NumPy-Discussion December 2014

numpy-discussion@python.org

52 participants
47 discussions

Re: [Numpy-discussion] example reading binary Fortran file
by Neil Martinsen-Burrell 22 Jul '21

22 Jul '21

David Froger <david.froger.info <at> gmail.com> writes: > Hy,My question is about reading Fortran binary file (oh no this question > again...) I've posted this before, but I finally got it cleaned up for the Cookbook. For this purpose I use a subclass of file that has methods for reading unformatted Fortran data. See http://www.scipy.org/Cookbook/FortranIO/FortranFile. I'd gladly see this in numpy or scipy somewhere, but I'm not sure where it belongs. > program makeArray > implicit none > integer,parameter:: nx=10,ny=20 > real(4),dimension(nx,ny):: ux,uy,p > integer :: i,j > open(11,file='uxuyp.bin',form='unformatted') > do i = 1,nx > do j = 1,ny > ux(i,j) = real(i*j) > uy(i,j) = real(i)/real(j) > p (i,j) = real(i) + real(j) > enddo > enddo > write(11) ux,uy > write(11) p > close(11) > end program makeArray When I run the above program compiled with gfortran on my Intel Mac, I can read it back with:: >>> import numpy as np >>> from fortranfile import FortranFile >>> f=FortranFile('uxuyp.bin', endian='<') >>> uxuy = f.readReals(prec='f') # 'f' for default reals >>> len(uxuy) 400 >>> ux = np.array(uxuy[:200]).reshape((20,10)).T >>> uy = np.array(uxuy[200:]).reshape((20,10)).T >>> p = f.readReals('f').reshape((20,10)).T >>> ux array([[ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20.], [ 2., 4., 6., 8., 10., 12., 14., 16., 18., 20., 22., 24., 26., 28., 30., 32., 34., 36., 38., 40.], [ 3., 6., 9., 12., 15., 18., 21., 24., 27., 30., 33., 36., 39., 42., 45., 48., 51., 54., 57., 60.], [ 4., 8., 12., 16., 20., 24., 28., 32., 36., 40., 44., 48., 52., 56., 60., 64., 68., 72., 76., 80.], [ 5., 10., 15., 20., 25., 30., 35., 40., 45., 50., 55., 60., 65., 70., 75., 80., 85., 90., 95., 100.], [ 6., 12., 18., 24., 30., 36., 42., 48., 54., 60., 66., 72., 78., 84., 90., 96., 102., 108., 114., 120.], [ 7.,Proxy-Connection: keep-alive Cache-Control: max-age=0 14., 21., 28., 35., 42., 49., 56., 63., 70., 77., 84., 91., 98., 105., 112., 119., 126., 133., 140.], [ 8., 16., 24., 32., 40., 48., 56., 64., 72., 80., 88., 96., 104., 112., 120., 128., 136., 144., 152., 160.], [ 9., 18., 27., 36., 45., 54., 63., 72., 81., 90., 99., 108., 117., 126., 135., 144., 153., 162., 171., 180.], [ 10., 20., 30., 40., 50., 60., 70., 80., 90., 100., 110., 120., 130., 140., 150., 160., 170., 180., 190., 200.]]) >>> uy array([[ 1. , 0.5 , 0.33333334, 0.25 , 0.2 , 0.16666667, 0.14285715, 0.125 , 0.11111111, 0.1 , 0.09090909, 0.08333334, 0.07692308, 0.07142857, 0.06666667, 0.0625 , 0.05882353, 0.05555556, 0.05263158, 0.05 ], [ 2. , 1. , 0.66666669, 0.5 , 0.40000001, 0.33333334, 0.2857143 , 0.25 , 0.22222222, 0.2 , 0.18181819, 0.16666667, 0.15384616, 0.14285715, 0.13333334, 0.125 , 0.11764706, 0.11111111, 0.10526316, 0.1 ], [ 3. , 1.5 , 1. , 0.75 , 0.60000002, 0.5 , 0.42857143, 0.375 , 0.33333334, 0.30000001, 0.27272728, 0.25 , 0.23076923, 0.21428572, 0.2 , 0.1875 , 0.17647059, 0.16666667, 0.15789473, 0.15000001], [ 4. , 2. , 1.33333337, 1. , 0.80000001, 0.66666669, 0.5714286 , 0.5 , 0.44444445, 0.40000001, 0.36363637, 0.33333334, 0.30769232, 0.2857143 , 0.26666668, 0.25 , 0.23529412, 0.22222222, 0.21052632, 0.2 ], [ 5. , 2.5 , 1.66666663, 1.25 , 1. , 0.83333331, 0.71428573, 0.625 , 0.55555558, 0.5 , 0.45454547, 0.41666666, 0.38461539, 0.35714287, 0.33333334, 0.3125 , 0.29411766, 0.27777779, 0.2631579 , 0.25 ], [ 6. , 3. , 2. , 1.5 , 1.20000005, 1. , 0.85714287, 0.75 , 0.66666669, 0.60000002, 0.54545456, 0.5 , 0.46153846, 0.42857143, 0.40000001, 0.375 , 0.35294119, 0.33333334, 0.31578946, 0.30000001], [ 7. , 3.5 , 2.33333325, 1.75 , 1.39999998, 1.16666663, 1. , 0.875 , 0.77777779, 0.69999999, 0.63636363, 0.58333331, 0.53846157, 0.5 , 0.46666667, 0.4375 , 0.41176471, 0.3888889 , 0.36842105, 0.34999999], [ 8. , 4. , 2.66666675, 2. , 1.60000002, 1.33333337, 1.14285719, 1. , 0.8888889 , 0.80000001, 0.72727275, 0.66666669, 0.61538464, 0.5714286 , 0.53333336, 0.5 , 0.47058824, 0.44444445, 0.42105263, 0.40000001], [ 9. , 4.5 , 3. , 2.25 , 1.79999995, 1.5 , 1.28571427, 1.125 , 1. , 0.89999998, 0.81818181, 0.75 , 0.69230771, 0.64285713, 0.60000002, 0.5625 , 0.52941179, 0.5 , 0.47368422, 0.44999999], [ 10. , 5. , 3.33333325, 2.5 , 2. , 1.66666663, 1.42857146, 1.25 , 1.11111116, 1. , 0.90909094, 0.83333331, 0.76923078, 0.71428573, 0.66666669, 0.625 , 0.58823532, 0.55555558, 0.52631581, 0.5 ]]) >>> p array([[ 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21.], [ 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.], [ 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23.], [ 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24.], [ 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.], [ 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26.], [ 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27.], [ 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28.], [ 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29.], [ 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30.]]) Note that you have to provide the shape information for ux and uy because fortran writes them together as a stream of 400 numbers. -Neil

