#:include "common.fypp"
module stdlib_linalg_blas_s
use stdlib_linalg_constants
use stdlib_linalg_blas_aux
implicit none(type,external)
private
public :: sp,dp,qp,lk,ilp
public :: stdlib_sasum
public :: stdlib_saxpy
public :: stdlib_scasum
public :: stdlib_scnrm2
public :: stdlib_scopy
public :: stdlib_sdot
public :: stdlib_sdsdot
public :: stdlib_sgbmv
public :: stdlib_sgemm
public :: stdlib_sgemv
public :: stdlib_sger
public :: stdlib_snrm2
public :: stdlib_srot
public :: stdlib_srotg
public :: stdlib_srotm
public :: stdlib_srotmg
public :: stdlib_ssbmv
public :: stdlib_sscal
public :: stdlib_sspmv
public :: stdlib_sspr
public :: stdlib_sspr2
public :: stdlib_sswap
public :: stdlib_ssymm
public :: stdlib_ssymv
public :: stdlib_ssyr
public :: stdlib_ssyr2
public :: stdlib_ssyr2k
public :: stdlib_ssyrk
public :: stdlib_stbmv
public :: stdlib_stbsv
public :: stdlib_stpmv
public :: stdlib_stpsv
public :: stdlib_strmm
public :: stdlib_strmv
public :: stdlib_strsm
public :: stdlib_strsv
! 32-bit real constants
real(sp), parameter, private :: negone = -1.00_sp
real(sp), parameter, private :: zero = 0.00_sp
real(sp), parameter, private :: half = 0.50_sp
real(sp), parameter, private :: one = 1.00_sp
real(sp), parameter, private :: two = 2.00_sp
real(sp), parameter, private :: three = 3.00_sp
real(sp), parameter, private :: four = 4.00_sp
real(sp), parameter, private :: eight = 8.00_sp
real(sp), parameter, private :: ten = 10.00_sp
! 32-bit complex constants
complex(sp), parameter, private :: czero = ( 0.0_sp,0.0_sp)
complex(sp), parameter, private :: chalf = ( 0.5_sp,0.0_sp)
complex(sp), parameter, private :: cone = ( 1.0_sp,0.0_sp)
complex(sp), parameter, private :: cnegone = (-1.0_sp,0.0_sp)
! 32-bit scaling constants
integer, parameter, private :: maxexp = maxexponent(zero)
integer, parameter, private :: minexp = minexponent(zero)
real(sp), parameter, private :: rradix = real(radix(zero),sp)
real(sp), parameter, private :: ulp = epsilon(zero)
real(sp), parameter, private :: eps = ulp*half
real(sp), parameter, private :: safmin = rradix**max(minexp-1,1-maxexp)
real(sp), parameter, private :: safmax = one/safmin
real(sp), parameter, private :: smlnum = safmin/ulp
real(sp), parameter, private :: bignum = safmax*ulp
real(sp), parameter, private :: rtmin = sqrt(smlnum)
real(sp), parameter, private :: rtmax = sqrt(bignum)
! 32-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(sp), parameter, private :: tsml = rradix**ceiling((minexp-1)*half)
real(sp), parameter, private :: tbig = rradix**floor((maxexp-digits(zero)+1)*half)
real(sp), parameter, private :: ssml = rradix**(-floor((minexp-digits(zero))*half))
real(sp), parameter, private :: sbig = rradix**(-ceiling((maxexp+digits(zero)-1)*half))
contains
pure real(sp) function stdlib_sasum(n,sx,incx)
!! SASUM takes the sum of the absolute values.
!! uses unrolled loops for increment 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, n
! Array Arguments
real(sp), intent(in) :: sx(*)
! =====================================================================
! Local Scalars
real(sp) :: stemp
integer(ilp) :: i, m, mp1, nincx
! Intrinsic Functions
intrinsic :: abs,mod
stdlib_sasum = zero
stemp = 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
stemp = stemp + abs(sx(i))
end do
if (n<6) then
stdlib_sasum = stemp
return
end if
end if
mp1 = m + 1
do i = mp1,n,6
stemp = stemp + abs(sx(i)) + abs(sx(i+1)) +abs(sx(i+2)) + abs(sx(i+3)) +abs(sx(i+&
4)) + abs(sx(i+5))
end do
else
! code for increment not equal to 1
nincx = n*incx
do i = 1,nincx,incx
stemp = stemp + abs(sx(i))
end do
end if
stdlib_sasum = stemp
return
end function stdlib_sasum
pure subroutine stdlib_saxpy(n,sa,sx,incx,sy,incy)
!! SAXPY 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(sp), intent(in) :: sa
integer(ilp), intent(in) :: incx, incy, n
! Array Arguments
real(sp), intent(in) :: sx(*)
real(sp), intent(inout) :: sy(*)
! =====================================================================
! Local Scalars
integer(ilp) :: i, ix, iy, m, mp1
! Intrinsic Functions
intrinsic :: mod
if (n<=0) return
if (sa==0.0_sp) 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
sy(i) = sy(i) + sa*sx(i)
end do
end if
if (n<4) return
mp1 = m + 1
do i = mp1,n,4
sy(i) = sy(i) + sa*sx(i)
sy(i+1) = sy(i+1) + sa*sx(i+1)
sy(i+2) = sy(i+2) + sa*sx(i+2)
sy(i+3) = sy(i+3) + sa*sx(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
sy(iy) = sy(iy) + sa*sx(ix)
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib_saxpy
pure real(sp) function stdlib_scasum(n,cx,incx)
!! SCASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and
!! returns a single precision result.
