stdlib_dtrsm Subroutine

     pure subroutine stdlib_dtrsm(side,uplo,transa,diag,m,n,alpha,a,lda,b,ldb)
     !! DTRSM solves one of the matrix equations
     !! op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,
     !! where alpha is a scalar, X and B are m by n matrices, A is a unit, or
     !! non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
     !! op( A ) = A   or   op( A ) = A**T.
     !! The matrix X is overwritten on B.
        ! -- reference blas level3 routine --
        ! -- reference blas is a software package provided by univ. of tennessee,    --
        ! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
           ! Scalar Arguments 
           real(dp), intent(in) :: alpha
           integer(ilp), intent(in) :: lda, ldb, m, n
           character, intent(in) :: diag, side, transa, uplo
           ! Array Arguments 
           real(dp), intent(in) :: a(lda,*)
           real(dp), intent(inout) :: b(ldb,*)
        ! =====================================================================
           ! Intrinsic Functions 
           intrinsic :: max
           ! Local Scalars 
           real(dp) :: temp
           integer(ilp) :: i, info, j, k, nrowa
           logical(lk) :: lside, nounit, upper
           
           ! test the input parameters.
           lside = stdlib_lsame(side,'L')
           if (lside) then
               nrowa = m
           else
               nrowa = n
           end if
           nounit = stdlib_lsame(diag,'N')
           upper = stdlib_lsame(uplo,'U')
           info = 0
           if ((.not.lside) .and. (.not.stdlib_lsame(side,'R'))) then
               info = 1
           else if ((.not.upper) .and. (.not.stdlib_lsame(uplo,'L'))) then
               info = 2
           else if ((.not.stdlib_lsame(transa,'N')) .and.(.not.stdlib_lsame(transa,'T')) .and.(&
                     .not.stdlib_lsame(transa,'C'))) then
               info = 3
           else if ((.not.stdlib_lsame(diag,'U')) .and. (.not.stdlib_lsame(diag,'N'))) &
                     then
               info = 4
           else if (m<0) then
               info = 5
           else if (n<0) then
               info = 6
           else if (lda<max(1,nrowa)) then
               info = 9
           else if (ldb<max(1,m)) then
               info = 11
           end if
           if (info/=0) then
               call stdlib_xerbla('DTRSM ',info)
               return
           end if
           ! quick return if possible.
           if (m==0 .or. n==0) return
           ! and when  alpha.eq.zero.
           if (alpha==zero) then
               do j = 1,n
                   do i = 1,m
                       b(i,j) = zero
                   end do
               end do
               return
           end if
           ! start the operations.
           if (lside) then
               if (stdlib_lsame(transa,'N')) then
                 ! form  b := alpha*inv( a )*b.
                   if (upper) then
                       do j = 1,n
                           if (alpha/=one) then
                               do i = 1,m
                                   b(i,j) = alpha*b(i,j)
                               end do
                           end if
                           do k = m,1,-1
                               if (b(k,j)/=zero) then
                                   if (nounit) b(k,j) = b(k,j)/a(k,k)
                                   do i = 1,k - 1
                                       b(i,j) = b(i,j) - b(k,j)*a(i,k)
                                   end do
                               end if
                           end do
                       end do
                   else
                       do j = 1,n
                           if (alpha/=one) then
                               do i = 1,m
                                   b(i,j) = alpha*b(i,j)
                               end do
                           end if
                           do k = 1,m
                               if (b(k,j)/=zero) then
                                   if (nounit) b(k,j) = b(k,j)/a(k,k)
                                   do i = k + 1,m
                                       b(i,j) = b(i,j) - b(k,j)*a(i,k)
                                   end do
                               end if
                           end do
                       end do
                   end if
               else
                 ! form  b := alpha*inv( a**t )*b.
                   if (upper) then
                       do j = 1,n
                           do i = 1,m
                               temp = alpha*b(i,j)
                               do k = 1,i - 1
                                   temp = temp - a(k,i)*b(k,j)
                               end do
                               if (nounit) temp = temp/a(i,i)
                               b(i,j) = temp
                           end do
                       end do
                   else
                       do j = 1,n
                           do i = m,1,-1
                               temp = alpha*b(i,j)
                               do k = i + 1,m
                                   temp = temp - a(k,i)*b(k,j)
                               end do
                               if (nounit) temp = temp/a(i,i)
                               b(i,j) = temp
                           end do
                       end do
                   end if
               end if
           else
               if (stdlib_lsame(transa,'N')) then
                 ! form  b := alpha*b*inv( a ).
                   if (upper) then
                       do j = 1,n
                           if (alpha/=one) then
                               do i = 1,m
                                   b(i,j) = alpha*b(i,j)
                               end do
                           end if
                           do k = 1,j - 1
                               if (a(k,j)/=zero) then
                                   do i = 1,m
                                       b(i,j) = b(i,j) - a(k,j)*b(i,k)
                                   end do
                               end if
                           end do
                           if (nounit) then
                               temp = one/a(j,j)
                               do i = 1,m
                                   b(i,j) = temp*b(i,j)
                               end do
                           end if
                       end do
                   else
                       do j = n,1,-1
                           if (alpha/=one) then
                               do i = 1,m
                                   b(i,j) = alpha*b(i,j)
                               end do
                           end if
                           do k = j + 1,n
                               if (a(k,j)/=zero) then
                                   do i = 1,m
                                       b(i,j) = b(i,j) - a(k,j)*b(i,k)
                                   end do
                               end if
                           end do
                           if (nounit) then
                               temp = one/a(j,j)
                               do i = 1,m
                                   b(i,j) = temp*b(i,j)
                               end do
                           end if
                       end do
                   end if
               else
                 ! form  b := alpha*b*inv( a**t ).
                   if (upper) then
                       do k = n,1,-1
                           if (nounit) then
                               temp = one/a(k,k)
                               do i = 1,m
                                   b(i,k) = temp*b(i,k)
                               end do
                           end if
                           do j = 1,k - 1
                               if (a(j,k)/=zero) then
                                   temp = a(j,k)
                                   do i = 1,m
                                       b(i,j) = b(i,j) - temp*b(i,k)
                                   end do
                               end if
                           end do
                           if (alpha/=one) then
                               do i = 1,m
                                   b(i,k) = alpha*b(i,k)
                               end do
                           end if
                       end do
                   else
                       do k = 1,n
                           if (nounit) then
                               temp = one/a(k,k)
                               do i = 1,m
                                   b(i,k) = temp*b(i,k)
                               end do
                           end if
                           do j = k + 1,n
                               if (a(j,k)/=zero) then
                                   temp = a(j,k)
                                   do i = 1,m
                                       b(i,j) = b(i,j) - temp*b(i,k)
                                   end do
                               end if
                           end do
                           if (alpha/=one) then
                               do i = 1,m
                                   b(i,k) = alpha*b(i,k)
                               end do
                           end if
                       end do
                   end if
               end if
           end if
           return
     end subroutine stdlib_dtrsm