Re: [Numpy-discussion] preferred way of testing empty arrays
On Fri, Jan 27, 2012 at 1:29 PM, Robert Kern wrote: > Well, if you really need to do this in more than one place, define a > utility function and call it a day. > > def should_not_plot(x): > if x is None: > return True > elif isinstance(x, np.ndarray): > return x.size == 0 > else: > return bool(x) I tend to do things like: def convert_to_plotable(x): if x is None: return None else: x = np.asarray(x) if b.size == 0: return None return x it does mean you need to check for None later anyway, but I like to convert to an array early in the process -- then you know you have either an array or None at that point. NOTE: you could also raise and handle an exception instead. -Chris -- Christopher Barker, Ph.D. Oceanographer Emergency Response Division NOAA/NOS/OR&R (206) 526-6959 voice 7600 Sand Point Way NE (206) 526-6329 fax Seattle, WA 98115 (206) 526-6317 main reception chris.bar...@noaa.gov ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] histogram help
Hi Ruby, I still do not fully understand your question but what I do in such cases is to construct a very simple array and test the functions. The help of numpy.histogram2d or numpy.histogramdd (for more than two dims) might help here. So I guess, basically you want to ignore the x,y positions and just look at the combined distribution of the Z values? In this case, you would just need the numpy.histogram (the 1d version). Note that the histogram returns the numbers and the bin-borders. bests Samuel On 30.01.2012, at 20:27, Ruby Stevenson wrote: > Sorry, I realize I didn't describe the problem completely clear or correct. > > the (x,y) in this case is just many co-ordinates, and each coordinate > has a list of values (Z value) associated with it. The bins are > allocated for the Z. > > I hope this clarify things a little. Thanks again. > > Ruby > > > > > On Mon, Jan 30, 2012 at 2:21 PM, Ruby Stevenson wrote: >> hi, all >> >> I am trying to figure out how to do histogram with numpy >> >> I have a three-dimension array A[x,y,z], another array (bins) has >> been allocated along Z dimension, z' >> >> how can I get the histogram of H[ x, y, z' ]? >> >> thanks for your help. >> >> Ruby > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] histogram help
Sorry, I realize I didn't describe the problem completely clear or correct. the (x,y) in this case is just many co-ordinates, and each coordinate has a list of values (Z value) associated with it. The bins are allocated for the Z. I hope this clarify things a little. Thanks again. Ruby On Mon, Jan 30, 2012 at 2:21 PM, Ruby Stevenson wrote: > hi, all > > I am trying to figure out how to do histogram with numpy > > I have a three-dimension array A[x,y,z], another array (bins) has > been allocated along Z dimension, z' > > how can I get the histogram of H[ x, y, z' ]? > > thanks for your help. > > Ruby ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] condense array along one dimension
I think this is exactly what I need. Thanks for your help, Olivier. Ruby On Fri, Jan 20, 2012 at 9:50 AM, Olivier Delalleau wrote: > What do you mean by "summarize"? > If for instance you want to sum along Y, just do > my_array.sum(axis=1) > > -=- Olivier > > 2012/1/20 Ruby Stevenson >> >> hi, all >> >> Say I have a three dimension array, X, Y, Z, how can I condense into >> two dimensions: for example, compute 2-D array with (X, Z) and >> summarize along Y dimensions ... is it possible? >> >> thanks >> >> Ruby >> ___ >> NumPy-Discussion mailing list >> NumPy-Discussion@scipy.org >> http://mail.scipy.org/mailman/listinfo/numpy-discussion > > > > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
> You'd want to update your mask appropriately to get everything you > want to select, one criteria at a time e.g.: > mask = a[:,0] == 1 > mask &= a[:,1] == 1960 > > Alternatively: > mask = (a[:,0] == 1) & (a[:,1] == 1960) > but be careful with the parens, & and | are normally high-priority > bitwise operators and if you leave the parens out, it will try to > bitwise-and 1 and a[:,1] and throw an error. > > If you've got a ton of parameters, you can combine these more > aesthetically with: > mask = (a[:,[0,1]] == [1, 1960]).all(axis=1) > > ~Brett Zach and Brett, Many thanks -- that is exactly what I need. Cheers, Ted ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