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C-API: multidimensional array indexing?
by Johann Bauer 31 Mar '16

31 Mar '16

Dear experts, is there a C-API function for numpy which implements Python's multidimensional indexing? Say, I have a 2d-array PyArrayObject * M; and an index int i; how do I extract the i-th row or column M[i,:] respectively M[:,i]? I am looking for a function which gives again a PyArrayObject * and which is a view to M (no copied data; the result should be another PyArrayObject whose data and strides points to the correct memory portion of M). I searched the API documentation, Google and mailing lists for quite a long time but didn't find anything. Can you help me? Thanks, Johann

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Generalize hstack/vstack --> stack; Block matrices like in matlab
by Stefan Otte 09 Jan '16

09 Jan '16

Hey, quite often I work with block matrices. Matlab offers the convenient notation [ a b; c d ] to stack matrices. The numpy equivalent is kinda clumsy: vstack([hstack([a,b]), hstack([c,d])]) I wrote the little function `stack` that does exactly that: stack([[a, b], [c, d]]) In my case `stack` replaced `hstack` and `vstack` almost completely. If you're interested in including it in numpy I created a pull request [1]. I'm looking forward to getting some feedback! Best, Stefan [1] https://github.com/numpy/numpy/pull/5057

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PR added: frozen dimensions in gufunc signatures
by Jaime Fernández del Río 23 Jun '15

23 Jun '15

Hi, I have just sent a PR (https://github.com/numpy/numpy/pull/5015), adding the possibility of having frozen dimensions in gufunc signatures. As a proof of concept, I have added a `cross1d` gufunc to `numpy.core.umath_tests`: In [1]: import numpy as np In [2]: from numpy.core.umath_tests import cross1d In [3]: cross1d.signature Out[3]: '(3),(3)->(3)' In [4]: a = np.random.rand(1000, 3) In [5]: b = np.random.rand(1000, 3) In [6]: np.allclose(np.cross(a, b), cross1d(a, b)) Out[6]: True In [7]: %timeit np.cross(a, b) 10000 loops, best of 3: 76.1 us per loop In [8]: %timeit cross1d(a, b) 100000 loops, best of 3: 13.1 us per loop In [9]: c = np.random.rand(1000, 2) In [10]: d = np.random.rand(1000, 2) In [11]: cross1d(c, d) --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-11-72c66212e40c> in <module>() ----> 1 cross1d(c, d) ValueError: cross1d: Operand 0 has a mismatch in its core dimension 0, with gufunc signature (3),(3)->(3) (size 2 is different from 3) The speed up over `np.cross` is nice, and while `np.cross` is not the best of examples, as it needs to handle more sizes, in many cases this will allow producing gufuncs that work without a Python wrapper redoing checks that are best left to the iterator, such as dimension sizes. It still needs tests, but before embarking on fully developing those, I wanted to make sure that there is an interest on this. I would also like to further enhance gufuncs providing computed dimensions, e.g. making it possible to e.g. define `pairwise_cross` with signature '(n, 3)->($m, 3)', where the $ indicates that m is a computed dimension, that would have to be calculated by a function passed to the gufunc constructor and stored in the gufunc object, based on the other core dimensions. In this case it would make $m be n*(n-1), so that all pairwise cross products between 3D vectors could be computed. The syntax with '$' is kind of crappy, so any suggestions on how to better express this in the signature are more than welcome, as well as any feedback on the merits (or lack of them) of implementing this. Jaime -- (\__/) ( O.o) ( > <) Este es Conejo. Copia a Conejo en tu firma y ayúdale en sus planes de dominación mundial.

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Problem with _dotblas.pyd when using Matplotlib for 3d plot
by Geoffrey Mégardon 19 Mar '15

