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This bug affected the various polynomial class methods fromroots due to
the ability to specify both window and domain. In that circumstance the
roots are mapped from the domain to the window by the substitution
`x = off + scl*x`. The polynomial that was being generated was monic in
the window before substitution, but if scl was not one it was not monic
considered as a function of the variable x in the domain. The fix is to
divide the generated coefficients by `scl ** deg` so that the scaling of
the highest degree term after substitution is canceled.
It might be better to make the scaling optional in the future, but this
fix makes the result match the documentation.
Closes #3467.
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The companion matrices returned by the various polynomial types was
a scalar in the degree one case instead of a 2-D array. Fix that and
add a test to check for that result.
Closes #3459.
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Now that only Python versions 2.6-2.7 and 3.2-3.3 are supported
some version checks are no longer needed. This patch removes them
so as to clean up the code.
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Add `print_function` to all `from __future__ import ...` statements
and use the python3 print function syntax everywhere.
Closes #3078.
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DOC: Formatting fixes using regex
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also other spacing or formatting mistakes
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The new import `absolute_import` is added the `from __future__ import`
statement and The 2to3 `import` fixer is run to make the imports
compatible. There are several things that need to be dealt with to make
this work.
1) Files meant to be run as scripts run in a different environment than
files imported as part of a package, and so changes to those files need
to be skipped. The affected script files are:
* all setup.py files
* numpy/core/code_generators/generate_umath.py
* numpy/core/code_generators/generate_numpy_api.py
* numpy/core/code_generators/generate_ufunc_api.py
2) Some imported modules are not available as they are created during
the build process and consequently 2to3 is unable to handle them
correctly. Files that import those modules need a bit of extra work.
The affected files are:
* core/__init__.py,
* core/numeric.py,
* core/_internal.py,
* core/arrayprint.py,
* core/fromnumeric.py,
* numpy/__init__.py,
* lib/npyio.py,
* lib/function_base.py,
* fft/fftpack.py,
* random/__init__.py
Closes #3172
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In python3 range is an iterator and `xrange` has been removed. This has
two consequence for code:
1) Where a list is needed `list(range(...))` must be used.
2) `xrange` must be replaced by `range`
Both of these changes also work in python2 and this patch makes both.
There are three places fixed that do not need it, but I left them in
so that the result would be `xrange` clean.
Closes #3092
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This should be harmless, as we already are division clean. However,
placement of this import takes some care. In the future a script
can be used to append new features without worry, at least until
such time as it exceeds a single line. Having that ability will
make it easier to deal with absolute imports and printing updates.
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This changes the `exec` command to the `exec` function.
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Instead of
if lhs.dtype.char in np.typecodes['Complex']:
use
if issubclass(lhs.dtype.type, np.complexfloating):
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The test uses the complex set of sample points [1, 1j, -1, -1j] whose
squared sum is exactly zero. This would fail before the column scaling
was fixed.
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The columns should be scaled using their 2-norm, but in the complex case
that was being incorrectly computed as the square root of the sum of the
squared elements rather than as the square root of the sum of their squared
real and imaginary parts.
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The original masked-NA-NEP branch contained a large number of changes
in addition to the core NA support. For example:
- ufunc.__call__ support for where= argument
- nditer support for arbitrary masks (in support of where=)
- ufunc.reduce support for simultaneous reduction over multiple axes
- a new "array assignment API"
- ndarray.diagonal() returning a view in all cases
- bug-fixes in __array_priority__ handling
- datetime test changes
etc. There's no consensus yet on what should be done with the
maskna-related part of this branch, but the rest is generally useful
and uncontroversial, so the goal of this branch is to identify exactly
which code changes are involved in maskna support.
The basic strategy used to create this patch was:
- Remove the new masking-related fields from ndarray, so no arrays
are masked
- Go through and remove all the code that this makes
dead/inaccessible/irrelevant, in a largely mechanical fashion. So
for example, if I saw 'if (PyArray_HASMASK(a)) { ... }' then that
whole block was obviously just dead code if no arrays have masks,
and I removed it. Likewise for function arguments like skipna that
are useless if there aren't any NAs to skip.
This changed the signature of a number of functions that were newly
exposed in the numpy public API. I've removed all such functions from
the public API, since releasing them with the NA-less signature in 1.7
would create pointless compatibility hassles later if and when we add
back the NA-related functionality. Most such functions are removed by
this commit; the exception is PyArray_ReduceWrapper, which requires
more extensive surgery, and will be handled in followup commits.
