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Wrapper functions to more user-friendly calling of certain math functions
whose output data-type is different than the input data-type in certain
domains of the input.
For example, for functions like `log` with branch cuts, the versions in this
module provide the mathematically valid answers in the complex plane::
>>> import math
>>> np.emath.log(-math.exp(1)) == (1+1j*math.pi)
True
Similarly, `sqrt`, other base logarithms, `power` and trig functions are
correctly handled. See their respective docstrings for specific examples.
� N)�asarray�any)�array_function_dispatch�
set_module)�isreal) �sqrt�log�log2�logn�log10�power�arccos�arcsin�arctanhg @c �r � t | j j t j t j
t j t j t j t j f� r | j t j � S | j t j � S )az Convert its input `arr` to a complex array.
The input is returned as a complex array of the smallest type that will fit
the original data: types like single, byte, short, etc. become csingle,
while others become cdouble.
A copy of the input is always made.
Parameters
----------
arr : array
Returns
-------
array
An array with the same input data as the input but in complex form.
Examples
--------
>>> import numpy as np
First, consider an input of type short:
>>> a = np.array([1,2,3],np.short)
>>> ac = np.lib.scimath._tocomplex(a); ac
array([1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64)
>>> ac.dtype
dtype('complex64')
If the input is of type double, the output is correspondingly of the
complex double type as well:
>>> b = np.array([1,2,3],np.double)
>>> bc = np.lib.scimath._tocomplex(b); bc
array([1.+0.j, 2.+0.j, 3.+0.j])
>>> bc.dtype
dtype('complex128')
Note that even if the input was complex to begin with, a copy is still
made, since the astype() method always copies:
>>> c = np.array([1,2,3],np.csingle)
>>> cc = np.lib.scimath._tocomplex(c); cc
array([1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64)
>>> c *= 2; c
array([2.+0.j, 4.+0.j, 6.+0.j], dtype=complex64)
>>> cc
array([1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64)
) �
issubclass�dtype�type�nt�single�byte�short�ubyte�ushort�csingle�astype�cdouble)�arrs �9C:\Python312\Lib\site-packages\numpy/lib/_scimath_impl.py�
_tocomplexr ! sg � �r �#�)�)�.�.�2�9�9�b�g�g�r�x�x����#%�9�9�b�j�j�#:� ;��z�z�"�*�*�%�%��z�z�"�*�*�%�%� c �f � t | � } t t | � | dk z � r t | � } | S )a� Convert `x` to complex if it has real, negative components.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> import numpy as np
>>> np.lib.scimath._fix_real_lt_zero([1,2])
array([1, 2])
>>> np.lib.scimath._fix_real_lt_zero([-1,2])
array([-1.+0.j, 2.+0.j])
r )r r r r ��xs r �_fix_real_lt_zeror% a s0 � �. ��
�A�
�6�!�9��A�� � � �q�M�� �Hr! c �Z � t | � } t t | � | dk z � r| dz } | S )a� Convert `x` to double if it has real, negative components.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> import numpy as np
>>> np.lib.scimath._fix_int_lt_zero([1,2])
array([1, 2])
>>> np.lib.scimath._fix_int_lt_zero([-1,2])
array([-1., 2.])
r g �?)r r r r# s r �_fix_int_lt_zeror' ~ s0 � �, ��
�A�
�6�!�9��A�� � �
��G�� �Hr! c �x � t | � } t t | � t | � dkD z � r t | � } | S )a� Convert `x` to complex if it has real components x_i with abs(x_i)>1.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> import numpy as np
>>> np.lib.scimath._fix_real_abs_gt_1([0,1])
array([0, 1])
>>> np.lib.scimath._fix_real_abs_gt_1([0,2])
array([0.+0.j, 2.+0.j])
� )r r r �absr r# s r �_fix_real_abs_gt_1r+ � s4 � �, ��
�A�
�6�!�9��A���
� #�$� �q�M�� �Hr! c � � | fS �N� r# s r �_unary_dispatcherr/ � s � �
�4�Kr! znumpy.lib.scimathc �B � t | � } t j | � S )a
Compute the square root of x.
For negative input elements, a complex value is returned
(unlike `numpy.sqrt` which returns NaN).
Parameters
----------
x : array_like
The input value(s).
Returns
-------
out : ndarray or scalar
The square root of `x`. If `x` was a scalar, so is `out`,
otherwise an array is returned.
See Also
--------
numpy.sqrt
Examples
--------
For real, non-negative inputs this works just like `numpy.sqrt`:
>>> import numpy as np
>>> np.emath.sqrt(1)
1.0
>>> np.emath.sqrt([1, 4])
array([1., 2.])
But it automatically handles negative inputs:
>>> np.emath.sqrt(-1)
1j
>>> np.emath.sqrt([-1,4])
array([0.+1.j, 2.+0.j])
Different results are expected because:
floating point 0.0 and -0.0 are distinct.