On Mon, Jan 30, 2012 at 11:31 AM, Ted To wrote: > On 01/30/2012 12:13 PM, Brett Olsen wrote: >> On Mon, Jan 30, 2012 at 10:57 AM, Ted To wrote: >>> Sure thing. To keep it simple suppose I have just a two dimensional >>> array (time,output): >>> [(1,2),(2,3),(3,4)] >>> I would like to look at all values of output for which, for example time==2. >>> >>> My actual application has a six dimensional array and I'd like to look >>> at the contents using one or more of the first three dimensions. >>> >>> Many thanks, >>> Ted >> >> Couldn't you just do something like this with boolean indexing: >> >> In [1]: import numpy as np >> >> In [2]: a = np.array([(1,2),(2,3),(3,4)]) >> >> In [3]: a >> Out[3]: >> array([[1, 2], >> [2, 3], >> [3, 4]]) >> >> In [4]: mask = a[:,0] == 2 >> >> In [5]: mask >> Out[5]: array([False, True, False], dtype=bool) >> >> In [6]: a[mask,1] >> Out[6]: array([3]) >> >> ~Brett > > Thanks! That works great if I only want to search over one index but I > can't quite figure out what to do with more than a single index. So > suppose I have a labeled, multidimensional array with labels 'month', > 'year' and 'quantity'. a[['month','year']] gives me an array of indices > but "a[['month','year']]==(1,1960)" produces "False". I'm sure I simply > don't know the proper syntax and I apologize for that -- I'm kind of new > to numpy. > > Ted You'd want to update your mask appropriately to get everything you want to select, one criteria at a time e.g.: mask = a[:,0] == 1 mask &= a[:,1] == 1960 Alternatively: mask = (a[:,0] == 1) & (a[:,1] == 1960) but be careful with the parens, & and | are normally high-priority bitwise operators and if you leave the parens out, it will try to bitwise-and 1 and a[:,1] and throw an error. If you've got a ton of parameters, you can combine these more aesthetically with: mask = (a[:,[0,1]] == [1, 1960]).all(axis=1) ~Brett ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
> Thanks! That works great if I only want to search over one index but I > can't quite figure out what to do with more than a single index. So > suppose I have a labeled, multidimensional array with labels 'month', > 'year' and 'quantity'. a[['month','year']] gives me an array of indices > but "a[['month','year']]==(1,1960)" produces "False". I'm sure I simply > don't know the proper syntax and I apologize for that -- I'm kind of new > to numpy. I think that your best bet is to form the boolean masks independently and then logical-and them together: mask = (a['month'] == 1) & (a['year'] == 1960) jan_60 = a[mask] Someone might have more insight here. Though I should note that if you have large data and are doing lots of "queries" like this, a more database-ish approach might be better. Something like sqlite's python bindings, or PyTables. Alternately, if your data are all time-series based things, PANDAS might be worth looking at. But the above approach should be just fine for non-huge datasets... Zach ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
On 01/30/2012 12:13 PM, Brett Olsen wrote: > On Mon, Jan 30, 2012 at 10:57 AM, Ted To wrote: >> Sure thing. To keep it simple suppose I have just a two dimensional >> array (time,output): >> [(1,2),(2,3),(3,4)] >> I would like to look at all values of output for which, for example time==2. >> >> My actual application has a six dimensional array and I'd like to look >> at the contents using one or more of the first three dimensions. >> >> Many thanks, >> Ted > > Couldn't you just do something like this with boolean indexing: > > In [1]: import numpy as np > > In [2]: a = np.array([(1,2),(2,3),(3,4)]) > > In [3]: a > Out[3]: > array([[1, 2], >[2, 3], >[3, 4]]) > > In [4]: mask = a[:,0] == 2 > > In [5]: mask > Out[5]: array([False, True, False], dtype=bool) > > In [6]: a[mask,1] > Out[6]: array([3]) > > ~Brett Thanks! That works great if I only want to search over one index but I can't quite figure out what to do with more than a single index. So suppose I have a labeled, multidimensional array with labels 'month', 'year' and 'quantity'. a[['month','year']] gives me an array of indices but "a[['month','year']]==(1,1960)" produces "False". I'm sure I simply don't know the proper syntax and I apologize for that -- I'm kind of new to numpy. Ted ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