! -- 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
complex(sp), intent(in) :: cx(*)
! =====================================================================
! Local Scalars
real(sp) :: stemp
integer(ilp) :: i, nincx
! Intrinsic Functions
intrinsic :: abs,aimag,real
stdlib_scasum = zero
stemp = zero
if (n<=0 .or. incx<=0) return
if (incx==1) then
! code for increment equal to 1
do i = 1,n
stemp = stemp + abs(real(cx(i),KIND=sp)) + abs(aimag(cx(i)))
end do
else
! code for increment not equal to 1
nincx = n*incx
do i = 1,nincx,incx
stemp = stemp + abs(real(cx(i),KIND=sp)) + abs(aimag(cx(i)))
end do
end if
stdlib_scasum = stemp
return
end function stdlib_scasum
pure function stdlib_scnrm2( n, x, incx )
!! SCNRM2 returns the euclidean norm of a vector via the function
!! name, so that
!! SCNRM2 := sqrt( x**H*x )
real(sp) :: stdlib_scnrm2
! -- reference blas level1 routine (version 3.9.1_sp) --
! -- 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._sp)
real(sp), parameter :: maxn = huge(0.0_sp)
! .. blue's scaling constants ..
! Scalar Arguments
integer(ilp), intent(in) :: incx, n
! Array Arguments
complex(sp), intent(in) :: x(*)
! Local Scalars
integer(ilp) :: i, ix
logical(lk) :: notbig
real(sp) :: abig, amed, asml, ax, scl, sumsq, ymax, ymin
! quick return if possible
stdlib_scnrm2 = 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(real(x(ix),KIND=sp))
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
ax = abs(aimag(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_scnrm2 = scl*sqrt( sumsq )
return
end function stdlib_scnrm2
pure subroutine stdlib_scopy(n,sx,incx,sy,incy)
!! SCOPY 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(sp), intent(in) :: sx(*)
real(sp), intent(out) :: sy(*)
! =====================================================================
! 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
sy(i) = sx(i)
end do
if (n<7) return
end if
mp1 = m + 1
do i = mp1,n,7
sy(i) = sx(i)
sy(i+1) = sx(i+1)
sy(i+2) = sx(i+2)
sy(i+3) = sx(i+3)
sy(i+4) = sx(i+4)
sy(i+5) = sx(i+5)
sy(i+6) = sx(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
sy(iy) = sx(ix)
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib_scopy
pure real(sp) function stdlib_sdot(n,sx,incx,sy,incy)
!! SDOT 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(sp), intent(in) :: sx(*), sy(*)
! =====================================================================
! Local Scalars
real(sp) :: stemp
integer(ilp) :: i, ix, iy, m, mp1
! Intrinsic Functions
intrinsic :: mod
stemp = zero
stdlib_sdot = 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
stemp = stemp + sx(i)*sy(i)
end do
if (n<5) then
stdlib_sdot=stemp
return
end if
end if
mp1 = m + 1
do i = mp1,n,5
stemp = stemp + sx(i)*sy(i) + sx(i+1)*sy(i+1) +sx(i+2)*sy(i+2) + sx(i+3)*sy(i+3) + &
sx(i+4)*sy(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
stemp = stemp + sx(ix)*sy(iy)
ix = ix + incx
iy = iy + incy
end do
end if
stdlib_sdot = stemp
return
end function stdlib_sdot
pure real(sp) function stdlib_sdsdot(n,sb,sx,incx,sy,incy)
!! Compute the inner product of two vectors with extended
!! precision accumulation.
!! Returns S.P. result with dot product accumulated in D.P.
!! SDSDOT = SB + sum for I = 0 to N-1 of SX(LX+I*INCX)*SY(LY+I*INCY),
!! where LX = 1 if INCX >= 0, else LX = 1+(1-N)*INCX, and LY is
!! defined in a similar way using 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(sp), intent(in) :: sb
integer(ilp), intent(in) :: incx, incy, n
! Array Arguments
real(sp), intent(in) :: sx(*), sy(*)
! Local Scalars
real(dp) :: dsdot
integer(ilp) :: i, kx, ky, ns
! Intrinsic Functions
intrinsic :: real
dsdot = sb
if (n<=0) then
stdlib_sdsdot = dsdot
return
end if
if (incx==incy .and. incx>0) then
! code for equal and positive increments.
ns = n*incx
do i = 1,ns,incx
dsdot = dsdot + real(sx(i),KIND=sp)*real(sy(i),KIND=sp)
end do
else
! code for unequal or nonpositive increments.
kx = 1
ky = 1
if (incx<0) kx = 1 + (1-n)*incx
if (incy<0) ky = 1 + (1-n)*incy
do i = 1,n
dsdot = dsdot + real(sx(kx),KIND=sp)*real(sy(ky),KIND=sp)
kx = kx + incx
ky = ky + incy
end do
end if
stdlib_sdsdot = dsdot
return
end function stdlib_sdsdot
pure subroutine stdlib_sgbmv(trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy)
!! SGBMV 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(sp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: incx, incy, kl, ku, lda, m, n
character, intent(in) :: trans
! Array Arguments
real(sp), intent(in) :: a(lda,*), x(*)
real(sp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
real(sp) :: 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('SGBMV ',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_sgbmv
pure subroutine stdlib_sgemm(transa,transb,m,n,k,alpha,a,lda,b,ldb,beta,c,ldc)
!! SGEMM 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(sp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: k, lda, ldb, ldc, m, n
character, intent(in) :: transa, transb
! Array Arguments
real(sp), intent(in) :: a(lda,*), b(ldb,*)
real(sp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: max
! Local Scalars
real(sp) :: 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('SGEMM ',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_sgemm
pure subroutine stdlib_sgemv(trans,m,n,alpha,a,lda,x,incx,beta,y,incy)
!! SGEMV 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(sp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: incx, incy, lda, m, n
character, intent(in) :: trans
! Array Arguments
real(sp), intent(in) :: a(lda,*), x(*)
real(sp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
real(sp) :: 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('SGEMV ',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_sgemv
pure subroutine stdlib_sger(m,n,alpha,x,incx,y,incy,a,lda)
!! SGER 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(sp), intent(in) :: alpha
integer(ilp), intent(in) :: incx, incy, lda, m, n
! Array Arguments
real(sp), intent(inout) :: a(lda,*)
real(sp), intent(in) :: x(*), y(*)
! =====================================================================
! Local Scalars
real(sp) :: 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('SGER ',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_sger
pure function stdlib_snrm2( n, x, incx )
!! SNRM2 returns the euclidean norm of a vector via the function
!! name, so that
!! SNRM2 := sqrt( x'*x ).
real(sp) :: stdlib_snrm2
! -- reference blas level1 routine (version 3.9.1_sp) --
! -- 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._sp)
real(sp), parameter :: maxn = huge(0.0_sp)
! .. blue's scaling constants ..
