Re: [Numpy-discussion] Porting numpy to Python3
On Friday 25 February 2011 18:54:13 Scott Sinclair wrote: On 25 February 2011 06:22, Algis Kabaila akaba...@pcug.org.au wrote: On Friday 25 February 2011 14:44:07 Algis Kabaila wrote: PS: a little investigation shows that my version of numpy is 1.3.0 and scipy is 0.7.2 - so ubuntu binaries are way behind the bleeding edge... ... and built for the system Python (2.6), so even if the Ubuntu binaries were more up to date you'd need to build your own Numpy for Python 3. Cheers, Scott ___ Scott, Good point! Thanks. Al. -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Porting numpy to Python3
On Saturday 26 February 2011 02:58:19 Bruce Southey wrote: On 02/25/2011 02:01 AM, Algis Kabaila wrote: I just build numpy and scipy from source so I do not know how you get Python 3 or which Ubuntu versions include recent numpy versions (there is a upcoming release that will probably contain a more recent numpy). It is very easy to install numpy and scipy from source on Linux although it is important that Blas/Lapack/Altas are built and installed correctly (I just use my distro's package). Please see the following link for more details: http://www.scipy.org/Installing_SciPy/Linux There was also a recent post on the list as well. Bruce Bruce, Thank you for the information. I had a look at the URL that you gave (Actually, I had already seen it in my wanderings on internet.) For me it is very important to hear from the users' perspective how easy or hard the installation was. Python 3 is readily available in most distros, certainly in ubuntu, so that is not a problem. In fact in ubuntu Python 2.6 happily coexists with Python 3.1 for one and the same user. Thank you for your help - greatly appreciated. OldAl. -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
[Numpy-discussion] Porting numpy to Python3
Are there plans to port numpy to Python3? In particular, when will the packages of Linear Algebra (viz matrix inversion) be available in Python 3 compatible modules. Because of the importance of numpy in many scientific endeavours is so great, information of the availability in Python 3 mode is very important and will be greatly appreciated. OldAl. -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Porting numpy to Python3
If there is, then its great news (for me). Where can I check it out? Thanks for responding - Al. On Friday 25 February 2011 13:14:31 Shao Hong wrote: Hi correct me if I am wrong, I thought there is package ported for python 3.1 already? -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Porting numpy to Python3
On Friday 25 February 2011 14:22:04 Bruce Southey wrote: Python 3.1+ support occurred with numpy 1.5 that was released last year (2010-08-31) - 1.5.1 is the current release. scipy 0.9 due very soon (release candidates are available at http://sourceforge.net/projects/scipy/) also supports Python 3 except for weave module. Bruce Bruce, The link http://sourceforge.net/projects/scipy/ responds with Whoops, we can't find that page. I use Linux kubuntu 10.10 (Maverick Meerkat) OS and installed numpy with lapac from the ubuntu binaries. As ubuntu 10.10 was released on 2010-10-10 10:x the version on numpy is probably earlier than 1.5, so presumably I have to either wait a couple of months for the next ubuntu release or install from source. Bruce, can you tell me how can I check the version of installed numpy? There probably is a __version__ or something like that which would enable to verify. Thanks for the answer - I unsuccessfully googled for the answer; I also recall my much earlier enquiries when the replies did not shed much light on the possible release date. Your reply is very much appreciated - thank you! Al. -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Porting numpy to Python3
On Friday 25 February 2011 14:44:07 Algis Kabaila wrote: On Friday 25 February 2011 14:22:04 Bruce Southey wrote: Python 3.1+ support occurred with numpy 1.5 that was released last year (2010-08-31) - 1.5.1 is the current release. scipy 0.9 due very soon (release candidates are available at http://sourceforge.net/projects/scipy/) also supports Python 3 except for weave module. Bruce Bruce, The link http://sourceforge.net/projects/scipy/ responds with Whoops, we can't find that page. I use Linux kubuntu 10.10 (Maverick Meerkat) OS and installed numpy with lapac from the ubuntu binaries. As ubuntu 10.10 was released on 2010-10-10 10:x the version on numpy is probably earlier than 1.5, so presumably I have to either wait a couple of months for the next ubuntu release or install from source. Bruce, can you tell me how can I check the version of installed numpy? There probably is a __version__ or something like that which would enable to verify. Thanks for the answer - I unsuccessfully googled for the answer; I also recall my much earlier enquiries when the replies did not shed much light on the possible release date. Your reply is very much appreciated - thank you! Al. PS: a little investigation shows that my version of numpy is 1.3.0 and scipy is 0.7.2 - so ubuntu binaries are way behind the bleeding edge... Al. -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Inversion of near singular matrices.
