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Alters 'data' in-place.
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Logic for the 1-d interpolation. The input
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Bounds_error is currently hardcoded to False since non-scipy ones don't
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Fills 'yvalues' in-place.
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Passed off to scipy.interpolate.interp1d. method is scipy's kind.
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z interpolation requires SciPy.Úscipy)Úextrar ©Ú interpolate)ra rb re rf ri rh rg )rS r] r^ r_ r` rd rd )r r¤ r¥ rc z;order needs to be specified and greater than 0; got order: Úk)r rÒ rÕ r. rµ Úbarycentric_interpolateÚkrogh_interpolateÚ_from_derivativesÚ_cubicspline_interpolateÚ_akima_interpolateÚpchip_interpolateÚinterp1dr r" ÚUnivariateSplineÚflagsÚ writeabler+ )rA ÚyÚnew_xrJ r¤ r¥ rk rp rÓ rÕ Ú alt_methodsÚinterp1d_methodsr ÚterpÚnew_ys r& rÅ rÅ % s} ð hÐ4Ð 5EÜ w¨eÕ4Ý!ä JJuÓ Eð #×:Ñ:Ø ×.Ñ.Ü -Ü 1Ü/Ü#Ø ×.Ñ.ñKòÐð Ð!Ñ!Ø \Ò !ØDàDØ×#Ñ#Ø qt¨
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Convenience function for interpolate.BPoly.from_derivatives.
|
|
Construct a piecewise polynomial in the Bernstein basis, compatible
|
with the specified values and derivatives at breakpoints.
|
|
Parameters
|
----------
|
xi : array-like
|
sorted 1D array of x-coordinates
|
yi : array-like or list of array-likes
|
yi[i][j] is the j-th derivative known at xi[i]
|
order: None or int or array-like of ints. Default: None.
|
Specifies the degree of local polynomials. If not None, some
|
derivatives are ignored.
|
der : int or list
|
How many derivatives to extract; None for all potentially nonzero
|
derivatives (that is a number equal to the number of points), or a
|
list of derivatives to extract. This number includes the function
|
value as 0th derivative.
|
extrapolate : bool, optional
|
Whether to extrapolate to ouf-of-bounds points based on first and last
|
intervals, or to return NaNs. Default: True.
|
|
See Also
|
--------
|
scipy.interpolate.BPoly.from_derivatives
|
|
Returns
|
-------
|
y : scalar or array-like
|
The result, of length R or length M or M by R.
|
r rÔ rz rw )ÚordersÚ extrapolate)rÒ rÕ ÚBPolyre Úreshape) ÚxiÚyirA rk Úderré rÕ rJ Úms r& rÙ rÙ l s? õR "ð × Ñ × /Ñ /FÙr2::b !Ó$¨UÀ ÔLAá Q4Kr( c óJ ddl m} |j | ||¬« } |||¬« S )aQ
|
Convenience function for akima interpolation.
|
xi and yi are arrays of values used to approximate some function f,
|
with ``yi = f(xi)``.
|
|
See `Akima1DInterpolator` for details.
|
|
Parameters
|
----------
|
xi : np.ndarray
|
A sorted list of x-coordinates, of length N.
|
yi : np.ndarray
|
A 1-D array of real values. `yi`'s length along the interpolation
|
axis must be equal to the length of `xi`. If N-D array, use axis
|
parameter to select correct axis.
|
x : np.ndarray
|
Of length M.
|
der : int, optional
|
How many derivatives to extract; None for all potentially
|
nonzero derivatives (that is a number equal to the number
|
of points), or a list of derivatives to extract. This number
|
includes the function value as 0th derivative.
|
axis : int, optional
|
Axis in the yi array corresponding to the x-coordinate values.
|
|
See Also
|
--------
|
scipy.interpolate.Akima1DInterpolator
|
|
Returns
|
-------
|
y : scalar or array-like
|
The result, of length R or length M or M by R,
|
|
r rÔ rx )Únu)rÒ rÕ ÚAkima1DInterpolator)rì rí rA rî ry rÕ ÚPs r& rÛ rÛ s+ õT "à×'Ñ'¨¨B°TÐ'Ó:Aá Q3<Ðr( c óJ ddl m} |j | ||||¬« } ||« S )ag
|
Convenience function for cubic spline data interpolator.
