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==================================
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A guide to masked arrays in NumPy
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==================================
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.. Contents::
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See http://www.scipy.org/scipy/numpy/wiki/MaskedArray (dead link)
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for updates of this document.
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History
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-------
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As a regular user of MaskedArray, I (Pierre G.F. Gerard-Marchant) became
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increasingly frustrated with the subclassing of masked arrays (even if
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I can only blame my inexperience). I needed to develop a class of arrays
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that could store some additional information along with numerical values,
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while keeping the possibility for missing data (picture storing a series
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of dates along with measurements, what would later become the `TimeSeries
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Scikit <http://projects.scipy.org/scipy/scikits/wiki/TimeSeries>`__
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(dead link).
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I started to implement such a class, but then quickly realized that
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any additional information disappeared when processing these subarrays
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(for example, adding a constant value to a subarray would erase its
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dates). I ended up writing the equivalent of *numpy.core.ma* for my
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particular class, ufuncs included. Everything went fine until I needed to
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subclass my new class, when more problems showed up: some attributes of
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the new subclass were lost during processing. I identified the culprit as
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MaskedArray, which returns masked ndarrays when I expected masked
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arrays of my class. I was preparing myself to rewrite *numpy.core.ma*
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when I forced myself to learn how to subclass ndarrays. As I became more
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familiar with the *__new__* and *__array_finalize__* methods,
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I started to wonder why masked arrays were objects, and not ndarrays,
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and whether it wouldn't be more convenient for subclassing if they did
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behave like regular ndarrays.
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The new *maskedarray* is what I eventually come up with. The
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main differences with the initial *numpy.core.ma* package are
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that MaskedArray is now a subclass of *ndarray* and that the
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*_data* section can now be any subclass of *ndarray*. Apart from a
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couple of issues listed below, the behavior of the new MaskedArray
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class reproduces the old one. Initially the *maskedarray*
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implementation was marginally slower than *numpy.ma* in some areas,
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but work is underway to speed it up; the expectation is that it can be
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made substantially faster than the present *numpy.ma*.
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Note that if the subclass has some special methods and
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attributes, they are not propagated to the masked version:
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this would require a modification of the *__getattribute__*
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method (first trying *ndarray.__getattribute__*, then trying
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*self._data.__getattribute__* if an exception is raised in the first
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place), which really slows things down.
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Main differences
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----------------
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* The *_data* part of the masked array can be any subclass of ndarray (but not recarray, cf below).
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* *fill_value* is now a property, not a function.
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* 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.
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* I got rid of the *share_mask* flag, I never understood its purpose.
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* *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.
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* in the same way, the comparison of two masked arrays is a masked array, not a boolean
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* *filled(a)* returns an array of the same subclass as *a._data*, and no test is performed on whether it is contiguous or not.
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* 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.
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* *cumsum* works as if the *_data* array was filled with 0. The mask is preserved, but not updated.
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* *cumprod* works as if the *_data* array was filled with 1. The mask is preserved, but not updated.
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New features
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------------
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This list is non-exhaustive...
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* the *mr_* function mimics *r_* for masked arrays.
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* the *anom* method returns the anomalies (deviations from the average)
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Using the new package with numpy.core.ma
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----------------------------------------
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I tried to make sure that the new package can understand old masked
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arrays. Unfortunately, there's no upward compatibility.
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For example:
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>>> import numpy.core.ma as old_ma
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>>> import maskedarray as new_ma
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>>> x = old_ma.array([1,2,3,4,5], mask=[0,0,1,0,0])
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>>> x
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array(data =
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[ 1 2 999999 4 5],
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mask =
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[False False True False False],
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fill_value=999999)
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>>> y = new_ma.array([1,2,3,4,5], mask=[0,0,1,0,0])
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>>> y
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array(data = [1 2 -- 4 5],
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mask = [False False True False False],
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fill_value=999999)
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>>> x==y
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array(data =
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[True True True True True],
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mask =
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[False False True False False],
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fill_value=?)
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>>> old_ma.getmask(x) == new_ma.getmask(x)
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array([True, True, True, True, True])
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>>> old_ma.getmask(y) == new_ma.getmask(y)
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array([True, True, False, True, True])
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>>> old_ma.getmask(y)
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False
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Using maskedarray with matplotlib
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---------------------------------
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Starting with matplotlib 0.91.2, the masked array importing will work with
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the maskedarray branch) as well as with earlier versions.
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By default matplotlib still uses numpy.ma, but there is an rcParams setting
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that you can use to select maskedarray instead. In the matplotlibrc file
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you will find::
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#maskedarray : False # True to use external maskedarray module
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# instead of numpy.ma; this is a temporary #
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setting for testing maskedarray.
