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stdlib_linalg_blas_q.fypp
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#:include "common.fypp"
#:if WITH_QP
module stdlib_linalg_blas_q
use stdlib_linalg_constants
use stdlib_linalg_blas_aux
use stdlib_linalg_blas_s
use stdlib_linalg_blas_c
use stdlib_linalg_blas_d
use stdlib_linalg_blas_z
implicit none(type,external)
private
public :: sp,dp,qp,lk,ilp
public :: stdlib_qasum
public :: stdlib_qaxpy
public :: stdlib_qcopy
public :: stdlib_qdot
public :: stdlib_qgbmv
public :: stdlib_qgemm
public :: stdlib_qgemv
public :: stdlib_qger
public :: stdlib_qnrm2
public :: stdlib_qrot
public :: stdlib_qrotg
public :: stdlib_qrotm
public :: stdlib_qrotmg
public :: stdlib_qsbmv
public :: stdlib_qscal
public :: stdlib_qsdot
public :: stdlib_qspmv
public :: stdlib_qspr
public :: stdlib_qspr2
public :: stdlib_qswap
public :: stdlib_qsymm
public :: stdlib_qsymv
public :: stdlib_qsyr
public :: stdlib_qsyr2
public :: stdlib_qsyr2k
public :: stdlib_qsyrk
public :: stdlib_qtbmv
public :: stdlib_qtbsv
public :: stdlib_qtpmv
public :: stdlib_qtpsv
public :: stdlib_qtrmm
public :: stdlib_qtrmv
public :: stdlib_qtrsm
public :: stdlib_qtrsv
public :: stdlib_qzasum
public :: stdlib_qznrm2
! 128-bit real constants
real(qp), parameter, private :: negone = -1.00_qp
real(qp), parameter, private :: zero = 0.00_qp
real(qp), parameter, private :: half = 0.50_qp
real(qp), parameter, private :: one = 1.00_qp
real(qp), parameter, private :: two = 2.00_qp
real(qp), parameter, private :: three = 3.00_qp
real(qp), parameter, private :: four = 4.00_qp
real(qp), parameter, private :: eight = 8.00_qp
real(qp), parameter, private :: ten = 10.00_qp
! 128-bit complex constants
complex(qp), parameter, private :: czero = ( 0.0_qp,0.0_qp)
complex(qp), parameter, private :: chalf = ( 0.5_qp,0.0_qp)
complex(qp), parameter, private :: cone = ( 1.0_qp,0.0_qp)
complex(qp), parameter, private :: cnegone = (-1.0_qp,0.0_qp)
! 128-bit scaling constants
integer, parameter, private :: maxexp = maxexponent(zero)
integer, parameter, private :: minexp = minexponent(zero)
real(qp), parameter, private :: rradix = real(radix(zero),qp)
real(qp), parameter, private :: ulp = epsilon(zero)
real(qp), parameter, private :: eps = ulp*half
real(qp), parameter, private :: safmin = rradix**max(minexp-1,1-maxexp)
real(qp), parameter, private :: safmax = one/safmin
real(qp), parameter, private :: smlnum = safmin/ulp
real(qp), parameter, private :: bignum = safmax*ulp
real(qp), parameter, private :: rtmin = sqrt(smlnum)
real(qp), parameter, private :: rtmax = sqrt(bignum)
! 128-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(qp), parameter, private :: tsml = rradix**ceiling((minexp-1)*half)
real(qp), parameter, private :: tbig = rradix**floor((maxexp-digits(zero)+1)*half)
real(qp), parameter, private :: ssml = rradix**(-floor((minexp-digits(zero))*half))
real(qp), parameter, private :: sbig = rradix**(-ceiling((maxexp+digits(zero)-1)*half))
contains
pure real(qp) function stdlib_qasum(n,dx,incx)
!! DASUM: takes the sum of the absolute values.
! -- 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(ilp), intent(in) :: incx, n
! Array Arguments
real(qp), intent(in) :: dx(*)
! =====================================================================
! Local Scalars
real(qp) :: dtemp
integer(ilp) :: i, m, mp1, nincx
! Intrinsic Functions
intrinsic :: abs,mod
stdlib_qasum = zero
dtemp = zero
if (n<=0 .or. incx<=0) return
if (incx==1) then
! code for increment equal to 1
! clean-up loop
m = mod(n,6)
if (m/=0) then
do i = 1,m
dtemp = dtemp + abs(dx(i))
end do
if (n<6) then
stdlib_qasum = dtemp
return
end if
end if
mp1 = m + 1
do i = mp1,n,6
dtemp = dtemp + abs(dx(i)) + abs(dx(i+1)) +abs(dx(i+2)) + abs(dx(i+3)) +abs(dx(i+&
4)) + abs(dx(i+5))
end do
else
! code for increment not equal to 1
nincx = n*incx
do i = 1,nincx,incx
dtemp = dtemp + abs(dx(i))
end do
end if
stdlib_qasum = dtemp
return
end function stdlib_qasum
pure subroutine stdlib_qaxpy(n,da,dx,incx,dy,incy)
!! DAXPY: constant times a vector plus a vector.
