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stdlib_linalg_blas_d.f90
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stdlib_linalg_blas_d.f90
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module stdlib_linalg_blas_d
use stdlib_linalg_constants
use stdlib_linalg_blas_aux
use stdlib_linalg_blas_s
implicit none(type, external)
private
public :: sp, dp, lk, ilp
public :: stdlib_dasum
public :: stdlib_daxpy
public :: stdlib_dcopy
public :: stdlib_ddot
public :: stdlib_dgbmv
public :: stdlib_dgemm
public :: stdlib_dgemv
public :: stdlib_dger
public :: stdlib_dnrm2
public :: stdlib_drot
public :: stdlib_drotg
public :: stdlib_drotm
public :: stdlib_drotmg
public :: stdlib_dsbmv
public :: stdlib_dscal
public :: stdlib_dsdot
public :: stdlib_dspmv
public :: stdlib_dspr
public :: stdlib_dspr2
public :: stdlib_dswap
public :: stdlib_dsymm
public :: stdlib_dsymv
public :: stdlib_dsyr
public :: stdlib_dsyr2
public :: stdlib_dsyr2k
public :: stdlib_dsyrk
public :: stdlib_dtbmv
public :: stdlib_dtbsv
public :: stdlib_dtpmv
public :: stdlib_dtpsv
public :: stdlib_dtrmm
public :: stdlib_dtrmv
public :: stdlib_dtrsm
public :: stdlib_dtrsv
public :: stdlib_dzasum
public :: stdlib_dznrm2
! 64-bit real constants
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)
! 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
! DASUM takes the sum of the absolute values.
real(dp) function stdlib_dasum(n, dx, incx)
! -- 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) :: incx, n
! .. array arguments ..
real(dp) :: dx(*)
! =====================================================================
! .. local scalars ..
real(dp) :: dtemp
integer(ilp) :: i, m, mp1, nincx
! .. intrinsic functions ..
intrinsic :: dabs, mod
stdlib_dasum = 0.0_dp
dtemp = 0.0_dp
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 + dabs(dx(i))
end do
if (n < 6) then
stdlib_dasum = dtemp
return
end if
end if
mp1 = m + 1
do i = mp1, n, 6
dtemp = dtemp + dabs(dx(i)) + dabs(dx(i + 1)) + dabs(dx(i + 2)) + dabs(dx(i + 3)) + dabs( &
dx(i + 4)) + dabs(dx(i + 5))
end do
else
! code for increment not equal to 1
nincx = n*incx
do i = 1, nincx, incx
dtemp = dtemp + dabs(dx(i))
end do
end if
stdlib_dasum = dtemp
return
! end of stdlib_dasum
end function stdlib_dasum
! DAXPY constant times a vector plus a vector.
! uses unrolled loops for increments equal to one.
subroutine stdlib_daxpy(n, da, dx, incx, dy, incy)
! -- 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) :: da
integer(ilp) :: incx, incy, n
! .. array arguments ..
real(dp) :: dx(*), dy(*)
! =====================================================================
! .. local scalars ..
integer(ilp) :: i, ix, iy, m, mp1
! .. intrinsic functions ..
intrinsic :: mod
if (n <= 0) return
if (da == 0.0_dp) 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 of stdlib_daxpy
end subroutine stdlib_daxpy
! DCOPY copies a vector, x, to a vector, y.
! uses unrolled loops for increments equal to 1.
subroutine stdlib_dcopy(n, dx, incx, dy, incy)
! -- 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) :: incx, incy, n
! .. array arguments ..
real(dp) :: dx(*), 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 of stdlib_dcopy
end subroutine stdlib_dcopy
! DDOT forms the dot product of two vectors.