19 Mar '15

Hi, I am on Windows 8.1, 64-bit, using the usual version of Anaconda-64-bit for windows. I just come from the mailing list of matplotlib: my PC is not able to do 3D plot with matplotlib. Python crashes completely if I try to plot something in 3D and to show it: "Python.exe has stopped working..." The main problem in resolving my issue is that the python traceback and the faulthandler package do not succeed in catching the errors. Only the Windows crash report allows us to see what happened before the crash. The windows report tells that the file _dotblas.pyd from numpy is likely responsible for the crash. So I tried a simple: import numpy; numpy.test() numpy.test() does not work! I dont get any traceback from python. It just crashes as before: "Python.exe has stopped working..." And again, the Windows report blames _dotblas.pyd :) Here the new Windows report for the numpy.test(), I highlighted the lines which blame _dotblas.pyd: Version=1 EventType=APPCRASH EventTime=130608138227608275 ReportType=2 Consent=1 UploadTime=130608138229728384 ReportIdentifier=216b16d2-6f5c-11e4-bec3-48d22435da2b IntegratorReportIdentifier=216b16d1-6f5c-11e4-bec3-48d22435da2b NsAppName=python.exe Response.BucketId=398b7eee350a0fd8a7a96f705d3488f6 Response.BucketTable=4 Response.LegacyBucketId=85979911964 Response.type=4 Sig[0].Name=Application Name Sig[0].Value=python.exe Sig[1].Name=Application Version Sig[1].Value=0.0.0.0 Sig[2].Name=Application Timestamp Sig[2].Value=53b4679e *Sig[3].Name=Fault Module NameSig[3].Value=_dotblas.pyd* Sig[4].Name=Fault Module Version Sig[4].Value=0.0.0.0 Sig[5].Name=Fault Module Timestamp Sig[5].Value=545678cb Sig[6].Name=Exception Code Sig[6].Value=c000001d Sig[7].Name=Exception Offset Sig[7].Value=0000000000324022 DynamicSig[1].Name=OS Version DynamicSig[1].Value=6.3.9600.2.0.0.768.101 DynamicSig[2].Name=Locale ID DynamicSig[2].Value=2057 DynamicSig[22].Name=Additional Information 1 DynamicSig[22].Value=f32f DynamicSig[23].Name=Additional Information 2 DynamicSig[23].Value=f32feb95f950f918532aa47b4372840e DynamicSig[24].Name=Additional Information 3 DynamicSig[24].Value=9882 DynamicSig[25].Name=Additional Information 4 DynamicSig[25].Value=98823b6c7f579b24e92112ab827fe4a1 UI[2]=C:\Anaconda\python.exe UI[3]=python.exe has stopped working UI[4]=Windows can check online for a solution to the problem. UI[5]=Check online for a solution and close the program UI[6]=Check online for a solution later and close the program UI[7]=Close the program LoadedModule[0]=C:\Anaconda\python.exe LoadedModule[1]=C:\WINDOWS\SYSTEM32\ntdll.dll LoadedModule[2]=C:\WINDOWS\system32\KERNEL32.DLL LoadedModule[3]=C:\WINDOWS\system32\KERNELBASE.dll