On Mon, Jan 30, 2012 at 10:57 AM, Ted To wrote: > Sure thing. To keep it simple suppose I have just a two dimensional > array (time,output): > [(1,2),(2,3),(3,4)] > I would like to look at all values of output for which, for example time==2. > > My actual application has a six dimensional array and I'd like to look > at the contents using one or more of the first three dimensions. > > Many thanks, > Ted Couldn't you just do something like this with boolean indexing: In [1]: import numpy as np In [2]: a = np.array([(1,2),(2,3),(3,4)]) In [3]: a Out[3]: array([[1, 2], [2, 3], [3, 4]]) In [4]: mask = a[:,0] == 2 In [5]: mask Out[5]: array([False, True, False], dtype=bool) In [6]: a[mask,1] Out[6]: array([3]) ~Brett ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
Sure thing. To keep it simple suppose I have just a two dimensional array (time,output): [(1,2),(2,3),(3,4)] I would like to look at all values of output for which, for example time==2. My actual application has a six dimensional array and I'd like to look at the contents using one or more of the first three dimensions. Many thanks, Ted On 01/30/2012 10:50 AM, Zachary Pincus wrote: > Ted, can you clarify what you're asking for? Maybe give a trivial example of > an array and the desired output? > > I'm pretty sure this is a slicing question though: >> If I have a three dimensional array a=(x,y,z), can I look at the values of z >> given particular values for x and y? > Given that element values are scalars in this case, and indices are (x,y,z) > triples, it seems likely that looking for "values of z" given an (x,y) pair > is an slicing-by-index question, no? > > For indexing-by-value, "fancy indexing" with boolean masks is usually the way > to go... again, Ted (or Chao), if you can describe your indexing needs in a > bit more detail, it's often easy to find a compact slicing and/or > fancy-indexing strategy that works well and reasonably efficiently. > > Zach > > > > On Jan 30, 2012, at 10:33 AM, Chao YUE wrote: > >> he is not asking for slicing. he is asking for how to index array by element >> value but not element index. >> >> 2012/1/30 Zachary Pincus >> a[x,y,:] >> >> Read the slicing part of the tutorial: >> http://www.scipy.org/Tentative_NumPy_Tutorial >> (section 1.6) >> >> And the documentation: >> http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html >> >> >> >> On Jan 30, 2012, at 10:25 AM, Ted To wrote: >> >>> Hi, >>> >>> Is there some straightforward way to access an array by values across a >>> subset of its dimensions? For example, if I have a three dimensional >>> array a=(x,y,z), can I look at the values of z given particular values >>> for x and y? >>> >>> Thanks, >>> Ted >>> ___ >>> NumPy-Discussion mailing list >>> NumPy-Discussion@scipy.org >>> http://mail.scipy.org/mailman/listinfo/numpy-discussion >> >> ___ >> NumPy-Discussion mailing list >> NumPy-Discussion@scipy.org >> http://mail.scipy.org/mailman/listinfo/numpy-discussion >> >> >> >> -- >> *** >> Chao YUE >> Laboratoire des Sciences du Climat et de l'Environnement (LSCE-IPSL) >> UMR 1572 CEA-CNRS-UVSQ >> Batiment 712 - Pe 119 >> 91191 GIF Sur YVETTE Cedex >> Tel: (33) 01 69 08 29 02; Fax:01.69.08.77.16 >> >> >> ___ >> NumPy-Discussion mailing list >> NumPy-Discussion@scipy.org >> http://mail.scipy.org/mailman/listinfo/numpy-discussion > > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
Ted, can you clarify what you're asking for? Maybe give a trivial example of an array and the desired output? I'm pretty sure this is a slicing question though: > If I have a three dimensional array a=(x,y,z), can I look at the values of z > given particular values for x and y? Given that element values are scalars in this case, and indices are (x,y,z) triples, it seems likely that looking for "values of z" given an (x,y) pair is an slicing-by-index question, no? For indexing-by-value, "fancy indexing" with boolean masks is usually the way to go... again, Ted (or Chao), if you can describe your indexing needs in a bit more detail, it's often easy to find a compact slicing and/or fancy-indexing strategy that works well and reasonably efficiently. Zach On Jan 30, 2012, at 10:33 AM, Chao YUE