|
|
See `scipy.interpolate.CubicSpline` for details.
|
|
Parameters
|
----------
|
xi : np.ndarray, shape (n,)
|
1-d array containing values of the independent variable.
|
Values must be real, finite and in strictly increasing order.
|
yi : np.ndarray
|
Array containing values of the dependent variable. It can have
|
arbitrary number of dimensions, but the length along ``axis``
|
(see below) must match the length of ``x``. Values must be finite.
|
x : np.ndarray, shape (m,)
|
axis : int, optional
|
Axis along which `y` is assumed to be varying. Meaning that for
|
``x[i]`` the corresponding values are ``np.take(y, i, axis=axis)``.
|
Default is 0.
|
bc_type : string or 2-tuple, optional
|
Boundary condition type. Two additional equations, given by the
|
boundary conditions, are required to determine all coefficients of
|
polynomials on each segment [2]_.
|
If `bc_type` is a string, then the specified condition will be applied
|
at both ends of a spline. Available conditions are:
|
* 'not-a-knot' (default): The first and second segment at a curve end
|
are the same polynomial. It is a good default when there is no
|
information on boundary conditions.
|
* 'periodic': The interpolated functions is assumed to be periodic
|
of period ``x[-1] - x[0]``. The first and last value of `y` must be
|
identical: ``y[0] == y[-1]``. This boundary condition will result in
|
``y'[0] == y'[-1]`` and ``y''[0] == y''[-1]``.
|
* 'clamped': The first derivative at curves ends are zero. Assuming
|
a 1D `y`, ``bc_type=((1, 0.0), (1, 0.0))`` is the same condition.
|
* 'natural': The second derivative at curve ends are zero. Assuming
|
a 1D `y`, ``bc_type=((2, 0.0), (2, 0.0))`` is the same condition.
|
If `bc_type` is a 2-tuple, the first and the second value will be
|
applied at the curve start and end respectively. The tuple values can
|
be one of the previously mentioned strings (except 'periodic') or a
|
tuple `(order, deriv_values)` allowing to specify arbitrary
|
derivatives at curve ends:
|
* `order`: the derivative order, 1 or 2.
|
* `deriv_value`: array-like containing derivative values, shape must
|
be the same as `y`, excluding ``axis`` dimension. For example, if
|
`y` is 1D, then `deriv_value` must be a scalar. If `y` is 3D with
|
the shape (n0, n1, n2) and axis=2, then `deriv_value` must be 2D
|
and have the shape (n0, n1).
|
extrapolate : {bool, 'periodic', None}, optional
|
If bool, determines whether to extrapolate to out-of-bounds points
|
based on first and last intervals, or to return NaNs. If 'periodic',
|
periodic extrapolation is used. If None (default), ``extrapolate`` is
|
set to 'periodic' for ``bc_type='periodic'`` and to True otherwise.
|
|
See Also
|
--------
|
scipy.interpolate.CubicHermiteSpline
|
|
Returns
|
-------
|
y : scalar or array-like
|
The result, of shape (m,)
|
|
References
|
----------
|
.. [1] `Cubic Spline Interpolation
|
<https://en.wikiversity.org/wiki/Cubic_Spline_Interpolation>`_
|
on Wikiversity.
|
.. [2] Carl de Boor, "A Practical Guide to Splines", Springer-Verlag, 1978.
|
r rÔ )ry Úbc_typeré )rÒ rÕ Ú CubicSpline)rì rí rA ry rõ ré rÕ ró s r& rÚ rÚ Ï s3 õZ "à× Ñ Ø
|
BT 7¸ ð ó Añ Q4Kr( c ó4 t | « }| }|j « szt d|¬« }|d}t d|¬« }| t | « }t | |||¬« |dk( r d|||d z n |d
|
k( rdx|d| ||d z d n t d « t j | |< yy) a«
|
Apply interpolation and limit_area logic to values along a to-be-specified axis.
|
|
Parameters
|
----------
|
values: np.ndarray
|
Input array.
|
method: str
|
Interpolation method. Could be "bfill" or "pad"
|
limit: int, optional
|
Index limit on interpolation.
|
limit_area: {'inside', 'outside'}
|
Limit area for interpolation.
|
|
Notes
|
-----
|
Modifies values in-place.
