*)
complex(dp), intent(inout) :: x(*)
! =====================================================================
! Local Scalars
complex(dp) :: temp
integer(${ik}$) :: i, info, ix, j, jx, kx
logical(lk) :: noconj, nounit
! Intrinsic Functions
intrinsic :: conjg,max
! test the input parameters.
info = 0
if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
info = 1
else if (.not.stdlib_lsame(trans,'N') .and. .not.stdlib_lsame(trans,'T') &
.and..not.stdlib_lsame(trans,'C')) then
info = 2
else if (.not.stdlib_lsame(diag,'U') .and. .not.stdlib_lsame(diag,'N')) then
info = 3
else if (n<0) then
info = 4
else if (lda<max(1,n)) then
info = 6
else if (incx==0) then
info = 8
end if
if (info/=0) then
call stdlib${ii}$_xerbla('ZTRSV ',info)
return
end if
! quick return if possible.
if (n==0) return
noconj = stdlib_lsame(trans,'T')
nounit = stdlib_lsame(diag,'N')
! set up the start point in x if the increment is not unity. this
! will be ( n - 1 )*incx too small for descending loops.
if (incx<=0) then
kx = 1 - (n-1)*incx
else if (incx/=1) then
kx = 1
end if
! start the operations. in this version the elements of a are
! accessed sequentially with cone pass through a.
if (stdlib_lsame(trans,'N')) then
! form x := inv( a )*x.
if (stdlib_lsame(uplo,'U')) then
if (incx==1) then
do j = n,1,-1
if (x(j)/=czero) then
if (nounit) x(j) = x(j)/a(j,j)
temp = x(j)
do i = j - 1,1,-1
x(i) = x(i) - temp*a(i,j)
end do
end if
end do
else
jx = kx + (n-1)*incx
do j = n,1,-1
if (x(jx)/=czero) then
if (nounit) x(jx) = x(jx)/a(j,j)
temp = x(jx)
ix = jx
do i = j - 1,1,-1
ix = ix - incx
x(ix) = x(ix) - temp*a(i,j)
end do
end if
jx = jx - incx
end do
end if
else
if (incx==1) then
do j = 1,n
if (x(j)/=czero) then
if (nounit) x(j) = x(j)/a(j,j)
temp = x(j)
do i = j + 1,n
x(i) = x(i) - temp*a(i,j)
end do
end if
end do
else
jx = kx
do j = 1,n
if (x(jx)/=czero) then
if (nounit) x(jx) = x(jx)/a(j,j)
temp = x(jx)
ix = jx
do i = j + 1,n
ix = ix + incx
x(ix) = x(ix) - temp*a(i,j)
end do
end if
jx = jx + incx
end do
end if
end if
else
! form x := inv( a**t )*x or x := inv( a**h )*x.
if (stdlib_lsame(uplo,'U')) then
if (incx==1) then
do j = 1,n
temp = x(j)
if (noconj) then
do i = 1,j - 1
temp = temp - a(i,j)*x(i)
end do
if (nounit) temp = temp/a(j,j)
else
do i = 1,j - 1
temp = temp - conjg(a(i,j))*x(i)
end do
if (nounit) temp = temp/conjg(a(j,j))
end if
x(j) = temp
end do
else
jx = kx
do j = 1,n
ix = kx
temp = x(jx)
if (noconj) then
do i = 1,j - 1
temp = temp - a(i,j)*x(ix)
ix = ix + incx
end do
if (nounit) temp = temp/a(j,j)
else
do i = 1,j - 1
temp = temp - conjg(a(i,j))*x(ix)
ix = ix + incx
end do
if (nounit) temp = temp/conjg(a(j,j))
end if
x(jx) = temp
jx = jx + incx
end do
end if
else
if (incx==1) then
do j = n,1,-1
temp = x(j)
if (noconj) then
do i = n,j + 1,-1
temp = temp - a(i,j)*x(i)
end do
if (nounit) temp = temp/a(j,j)
else
do i = n,j + 1,-1
temp = temp - conjg(a(i,j))*x(i)
end do
if (nounit) temp = temp/conjg(a(j,j))
end if
x(j) = temp
end do
else
kx = kx + (n-1)*incx
jx = kx
do j = n,1,-1
ix = kx
temp = x(jx)
if (noconj) then
do i = n,j + 1,-1
temp = temp - a(i,j)*x(ix)
ix = ix - incx
end do
if (nounit) temp = temp/a(j,j)
else
do i = n,j + 1,-1
temp = temp - conjg(a(i,j))*x(ix)
ix = ix - incx
end do
if (nounit) temp = temp/conjg(a(j,j))
end if
x(jx) = temp
jx = jx - incx
end do
end if
end if
end if
return
end subroutine stdlib${ii}$_ztrsv
#:endfor
end module stdlib_linalg_blas_z
