[SciPy-dev] Reliability of results

[Nils Wagner]

Hi all,

We should take care of using linalg.inv blindly (test_inv.py).

So how can we improve the behaviour of linalg.solve, linalg.lu,
linalg.inv etc.
with respect to  "nearly" singular  matrices (floating point arithmetic) ?

Any pointer would be appreciated.

Is it possibe to add the condition number to the output of linalg.solve,
linalg.inv, ... ?

For example linalg.lstsq returns the singular values.

lstsq(a, b, cond=None, overwrite_a=0, overwrite_b=0)
    lstsq(a, b, cond=None, overwrite_a=0, overwrite_b=0) -> x,resids,rank,s

    Return least-squares solution of a * x = b.

    Inputs:

      a -- An M x N matrix.
      b -- An M x nrhs matrix or M vector.
      cond -- Used to determine effective rank of a.

    Outputs:

      x -- The solution (N x nrhs matrix) to the minimization problem:
                  2-norm(| b - a * x |) -> min
      resids -- The residual sum-of-squares for the solution matrix x
                (only if M>N and rank==N).
      rank -- The effective rank of a.
      s -- Singular values of a in decreasing order. The condition number
           of a is abs(s[0]/s[-1]).

                                           Nils
 

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