Sat, 16 May 2009 14:02:34 +0000, Pauli Virtanen wrote:

Hi,

Sat, 16 May 2009 16:01:00 +0300, Quilby wrote: [clip]

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http://www.scipy.org/doc/numpy_api_docs/numpy.linalg.linalg.html#lstsq [clip]

Could we take these old Endo-generated docs down, and make the URL redirect to docs.scipy.org?

I went and removed the links to them from http://www.scipy.org/Documentation -- Pauli Virtanen

Right the dimensions I gave were wrong. What do I need to do for m>=n (more rows than columns)? Can I use the same function? When I run the script written by Nils (thanks!) I get: from numpy.random import rand, seed ImportError: No module named random But importing numpy works ok. What do I need to install? Thanks again! On Sun, May 17, 2009 at 1:51 AM, Alan G Isaac wrote:

On 5/16/2009 9:01 AM Quilby apparently wrote:

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Ax = y Where A is a rational m*n matrix (m<=n), and x and y are vectors of the right size. I know A and y, I don't know what x is equal to. I also know that there is no x where Ax equals exactly y.

If m<=n, that can only be true if there are not m linearly independent columns of A. Are you sure you have the dimensions right?

Alan Isaac

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Alternatively, to solve A x = b you could do import numpy import numpy.linalg B = numpy.dot(A.T, A) c = numpy.dot(A.T, b) x = numpy.linalg(B,c) This is not the most efficient way to do it but at least you know exactly what's going on in your code. On Sun, May 17, 2009 at 7:21 PM, wrote:

On Sun, May 17, 2009 at 12:14 PM, Quilby wrote:

...

Right the dimensions I gave were wrong. What do I need to do for m>=n (more rows than columns)? Can I use the same function?

When I run the script written by Nils (thanks!) I get: from numpy.random import rand, seed ImportError: No module named random

But importing numpy works ok. What do I need to install?

This should be working without extra install. You could run the test suite, numpy.test(), to see whether your install is ok.

Otherwise, you would need to provide more information, numpy version, ....

np.lstsq works for m>n, mn (more observations than parameters) is the standard least squares estimation problem.

Josef

...

Thanks again!

On Sun, May 17, 2009 at 1:51 AM, Alan G Isaac wrote:

...

On 5/16/2009 9:01 AM Quilby apparently wrote:

...

Ax = y Where A is a rational m*n matrix (m<=n), and x and y are vectors of the right size. I know A and y, I don't know what x is equal to. I also know that there is no x where Ax equals exactly y.

If m<=n, that can only be true if there are not m linearly independent columns of A. Are you sure you have the dimensions right?

Alan Isaac

_______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion

2009/5/18 Stéfan van der Walt :

2009/5/18 Sebastian Walter :

...

B = numpy.dot(A.T, A)

This multiplication should be avoided whenever possible -- you are effectively squaring your condition number. Indeed.

In the case where you have more rows than columns, use least squares. For square matrices use solve. For large sparse matrices, use GMRES or any of the others available in scipy.sparse.linalg.

It is my impression that this is a linear algebra and not a numerics question.

Regards Stéfan _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion

On Mon, May 18, 2009 at 10:55 AM, Charles R Harris wrote:

2009/5/18 Stéfan van der Walt

...

2009/5/18 Sebastian Walter :

...

B = numpy.dot(A.T, A)

This multiplication should be avoided whenever possible -- you are effectively squaring your condition number.

Although the condition number doesn't mean much unless the columns are normalized. Having badly scaled columns can lead to problems with lstsq because of its default cutoff based on the condition number.

Chuck

Do you know if any of the linalg methods, np.linalg.lstsq or scipy.linalg.lstsq, do any normalization internally to improve numerical accuracy? I saw automatic internal normalization (e.g. rescaling) for some econometrics methods, and was wondering whether we should do this also in stats.models or whether scipy.linalg is already taking care of this. I have only vague knowledge of the numerical precision of different linear algebra methods. Thanks, Josef