!! uses unrolled loops for increments equal to one.
! -- 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(qp), intent(in) :: da
integer(ilp), intent(in) :: incx, incy, n
! Array Arguments
real(qp), intent(in) :: dx(*)
real(qp), intent(inout) :: dy(*)
! =====================================================================
! Local Scalars
integer(ilp) :: i, ix, iy, m, mp1
! Intrinsic Functions
intrinsic :: mod
if (n<=0) return
if (da==0.0_qp) return
if (incx==1 .and. incy==1) then
! code for both increments equal to 1
! clean-up loop
m = mod(n,4)
if (m/=0) then
do i = 1,m
dy(i) = dy(i) + da*dx(i)
end do
end if
if (n<4) return
mp1 = m + 1
do i = mp1,n,4
dy(i) = dy(i) + da*dx(i)
dy(i+1) = dy(i+1) + da*dx(i+1)
dy(i+2) = dy(i+2) + da*dx(i+2)
dy(i+3) = dy(i+3) + da*dx(i+3)
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
dy(iy) = dy(iy) + da*dx(ix)
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib_qaxpy
pure subroutine stdlib_qcopy(n,dx,incx,dy,incy)
!! DCOPY: copies a vector, x, to a vector, y.
!! uses unrolled loops for increments equal to 1.
! -- 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(ilp), intent(in) :: incx, incy, n
! Array Arguments
real(qp), intent(in) :: dx(*)
real(qp), intent(out) :: dy(*)
! =====================================================================
! Local Scalars
integer(ilp) :: i, ix, iy, m, mp1
! Intrinsic Functions
intrinsic :: mod
if (n<=0) return
if (incx==1 .and. incy==1) then
! code for both increments equal to 1
! clean-up loop
m = mod(n,7)
if (m/=0) then
do i = 1,m
dy(i) = dx(i)
end do
if (n<7) return
end if
mp1 = m + 1
do i = mp1,n,7
dy(i) = dx(i)
dy(i+1) = dx(i+1)
dy(i+2) = dx(i+2)
dy(i+3) = dx(i+3)
dy(i+4) = dx(i+4)
dy(i+5) = dx(i+5)
dy(i+6) = dx(i+6)
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
dy(iy) = dx(ix)
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib_qcopy
pure real(qp) function stdlib_qdot(n,dx,incx,dy,incy)
!! DDOT: forms the dot product of two vectors.
!! uses unrolled loops for increments equal to one.
! -- 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(ilp), intent(in) :: incx, incy, n
! Array Arguments
real(qp), intent(in) :: dx(*), dy(*)
! =====================================================================
! Local Scalars
real(qp) :: dtemp
integer(ilp) :: i, ix, iy, m, mp1
! Intrinsic Functions
intrinsic :: mod
stdlib_qdot = zero
dtemp = zero
if (n<=0) return
if (incx==1 .and. incy==1) then
! code for both increments equal to 1
! clean-up loop
m = mod(n,5)
if (m/=0) then
do i = 1,m
dtemp = dtemp + dx(i)*dy(i)
end do
if (n<5) then
stdlib_qdot=dtemp
return
end if
end if
mp1 = m + 1
do i = mp1,n,5
dtemp = dtemp + dx(i)*dy(i) + dx(i+1)*dy(i+1) +dx(i+2)*dy(i+2) + dx(i+3)*dy(i+3) + &
dx(i+4)*dy(i+4)
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
dtemp = dtemp + dx(ix)*dy(iy)
ix = ix + incx
iy = iy + incy
end do
end if
stdlib_qdot = dtemp
return
end function stdlib_qdot
pure subroutine stdlib_qgbmv(trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy)
!! DGBMV: performs one of the matrix-vector operations
!! y := alpha*A*x + beta*y, or y := alpha*A**T*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
real(qp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: incx, incy, kl, ku, lda, m, n
character, intent(in) :: trans
! Array Arguments
real(qp), intent(in) :: a(lda,*), x(*)
real(qp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
real(qp) :: temp
integer(ilp) :: i, info, ix, iy, j, jx, jy, k, kup1, kx, ky, lenx, leny
! Intrinsic Functions
intrinsic :: 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_xerbla('DGBMV ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or.((alpha==zero).and. (beta==one))) return
! 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 one pass through the band part of a.
