See http://code.google.com/p/macvim/wiki/FAQ for instructions on how to install vim-latex(or known as latex-suite) on macvim.
However, on my Mac OS X Lion, there seems to be a problem with \lv using the default setting. When commanding \lv a pile of error messages jumped out. The fix I found is the following: go to ftplugin/latex-suite, open texrc, uncomment the line
TexLet g:Tex_TreatMacViewerAsUNIX = 1
and add here or to .vimrc the following:
TexLet g:Tex_ViewRule_pdf = ‘open -a Skim’
I use Skim as my pdf viewer. These two resolve the problem.
It may seem that one should go to LAPACK and find a routine that does just this job. However, it turns out that LAPACK does not really have such a routine. So a little bit of detour is needed. If you want to deal with a general, complex matrix, not symmetric, not Hermitian, then the way to go is using Gauss elimination(GE). LAPACK provides routines to find the LU decomposition of a matrix, which is essentially GE and can be used to compute the determinant. Here is the code snippet:
1 complex(kind=8) function det(N, mat)
2 implicit none
3 integer(kind=8), intent(in) :: N
4 complex(kind=8), intent(inout), dimension(:,:) :: mat
5 integer(kind=8) :: i, info
6 integer, allocatable :: ipiv(:)
7 real(kind=8) :: sgn
8
9 allocate(ipiv(N))
10
11 ipiv = 0
12
13 call zgetrf(N, N, mat, N, ipiv, info)
14
15 det = ONE
16 do i = 1, N
17 det = det*mat(i, i)
18 end do
19 sgn = ONE
20 do i = 1, N
21 if(ipiv(i) /= i) then
22 sgn = -sgn
23 end if
24 end do
25 det = sgn*det
26 end function det