LoadedModule[4]=C:\Anaconda\python27.dll LoadedModule[5]=C:\WINDOWS\WinSxS\amd64_microsoft.vc90.crt_1fc8b3b9a1e18e3b_9.0.30729.8387_none_08e793bfa83a89b5\MSVCR90.dll LoadedModule[6]=C:\WINDOWS\system32\USER32.dll LoadedModule[7]=C:\WINDOWS\system32\ADVAPI32.dll LoadedModule[8]=C:\WINDOWS\system32\SHELL32.dll LoadedModule[9]=C:\WINDOWS\system32\GDI32.dll LoadedModule[10]=C:\WINDOWS\system32\msvcrt.dll LoadedModule[11]=C:\WINDOWS\SYSTEM32\sechost.dll LoadedModule[12]=C:\WINDOWS\system32\RPCRT4.dll LoadedModule[13]=C:\WINDOWS\SYSTEM32\combase.dll LoadedModule[14]=C:\WINDOWS\system32\SHLWAPI.dll LoadedModule[15]=C:\WINDOWS\system32\IMM32.DLL LoadedModule[16]=C:\WINDOWS\system32\MSCTF.dll LoadedModule[17]=C:\Anaconda\DLLs\_socket.pyd LoadedModule[18]=C:\WINDOWS\system32\WS2_32.dll LoadedModule[19]=C:\WINDOWS\system32\NSI.dll LoadedModule[20]=C:\Anaconda\DLLs\_ssl.pyd LoadedModule[21]=C:\Anaconda\DLLs\_ctypes.pyd LoadedModule[22]=C:\WINDOWS\system32\ole32.dll LoadedModule[23]=C:\WINDOWS\system32\OLEAUT32.dll LoadedModule[24]=C:\Anaconda\DLLs\_hashlib.pyd LoadedModule[25]=C:\WINDOWS\SYSTEM32\CRYPTSP.dll LoadedModule[26]=C:\WINDOWS\system32\rsaenh.dll LoadedModule[27]=C:\WINDOWS\SYSTEM32\bcrypt.dll LoadedModule[28]=C:\WINDOWS\SYSTEM32\CRYPTBASE.dll LoadedModule[29]=C:\WINDOWS\SYSTEM32\bcryptPrimitives.dll LoadedModule[30]=C:\Users\User\AppData\Roaming\Python-Eggs\faulthandler-2.4-py2.7-win-amd64.egg-tmp\faulthandler.pyd LoadedModule[31]=C:\Anaconda\lib\site-packages\numpy\core\multiarray.pyd LoadedModule[32]=C:\Anaconda\lib\site-packages\numpy\core\umath.pyd LoadedModule[33]=C:\Anaconda\lib\site-packages\numpy\core\_dotblas.pyd LoadedModule[34]=C:\Anaconda\lib\site-packages\numpy\core\libiomp5md.dll LoadedModule[35]=C:\Anaconda\lib\site-packages\numpy\core\scalarmath.pyd LoadedModule[36]=C:\Anaconda\lib\site-packages\numpy\lib\_compiled_base.pyd LoadedModule[37]=C:\Anaconda\lib\site-packages\numpy\linalg\lapack_lite.pyd LoadedModule[38]=C:\Anaconda\lib\site-packages\numpy\linalg\_umath_linalg.pyd LoadedModule[39]=C:\Anaconda\lib\site-packages\numpy\fft\fftpack_lite.pyd LoadedModule[40]=C:\Anaconda\lib\site-packages\numpy\random\mtrand.pyd LoadedModule[41]=C:\Anaconda\DLLs\_multiprocessing.pyd State[0].Key=Transport.DoneStage1 State[0].Value=1 FriendlyEventName=Stopped working ConsentKey=APPCRASH AppName=python.exe AppPath=C:\Anaconda\python.exe NsPartner=windows NsGroup=windows8 ApplicationIdentity=5B036AF1EC2E20F320DBF28D119DE93D Any idea, of what I can do? I try to reinstall anaconda, I also try conda remove numpy and conda install numpy. That does not seem to change anything. -- -- MEGARDON Geoffrey