! Scalar Arguments
integer(ilp), intent(in) :: incx, n
! Array Arguments
real(sp), intent(in) :: x(*)
! Local Scalars
integer(ilp) :: i, ix
logical(lk) :: notbig
real(sp) :: abig, amed, asml, ax, scl, sumsq, ymax, ymin
! quick return if possible
stdlib_snrm2 = 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_snrm2 = scl*sqrt( sumsq )
return
end function stdlib_snrm2
pure subroutine stdlib_srot(n,sx,incx,sy,incy,c,s)
!! 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(sp), intent(in) :: c, s
integer(ilp), intent(in) :: incx, incy, n
! Array Arguments
real(sp), intent(inout) :: sx(*), sy(*)
! =====================================================================
! Local Scalars
real(sp) :: stemp
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
stemp = c*sx(i) + s*sy(i)
sy(i) = c*sy(i) - s*sx(i)
sx(i) = stemp
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
stemp = c*sx(ix) + s*sy(iy)
sy(iy) = c*sy(iy) - s*sx(ix)
sx(ix) = stemp
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib_srot
pure subroutine stdlib_srotg( 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._sp)
! Scaling Constants
! Scalar Arguments
real(sp), intent(inout) :: a, b
real(sp), intent(out) :: c, s
! Local Scalars
real(sp) :: anorm, bnorm, scl, sigma, r, z
anorm = abs(a)
bnorm = abs(b)
if( bnorm == zero ) then
c = one
s = zero
b = zero
else if( anorm == zero ) then
c = zero
s = one
a = b
b = one
else
scl = min( safmax, max( safmin, anorm, bnorm ) )
if( anorm > bnorm ) then
sigma = sign(one,a)
else
sigma = sign(one,b)
end if
r = sigma*( scl*sqrt((a/scl)**2 + (b/scl)**2) )
c = a/r
s = b/r
if( anorm > bnorm ) then
z = s
else if( c /= zero ) then
z = one/c
else
z = one
end if
a = r
b = z
end if
return
end subroutine stdlib_srotg
pure subroutine stdlib_srotm(n,sx,incx,sy,incy,sparam)
!! SROTM applies the modified Givens transformation, \(H\), to the 2-by-N matrix
!! $$ \left[ \begin{array}{c}SX^T\\SY^T\\ \end{array} \right], $$
!! where \(^T\) indicates transpose. The elements of \(SX\) are in
!! SX(LX+I*INCX), I = 0:N-1, where LX = 1 if INCX >= 0, else LX = (-INCX)*N,
!! and similarly for SY using LY and INCY.
!! With SPARAM(1)=SFLAG, \(H\) has one of the following forms:
!! $$ H=\underbrace{\begin{bmatrix}SH_{11} & SH_{12}\\SH_{21} & SH_{22}\end{bmatrix}}_{SFLAG=-1},
!! \underbrace{\begin{bmatrix}1 & SH_{12}\\SH_{21} & 1\end{bmatrix}}_{SFLAG=0},
!! \underbrace{\begin{bmatrix}SH_{11} & 1\\-1 & SH_{22}\end{bmatrix}}_{SFLAG=1},
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{SFLAG=-2}. $$
!! See SROTMG for a description of data storage in SPARAM.
! -- 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(sp), intent(in) :: sparam(5)
real(sp), intent(inout) :: sx(*), sy(*)
! =====================================================================
! Local Scalars
real(sp) :: sflag, sh11, sh12, sh21, sh22, two, w, z, zero
integer(ilp) :: i, kx, ky, nsteps
! Data Statements
zero = 0.0_sp
two = 2.0_sp
sflag = sparam(1)
if (n<=0 .or. (sflag+two==zero)) return
if (incx==incy.and.incx>0) then
nsteps = n*incx
if (sflag<zero) then
sh11 = sparam(2)
sh12 = sparam(4)
sh21 = sparam(3)
sh22 = sparam(5)
do i = 1,nsteps,incx
w = sx(i)
z = sy(i)
sx(i) = w*sh11 + z*sh12
sy(i) = w*sh21 + z*sh22
end do
else if (sflag==zero) then
sh12 = sparam(4)
sh21 = sparam(3)
do i = 1,nsteps,incx
w = sx(i)
z = sy(i)
sx(i) = w + z*sh12
sy(i) = w*sh21 + z
end do
else
sh11 = sparam(2)
sh22 = sparam(5)
do i = 1,nsteps,incx
w = sx(i)
z = sy(i)
sx(i) = w*sh11 + z
sy(i) = -w + sh22*z
end do
end if
else
kx = 1
ky = 1
if (incx<0) kx = 1 + (1-n)*incx
if (incy<0) ky = 1 + (1-n)*incy
if (sflag<zero) then
sh11 = sparam(2)
sh12 = sparam(4)
sh21 = sparam(3)
sh22 = sparam(5)
do i = 1,n
w = sx(kx)
z = sy(ky)
sx(kx) = w*sh11 + z*sh12
sy(ky) = w*sh21 + z*sh22
kx = kx + incx
ky = ky + incy
end do
else if (sflag==zero) then
sh12 = sparam(4)
sh21 = sparam(3)
do i = 1,n
w = sx(kx)
z = sy(ky)
sx(kx) = w + z*sh12
sy(ky) = w*sh21 + z
kx = kx + incx
ky = ky + incy
end do
else
sh11 = sparam(2)
sh22 = sparam(5)
do i = 1,n
w = sx(kx)
z = sy(ky)
sx(kx) = w*sh11 + z
sy(ky) = -w + sh22*z
kx = kx + incx
ky = ky + incy
end do
end if
end if
return
end subroutine stdlib_srotm
pure subroutine stdlib_srotmg(sd1,sd2,sx1,sy1,sparam)
!! SROTMG Constructs the modified Givens transformation matrix \(H\) which zeros the
!! second component of the 2-vector
!! $$ \left[ {\sqrt{SD_1}\cdot SX_1,\sqrt{SD_2}\cdot SY_2} \right]^T. $$
!! With SPARAM(1)=SFLAG, \(H\) has one of the following forms:
!! $$ H=\underbrace{\begin{bmatrix}SH_{11} & SD_{12}\\SH_{21} & SH_{22}\end{bmatrix}}_{SFLAG=-1},
!! \underbrace{\begin{bmatrix}1 & SH_{12}\\SH_{21} & 1\end{bmatrix}}_{SFLAG=0},
!! \underbrace{\begin{bmatrix}SH_{11} & 1\\-1 & SH_{22}\end{bmatrix}}_{SFLAG=1},
!! \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{SFLAG=2}. $$
!! Locations 2-4 of SPARAM contain SH11, SH21, SH12 and SH22 respectively.
