| ================================== |
| A Guide to Masked Arrays in NumPy |
| ================================== |
|
|
| .. Contents:: |
|
|
| See http://www.scipy.org/scipy/numpy/wiki/MaskedArray (dead link) |
| for updates of this document. |
|
|
|
|
| History |
| |
|
|
| As a regular user of MaskedArray, I (Pierre G.F. Gerard-Marchant) became |
| increasingly frustrated with the subclassing of masked arrays (even if |
| I can only blame my inexperience). I needed to develop a class of arrays |
| that could store some additional information along with numerical values, |
| while keeping the possibility for missing data (picture storing a series |
| of dates along with measurements, what would later become the `TimeSeries |
| Scikit <http://projects.scipy.org/scipy/scikits/wiki/TimeSeries>`__ |
| (dead link). |
|
|
| I started to implement such a class, but then quickly realized that |
| any additional information disappeared when processing these subarrays |
| (for example, adding a constant value to a subarray would erase its |
| dates). I ended up writing the equivalent of *numpy.core.ma* for my |
| particular class, ufuncs included. Everything went fine until I needed to |
| subclass my new class, when more problems showed up: some attributes of |
| the new subclass were lost during processing. I identified the culprit as |
| MaskedArray, which returns masked ndarrays when I expected masked |
| arrays of my class. I was preparing myself to rewrite *numpy.core.ma* |
| when I forced myself to learn how to subclass ndarrays. As I became more |
| familiar with the *__new__* and *__array_finalize__* methods, |
| I started to wonder why masked arrays were objects, and not ndarrays, |
| and whether it wouldn't be more convenient for subclassing if they did |
| behave like regular ndarrays. |
| |
| The new *maskedarray* is what I eventually come up with. The |
| main differences with the initial *numpy.core.ma* package are |
| that MaskedArray is now a subclass of *ndarray* and that the |
| *_data* section can now be any subclass of *ndarray*. Apart from a |
| couple of issues listed below, the behavior of the new MaskedArray |
| class reproduces the old one. Initially the *maskedarray* |
| implementation was marginally slower than *numpy.ma* in some areas, |
| but work is underway to speed it up; the expectation is that it can be |
| made substantially faster than the present *numpy.ma*. |
| |
| |
| Note that if the subclass has some special methods and |
| attributes, they are not propagated to the masked version: |
| this would require a modification of the *__getattribute__* |
| method (first trying *ndarray.__getattribute__*, then trying |
| *self._data.__getattribute__* if an exception is raised in the first |
| place), which really slows things down. |
| |
| Main differences |
| ---------------- |
| |
| * The *_data* part of the masked array can be any subclass of ndarray (but not recarray, cf below). |
| * *fill_value* is now a property, not a function. |
| * in the majority of cases, the mask is forced to *nomask* when no value is actually masked. A notable exception is when a masked array (with no masked values) has just been unpickled. |
| * I got rid of the *share_mask* flag, I never understood its purpose. |
| * *put*, *putmask* and *take* now mimic the ndarray methods, to avoid unpleasant surprises. Moreover, *put* and *putmask* both update the mask when needed. * if *a* is a masked array, *bool(a)* raises a *ValueError*, as it does with ndarrays. |
| * in the same way, the comparison of two masked arrays is a masked array, not a boolean |
| * *filled(a)* returns an array of the same subclass as *a._data*, and no test is performed on whether it is contiguous or not. |
| * the mask is always printed, even if it's *nomask*, which makes things easy (for me at least) to remember that a masked array is used. |
| * *cumsum* works as if the *_data* array was filled with 0. The mask is preserved, but not updated. |
| * *cumprod* works as if the *_data* array was filled with 1. The mask is preserved, but not updated. |
|
|
| New features |
| |
|
|
| This list is non-exhaustive... |
|
|
| * the *mr_* function mimics *r_* for masked arrays. |
| * the *anom* method returns the anomalies (deviations from the average) |
|
|
| Using the new package with numpy.core.ma |
| |
|
|
| I tried to make sure that the new package can understand old masked |
| arrays. Unfortunately, there's no upward compatibility. |
| |
| For example: |
| |
| >>> import numpy.core.ma as old_ma |
| >>> import maskedarray as new_ma |
| >>> x = old_ma.array([1,2,3,4,5], mask=[0,0,1,0,0]) |
| >>> x |
| array(data = |
| [ 1 2 999999 4 5], |
| mask = |
| [False False True False False], |
| fill_value=999999) |
| >>> y = new_ma.array([1,2,3,4,5], mask=[0,0,1,0,0]) |
| >>> y |
| array(data = [1 2 -- 4 5], |
| mask = [False False True False False], |
| fill_value=999999) |
| >>> x==y |
| array(data = |
| [True True True True True], |
| mask = |
| [False False True False False], |
| fill_value=?) |
| >>> old_ma.getmask(x) == new_ma.getmask(x) |
| array([True, True, True, True, True]) |
| >>> old_ma.getmask(y) == new_ma.getmask(y) |
| array([True, True, False, True, True]) |
| >>> old_ma.getmask(y) |