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Numpy 'None' comparison FutureWarning
by Demitri Muna 31 Jan '15

31 Jan '15

Hi, I just encountered the following in my code: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future. I'm very concerned about this. This is a very common programming pattern (lazy loading): class A(object): def __init__(self): self._some_array = None @property def some_array(self): if self._some_array == None: # perform some expensive setup of array return self._some_array It seems to me that the new behavior will break this pattern. I think that redefining the "==" operator is a little too aggressive here. It strikes me as very nonstandard and not at all obvious to someone reading the code that the comparison is a very special case for numpy objects. Unless there's some aspect I'm missing here, I think an element-wise comparator should be more explicit. Cheers, Demitri _________________________________________ Demitri Muna Department of Astronomy Le Ohio State University http://trillianverse.org http://scicoder.org

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New function `count_unique` to generate contingency tables.
by Warren Weckesser 25 Jan '15

25 Jan '15

I created a pull request (https://github.com/numpy/numpy/pull/4958) that defines the function `count_unique`. `count_unique` generates a contingency table from a collection of sequences. For example, In [7]: x = [1, 1, 1, 1, 2, 2, 2, 2, 2] In [8]: y = [3, 4, 3, 3, 3, 4, 5, 5, 5] In [9]: (xvals, yvals), counts = count_unique(x, y) In [10]: xvals Out[10]: array([1, 2]) In [11]: yvals Out[11]: array([3, 4, 5]) In [12]: counts Out[12]: array([[3, 1, 0], [1, 1, 3]]) It can be interpreted as a multi-argument generalization of `np.unique(x, return_counts=True)`. It overlaps with Pandas' `crosstab`, but I think this is a pretty fundamental counting operation that fits in numpy. Matlab's `crosstab` (http://www.mathworks.com/help/stats/crosstab.html) and R's `table` perform the same calculation (with a few more bells and whistles). For comparison, here's Pandas' `crosstab` (same `x` and `y` as above): In [28]: import pandas as pd In [29]: xs = pd.Series(x) In [30]: ys = pd.Series(y) In [31]: pd.crosstab(xs, ys) Out[31]: col_0 3 4 5 row_0 1 3 1 0 2 1 1 3 And here is R's `table`: > x <- c(1,1,1,1,2,2,2,2,2) > y <- c(3,4,3,3,3,4,5,5,5) > table(x, y) y x 3 4 5 1 3 1 0 2 1 1 3 Is there any interest in adding this (or some variation of it) to numpy? Warren