For more control, explicitly use complex() as follows:
>>> np.emath.sqrt(complex(-4.0, 0.0))
2j
>>> np.emath.sqrt(complex(-4.0, -0.0))
-2j
)r% �nxr r# s r r r � s � �h �!� �A�
�7�7�1�:�r! c �B � t | � } t j | � S )a�
Compute the natural logarithm of `x`.
Return the "principal value" (for a description of this, see `numpy.log`)
of :math:`log_e(x)`. For real `x > 0`, this is a real number (``log(0)``
returns ``-inf`` and ``log(np.inf)`` returns ``inf``). Otherwise, the
complex principle value is returned.
Parameters
----------
x : array_like
The value(s) whose log is (are) required.
Returns
-------
out : ndarray or scalar
The log of the `x` value(s). If `x` was a scalar, so is `out`,
otherwise an array is returned.
See Also
--------
numpy.log
Notes
-----
For a log() that returns ``NAN`` when real `x < 0`, use `numpy.log`
(note, however, that otherwise `numpy.log` and this `log` are identical,
i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and,
notably, the complex principle value if ``x.imag != 0``).
Examples
--------
>>> import numpy as np
>>> np.emath.log(np.exp(1))
1.0
Negative arguments are handled "correctly" (recall that
``exp(log(x)) == x`` does *not* hold for real ``x < 0``):
>>> np.emath.log(-np.exp(1)) == (1 + np.pi * 1j)
True
�r% r1 r r# s r r r � s � �\ �!� �A�
�6�6�!�9�r! c �B � t | � } t j | � S )a
Compute the logarithm base 10 of `x`.
Return the "principal value" (for a description of this, see
`numpy.log10`) of :math:`log_{10}(x)`. For real `x > 0`, this
is a real number (``log10(0)`` returns ``-inf`` and ``log10(np.inf)``
returns ``inf``). Otherwise, the complex principle value is returned.
Parameters
----------
x : array_like or scalar
The value(s) whose log base 10 is (are) required.
Returns
-------
out : ndarray or scalar
The log base 10 of the `x` value(s). If `x` was a scalar, so is `out`,
otherwise an array object is returned.
See Also
--------
numpy.log10
Notes
-----
For a log10() that returns ``NAN`` when real `x < 0`, use `numpy.log10`
(note, however, that otherwise `numpy.log10` and this `log10` are
identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`,
and, notably, the complex principle value if ``x.imag != 0``).
Examples
--------
>>> import numpy as np
(We set the printing precision so the example can be auto-tested)
>>> np.set_printoptions(precision=4)
>>> np.emath.log10(10**1)
1.0
>>> np.emath.log10([-10**1, -10**2, 10**2])
array([1.+1.3644j, 2.+1.3644j, 2.+0.j ])
)r% r1 r r# s r r r $ s � �` �!� �A�
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�q�7�Nr! c � � t |� }t | � } t j |� t j | � z S )a�
Take log base n of x.
If `x` contains negative inputs, the answer is computed and returned in the
complex domain.
Parameters
----------
n : array_like
The integer base(s) in which the log is taken.
x : array_like
The value(s) whose log base `n` is (are) required.
Returns
-------
out : ndarray or scalar
The log base `n` of the `x` value(s). If `x` was a scalar, so is
`out`, otherwise an array is returned.
Examples
--------
>>> import numpy as np
>>> np.set_printoptions(precision=4)
>>> np.emath.logn(2, [4, 8])
array([2., 3.])
>>> np.emath.logn(2, [-4, -8, 8])
array([2.+4.5324j, 3.+4.5324j, 3.+0.j ])
r3 r6 s r r r \ s4 � �B �!� �A��!� �A�
�6�6�!�9�R�V�V�A�Y� � r! c �B � t | � } t j | � S )a�
Compute the logarithm base 2 of `x`.
Return the "principal value" (for a description of this, see
`numpy.log2`) of :math:`log_2(x)`. For real `x > 0`, this is
a real number (``log2(0)`` returns ``-inf`` and ``log2(np.inf)`` returns
``inf``). Otherwise, the complex principle value is returned.
Parameters
----------
x : array_like
The value(s) whose log base 2 is (are) required.
Returns
-------
out : ndarray or scalar
The log base 2 of the `x` value(s). If `x` was a scalar, so is `out`,
otherwise an array is returned.
See Also
--------
numpy.log2
Notes
-----
For a log2() that returns ``NAN`` when real `x < 0`, use `numpy.log2`
(note, however, that otherwise `numpy.log2` and this `log2` are
identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`,
and, notably, the complex principle value if ``x.imag != 0``).
Examples
--------
We set the printing precision so the example can be auto-tested:
>>> np.set_printoptions(precision=4)
>>> np.emath.log2(8)
3.0
>>> np.emath.log2([-4, -8, 8])
array([2.+4.5324j, 3.+4.5324j, 3.+0.j ])
)r% r1 r
r# s r r
r
� s � �\ �!� �A�
�7�7�1�:�r! c �
� | |fS r- r. �r$ �ps r �_power_dispatcherr> � s � �
�q�6�Mr! c �Z � t | � } t |� }t j | |� S )a-
Return x to the power p, (x**p).