! first form y := beta*y.
if (beta/=one) then
if (incy==1) then
if (beta==zero) then
do i = 1,leny
y(i) = zero
end do
else
do i = 1,leny
y(i) = beta*y(i)
end do
end if
else
iy = ky
if (beta==zero) then
do i = 1,leny
y(iy) = zero
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==zero) 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.
jy = ky
if (incx==1) then
do j = 1,n
temp = zero
k = kup1 - j
do i = max(1,j-ku),min(m,j+kl)
temp = temp + a(k+i,j)*x(i)
end do
y(jy) = y(jy) + alpha*temp
jy = jy + incy
end do
else
do j = 1,n
temp = zero
ix = kx
k = kup1 - j
do i = max(1,j-ku),min(m,j+kl)
temp = temp + a(k+i,j)*x(ix)
ix = ix + incx
end do
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_qgbmv
pure subroutine stdlib_qgemm(transa,transb,m,n,k,alpha,a,lda,b,ldb,beta,c,ldc)
!! DGEMM: 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,
!! 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
real(qp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: k, lda, ldb, ldc, m, n
character, intent(in) :: transa, transb
! Array Arguments
real(qp), intent(in) :: a(lda,*), b(ldb,*)
real(qp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: max
! Local Scalars
real(qp) :: temp
integer(ilp) :: i, info, j, l, nrowa, nrowb
logical(lk) :: nota, notb
! set nota and notb as true if a and b respectively are not
! transposed 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')
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.stdlib_lsame(transa,'C')) .and.(.not.stdlib_lsame(transa,&
'T'))) then
info = 1
else if ((.not.notb) .and. (.not.stdlib_lsame(transb,'C')) .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_xerbla('DGEMM ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or.(((alpha==zero).or. (k==0)).and. (beta==one))) &
return
! and if alpha.eq.zero.
if (alpha==zero) then
if (beta==zero) then
do j = 1,n
do i = 1,m
c(i,j) = zero
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==zero) then
do i = 1,m
c(i,j) = zero
end do
else if (beta/=one) 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
! form c := alpha*a**t*b + beta*c
do j = 1,n
do i = 1,m
temp = zero
do l = 1,k
temp = temp + a(l,i)*b(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
else
if (nota) then
! form c := alpha*a*b**t + beta*c
do j = 1,n
if (beta==zero) then
do i = 1,m
c(i,j) = zero
end do
else if (beta/=one) 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
else
! form c := alpha*a**t*b**t + beta*c
do j = 1,n
do i = 1,m
temp = zero
do l = 1,k
temp = temp + a(l,i)*b(j,l)
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_qgemm
pure subroutine stdlib_qgemv(trans,m,n,alpha,a,lda,x,incx,beta,y,incy)
!! DGEMV: performs one of the matrix-vector operations
!! y := alpha*A*x + beta*y, or y := alpha*A**T*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
real(qp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: incx, incy, lda, m, n
character, intent(in) :: trans
! Array Arguments
real(qp), intent(in) :: a(lda,*), x(*)
real(qp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
real(qp) :: temp
integer(ilp) :: i, info, ix, iy, j, jx, jy, kx, ky, lenx, leny
! Intrinsic Functions
intrinsic :: 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_xerbla('DGEMV ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or.((alpha==zero).and. (beta==one))) return
! 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 one pass through a.
! first form y := beta*y.
if (beta/=one) then
if (incy==1) then
if (beta==zero) then
do i = 1,leny
y(i) = zero
end do
else
do i = 1,leny
y(i) = beta*y(i)
end do
end if
else
iy = ky
if (beta==zero) then
do i = 1,leny
y(iy) = zero
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==zero) 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.
jy = ky
if (incx==1) then
do j = 1,n
temp = zero
do i = 1,m
temp = temp + a(i,j)*x(i)
end do
y(jy) = y(jy) + alpha*temp
jy = jy + incy
end do
else
do j = 1,n
temp = zero
ix = kx
do i = 1,m
temp = temp + a(i,j)*x(ix)
ix = ix + incx
end do
y(jy) = y(jy) + alpha*temp
jy = jy + incy
end do
end if
end if
return
end subroutine stdlib_qgemv
pure subroutine stdlib_qger(m,n,alpha,x,incx,y,incy,a,lda)
!! DGER: 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
real(qp), intent(in) :: alpha
integer(ilp), intent(in) :: incx, incy, lda, m, n
! Array Arguments
real(qp), intent(inout) :: a(lda,*)
real(qp), intent(in) :: x(*), y(*)
! =====================================================================
! Local Scalars
real(qp) :: temp
integer(ilp) :: 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_xerbla('DGER ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or. (alpha==zero)) return
! start the operations. in this version the elements of a are
! accessed sequentially with one 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)/=zero) 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)/=zero) 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_qger
pure function stdlib_qnrm2( n, x, incx )
!! DNRM2: returns the euclidean norm of a vector via the function
!! name, so that
!! DNRM2 := sqrt( x'*x )
real(qp) :: stdlib_qnrm2
! -- reference blas level1 routine (version 3.9.1_qp) --
! -- reference blas is a software package provided by univ. of tennessee, --
! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
! march 2021
! Constants
integer, parameter :: wp = kind(1._qp)
real(qp), parameter :: maxn = huge(0.0_qp)
! .. blue's scaling constants ..