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Add a function to broadcast arrays to a given shape to numpy's stride_tricks?
by Stephan Hoyer 03 Jan '15

03 Jan '15

I recently wrote function to manually broadcast an ndarray to a given shape according to numpy's broadcasting rules (using strides): https://github.com/xray/xray/commit/7aee4a3ed2dfd3b9aff7f3c5c6c68d51df2e3ff3 The same functionality can be done pretty straightforwardly with np.broadcast_arrays, but that function does both too much (I don't actually have a second array that needs to be broadcast) and not enough (I need to create a dummy array to broadcast against it). This approach is simpler, and also, according to my benchmarks, about 3x faster than np.broadcast_arrays: In [1]: import xray In [2]: import numpy as np In [3]: x = np.random.randn(4) In [4]: y = np.empty((2, 3, 4)) In [5]: %timeit xray.core.utils.as_shape(x, y.shape) 100000 loops, best of 3: 17 µs per loop In [6]: %timeit np.broadcast_arrays(x, y)[0] 10000 loops, best of 3: 47.4 µs per loop Would this be a welcome addition to numpy's lib.stride_tricks? If so, I will put together a PR. In my search, I turned up a Stack Overflow post looking for similar functionality: https://stackoverflow.com/questions/11622692/is-there-a-better-way-to-broad… Cheers, Stephan

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npymath on Windows
by Matthew Brett 02 Jan '15

02 Jan '15

Hi, Sorry for this ignorant email, but we got confused trying to use 'libnpymath.a' from the mingw builds of numpy: We were trying to link against the mingw numpy 'libnpymath.a' using Visual Studio C, but this give undefined symbols from 'libnpymath.a' like this: npymath.lib(npy_math.o) : error LNK2019: unresolved external symbol _atanf referenced in function _npy_atanf npymath.lib(npy_math.o) : error LNK2019: unresolved external symbol _acosf referenced in function _npy_acosf npymath.lib(npy_math.o) : error LNK2019: unresolved external symbol _asinf referenced in function _npy_asinf (see : http://nipy.bic.berkeley.edu/builders/dipy-bdist32-33/builds/73/steps/shell…) npymath.lib from Christophe Gohlke's (MSVC compiled) numpies does not give such an error. Sure enough, 'npymath.lib' shows these lines from `dumpbin /all npymath.lib`: 00000281 REL32 00000000 4F asinf 00000291 REL32 00000000 51 acosf 000002A1 REL32 00000000 53 atanf whereas `dumpbin /all libnpymath.a` shows these kinds of lines: 000008E5 REL32 00000000 86 _asinf 000008F5 REL32 00000000 85 _acosf 00000905 REL32 00000000 84 _atanf As far as I can see, 'acosf' is defined in the msvc runtime library. I guess that '_acosf' is defined in some mingw runtime library? Is there any way of making a npymath library that will pick up the msvc math and so may work with both msvc and mingw? Sorry again if that's a dumb question, Matthew

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Access dtype kind from cython
by Valentin Haenel 01 Jan '15

01 Jan '15

Hi, how do I access the kind of the data from cython, i.e. the single character string: 'b' boolean 'i' (signed) integer 'u' unsigned integer 'f' floating-point 'c' complex-floating point 'O' (Python) objects 'S', 'a' (byte-)string 'U' Unicode 'V' raw data (void) In regular Python I can do: In [7]: d = np.dtype('S') In [8]: d.kind Out[8]: 'S' Looking at the definition of dtype that comes with cython, I see: ctypedef class numpy.dtype [object PyArray_Descr]: # Use PyDataType_* macros when possible, however there are no macros # for accessing some of the fields, so some are defined. Please # ask on cython-dev if you need more. cdef int type_num cdef int itemsize "elsize" cdef char byteorder cdef object fields cdef tuple names I.e. no kind. Also, i looked for an appropriate PyDataType_* macro but couldn't find one. Perhaps there is something simple I could use? best, V-

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NumPy-Discussion December 2014