!! (Values of 1.0, -1.0, or 0.0 implied by the value of SPARAM(1) are not stored in SPARAM.)
!! The values of parameters GAMSQ and RGAMSQ may be inexact. This is OK as they are only
!! used for testing the size of DD1 and DD2. All actual scaling of data is done using GAM.
! -- 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(sp), intent(inout) :: sd1, sd2, sx1
real(sp), intent(in) :: sy1
! Array Arguments
real(sp), intent(out) :: sparam(5)
! =====================================================================
! Local Scalars
real(sp) :: gam, gamsq, one, rgamsq, sflag, sh11, sh12, sh21, sh22, sp1, sp2, sq1, sq2,&
stemp, su, two, zero
! Intrinsic Functions
intrinsic :: abs
! Data Statements
zero = 0.0_sp
one = 1.0_sp
two = 2.0_sp
gam = 4096.0_sp
gamsq = 1.67772e7_sp
rgamsq = 5.96046e-8_sp
if (sd1<zero) then
! go zero-h-d-and-sx1..
sflag = -one
sh11 = zero
sh12 = zero
sh21 = zero
sh22 = zero
sd1 = zero
sd2 = zero
sx1 = zero
else
! case-sd1-nonnegative
sp2 = sd2*sy1
if (sp2==zero) then
sflag = -two
sparam(1) = sflag
return
end if
! regular-case..
sp1 = sd1*sx1
sq2 = sp2*sy1
sq1 = sp1*sx1
if (abs(sq1)>abs(sq2)) then
sh21 = -sy1/sx1
sh12 = sp2/sp1
su = one - sh12*sh21
if (su>zero) then
sflag = zero
sd1 = sd1/su
sd2 = sd2/su
sx1 = sx1*su
else
! this code path if here for safety. we do not expect this
! condition to ever hold except in edge cases with rounding
! errors. see doi: 10.1145/355841.355847
sflag = -one
sh11 = zero
sh12 = zero
sh21 = zero
sh22 = zero
sd1 = zero
sd2 = zero
sx1 = zero
end if
else
if (sq2<zero) then
! go zero-h-d-and-sx1..
sflag = -one
sh11 = zero
sh12 = zero
sh21 = zero
sh22 = zero
sd1 = zero
sd2 = zero
sx1 = zero
else
sflag = one
sh11 = sp1/sp2
sh22 = sx1/sy1
su = one + sh11*sh22
stemp = sd2/su
sd2 = sd1/su
sd1 = stemp
sx1 = sy1*su
end if
end if
! procedure..scale-check
if (sd1/=zero) then
do while ((sd1<=rgamsq) .or. (sd1>=gamsq))
if (sflag==zero) then
sh11 = one
sh22 = one
sflag = -one
else
sh21 = -one
sh12 = one
sflag = -one
end if
if (sd1<=rgamsq) then
sd1 = sd1*gam**2
sx1 = sx1/gam
sh11 = sh11/gam
sh12 = sh12/gam
else
sd1 = sd1/gam**2
sx1 = sx1*gam
sh11 = sh11*gam
sh12 = sh12*gam
end if
enddo
end if
if (sd2/=zero) then
do while ( (abs(sd2)<=rgamsq) .or. (abs(sd2)>=gamsq) )
if (sflag==zero) then
sh11 = one
sh22 = one
sflag = -one
else
sh21 = -one
sh12 = one
sflag = -one
end if
if (abs(sd2)<=rgamsq) then
sd2 = sd2*gam**2
sh21 = sh21/gam
sh22 = sh22/gam
else
sd2 = sd2/gam**2
sh21 = sh21*gam
sh22 = sh22*gam
end if
end do
end if
end if
if (sflag<zero) then
sparam(2) = sh11
sparam(3) = sh21
sparam(4) = sh12
sparam(5) = sh22
else if (sflag==zero) then
sparam(3) = sh21
sparam(4) = sh12
else
sparam(2) = sh11
sparam(5) = sh22
end if
sparam(1) = sflag
return
end subroutine stdlib_srotmg
pure subroutine stdlib_ssbmv(uplo,n,k,alpha,a,lda,x,incx,beta,y,incy)
!! SSBMV 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 symmetric 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
real(sp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: incx, incy, k, lda, n
character, intent(in) :: uplo
! Array Arguments
real(sp), intent(in) :: a(lda,*), x(*)
real(sp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
real(sp) :: temp1, temp2
integer(ilp) :: i, info, ix, iy, j, jx, jy, kplus1, kx, ky, l
! Intrinsic Functions
intrinsic :: 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_xerbla('SSBMV ',info)
return
end if
! quick return if possible.
if ((n==0) .or. ((alpha==zero).and. (beta==one))) 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 one pass through a.