! uses unrolled loops for increments equal to one.
real(dp) function stdlib_ddot(n, dx, incx, dy, incy)
! -- 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) :: incx, incy, n
! .. array arguments ..
real(dp) :: dx(*), dy(*)
! =====================================================================
! .. local scalars ..
real(dp) :: dtemp
integer(ilp) :: i, ix, iy, m, mp1
! .. intrinsic functions ..
intrinsic :: mod
stdlib_ddot = 0.0_dp
dtemp = 0.0_dp
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_ddot = 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_ddot = dtemp
return
! end of stdlib_ddot
end function stdlib_ddot
! 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.
subroutine stdlib_dgbmv(trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
! -- 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) :: alpha, beta
integer(ilp) :: incx, incy, kl, ku, lda, m, n
character :: trans
! .. array arguments ..
real(dp) :: a(lda, *), x(*), y(*)
! =====================================================================
! .. local scalars ..
real(dp) :: 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('stdlib_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 of stdlib_dgbmv
end subroutine stdlib_dgbmv
! 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.
subroutine stdlib_dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
! -- 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) :: alpha, beta
integer(ilp) :: k, lda, ldb, ldc, m, n
character :: transa, transb
! .. array arguments ..
real(dp) :: a(lda, *), b(ldb, *), c(ldc, *)
! =====================================================================
! .. intrinsic functions ..
intrinsic :: max
! .. local scalars ..
real(dp) :: 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('stdlib_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 of stdlib_dgemm
end subroutine stdlib_dgemm
! 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.
subroutine stdlib_dgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
! -- 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) :: alpha, beta
integer(ilp) :: incx, incy, lda, m, n
character :: trans
! .. array arguments ..
real(dp) :: a(lda, *), x(*), y(*)
! =====================================================================
! .. local scalars ..
real(dp) :: 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('stdlib_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 of stdlib_dgemv
end subroutine stdlib_dgemv
! 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.
subroutine stdlib_dger(m, n, alpha, x, incx, y, incy, a, lda)
! -- 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) :: alpha
integer(ilp) :: incx, incy, lda, m, n
! .. array arguments ..
real(dp) :: a(lda, *), x(*), y(*)
! =====================================================================
! .. local scalars ..
real(dp) :: 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('stdlib_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 of stdlib_dger
end subroutine stdlib_dger
! !
! DNRM2 returns the euclidean norm of a vector via the function
! name, so that
! DNRM2 := sqrt( x'*x )
function stdlib_dnrm2(n, x, incx)
integer, parameter :: wp = kind(1._dp)
real(dp) :: stdlib_dnrm2
! -- reference blas level1 routine (version 3.9.1) --
! -- 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 ..
real(dp), parameter :: zero = 0.0_dp
real(dp), parameter :: one = 1.0_dp
real(dp), parameter :: maxn = huge(0.0_dp)
! .. blue's scaling constants ..
real(dp), parameter :: tsml = real(radix(0._dp), wp)**ceiling((minexponent(0._dp) - 1) &
*0.5_dp)
real(dp), parameter :: tbig = real(radix(0._dp), wp)**floor((maxexponent(0._dp) - &
digits(0._dp) + 1)*0.5_dp)
real(dp), parameter :: ssml = real(radix(0._dp), wp)**(-floor((minexponent(0._dp) - &
digits(0._dp))*0.5_dp))
real(dp), parameter :: sbig = real(radix(0._dp), wp)**(-ceiling((maxexponent(0._dp) &
+ digits(0._dp) - 1)*0.5_dp))
! .. scalar arguments ..
integer :: incx, n
! .. array arguments ..
real(dp) :: x(*)
! .. local scalars ..
integer :: i, ix
logical :: notbig
real(dp) :: abig, amed, asml, ax, scl, sumsq, ymax, ymin
! quick return if possible
stdlib_dnrm2 = 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_dnrm2 = scl*sqrt(sumsq)
return
end function stdlib_dnrm2
! DROT applies a plane rotation.
subroutine stdlib_drot(n, dx, incx, dy, incy, c, s)
! -- 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) :: c, s
integer(ilp) :: incx, incy, n
! .. array arguments ..
real(dp) :: dx(*), dy(*)
! =====================================================================
! .. local scalars ..
real(dp) :: 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 of stdlib_drot
end subroutine stdlib_drot
! !
! 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).
subroutine stdlib_drotg(a, b, c, s)
integer, parameter :: wp = kind(1._dp)
! -- reference blas level1 routine --
! -- reference blas is a software package provided by univ. of tennessee, --