If `x` contains negative values, the output is converted to the
complex domain.
Parameters
----------
x : array_like
The input value(s).
p : array_like of ints
The power(s) to which `x` is raised. If `x` contains multiple values,
`p` has to either be a scalar, or contain the same number of values
as `x`. In the latter case, the result is
``x[0]**p[0], x[1]**p[1], ...``.
Returns
-------
out : ndarray or scalar
The result of ``x**p``. If `x` and `p` are scalars, so is `out`,
otherwise an array is returned.
See Also
--------
numpy.power
Examples
--------
>>> import numpy as np
>>> np.set_printoptions(precision=4)
>>> np.emath.power(2, 2)
4
>>> np.emath.power([2, 4], 2)
array([ 4, 16])
>>> np.emath.power([2, 4], -2)
array([0.25 , 0.0625])
>>> np.emath.power([-2, 4], 2)
array([ 4.-0.j, 16.+0.j])
>>> np.emath.power([2, 4], [2, 4])
array([ 4, 256])
)r% r' r1 r
r< s r r
r
� s) � �d �!� �A����A�
�8�8�A�q�>�r! c �B � t | � } t j | � S )a�
Compute the inverse cosine of x.
Return the "principal value" (for a description of this, see
`numpy.arccos`) of the inverse cosine of `x`. For real `x` such that
`abs(x) <= 1`, this is a real number in the closed interval
:math:`[0, \pi]`. Otherwise, the complex principle value is returned.
Parameters
----------
x : array_like or scalar
The value(s) whose arccos is (are) required.
Returns
-------
out : ndarray or scalar
The inverse cosine(s) of the `x` value(s). If `x` was a scalar, so
is `out`, otherwise an array object is returned.
See Also
--------
numpy.arccos
Notes
-----
For an arccos() that returns ``NAN`` when real `x` is not in the
interval ``[-1,1]``, use `numpy.arccos`.
Examples
--------
>>> import numpy as np
>>> np.set_printoptions(precision=4)
>>> np.emath.arccos(1) # a scalar is returned
0.0
>>> np.emath.arccos([1,2])
array([0.-0.j , 0.-1.317j])
)r+ r1 r r# s r r r � s � �V �1� �A�
�9�9�Q�<�r! c �B � t | � } t j | � S )a�
Compute the inverse sine of x.
Return the "principal value" (for a description of this, see
`numpy.arcsin`) of the inverse sine of `x`. For real `x` such that
`abs(x) <= 1`, this is a real number in the closed interval
:math:`[-\pi/2, \pi/2]`. Otherwise, the complex principle value is
returned.
Parameters
----------
x : array_like or scalar
The value(s) whose arcsin is (are) required.
Returns
-------
out : ndarray or scalar
The inverse sine(s) of the `x` value(s). If `x` was a scalar, so
is `out`, otherwise an array object is returned.
See Also
--------
numpy.arcsin
Notes
-----
For an arcsin() that returns ``NAN`` when real `x` is not in the
interval ``[-1,1]``, use `numpy.arcsin`.
Examples
--------
>>> import numpy as np
>>> np.set_printoptions(precision=4)
>>> np.emath.arcsin(0)
0.0
>>> np.emath.arcsin([0,1])
array([0. , 1.5708])
)r+ r1 r r# s r r r s � �X �1� �A�
�9�9�Q�<�r! c �B � t | � } t j | � S )a,
Compute the inverse hyperbolic tangent of `x`.
Return the "principal value" (for a description of this, see
`numpy.arctanh`) of ``arctanh(x)``. For real `x` such that
``abs(x) < 1``, this is a real number. If `abs(x) > 1`, or if `x` is
complex, the result is complex. Finally, `x = 1` returns``inf`` and
``x=-1`` returns ``-inf``.
Parameters
----------
x : array_like
The value(s) whose arctanh is (are) required.
Returns
-------
out : ndarray or scalar
The inverse hyperbolic tangent(s) of the `x` value(s). If `x` was
a scalar so is `out`, otherwise an array is returned.
See Also
--------
numpy.arctanh
Notes
-----
For an arctanh() that returns ``NAN`` when real `x` is not in the
interval ``(-1,1)``, use `numpy.arctanh` (this latter, however, does
return +/-inf for ``x = +/-1``).
Examples
--------
>>> import numpy as np
>>> np.set_printoptions(precision=4)
>>> np.emath.arctanh(0.5)
0.5493061443340549
>>> from numpy.testing import suppress_warnings
>>> with suppress_warnings() as sup:
... sup.filter(RuntimeWarning)
... np.emath.arctanh(np.eye(2))
array([[inf, 0.],
[ 0., inf]])
>>> np.emath.arctanh([1j])
array([0.+0.7854j])
)r+ r1 r r# s r r r N s � �h �1� �A�
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