wrote: > he is not asking for slicing. he is asking for how to index array by element > value but not element index. > > 2012/1/30 Zachary Pincus > a[x,y,:] > > Read the slicing part of the tutorial: > http://www.scipy.org/Tentative_NumPy_Tutorial > (section 1.6) > > And the documentation: > http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html > > > > On Jan 30, 2012, at 10:25 AM, Ted To wrote: > > > Hi, > > > > Is there some straightforward way to access an array by values across a > > subset of its dimensions? For example, if I have a three dimensional > > array a=(x,y,z), can I look at the values of z given particular values > > for x and y? > > > > Thanks, > > Ted > > ___ > > NumPy-Discussion mailing list > > NumPy-Discussion@scipy.org > > http://mail.scipy.org/mailman/listinfo/numpy-discussion > > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > > > > -- > *** > Chao YUE > Laboratoire des Sciences du Climat et de l'Environnement (LSCE-IPSL) > UMR 1572 CEA-CNRS-UVSQ > Batiment 712 - Pe 119 > 91191 GIF Sur YVETTE Cedex > Tel: (33) 01 69 08 29 02; Fax:01.69.08.77.16 > > > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
he is not asking for slicing. he is asking for how to index array by element value but not element index. 2012/1/30 Zachary Pincus > a[x,y,:] > > Read the slicing part of the tutorial: > http://www.scipy.org/Tentative_NumPy_Tutorial > (section 1.6) > > And the documentation: > http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html > > > > On Jan 30, 2012, at 10:25 AM, Ted To wrote: > > > Hi, > > > > Is there some straightforward way to access an array by values across a > > subset of its dimensions? For example, if I have a three dimensional > > array a=(x,y,z), can I look at the values of z given particular values > > for x and y? > > > > Thanks, > > Ted > > ___ > > NumPy-Discussion mailing list > > NumPy-Discussion@scipy.org > > http://mail.scipy.org/mailman/listinfo/numpy-discussion > > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > -- *** Chao YUE Laboratoire des Sciences du Climat et de l'Environnement (LSCE-IPSL) UMR 1572 CEA-CNRS-UVSQ Batiment 712 - Pe 119 91191 GIF Sur YVETTE Cedex Tel: (33) 01 69 08 29 02; Fax:01.69.08.77.16 ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
a[x,y,:] Read the slicing part of the tutorial: http://www.scipy.org/Tentative_NumPy_Tutorial (section 1.6) And the documentation: http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html On Jan 30, 2012, at 10:25 AM, Ted To wrote: > Hi, > > Is there some straightforward way to access an array by values across a > subset of its dimensions? For example, if I have a three dimensional > array a=(x,y,z), can I look at the values of z given particular values > for x and y? > > Thanks, > Ted > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
On Mon, Jan 30, 2012 at 3:25 PM, Ted To wrote: > Is there some straightforward way to access an array by values across a > subset of its dimensions? For example, if I have a three dimensional > array a=(x,y,z), can I look at the values of z given particular values > for x and y? a[x, y, :] should get you what you want I believe.. Malcolm ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Addressing arrays
I am afraid you have to write index inquire function by yourself. I did like this. chao 2012/1/30 Ted To > Hi, > > Is there some straightforward way to access an array by values across a > subset of its dimensions? For example, if I have a three dimensional > array a=(x,y,z), can I look at the values of z given particular values > for x and y? > > Thanks, > Ted > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > -- *** Chao YUE Laboratoire des Sciences du Climat et de l'Environnement (LSCE-IPSL) UMR 1572 CEA-CNRS-UVSQ Batiment 712 - Pe 119 91191 GIF Sur YVETTE Cedex Tel: (33) 01 69 08 29 02; Fax:01.69.08.77.16 ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
[Numpy-discussion] Addressing arrays
Hi, Is there some straightforward way to access an array by values across a subset of its dimensions? For example, if I have a three dimensional array a=(x,y,z), can I look at the values of z given particular values for x and y? Thanks, Ted ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Unrealistic expectations of class Polynomial or a bug?