! first form y := beta*y.
if (beta/=one) then
if (incy==1) then
if (beta==zero) then
do i = 1,n
y(i) = zero
end do
else
do i = 1,n
y(i) = beta*y(i)
end do
end if
else
iy = ky
if (beta==zero) then
do i = 1,n
y(iy) = zero
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==zero) 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 = zero
l = kplus1 - j
do i = max(1,j-k),j - 1
y(i) = y(i) + temp1*a(l+i,j)
temp2 = temp2 + a(l+i,j)*x(i)
end do
y(j) = y(j) + temp1*a(kplus1,j) + alpha*temp2
end do
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = zero
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 + a(l+i,j)*x(ix)
ix = ix + incx
iy = iy + incy
end do
y(jy) = y(jy) + temp1*a(kplus1,j) + 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 = zero
y(j) = y(j) + temp1*a(1,j)
l = 1 - j
do i = j + 1,min(n,j+k)
y(i) = y(i) + temp1*a(l+i,j)
temp2 = temp2 + 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 = zero
y(jy) = y(jy) + temp1*a(1,j)
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 + 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_ssbmv
pure subroutine stdlib_sscal(n,sa,sx,incx)
!! SSCAL scales a vector by a constant.
!! uses unrolled loops for increment 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
real(sp), intent(in) :: sa
integer(ilp), intent(in) :: incx, n
! Array Arguments
real(sp), intent(inout) :: sx(*)
! =====================================================================
! Local Scalars
integer(ilp) :: i, m, mp1, nincx
! Intrinsic Functions
intrinsic :: mod
if (n<=0 .or. incx<=0) return
if (incx==1) then
! code for increment equal to 1
! clean-up loop
m = mod(n,5)
if (m/=0) then
do i = 1,m
sx(i) = sa*sx(i)
end do
if (n<5) return
end if
mp1 = m + 1
do i = mp1,n,5
sx(i) = sa*sx(i)
sx(i+1) = sa*sx(i+1)
sx(i+2) = sa*sx(i+2)
sx(i+3) = sa*sx(i+3)
sx(i+4) = sa*sx(i+4)
end do
else
! code for increment not equal to 1
nincx = n*incx
do i = 1,nincx,incx
sx(i) = sa*sx(i)
end do
end if
return
end subroutine stdlib_sscal
pure subroutine stdlib_sspmv(uplo,n,alpha,ap,x,incx,beta,y,incy)
!! SSPMV 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 symmetric 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(sp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: incx, incy, n
character, intent(in) :: uplo
! Array Arguments
real(sp), intent(in) :: ap(*), x(*)
real(sp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
real(sp) :: temp1, temp2
integer(ilp) :: i, info, ix, iy, j, jx, jy, k, kk, kx, ky
! 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_xerbla('SSPMV ',info)
return
end if
! quick return if possible.
if ((n==0) .or. ((alpha==zero).and. (beta==one))) 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 one pass through ap.
! first form y := beta*y.
if (beta/=one) then
if (incy==1) then
if (beta==zero) then
do i = 1,n
y(i) = zero
end do
else
do i = 1,n
y(i) = beta*y(i)
end do
end if
else
iy = ky
if (beta==zero) then
do i = 1,n
y(iy) = zero
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==zero) 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 = zero
k = kk
do i = 1,j - 1
y(i) = y(i) + temp1*ap(k)
temp2 = temp2 + ap(k)*x(i)
k = k + 1
end do
y(j) = y(j) + temp1*ap(kk+j-1) + alpha*temp2
kk = kk + j
end do
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = zero
ix = kx
iy = ky
do k = kk,kk + j - 2
y(iy) = y(iy) + temp1*ap(k)
temp2 = temp2 + ap(k)*x(ix)
ix = ix + incx
iy = iy + incy
end do
y(jy) = y(jy) + temp1*ap(kk+j-1) + 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 = zero
y(j) = y(j) + temp1*ap(kk)
k = kk + 1
do i = j + 1,n
y(i) = y(i) + temp1*ap(k)
temp2 = temp2 + 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 = zero
y(jy) = y(jy) + temp1*ap(kk)
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 + 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_sspmv
pure subroutine stdlib_sspr(uplo,n,alpha,x,incx,ap)
!! SSPR performs the symmetric rank 1 operation
!! A := alpha*x*x**T + A,
!! where alpha is a real scalar, x is an n element vector and A is an
!! n by n symmetric 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(sp), intent(in) :: alpha
integer(ilp), intent(in) :: incx, n
character, intent(in) :: uplo
! Array Arguments
real(sp), intent(inout) :: ap(*)
real(sp), intent(in) :: x(*)
! =====================================================================
! Local Scalars
real(sp) :: temp
integer(ilp) :: i, info, ix, j, jx, k, kk, kx
! 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_xerbla('SSPR ',info)
return
end if
! quick return if possible.
if ((n==0) .or. (alpha==zero)) 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 one 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)/=zero) then
temp = alpha*x(j)
k = kk
do i = 1,j
ap(k) = ap(k) + x(i)*temp
k = k + 1
end do
end if
kk = kk + j
end do
else
jx = kx
do j = 1,n
if (x(jx)/=zero) then
temp = alpha*x(jx)
ix = kx
do k = kk,kk + j - 1
ap(k) = ap(k) + x(ix)*temp
ix = ix + incx
end do
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)/=zero) then
temp = alpha*x(j)
k = kk
do i = j,n
ap(k) = ap(k) + x(i)*temp
k = k + 1
end do
end if
kk = kk + n - j + 1
end do
else
jx = kx
do j = 1,n
if (x(jx)/=zero) then
temp = alpha*x(jx)
ix = jx
do k = kk,kk + n - j
ap(k) = ap(k) + x(ix)*temp
ix = ix + incx
end do
end if
jx = jx + incx
kk = kk + n - j + 1
end do
end if
end if
return
end subroutine stdlib_sspr
pure subroutine stdlib_sspr2(uplo,n,alpha,x,incx,y,incy,ap)
!! SSPR2 performs the symmetric rank 2 operation
!! A := alpha*x*y**T + alpha*y*x**T + A,
!! where alpha is a scalar, x and y are n element vectors and A is an
!! n by n symmetric 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(sp), intent(in) :: alpha
integer(ilp), intent(in) :: incx, incy, n
character, intent(in) :: uplo
! Array Arguments
real(sp), intent(inout) :: ap(*)
real(sp), intent(in) :: x(*), y(*)
! =====================================================================
! Local Scalars
real(sp) :: temp1, temp2
integer(ilp) :: i, info, ix, iy, j, jx, jy, k, kk, kx, ky
! 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_xerbla('SSPR2 ',info)
return
end if
! quick return if possible.