|
rt r» Nr ru )rJ r r r Frw r z*limit_area should be 'inside' or 'outside')r r¼ r r! Úpad_or_backfill_inplacer" r. rÆ )r\ rJ r r rÇ r~ rt ru s r& Ú _interpolate_with_limit_arearù % s¼ ô2 6lGØxHà ;;=Ü W°xÔ@Ø =ØEÜ F°XÔ>Ø <Üv;Dä Ø ØØØ!õ
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ð Ò !Ø(-GED 1HÑ %Ø 9Ò $Ø49Ð 9GFUOg d¨Q¡h jÑ 1ä Ð IÓJÐ Jä &&wð- r( c óü |dk( rd nd }| j dk( r7|dk7 r t d« | j t d| j z « « } t |« } || « }t |d¬« } ||||¬ « y
|
) a
|
Perform an actual interpolation of values, values will be make 2-d if
|
needed fills inplace, returns the result.
|
|
Parameters
|
----------
|
values: np.ndarray
|
Input array.
|
method: str, default "pad"
|
Interpolation method. Could be "bfill" or "pad"
|
axis: 0 or 1
|
Interpolation axis
|
limit: int, optional
|
Index limit on interpolation.
|
limit_area: str, optional
|
Limit area for interpolation. Can be "inside" or "outside"
|
|
Notes
|
-----
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Modifies values in-place.
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Wrapper to handle datetime64 and timedelta64 dtypes.
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j « z
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dz
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}|dk( rd| d| d| |dz d y|dk( r d| |dz | yy)a× Prepare 1d mask for ffill/bfill with limit_area.
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Caller is responsible for checking at least one value of mask is False.
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When called, mask will no longer faithfully represent when
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the corresponding are NA or not.
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Parameters
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----------
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mask : np.ndarray[bool, ndim=1]
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Mask representing NA values when filling.
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limit_area : { "outside", "inside" }
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Whether to limit filling to outside or inside the outer most non-NA value.
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z }nQt j j |d¬« t j j |ddd
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z }d| |j < y)a Prepare 2d mask for ffill/bfill with limit_area.
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When called, mask will no longer faithfully represent when
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the corresponding are NA or not.
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Parameters
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----------
|
mask : np.ndarray[bool, ndim=1]
|
Mask representing NA values when filling.
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limit_area : { "outside", "inside" }
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Whether to limit filling to outside or inside the outer most non-NA value.
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r r rx Nrz F)rÿ r. ÚmaximumÚ
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accumulate)r$ r r" Úla_masks r& r r sÄ ð wHØYÒ ô JJ× !Ñ ! (°Ð !Ó 3Üjj×#Ñ# H©T¨r¨T¡N¸Ð#Ó;¹D¸b¸DÑAñ Bñ ô ZZ× "Ñ " 8°!Ð "Ó 4Ð 4Üzz×$Ñ$ X©d°¨d¡^¸!Ð$Ó<¹T¸r¸TÑBÐBñ Cð ð DOr( ©rP rR c óT t | « } |dk( r t | S t t d| S )Nrw r' )rK Ú _fill_methodsr r )rJ r{ s r& r r * s. Ü vÓ &FØ qyÜ VÑ$Ð$ܬ Ñ 5°fÑ =Ð=r( c ó" | y t | d¬« S )NTrD )rK )rJ s r& Úclean_reindex_fill_methodr+ 1 s Ø ~ØÜ V°4Ô 8Ð8r( c óT t | « t « }t « }dfd }|0|dk( r"t t j | « d « }n || |« }|J|dk( r|S t || ddd
|« « }t dz
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t j
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|« z
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« }|dk( r|S ||z S )ak
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Get indexers of values that won't be filled
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because they exceed the limits.
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Parameters
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----------
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invalid : np.ndarray[bool]
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fw_limit : int or None
|
forward limit to index
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bw_limit : int or None
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backward limit to index
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Returns
|
-------
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set of indexers
|
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Notes
|
-----
|
This is equivalent to the more readable, but slower
|
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.. code-block:: python
|
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def _interp_limit(invalid, fw_limit, bw_limit):
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for x in np.where(invalid)[0]:
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if invalid[max(0, x - fw_limit):x + bw_limit + 1].all():
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yield x
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