On Sat, Jan 28, 2012 at 11:14 PM, Charles R Harris < charlesr.har...@gmail.com> wrote: > > > On Sat, Jan 28, 2012 at 11:15 AM, eat wrote: > >> Hi, >> >> Short demonstration of the issue: >> In []: sys.version >> Out[]: '2.7.2 (default, Jun 12 2011, 15:08:59) [MSC v.1500 32 bit >> (Intel)]' >> In []: np.version.version >> Out[]: '1.6.0' >> >> In []: from numpy.polynomial import Polynomial as Poly >> In []: def p_tst(c): >>..: p= Poly(c) >>..: r= p.roots() >>..: return sort(abs(p(r))) >>..: >> >> Now I would expect a result more like: >> In []: p_tst(randn(123))[-3:] >> Out[]: array([ 3.41987203e-07, 2.82123675e-03, 2.82123675e-03]) >> >> be the case, but actually most result seems to be more like: >> In []: p_tst(randn(123))[-3:] >> Out[]: array([ 9.09325898e+13, 9.09325898e+13, 1.29387029e+72]) >> In []: p_tst(randn(123))[-3:] >> Out[]: array([ 8.60862087e-11, 8.60862087e-11, 6.58784520e+32]) >> In []: p_tst(randn(123))[-3:] >> Out[]: array([ 2.00545673e-09, 3.25537709e+32, 3.25537709e+32]) >> In []: p_tst(randn(123))[-3:] >> Out[]: array([ 3.22753481e-04, 1.87056454e+00, 1.87056454e+00]) >> In []: p_tst(randn(123))[-3:] >> Out[]: array([ 2.98556327e+08, 2.98556327e+08, 8.23588003e+12]) >> >> So, does this phenomena imply that >> - I'm testing with too high order polynomials (if so, does there exists a >> definite upper limit of polynomial order I'll not face this issue) >> or >> - it's just the 'nature' of computations with float values (if so, >> probably I should be able to tackle this regardless of the polynomial order) >> or >> - it's a nasty bug in class Polynomial >> >> > It's a defect. You will get all the roots and the number will equal the > degree. I haven't decided what the best way to deal with this is, but my > thoughts have trended towards specifying an interval with the default being > the domain. If you have other thoughts I'd be glad for the feedback. > > For the problem at hand, note first that you are specifying the > coefficients, not the roots as was the case with poly1d. Second, as a rule > of thumb, plain old polynomials will generally only be good for degree < 22 > due to being numerically ill conditioned. If you are really looking to use > high degrees, Chebyshev or Legendre will work better, although you will > probably need to explicitly specify the domain. If you want to specify the > polynomial using roots, do Poly.fromroots(...). Third, for the high degrees > you are probably screwed anyway for degree 123, since the accuracy of the > root finding will be limited, especially for roots that can cluster, and > any root that falls even a little bit outside the interval [-1,1] (the > default domain) is going to evaluate to a big number simply because the > polynomial is going to h*ll at a rate you wouldn't believe ;) > > For evenly spaced roots in [-1, 1] and using Chebyshev polynomials, things > look good for degree 50, get a bit loose at degree 75 but can be fixed up > with one iteration of Newton, and blow up at degree 100. I think that's > pretty good, actually, doing better would require a lot more work. There > are some zero finding algorithms out there that might do better if someone > wants to give it a shot. > > In [20]: p = Cheb.fromroots(linspace(-1, 1, 50)) > > In [21]: sort(abs(p(p.roots( > Out[21]: > array([ 6.20385459e-25, 1.65436123e-24, 2.06795153e-24, > 5.79026429e-24, 5.89366186e-24, 6.44916482e-24, > 6.44916482e-24, 6.77254127e-24, 6.97933642e-24, > 7.25459208e-24, 1.00295649e-23, 1.37391414e-23, > 1.37391414e-23, 1.63368171e-23, 2.39882378e-23, > 3.30872245e-23, 4.38405725e-23, 4.49502653e-23, > 4.49502653e-23, 5.58346913e-23, 8.35452419e-23, > 9.38407760e-23, 9.38407760e-23, 1.03703218e-22, > 1.03703218e-22, 1.23249911e-22, 1.75197880e-22, > 1.75197880e-22, 3.07711188e-22, 3.09821786e-22, > 3.09821786e-22, 4.56625520e-22, 4.56625520e-22, > 4.69638303e-22, 4.69638303e-22, 5.96448724e-22, > 5.96448724e-22, 1.24076485e-21, 1.24076485e-21, > 1.59972624e-21, 1.59972624e-21, 1.62930347e-21, > 1.62930347e-21, 1.73773328e-21, 1.73773328e-21, > 1.87935435e-21, 2.30287083e-21, 2.48815928e-21, > 2.85411753e-21, 2.85411753e-21]) > Thanks, for a very informative feedback. I'll study those orthogonal polynomials more detail. Regards, - eat > > > Chuck > > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > > ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