! Scalar Arguments
integer(ilp), intent(in) :: incx, n
! Array Arguments
real(qp), intent(in) :: x(*)
! Local Scalars
integer(ilp) :: i, ix
logical(lk) :: notbig
real(qp) :: abig, amed, asml, ax, scl, sumsq, ymax, ymin
! quick return if possible
stdlib_qnrm2 = zero
if( n <= 0 ) return
scl = one
sumsq = zero
! compute the sum of squares in 3 accumulators:
! abig -- sums of squares scaled down to avoid overflow
! asml -- sums of squares scaled up to avoid underflow
! amed -- sums of squares that do not require scaling
! the thresholds and multipliers are
! tbig -- values bigger than this are scaled down by sbig
! tsml -- values smaller than this are scaled up by ssml
notbig = .true.
asml = zero
amed = zero
abig = zero
ix = 1
if( incx < 0 ) ix = 1 - (n-1)*incx
do i = 1, n
ax = abs(x(ix))
if (ax > tbig) then
abig = abig + (ax*sbig)**2
notbig = .false.
else if (ax < tsml) then
if (notbig) asml = asml + (ax*ssml)**2
else
amed = amed + ax**2
end if
ix = ix + incx
end do
! combine abig and amed or amed and asml if more than one
! accumulator was used.
if (abig > zero) then
! combine abig and amed if abig > 0.
if ( (amed > zero) .or. (amed > maxn) .or. (amed /= amed) ) then
abig = abig + (amed*sbig)*sbig
end if
scl = one / sbig
sumsq = abig
else if (asml > zero) then
! combine amed and asml if asml > 0.
if ( (amed > zero) .or. (amed > maxn) .or. (amed /= amed) ) then
amed = sqrt(amed)
asml = sqrt(asml) / ssml
if (asml > amed) then
ymin = amed
ymax = asml
else
ymin = asml
ymax = amed
end if
scl = one
sumsq = ymax**2*( one + (ymin/ymax)**2 )
else
scl = one / ssml
sumsq = asml
end if
else
! otherwise all values are mid-range
scl = one
sumsq = amed
end if
stdlib_qnrm2 = scl*sqrt( sumsq )
return
end function stdlib_qnrm2
pure subroutine stdlib_qrot(n,dx,incx,dy,incy,c,s)
!! DROT: applies a plane rotation.
! -- 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(qp), intent(in) :: c, s
integer(ilp), intent(in) :: incx, incy, n
! Array Arguments
real(qp), intent(inout) :: dx(*), dy(*)
! =====================================================================
! Local Scalars
real(qp) :: dtemp
integer(ilp) :: 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
dtemp = c*dx(i) + s*dy(i)
dy(i) = c*dy(i) - s*dx(i)
dx(i) = dtemp
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
dtemp = c*dx(ix) + s*dy(iy)
dy(iy) = c*dy(iy) - s*dx(ix)
dx(ix) = dtemp
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib_qrot
pure subroutine stdlib_qrotg( a, b, c, s )
!! The computation uses the formulas
!! sigma = sgn(a) if |a| > |b|
!! = sgn(b) if |b| >= |a|
!! r = sigma*sqrt( a**2 + b**2 )
!! c = 1; s = 0 if r = 0
!! c = a/r; s = b/r if r != 0
!! The subroutine also computes
!! z = s if |a| > |b|,
!! = 1/c if |b| >= |a| and c != 0
!! = 1 if c = 0
!! This allows c and s to be reconstructed from z as follows:
!! If z = 1, set c = 0, s = 1.
!! If |z| < 1, set c = sqrt(1 - z**2) and s = z.
!! If |z| > 1, set c = 1/z and s = sqrt( 1 - c**2).
! -- 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..--
! Constants
integer, parameter :: wp = kind(1._qp)
! Scaling Constants
! Scalar Arguments
real(qp), intent(inout) :: a, b
real(qp), intent(out) :: c, s
! Local Scalars
real(qp) :: anorm, bnorm, scl, sigma, r, z
anorm = abs(a)
bnorm = abs(b)