if ((n==0) .or. (alpha==zero)) 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 one 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)/=zero) .or. (y(j)/=zero)) then
temp1 = alpha*y(j)
temp2 = alpha*x(j)
k = kk
do i = 1,j
ap(k) = ap(k) + x(i)*temp1 + y(i)*temp2
k = k + 1
end do
end if
kk = kk + j
end do
else
do j = 1,n
if ((x(jx)/=zero) .or. (y(jy)/=zero)) then
temp1 = alpha*y(jy)
temp2 = alpha*x(jx)
ix = kx
iy = ky
do k = kk,kk + j - 1
ap(k) = ap(k) + x(ix)*temp1 + y(iy)*temp2
ix = ix + incx
iy = iy + incy
end do
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)/=zero) .or. (y(j)/=zero)) then
temp1 = alpha*y(j)
temp2 = alpha*x(j)
k = kk
do i = j,n
ap(k) = ap(k) + x(i)*temp1 + y(i)*temp2
k = k + 1
end do
end if
kk = kk + n - j + 1
end do
else
do j = 1,n
if ((x(jx)/=zero) .or. (y(jy)/=zero)) then
temp1 = alpha*y(jy)
temp2 = alpha*x(jx)
ix = jx
iy = jy
do k = kk,kk + n - j
ap(k) = ap(k) + x(ix)*temp1 + y(iy)*temp2
ix = ix + incx
iy = iy + incy
end do
end if
jx = jx + incx
jy = jy + incy
kk = kk + n - j + 1
end do
end if
end if
return
end subroutine stdlib_sspr2
pure subroutine stdlib_sswap(n,sx,incx,sy,incy)
!! SSWAP interchanges two vectors.
!! 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(sp), intent(inout) :: sx(*), sy(*)
! =====================================================================
! Local Scalars
real(sp) :: stemp
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,3)
if (m/=0) then
do i = 1,m
stemp = sx(i)
sx(i) = sy(i)
sy(i) = stemp
end do
if (n<3) return
end if
mp1 = m + 1
do i = mp1,n,3
stemp = sx(i)
sx(i) = sy(i)
sy(i) = stemp
stemp = sx(i+1)
sx(i+1) = sy(i+1)
sy(i+1) = stemp
stemp = sx(i+2)
sx(i+2) = sy(i+2)
sy(i+2) = stemp
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
stemp = sx(ix)
sx(ix) = sy(iy)
sy(iy) = stemp
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine stdlib_sswap
pure subroutine stdlib_ssymm(side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc)
!! SSYMM 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
real(sp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: lda, ldb, ldc, m, n
character, intent(in) :: side, uplo
! Array Arguments
real(sp), intent(in) :: a(lda,*), b(ldb,*)
real(sp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: max
! Local Scalars
real(sp) :: temp1, temp2
integer(ilp) :: 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_xerbla('SSYMM ',info)
return
end if
! quick return if possible.
if ((m==0) .or. (n==0) .or.((alpha==zero).and. (beta==one))) return
! and when 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 (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 = zero
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==zero) 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 = zero
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==zero) 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==zero) 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_ssymm
pure subroutine stdlib_ssymv(uplo,n,alpha,a,lda,x,incx,beta,y,incy)
!! SSYMV 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 symmetric 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(sp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: incx, incy, lda, n
character, intent(in) :: uplo
! Array Arguments
real(sp), intent(in) :: a(lda,*), x(*)
real(sp), intent(inout) :: y(*)
! =====================================================================
! Local Scalars
real(sp) :: temp1, temp2
integer(ilp) :: i, info, ix, iy, j, jx, jy, kx, ky
! Intrinsic Functions
intrinsic :: 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_xerbla('SSYMV ',info)
return
end if
! quick return if possible.
if ((n==0) .or. ((alpha==zero).and. (beta==one))) 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 one pass through the triangular part
! of a.
! first form y := beta*y.
if (beta/=one) then
if (incy==1) then
if (beta==zero) then
do i = 1,n
y(i) = zero
end do
else
do i = 1,n
y(i) = beta*y(i)
end do
end if
else
iy = ky
if (beta==zero) then
do i = 1,n
y(iy) = zero
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==zero) 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 = zero
do i = 1,j - 1
y(i) = y(i) + temp1*a(i,j)
temp2 = temp2 + a(i,j)*x(i)
end do
y(j) = y(j) + temp1*a(j,j) + alpha*temp2
end do
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = zero
ix = kx
iy = ky
do i = 1,j - 1
y(iy) = y(iy) + temp1*a(i,j)
temp2 = temp2 + a(i,j)*x(ix)
ix = ix + incx
iy = iy + incy
end do
y(jy) = y(jy) + temp1*a(j,j) + 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 = zero
y(j) = y(j) + temp1*a(j,j)
do i = j + 1,n
y(i) = y(i) + temp1*a(i,j)
temp2 = temp2 + 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 = zero
y(jy) = y(jy) + temp1*a(j,j)
ix = jx
iy = jy
do i = j + 1,n
ix = ix + incx
iy = iy + incy
y(iy) = y(iy) + temp1*a(i,j)
temp2 = temp2 + 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_ssymv
pure subroutine stdlib_ssyr(uplo,n,alpha,x,incx,a,lda)
!! SSYR performs the symmetric rank 1 operation
!! A := alpha*x*x**T + A,
!! where alpha is a real scalar, x is an n element vector and A is an
!! n by n symmetric 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(sp), intent(in) :: alpha
integer(ilp), intent(in) :: incx, lda, n
character, intent(in) :: uplo
! Array Arguments
real(sp), intent(inout) :: a(lda,*)
real(sp), intent(in) :: x(*)
! =====================================================================
! Local Scalars
real(sp) :: temp
integer(ilp) :: i, info, ix, j, jx, kx
! Intrinsic Functions
intrinsic :: 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_xerbla('SSYR ',info)
return
end if
! quick return if possible.
