[Numpy-discussion] SVD errors

[Pauli Virtanen]

Mon, 02 Feb 2009 18:27:05 -0600, Robert Kern wrote:
> On Mon, Feb 2, 2009 at 18:21,  <mtrumpis at berkeley.edu> wrote:
>> Hello list.. I've run into two SVD errors over the last few days. Both
>> errors are identical in numpy/scipy.
>>
>> I've submitted a ticket for the 1st problem (numpy ticket #990).
>> Summary is: some builds of the lapack_lite module linking against
>> system LAPACK (not the bundled dlapack_lite.o, etc) give a
>> "LinAlgError: SVD did not converge" exception on my matrix. This error
>> does occur using Mac's Accelerate framework LAPACK, and a coworker's
>> Ubuntu LAPACK version. It does not seem to happen using ATLAS LAPACK
>> (nor using Octave/Matlab on said Ubuntu)
> 
> These are almost certainly issues with the particular implementations of
> LAPACK that you are using. I don't think there is anything we can do
> from numpy or scipy to change this.

Yes, this is almost certainly a LAPACK problem. If in doubt, you can test 
it with the following F90 program (be sure to link it against the same 
LAPACK as Numpy). Save the matrices with 'np.savetxt("foo.txt", x.ravel
())' and run './test < foo.txt'.

----
program test
    implicit none
    integer, parameter :: N = 128
    double precision :: A(N*N), S(N), U(N,N), Vh(N,N)
    double precision, allocatable :: WORK(:)
    double precision :: tmp
    integer :: IWORK(8*N)
    integer :: INFO = 0, LWORK

    read(*,*) A
    A = reshape(transpose(reshape(A, (/N, N/))), (/ N*N /))
    call dgesdd('A', N, N, A, N, S, U, N, Vh, N, tmp, -1, IWORK, INFO)
    LWORK = tmp
    if (info .ne. 0) stop 'lwork query failed'
    write(*,*) 'lwork:', lwork
    allocate(WORK(LWORK))
    call dgesdd('A', N, N, A, N, S, U, N, Vh, N, WORK, LWORK, IWORK, INFO)
    write(*,*) 'info:', INFO
    write(*,*) 'min(S):', minval(S)
    if (INFO .ne. 0) then
        write(*,*) ' -> SVD failed to converge'
    end if
    if (minval(S) .lt. 0) then
        write(*,*) ' -> negative singular value'
    end if
end program
----