On Tuesday 01 February 2011 03:27:22 Sturla Molden wrote: Den 31.01.2011 03:05, skrev Algis Kabaila: Actually, the structural engineer has no interest in trying to invert a singular matrix. However he/she is interested (or should be interested :) ) when the square response matrix might approach singularity for this would signal instability. I am sorry for having confused the issue by mentioning statistics. The mathematics (linear algebra) is of course the same. A singular matrix cannot be inverted by definition. The methods mentioned (SVD, Tikohonov regularization), as well as the transforms mentioned by Paul, will let you avoid numerical instability when matrices approach singularity (i.e. are very ill-conditioned). OT: I think I know what structural engineering is. Back in 1994 I had to take a class in statikk (not sure what that translates to in English), with a textbook by Fritjof Irgens. From what I remember we did vector calculus to ensure the forces in a construction summed to 0, so that Newton's first law of motion would apply. It's unhealthy to be inside a building otherwise ;-) Sturla Molden I would guess that statikk is statics, the subject of conditions of equilibrium. Yes, teaching is not for the faint hearted... Particularly in foreign areas. Just to put your mind at ese - it is important to have some idea of statistics even in simplest engineering structures, such as those made up of statically determinate trusses. (A truss is made up of members that are pin jointed, or are imagined to be pin jointed. Because of the pin joints, each member can only be subjected to an axial force. My next code snippet will show the vagaries of analisis of statically determinate trusses). Before I can really ask my next question, I should know what matrix norms are used for the calculation of matrix condition number in numpy.linalg. You see, I tried to compare it with a condition number found in an undergraduate text book and got a totally different number. So if you know that and are able to explain it in simple terms so that even engineers can understand it, it will be greatly appreciated. Al. -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Inversion of near singular matrices.
And if you are trying to solve a least-squares, I think that you should be using a ridge (or Tikhonov) regularisation: http://en.wikipedia.org/wiki/Tikhonov_regularization read in particular the paragraph above the table of content: you are most likely interested in Gamma = alpha identity, where you set alpha to be say 1% (or .1%) of the largest eigenvalue of A^t A. Gael First of all I want to thank all who have contributed to this discussion. It has been nothing less than inspiring! However, it has drifted to areas in which I lack expertese and interest. My interest is in structural analysis of engineering structures. The structure response is generally characterised by a square matrix with real elements. Actually, the structural engineer has no interest in trying to invert a singular matrix. However he/she is interested (or should be interested :) ) when the square response matrix might approach singularity for this would signal instability. He/She knows what the result of instability would be - a disaster! It is my fault not to have stated the problem with adequate clarity and I intend to do that as soon as I can. Thank you again for all your valuable contributions. Al. -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
[Numpy-discussion] Inversion of near singular matrices.
Hi, I am interested in determining if a matrix is singular or nearly singular - very ill conditioned. The problem occurs in structural engineering applications. My OS is kubuntu 10.10 (32 bit) Python 2.6.6 numpy and numpy.linalg binaries from ubuntu repositories. The attached tar ball has a little CLI script that generates singular or near singular matrices (because of the inevitable roundoffs) for matrices with elements from sequence 1, 2, 3, 4 etc. The dimension of matrix nn can be passed as command line parameter via sys.argv[1] . If argv[1] does not exist, the 5x5 default matrix is used. for nn = 3 and 4 numpy does not raise an exception for nn = 5 it does raise an exception for nn = 6, 7 np not raises exception for nn = 8 np does raise exception for nn = 9 np does not raise exception for higher nn values np mostly raises the exception, but for nn = 23 and nn=120 it does NOT raise the exception. It is worht noting that in practical problems of engineering analyisis the ill conditioned matrix is not exact - there always are approximations and roundoff errors. So my question is: how can one reliably detect singularity (or near singularity) and raise an exception? Many thanks for your attention, Al. -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf inversion.tar.gz Description: application/compressed-tar ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Inversion of near singular matrices.
