3
���h�9 � @ s0 d Z ddljjZddljjZddlmZm Z ddl
m Z ddl m
Z
dddd d
d d d
dg Zejd�Zdd� Zdd� Zdd� Zdd� Zdd� Ze e�dd� �Ze e�dd� �Ze e�d d
� �Zd d � Ze e�d d � �Ze e�d d� �Zd!d"� Ze e�d#d � �Z e e�d$d � �Z e e�d%d
� �Z e e�d&d� �Z dS )'aD
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
>>> from numpy.lib import scimath
>>> scimath.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)�isreal�sqrt�log�log2�logn�log10�power�arccos�arcsin�arctanhg @c C sB t | jjtjtjtjtjtjtj f�r2| j
tj �S | j
tj �S dS )a_ 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
--------
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)
N) �
issubclassZdtype�type�ntZsingleZbyte�shortZubyteZushortZcsingleZastypeZcdouble)Zarr� r �2/tmp/pip-build-5_djhm0z/numpy/numpy/lib/scimath.py�
_tocomplex" s 8 r c C s( t | �} tt| �| dk @ �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
--------
>>> 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 )�xr r r �_fix_real_lt_zeroa s r c C s( t | �} tt| �| dk @ �r$| d } | 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
--------
>>> 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 r r r �_fix_int_lt_zero} s r c C s, t | �} tt| �t| �dk@ �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
--------
>>> 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 r r r �_fix_real_abs_gt_1� s r c C s | fS )Nr )r r r r �_unary_dispatcher� s r c C s t | �} tj| �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`:
>>> np.lib.scimath.sqrt(1)
1.0
>>> np.lib.scimath.sqrt([1, 4])
array([1., 2.])
But it automatically handles negative inputs:
>>> np.lib.scimath.sqrt(-1)
1j
>>> np.lib.scimath.sqrt([-1,4])
array([0.+1.j, 2.+0.j])
)r �nxr )r r r r r � s (c C s t | �} tj| �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
--------
>>> 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 r r )r r r r r � s ,c C s t | �} tj| �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
--------
(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 r r
)r r r r r
s .c C s | |fS )Nr )�nr r r r �_logn_dispatcherE s r c C s$ t |�}t | �} tj|�tj| � 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
--------
>>> np.set_printoptions(precision=4)
>>> np.lib.scimath.logn(2, [4, 8])
array([2., 3.])
>>> np.lib.scimath.logn(2, [-4, -8, 8])
array([2.+4.5324j, 3.+4.5324j, 3.+0.j ])
)r r r )r r r r r r I s c C s t | �} tj| �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 r r )r r r r r m s ,c C s | |fS )Nr )r �pr r r �_power_dispatcher� s r! c C s t | �} t|�}tj| |�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
--------
>>> np.set_printoptions(precision=4)
>>> np.lib.scimath.power([2, 4], 2)
array([ 4, 16])
>>> np.lib.scimath.power([2, 4], -2)
array([0.25 , 0.0625])
>>> np.lib.scimath.power([-2, 4], 2)
array([ 4.-0.j, 16.+0.j])
)r r r r )r r r r r r � s (c C s t | �} tj| �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
--------
>>> 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 r r )r r r r r � s )c C s t | �} tj| �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
--------
>>> np.set_printoptions(precision=4)
>>> np.emath.arcsin(0)
0.0
>>> np.emath.arcsin([0,1])
array([0. , 1.5708])
)r r r
)r r r r r
� s *c C s t | �} tj| �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
--------
>>> np.set_printoptions(precision=4)
>>> 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 r r )r r r r r ) s /) �__doc__Znumpy.core.numeric�core�numericr Znumpy.core.numerictypesZ numerictypesr r r Znumpy.core.overridesr Znumpy.lib.type_checkr �__all__r Z_ln2r r r r r r r
r r r r! r r r
r r r r r �<module> s0
? ,02$0--. |