[Numpy-discussion] lstsq underdetermined behaviour

[Romesh Abeysuriya]

Thanks both! Yes, I guess it's typically 'least squares' referring to
the residual vector, and 'minimum norm' referring to the solution
vector. That's certainly how the documentation for `dgelsd` frames it.
In my case, the minimum norm solution can be sensibly interpreted (and
in particular, it guarantees that the solution is 0 for missing
variables), so it's great to know that I can rely on this being
returned

Cheers,
Romesh



On Mon, Nov 19, 2018 at 12:30 PM Charles R Harris
<charlesr.harris at gmail.com> wrote:
>
>
>
> On Sun, Nov 18, 2018 at 9:24 PM Eric Wieser <wieser.eric+numpy at gmail.com> wrote:
>>
>> > In 1.15 the call is instead to `_umath_linalg.lstsq_m` and I'm not sure what this actually ends up doing - does this end up being the same as `dgelsd`?
>>
>> When the arguments are real, yes. What changed is that the dispatching now happens in C, which was done as a step towards the incomplete https://github.com/numpy/numpy/issues/8720.
>>
>> I'm not an expert - but aren't "minimum norm" and "least squares" two ways to state the same thing?
>>
>
> If there aren't enough data points to uniquely determine the minimizing solution, the solution vector of shortest length is returned. In practice it is pretty useless because it depends on the column scaling and there is generally no natural metric in the solution space.
>
> <snip>
>
> Chuck
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