if ((n==0) .or. (alpha==zero)) 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 one 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)/=zero) then
temp = alpha*x(j)
do i = 1,j
a(i,j) = a(i,j) + x(i)*temp
end do
end if
end do
else
jx = kx
do j = 1,n
if (x(jx)/=zero) then
temp = alpha*x(jx)
ix = kx
do i = 1,j
a(i,j) = a(i,j) + x(ix)*temp
ix = ix + incx
end do
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)/=zero) then
temp = alpha*x(j)
do i = j,n
a(i,j) = a(i,j) + x(i)*temp
end do
end if
end do
else
jx = kx
do j = 1,n
if (x(jx)/=zero) then
temp = alpha*x(jx)
ix = jx
do i = j,n
a(i,j) = a(i,j) + x(ix)*temp
ix = ix + incx
end do
end if
jx = jx + incx
end do
end if
end if
return
end subroutine stdlib_ssyr
pure subroutine stdlib_ssyr2(uplo,n,alpha,x,incx,y,incy,a,lda)
!! SSYR2 performs the symmetric rank 2 operation
!! A := alpha*x*y**T + alpha*y*x**T + A,
!! where alpha is a scalar, x and y are n element vectors and A is an n
!! by n symmetric 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(sp), intent(in) :: alpha
integer(ilp), intent(in) :: incx, incy, lda, n
character, intent(in) :: uplo
! Array Arguments
real(sp), intent(inout) :: a(lda,*)
real(sp), intent(in) :: x(*), y(*)
! =====================================================================
! Local Scalars
real(sp) :: temp1, temp2
integer(ilp) :: i, info, ix, iy, j, jx, jy, kx, ky
! Intrinsic Functions
intrinsic :: 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_xerbla('SSYR2 ',info)
return
end if
! quick return if possible.
if ((n==0) .or. (alpha==zero)) 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 one 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)/=zero) .or. (y(j)/=zero)) then
temp1 = alpha*y(j)
temp2 = alpha*x(j)
do i = 1,j
a(i,j) = a(i,j) + x(i)*temp1 + y(i)*temp2
end do
end if
end do
else
do j = 1,n
if ((x(jx)/=zero) .or. (y(jy)/=zero)) then
temp1 = alpha*y(jy)
temp2 = alpha*x(jx)
ix = kx
iy = ky
do i = 1,j
a(i,j) = a(i,j) + x(ix)*temp1 + y(iy)*temp2
ix = ix + incx
iy = iy + incy
end do
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)/=zero) .or. (y(j)/=zero)) then
temp1 = alpha*y(j)
temp2 = alpha*x(j)
do i = j,n
a(i,j) = a(i,j) + x(i)*temp1 + y(i)*temp2
end do
end if
end do
else
do j = 1,n
if ((x(jx)/=zero) .or. (y(jy)/=zero)) then
temp1 = alpha*y(jy)
temp2 = alpha*x(jx)
ix = jx
iy = jy
do i = j,n
a(i,j) = a(i,j) + x(ix)*temp1 + y(iy)*temp2
ix = ix + incx
iy = iy + incy
end do
end if
jx = jx + incx
jy = jy + incy
end do
end if
end if
return
end subroutine stdlib_ssyr2
pure subroutine stdlib_ssyr2k(uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc)
!! SSYR2K 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
real(sp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: k, lda, ldb, ldc, n
character, intent(in) :: trans, uplo
! Array Arguments
real(sp), intent(in) :: a(lda,*), b(ldb,*)
real(sp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: max
! Local Scalars
real(sp) :: temp1, temp2
integer(ilp) :: 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')) .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_xerbla('SSYR2K',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
c(i,j) = beta*c(i,j)
end do
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
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==zero) then
do i = 1,j
c(i,j) = zero
end do
else if (beta/=one) then
do i = 1,j
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
if ((a(j,l)/=zero) .or. (b(j,l)/=zero)) 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==zero) then
do i = j,n
c(i,j) = zero
end do
else if (beta/=one) then
do i = j,n
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
if ((a(j,l)/=zero) .or. (b(j,l)/=zero)) 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 = zero
temp2 = zero
do l = 1,k
temp1 = temp1 + a(l,i)*b(l,j)
temp2 = temp2 + b(l,i)*a(l,j)
end do
if (beta==zero) 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 = zero
temp2 = zero
do l = 1,k
temp1 = temp1 + a(l,i)*b(l,j)
temp2 = temp2 + b(l,i)*a(l,j)
end do
if (beta==zero) 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_ssyr2k
pure subroutine stdlib_ssyrk(uplo,trans,n,k,alpha,a,lda,beta,c,ldc)
!! SSYRK 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
real(sp), intent(in) :: alpha, beta
integer(ilp), intent(in) :: k, lda, ldc, n
character, intent(in) :: trans, uplo
! Array Arguments
real(sp), intent(in) :: a(lda,*)
real(sp), intent(inout) :: c(ldc,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: max
! Local Scalars
real(sp) :: temp
integer(ilp) :: 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')) .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_xerbla('SSYRK ',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
c(i,j) = beta*c(i,j)
end do
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
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==zero) then
do i = 1,j
c(i,j) = zero
end do
else if (beta/=one) then
do i = 1,j
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
if (a(j,l)/=zero) 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==zero) then
do i = j,n
c(i,j) = zero
end do
else if (beta/=one) then
do i = j,n
c(i,j) = beta*c(i,j)
end do
end if
do l = 1,k
if (a(j,l)/=zero) 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 = zero
do l = 1,k
temp = temp + 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
else
do j = 1,n
do i = j,n
temp = zero
do l = 1,k
temp = temp + 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_ssyrk
pure subroutine stdlib_stbmv(uplo,trans,diag,n,k,a,lda,x,incx)
!! STBMV performs one of the matrix-vector operations
!! x := A*x, or x := A**T*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(ilp), intent(in) :: incx, k, lda, n
character, intent(in) :: diag, trans, uplo
! Array Arguments
real(sp), intent(in) :: a(lda,*)
real(sp), intent(inout) :: x(*)
! =====================================================================
! Local Scalars
real(sp) :: temp
integer(ilp) :: i, info, ix, j, jx, kplus1, kx, l
logical(lk) :: nounit
! Intrinsic Functions
intrinsic :: 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_xerbla('STBMV ',info)
return
end if
! quick return if possible.
if (n==0) return
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 one 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)/=zero) 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)/=zero) 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)/=zero) 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)/=zero) 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.