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Uncomment and set to True to select maskedarray everywhere.
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Alternatively, you can test a script with maskedarray by using a
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command-line option, e.g.::
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python simple_plot.py --maskedarray
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Masked records
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--------------
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Like *numpy.ma.core*, the *ndarray*-based implementation
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of MaskedArray is limited when working with records: you can
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mask any record of the array, but not a field in a record. If you
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need this feature, you may want to give the *mrecords* package
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a try (available in the *maskedarray* directory in the scipy
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sandbox). This module defines a new class, *MaskedRecord*. An
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instance of this class accepts a *recarray* as data, and uses two
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masks: the *fieldmask* has as many entries as records in the array,
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each entry with the same fields as a record, but of boolean types:
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they indicate whether the field is masked or not; a record entry
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is flagged as masked in the *mask* array if all the fields are
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masked. A few examples in the file should give you an idea of what
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can be done. Note that *mrecords* is still experimental...
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Optimizing maskedarray
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----------------------
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Should masked arrays be filled before processing or not?
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--------------------------------------------------------
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In the current implementation, most operations on masked arrays involve
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the following steps:
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* the input arrays are filled
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* the operation is performed on the filled arrays
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* the mask is set for the results, from the combination of the input masks and the mask corresponding to the domain of the operation.
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For example, consider the division of two masked arrays::
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import numpy
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import maskedarray as ma
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x = ma.array([1,2,3,4],mask=[1,0,0,0], dtype=numpy.float64)
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y = ma.array([-1,0,1,2], mask=[0,0,0,1], dtype=numpy.float64)
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The division of x by y is then computed as::
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d1 = x.filled(0) # d1 = array([0., 2., 3., 4.])
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d2 = y.filled(1) # array([-1., 0., 1., 1.])
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m = ma.mask_or(ma.getmask(x), ma.getmask(y)) # m =
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array([True,False,False,True])
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dm = ma.divide.domain(d1,d2) # array([False, True, False, False])
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result = (d1/d2).view(MaskedArray) # masked_array([-0. inf, 3., 4.])
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result._mask = logical_or(m, dm)
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Note that a division by zero takes place. To avoid it, we can consider
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to fill the input arrays, taking the domain mask into account, so that::
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d1 = x._data.copy() # d1 = array([1., 2., 3., 4.])
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d2 = y._data.copy() # array([-1., 0., 1., 2.])
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dm = ma.divide.domain(d1,d2) # array([False, True, False, False])
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numpy.putmask(d2, dm, 1) # d2 = array([-1., 1., 1., 2.])
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m = ma.mask_or(ma.getmask(x), ma.getmask(y)) # m =
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array([True,False,False,True])
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result = (d1/d2).view(MaskedArray) # masked_array([-1. 0., 3., 2.])
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result._mask = logical_or(m, dm)
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Note that the *.copy()* is required to avoid updating the inputs with
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*putmask*. The *.filled()* method also involves a *.copy()*.
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A third possibility consists in avoid filling the arrays::
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d1 = x._data # d1 = array([1., 2., 3., 4.])
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d2 = y._data # array([-1., 0., 1., 2.])
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dm = ma.divide.domain(d1,d2) # array([False, True, False, False])
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m = ma.mask_or(ma.getmask(x), ma.getmask(y)) # m =
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array([True,False,False,True])
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result = (d1/d2).view(MaskedArray) # masked_array([-1. inf, 3., 2.])
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result._mask = logical_or(m, dm)
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Note that here again the division by zero takes place.
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A quick benchmark gives the following results:
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* *numpy.ma.divide* : 2.69 ms per loop
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* classical division : 2.21 ms per loop
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* division w/ prefilling : 2.34 ms per loop
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* division w/o filling : 1.55 ms per loop
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So, is it worth filling the arrays beforehand ? Yes, if we are interested
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in avoiding floating-point exceptions that may fill the result with infs
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and nans. No, if we are only interested into speed...
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Thanks
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------
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I'd like to thank Paul Dubois, Travis Oliphant and Sasha for the
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original masked array package: without you, I would never have started
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that (it might be argued that I shouldn't have anyway, but that's
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another story...). I also wish to extend these thanks to Reggie Dugard
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and Eric Firing for their suggestions and numerous improvements.
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Revision notes
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--------------
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* 08/25/2007 : Creation of this page
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* 01/23/2007 : The package has been moved to the SciPy sandbox, and is regularly updated: please check out your SVN version!
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