stdlib_zgemm Subroutine

     pure subroutine stdlib_zgemm(transa,transb,m,n,k,alpha,a,lda,b,ldb,beta,c,ldc)
     !! ZGEMM 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   or   op( X ) = X**H,
     !! 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 
           complex(dp), intent(in) :: alpha, beta
           integer(ilp), intent(in) :: k, lda, ldb, ldc, m, n
           character, intent(in) :: transa, transb
           ! Array Arguments 
           complex(dp), intent(in) :: a(lda,*), b(ldb,*)
           complex(dp), intent(inout) :: c(ldc,*)
        ! =====================================================================
           ! Intrinsic Functions 
           intrinsic :: conjg,max
           ! Local Scalars 
           complex(dp) :: temp
           integer(ilp) :: i, info, j, l, nrowa, nrowb
           logical(lk) :: conja, conjb, nota, notb
           
           
           ! set  nota  and  notb  as  true if  a  and  b  respectively are not
           ! conjugated or transposed, set  conja and conjb  as true if  a  and
           ! b  respectively are to be  transposed but  not conjugated  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')
           conja = stdlib_lsame(transa,'C')
           conjb = stdlib_lsame(transb,'C')
           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.conja) .and.(.not.stdlib_lsame(transa,'T'))) then
               info = 1
           else if ((.not.notb) .and. (.not.conjb) .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('ZGEMM ',info)
               return
           end if
           ! quick return if possible.
           if ((m==0) .or. (n==0) .or.(((alpha==czero).or. (k==0)).and. (beta==cone))) &
                     return
           ! and when  alpha.eq.czero.
           if (alpha==czero) then
               if (beta==czero) then
                   do j = 1,n
                       do i = 1,m
                           c(i,j) = czero
                       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==czero) then
                           do i = 1,m
                               c(i,j) = czero
                           end do
                       else if (beta/=cone) 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 if (conja) then
                 ! form  c := alpha*a**h*b + beta*c.
                   do j = 1,n
                       do i = 1,m
                           temp = czero
                           do l = 1,k
                               temp = temp + conjg(a(l,i))*b(l,j)
                           end do
                           if (beta==czero) then
                               c(i,j) = alpha*temp
                           else
                               c(i,j) = alpha*temp + beta*c(i,j)
                           end if
                       end do
                   end do
               else
                 ! form  c := alpha*a**t*b + beta*c
                   do j = 1,n
                       do i = 1,m
                           temp = czero
                           do l = 1,k
                               temp = temp + a(l,i)*b(l,j)
                           end do
                           if (beta==czero) 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
               if (conjb) then
                 ! form  c := alpha*a*b**h + beta*c.
                   do j = 1,n
                       if (beta==czero) then
                           do i = 1,m
                               c(i,j) = czero
                           end do
                       else if (beta/=cone) then
                           do i = 1,m
                               c(i,j) = beta*c(i,j)
                           end do
                       end if
                       do l = 1,k
                           temp = alpha*conjg(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*b**t + beta*c
                   do j = 1,n
                       if (beta==czero) then
                           do i = 1,m
                               c(i,j) = czero
                           end do
                       else if (beta/=cone) 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
               end if
           else if (conja) then
               if (conjb) then
                 ! form  c := alpha*a**h*b**h + beta*c.
                   do j = 1,n
                       do i = 1,m
                           temp = czero
                           do l = 1,k
                               temp = temp + conjg(a(l,i))*conjg(b(j,l))
                           end do
                           if (beta==czero) then
                               c(i,j) = alpha*temp
                           else
                               c(i,j) = alpha*temp + beta*c(i,j)
                           end if
                       end do
                   end do
               else
                 ! form  c := alpha*a**h*b**t + beta*c
                   do j = 1,n
                       do i = 1,m
                           temp = czero
                           do l = 1,k
                               temp = temp + conjg(a(l,i))*b(j,l)
                           end do
                           if (beta==czero) 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 (conjb) then
                 ! form  c := alpha*a**t*b**h + beta*c
                   do j = 1,n
                       do i = 1,m
                           temp = czero
                           do l = 1,k
                               temp = temp + a(l,i)*conjg(b(j,l))
                           end do
                           if (beta==czero) then
                               c(i,j) = alpha*temp
                           else
                               c(i,j) = alpha*temp + beta*c(i,j)
                           end if
                       end do
                   end do
               else
                 ! form  c := alpha*a**t*b**t + beta*c
                   do j = 1,n
                       do i = 1,m
                           temp = czero
                           do l = 1,k
                               temp = temp + a(l,i)*b(j,l)
                           end do
                           if (beta==czero) 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_zgemm