I also removed the new ndarray.setasflat method. Reason: a comment
noted that the only reason this was added was to allow easier testing
of one branch of PyArray_CopyAsFlat. That branch is now the main
branch, so that isn't an issue. Nonetheless this function is arguably
useful, so perhaps it should have remained, but I judged that since
numpy's API is already hairier than we would like, it's not a good
idea to add extra hair "just in case". (Also AFAICT the test for this
method in test_maskna was actually incorrect, as noted here:
https://github.com/njsmith/numpyNEP/blob/master/numpyNEP.py
so I'm not confident that it ever worked in master, though I haven't
had a chance to follow-up on this.)
I also removed numpy.count_reduce_items, since without skipna it
became trivial.
I believe that these are the only exceptions to the "remove dead code"
strategy.
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Use divmod instead of // and % separately.
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The original method was overly sensitive to roundoff. Of the two
approaches considered, gauss integration or binary subdivision of
the roots, the latter is more compatible with using other number
representations such as mpmath. No method is going to be suitable
for large numbers of arbitrary zeros but the current method is a
significant improvement.
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And don't use the 'exec' statement to write the tests.
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The tests were all generator based and that produced the same message
for all the tests when they were run in verbose mode. The quick fix
was to use the generator to write named test functions for all the tests.
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Test that those combinations raise ValueError for the arithmetic operations
of the convenience classes.
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In particular for arithmetic where one could end up with a Polynomial
type with Chebyshev coefficients after an addition. It is unlikely that
that would be done on purpose.
The PolyDomain error message was also replaced by a TypeError with
an appropriate message. That seems like a better choice.
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The old functions could use a review, but that isn't pressing.
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Step 1 in the polynomial package documentation revisions.
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This is the first step in cleaning up the polynomial documentation
and writing an instructional section on the convenience classes.
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This works around changes in the treatment of __array_priority__ that
were part of commit 32b32c2. Previously the rop's of the right hand
object were called whenever it had the __array_priority__ attribute
and was not an ndarray or derived thereof. After the change the
object needed to have greater priority, in this case > 0. It isn't
clear that the new behavior is the correct one and if it is reverted
then setting __array_priority__ back to 0 will provide a test for that
decision.
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There are currently errors that will be fixed if pull #178 goes in.
The tests were also changed to use generators, which makes them
run noticeably slower but give better error messages and makes the
tests a bit cleaner.
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A new test file, test_classes, has been added so that conversions
between all the class types can be tested. Several tests common to
all the classes were also moved to this file. Ideally all the common
tests will be moved, but that isn't done yet.
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The new basis method is a convenient way to return an instance of the basis
function of given degree for the class. It is intended mostly for
pedagogical purposes.
The new cast method provides an alternate way to convert an instance of one
polynomial class to another. It complements the convert instance method.
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The new functions for Gauss quadrature are of the form xxxgauss, where xxx
is any of cheb, leg, lag, herm, herme. They return the Gauss points and
weights for Gauss quadrature of the various orthogonal polynomial types
given the degree. They are tested to work up to degree 100.
The new functions for the weight are of the form xxxweight, where xxx is
any of cheb, leg, lag, herm, herme. They return the value of the weight
function for the various orthogonal polynomial types given and array of
points.
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The new companion matrices are related to the old by a
similarity transformation that makes them better conditioned
for root finding. In particular, the companion matrices for
the orthogonal polynomials are symmetric when the zeros of a
single polynomial term is wanted. This produces better zeros
for use in Gauss quadrature.
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Test the multi-dimensional coefficient array functionality.
Reorganize and cleanup some previous tests.
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Where xxx is one of poly, cheb, leg, lag, herm, herme:
Refactor xxxval2d, xxxval3d, xxxgrid2d, and xxxgrid3d for clarity.
Check that coordinate arrays are compatible in xxxval2d, xxxval3d.
Work around einsum bug that affected xxxvander3d.
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The coefficients used were [1] + [0]*i instead of [0]*i + [1].
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An axis keyword was added to the function signatures of xxxder and
xxxint, where xxx is any of poly, cheb, leg, lag, herm, herme. The
evaluation method for the Chebeshev series was also changed to avoid
using z_series and to more closely resemble the other implementations.
At some point the z_series will be removed from the chebyshev module
and only used for trigonometric series.
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are useful for least squares fits to data depending on two or three variables using the various polynomial basis.
The new functions have names polyvander2d, and polyvander3d,
where 'poly' can be replaced by any of 'leg', 'cheb', 'lag',
'herm', or 'herme'.
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coefficient arrays can be used. Add functions for evaluation of 2D and 3D polynomial series evaluated either on a specified set of points or on a cartesian product of 1D points.
The new functions have names polyval2d, polygrid2d, polyval3d, and
polygrid3d, where 'poly' can be replaced by any of 'leg', 'cheb', 'lag',
'herm', or 'herme'. These additional functions should cover the common
multidimensional cases and provide examples for anyone who wants to go to
higher dimensions.
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