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 (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
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 (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
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 (nounit) temp = temp*a(1,j)
do i = j + 1,min(n,j+k)
temp = temp + a(l+i,j)*x(i)
end do
x(j) = temp
end do
else
jx = kx
do j = 1,n
temp = x(jx)
kx = kx + incx
ix = kx
l = 1 - j
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
x(jx) = temp
jx = jx + incx
end do
end if
end if
end if
return
end subroutine stdlib_stbmv
pure subroutine stdlib_stbsv(uplo,trans,diag,n,k,a,lda,x,incx)
!! STBSV solves one of the systems of equations
!! A*x = b, or A**T*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(ilp), intent(in) :: incx, k, lda, n
character, intent(in) :: diag, trans, uplo
! Array Arguments
real(sp), intent(in) :: a(lda,*)
real(sp), intent(inout) :: x(*)
! =====================================================================
! Local Scalars
real(sp) :: temp
integer(ilp) :: i, info, ix, j, jx, kplus1, kx, l
logical(lk) :: nounit
! Intrinsic Functions
intrinsic :: 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_xerbla('STBSV ',info)
return
end if
! quick return if possible.
if (n==0) return
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 one 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)/=zero) 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)/=zero) 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)/=zero) 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)/=zero) 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.
if (stdlib_lsame(uplo,'U')) then
kplus1 = k + 1
if (incx==1) then
do j = 1,n
temp = x(j)
l = kplus1 - j
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)
x(j) = temp
end do
else
jx = kx
do j = 1,n
temp = x(jx)
ix = kx
l = kplus1 - j
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)
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
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)
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
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)
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_stbsv
pure subroutine stdlib_stpmv(uplo,trans,diag,n,ap,x,incx)
!! STPMV performs one of the matrix-vector operations
!! x := A*x, or x := A**T*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(ilp), intent(in) :: incx, n
character, intent(in) :: diag, trans, uplo
! Array Arguments
real(sp), intent(in) :: ap(*)
real(sp), intent(inout) :: x(*)
! =====================================================================
! Local Scalars
real(sp) :: temp
integer(ilp) :: i, info, ix, j, jx, k, kk, kx
logical(lk) :: nounit
! 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_xerbla('STPMV ',info)
return
end if
! quick return if possible.
if (n==0) return
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 one 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)/=zero) 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)/=zero) 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)/=zero) 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)/=zero) 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.
if (stdlib_lsame(uplo,'U')) then
kk = (n* (n+1))/2
if (incx==1) then
do j = n,1,-1
temp = x(j)
if (nounit) temp = temp*ap(kk)
k = kk - 1
do i = j - 1,1,-1
temp = temp + ap(k)*x(i)
k = k - 1
end do
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 (nounit) temp = temp*ap(kk)
do k = kk - 1,kk - j + 1,-1
ix = ix - incx
temp = temp + ap(k)*x(ix)
end do
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)
if (nounit) temp = temp*ap(kk)
k = kk + 1
do i = j + 1,n
temp = temp + ap(k)*x(i)
k = k + 1
end do
x(j) = temp
kk = kk + (n-j+1)
end do
else
jx = kx
do j = 1,n
temp = x(jx)
ix = jx
if (nounit) temp = temp*ap(kk)
do k = kk + 1,kk + n - j
ix = ix + incx
temp = temp + ap(k)*x(ix)
end do
x(jx) = temp
jx = jx + incx
kk = kk + (n-j+1)
end do
end if
end if
end if
return
end subroutine stdlib_stpmv
pure subroutine stdlib_stpsv(uplo,trans,diag,n,ap,x,incx)
!! STPSV solves one of the systems of equations
!! A*x = b, or A**T*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(ilp), intent(in) :: incx, n
character, intent(in) :: diag, trans, uplo
! Array Arguments
real(sp), intent(in) :: ap(*)
real(sp), intent(inout) :: x(*)
! =====================================================================
! Local Scalars
real(sp) :: temp
integer(ilp) :: i, info, ix, j, jx, k, kk, kx
logical(lk) :: nounit
! 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_xerbla('STPSV ',info)
return
end if
! quick return if possible.
if (n==0) return
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 one 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)/=zero) 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)/=zero) 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)/=zero) 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)/=zero) 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.
if (stdlib_lsame(uplo,'U')) then
kk = 1
if (incx==1) then
do j = 1,n
temp = x(j)
k = kk
do i = 1,j - 1
temp = temp - ap(k)*x(i)
k = k + 1
end do
if (nounit) temp = temp/ap(kk+j-1)
x(j) = temp
kk = kk + j
end do
else
jx = kx
do j = 1,n
temp = x(jx)
ix = kx
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)
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
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)
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
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)
x(jx) = temp
jx = jx - incx
kk = kk - (n-j+1)
end do
end if
end if
end if
return
end subroutine stdlib_stpsv
pure subroutine stdlib_strmm(side,uplo,transa,diag,m,n,alpha,a,lda,b,ldb)
!! STRMM 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.
! -- 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(sp), intent(in) :: alpha
integer(ilp), intent(in) :: lda, ldb, m, n
character, intent(in) :: diag, side, transa, uplo
! Array Arguments
real(sp), intent(in) :: a(lda,*)
real(sp), intent(inout) :: b(ldb,*)
! =====================================================================
! Intrinsic Functions
intrinsic :: max
! Local Scalars
real(sp) :: temp
integer(ilp) :: i, info, j, k, nrowa
logical(lk) :: lside, nounit, upper
