stdlib_ztpsv Subroutine

     pure subroutine stdlib_ztpsv(uplo,trans,diag,n,ap,x,incx)
     !! ZTPSV solves one of the systems of equations
     !! A*x = b,   or   A**T*x = b,   or   A**H*x = b,
     !! where b and x are n element vectors and A is an n by n unit, or
     !! non-unit, upper or lower triangular matrix, supplied in packed form.
     !! No test for singularity or near-singularity is included in this
     !! routine. Such tests must be performed before calling this routine.
        ! -- reference blas level2 routine --
        ! -- reference blas is a software package provided by univ. of tennessee,    --
        ! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
           ! Scalar Arguments 
           integer(ilp), intent(in) :: incx, n
           character, intent(in) :: diag, trans, uplo
           ! Array Arguments 
           complex(dp), intent(in) :: ap(*)
           complex(dp), intent(inout) :: x(*)
        ! =====================================================================
           
           ! Local Scalars 
           complex(dp) :: temp
           integer(ilp) :: i, info, ix, j, jx, k, kk, kx
           logical(lk) :: noconj, nounit
           ! Intrinsic Functions 
           intrinsic :: conjg
           ! test the input parameters.
           info = 0
           if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
               info = 1
           else if (.not.stdlib_lsame(trans,'N') .and. .not.stdlib_lsame(trans,'T') &
                     .and..not.stdlib_lsame(trans,'C')) then
               info = 2
           else if (.not.stdlib_lsame(diag,'U') .and. .not.stdlib_lsame(diag,'N')) then
               info = 3
           else if (n<0) then
               info = 4
           else if (incx==0) then
               info = 7
           end if
           if (info/=0) then
               call stdlib_xerbla('ZTPSV ',info)
               return
           end if
           ! quick return if possible.
           if (n==0) return
           noconj = stdlib_lsame(trans,'T')
           nounit = stdlib_lsame(diag,'N')
           ! set up the start point in x if the increment is not unity. this
           ! will be  ( n - 1 )*incx  too small for descending loops.
           if (incx<=0) then
               kx = 1 - (n-1)*incx
           else if (incx/=1) then
               kx = 1
           end if
           ! start the operations. in this version the elements of ap are
           ! accessed sequentially with cone pass through ap.
           if (stdlib_lsame(trans,'N')) then
              ! form  x := inv( a )*x.
               if (stdlib_lsame(uplo,'U')) then
                   kk = (n* (n+1))/2
                   if (incx==1) then
                       do j = n,1,-1
                           if (x(j)/=czero) then
                               if (nounit) x(j) = x(j)/ap(kk)
                               temp = x(j)
                               k = kk - 1
                               do i = j - 1,1,-1
                                   x(i) = x(i) - temp*ap(k)
                                   k = k - 1
                               end do
                           end if
                           kk = kk - j
                       end do
                   else
                       jx = kx + (n-1)*incx
                       do j = n,1,-1
                           if (x(jx)/=czero) then
                               if (nounit) x(jx) = x(jx)/ap(kk)
                               temp = x(jx)
                               ix = jx
                               do k = kk - 1,kk - j + 1,-1
                                   ix = ix - incx
                                   x(ix) = x(ix) - temp*ap(k)
                               end do
                           end if
                           jx = jx - incx
                           kk = kk - j
                       end do
                   end if
               else
                   kk = 1
                   if (incx==1) then
                       do j = 1,n
                           if (x(j)/=czero) then
                               if (nounit) x(j) = x(j)/ap(kk)
                               temp = x(j)
                               k = kk + 1
                               do i = j + 1,n
                                   x(i) = x(i) - temp*ap(k)
                                   k = k + 1
                               end do
                           end if
                           kk = kk + (n-j+1)
                       end do
                   else
                       jx = kx
                       do j = 1,n
                           if (x(jx)/=czero) then
                               if (nounit) x(jx) = x(jx)/ap(kk)
                               temp = x(jx)
                               ix = jx
                               do k = kk + 1,kk + n - j
                                   ix = ix + incx
                                   x(ix) = x(ix) - temp*ap(k)
                               end do
                           end if
                           jx = jx + incx
                           kk = kk + (n-j+1)
                       end do
                   end if
               end if
           else
              ! form  x := inv( a**t )*x  or  x := inv( a**h )*x.
               if (stdlib_lsame(uplo,'U')) then
                   kk = 1
                   if (incx==1) then
                       do j = 1,n
                           temp = x(j)
                           k = kk
                           if (noconj) then
                               do i = 1,j - 1
                                   temp = temp - ap(k)*x(i)
                                   k = k + 1
                               end do
                               if (nounit) temp = temp/ap(kk+j-1)
                           else
                               do i = 1,j - 1
                                   temp = temp - conjg(ap(k))*x(i)
                                   k = k + 1
                               end do
                               if (nounit) temp = temp/conjg(ap(kk+j-1))
                           end if
                           x(j) = temp
                           kk = kk + j
                       end do
                   else
                       jx = kx
                       do j = 1,n
                           temp = x(jx)
                           ix = kx
                           if (noconj) then
                               do k = kk,kk + j - 2
                                   temp = temp - ap(k)*x(ix)
                                   ix = ix + incx
                               end do
                               if (nounit) temp = temp/ap(kk+j-1)
                           else
                               do k = kk,kk + j - 2
                                   temp = temp - conjg(ap(k))*x(ix)
                                   ix = ix + incx
                               end do
                               if (nounit) temp = temp/conjg(ap(kk+j-1))
                           end if
                           x(jx) = temp
                           jx = jx + incx
                           kk = kk + j
                       end do
                   end if
               else
                   kk = (n* (n+1))/2
                   if (incx==1) then
                       do j = n,1,-1
                           temp = x(j)
                           k = kk
                           if (noconj) then
                               do i = n,j + 1,-1
                                   temp = temp - ap(k)*x(i)
                                   k = k - 1
                               end do
                               if (nounit) temp = temp/ap(kk-n+j)
                           else
                               do i = n,j + 1,-1
                                   temp = temp - conjg(ap(k))*x(i)
                                   k = k - 1
                               end do
                               if (nounit) temp = temp/conjg(ap(kk-n+j))
                           end if
                           x(j) = temp
                           kk = kk - (n-j+1)
                       end do
                   else
                       kx = kx + (n-1)*incx
                       jx = kx
                       do j = n,1,-1
                           temp = x(jx)
                           ix = kx
                           if (noconj) then
                               do k = kk,kk - (n- (j+1)),-1
                                   temp = temp - ap(k)*x(ix)
                                   ix = ix - incx
                               end do
                               if (nounit) temp = temp/ap(kk-n+j)
                           else
                               do k = kk,kk - (n- (j+1)),-1
                                   temp = temp - conjg(ap(k))*x(ix)
                                   ix = ix - incx
                               end do
                               if (nounit) temp = temp/conjg(ap(kk-n+j))
                           end if
                           x(jx) = temp
                           jx = jx - incx
                           kk = kk - (n-j+1)
                       end do
                   end if
               end if
           end if
           return
     end subroutine stdlib_ztpsv