On Saturday 29 January 2011 22:47:23 Stuart Brorson wrote: So my question is: how can one reliably detect singularity (or near singularity) and raise an exception? Matrix condition number: http://docs.scipy.org/doc/numpy/reference/generated/numpy.lin alg.cond.html http://en.wikipedia.org/wiki/Condition_number Stuart Stuart, Thank you for the wonderful pointer to good information. When I was writing my PhD in 1966, there was little if anything known about the condition mumbers. Your judiciously chosen references put me on the track to search some information about it. Internet is wonderful - there are some well written material there to keep me quietly reading for a while... Thank you, Al. (aka OldAl) -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Inversion of near singular matrices.
On Sunday 30 January 2011 09:10:30 Sturla Molden wrote: Den 29.01.2011 12:40, skrev Algis Kabaila: So my question is: how can one reliably detect singularity (or near singularity) and raise an exception? Use an SVD, examine the singular values. I gather that SVD is the Singular Value Decomposition, but I have no idea how to perform such decomposition. Would you care to refer me to some simple source material? I have been advised to watch the condition numbers. No doubt, SVD and condition numbers are related. The references about condition numbers are very interesting and I intend to follow them in the first instance. In statistics we sometimes see ill-conditioning of covariance matrices. Another way to deal with multicollinearity besides SVD/PCA is regularisation. Simply adding a small bias k*I to the diagonal might fix the problem (cf. ridge regression). In the Levenberg-Marquardt algorithm used to fit non-linear least squares models (cf. scipy.optimize.leastsq), the bias k to the diagonal of the Jacobian is changed adaptively. One might also know in advance if a covariance matrix could be ill-conditioned (the number of samples is small compared to the number of dimensions) or singular (less data than parameters). That is, sometimes we don't even need to look at the matrix to give the correct diagnosis. Another widely used strategy is to use Cholesky factorization on covariance matrices. It is always stable unless there is a singularity, for which it will fail (NumPy will raise a LinAlgError exception). Cholesky is therefore safer to use for inverting covariance matrices than LU (as well as faster). If Cholesky fails one might fallback to SVD or regularisation to correct the problem. Sturla My knowledge of statistics is rather limited, though our son Dr. Paul Kabaila is a specialist in that area. My interests lie in the area of Analysis of Engineering Structures - it saves my brain from falling to a permafrost like sleep :) Thank you for your reply - greatly appreciated. Al. PS: Paul, I thought there is a minuscule chance that this is of some interest to you. Tete. -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Inversion of near singular matrices.
On Sunday 30 January 2011 16:35:15 Charles R Harris wrote: On Sat, Jan 29, 2011 at 10:11 PM, Algis Kabaila akaba...@pcug.org.auwrote: On Sunday 30 January 2011 09:10:30 Sturla Molden wrote: Den 29.01.2011 12:40, skrev Algis Kabaila: So my question is: how can one reliably detect singularity (or near singularity) and raise an exception? Use an SVD, examine the singular values. I gather that SVD is the Singular Value Decomposition, but I have no idea how to perform such decomposition. snip Use numpy.linalg.svd. The condition number is the ratio of the largest singular value to the smallest. snip Chuck Why not simply numply.linalg.cond? This gives the condition number directly (and presumably performs the inspection of sv's). Or do you think that sv's give more useful information? Thanks for writing - I find it all rather fascinating... Gratefully, Al. -- Algis http://akabaila.pcug.org.au/StructuralAnalysis.pdf ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