| False |
| |
| |
| Using maskedarray with matplotlib |
| --------------------------------- |
| |
| Starting with matplotlib 0.91.2, the masked array importing will work with |
| the maskedarray branch) as well as with earlier versions. |
| |
| By default matplotlib still uses numpy.ma, but there is an rcParams setting |
| that you can use to select maskedarray instead. In the matplotlibrc file |
| you will find:: |
| |
| #maskedarray : False # True to use external maskedarray module |
| # instead of numpy.ma; this is a temporary # |
| setting for testing maskedarray. |
| |
| |
| Uncomment and set to True to select maskedarray everywhere. |
| Alternatively, you can test a script with maskedarray by using a |
| command-line option, e.g.:: |
| |
| python simple_plot.py --maskedarray |
| |
| |
| Masked records |
| -------------- |
| |
| Like *numpy.core.ma*, the *ndarray*-based implementation |
| of MaskedArray is limited when working with records: you can |
| mask any record of the array, but not a field in a record. If you |
| need this feature, you may want to give the *mrecords* package |
| a try (available in the *maskedarray* directory in the scipy |
| sandbox). This module defines a new class, *MaskedRecord*. An |
| instance of this class accepts a *recarray* as data, and uses two |
| masks: the *fieldmask* has as many entries as records in the array, |
| each entry with the same fields as a record, but of boolean types: |
| they indicate whether the field is masked or not; a record entry |
| is flagged as masked in the *mask* array if all the fields are |
| masked. A few examples in the file should give you an idea of what |
| can be done. Note that *mrecords* is still experimental... |
| |
| Optimizing maskedarray |
| ---------------------- |
| |
| Should masked arrays be filled before processing or not? |
| -------------------------------------------------------- |
| |
| In the current implementation, most operations on masked arrays involve |
| the following steps: |
| |
| * the input arrays are filled |
| * the operation is performed on the filled arrays |
| * the mask is set for the results, from the combination of the input masks and the mask corresponding to the domain of the operation. |
| |
| For example, consider the division of two masked arrays:: |
| |
| import numpy |
| import maskedarray as ma |
| x = ma.array([1,2,3,4],mask=[1,0,0,0], dtype=numpy.float_) |
| y = ma.array([-1,0,1,2], mask=[0,0,0,1], dtype=numpy.float_) |
| |
| The division of x by y is then computed as:: |
| |
| d1 = x.filled(0) # d1 = array([0., 2., 3., 4.]) |
| d2 = y.filled(1) # array([-1., 0., 1., 1.]) |
| m = ma.mask_or(ma.getmask(x), ma.getmask(y)) # m = |
| array([True,False,False,True]) |
| dm = ma.divide.domain(d1,d2) # array([False, True, False, False]) |
| result = (d1/d2).view(MaskedArray) # masked_array([-0. inf, 3., 4.]) |
| result._mask = logical_or(m, dm) |
| |
| Note that a division by zero takes place. To avoid it, we can consider |
| to fill the input arrays, taking the domain mask into account, so that:: |
| |
| d1 = x._data.copy() # d1 = array([1., 2., 3., 4.]) |
| d2 = y._data.copy() # array([-1., 0., 1., 2.]) |
| dm = ma.divide.domain(d1,d2) # array([False, True, False, False]) |
| numpy.putmask(d2, dm, 1) # d2 = array([-1., 1., 1., 2.]) |
| m = ma.mask_or(ma.getmask(x), ma.getmask(y)) # m = |
| array([True,False,False,True]) |
| result = (d1/d2).view(MaskedArray) # masked_array([-1. 0., 3., 2.]) |
| result._mask = logical_or(m, dm) |
| |
| Note that the *.copy()* is required to avoid updating the inputs with |
| *putmask*. The *.filled()* method also involves a *.copy()*. |
| |
| A third possibility consists in avoid filling the arrays:: |
| |
| d1 = x._data # d1 = array([1., 2., 3., 4.]) |
| d2 = y._data # array([-1., 0., 1., 2.]) |
| dm = ma.divide.domain(d1,d2) # array([False, True, False, False]) |
| m = ma.mask_or(ma.getmask(x), ma.getmask(y)) # m = |
| array([True,False,False,True]) |
| result = (d1/d2).view(MaskedArray) # masked_array([-1. inf, 3., 2.]) |
| result._mask = logical_or(m, dm) |
| |
| Note that here again the division by zero takes place. |
| |
| A quick benchmark gives the following results: |
| |
| * *numpy.ma.divide* : 2.69 ms per loop |
| * classical division : 2.21 ms per loop |
| * division w/ prefilling : 2.34 ms per loop |
| * division w/o filling : 1.55 ms per loop |
| |
| So, is it worth filling the arrays beforehand ? Yes, if we are interested |
| in avoiding floating-point exceptions that may fill the result with infs |
| and nans. No, if we are only interested into speed... |
| |
| |
| Thanks |
| ------ |
| |
| I'd like to thank Paul Dubois, Travis Oliphant and Sasha for the |
| original masked array package: without you, I would never have started |
| that (it might be argued that I shouldn't have anyway, but that's |
| another story...). I also wish to extend these thanks to Reggie Dugard |
| and Eric Firing for their suggestions and numerous improvements. |
|
|
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| Revision notes |
| |
|
|
| * 08/25/2007 : Creation of this page |
| * 01/23/2007 : The package has been moved to the SciPy sandbox, and is regularly updated: please check out your SVN version! |
|
|
