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Edit File: scimath.cpython-311.pyc
� ��bg�: � � � d Z ddlmc mZ ddlmc mZ ddlmZm Z ddl m Z ddl m Z g d�Z ej d� � Zd� Zd � Zd � Zd � Zd � Z e e� � d � � � Z e e� � d� � � Z e e� � d� � � Zd� Z e e� � d� � � Z e e� � d� � � Zd� Z e e� � d� � � Z e e� � d� � � Z e e� � d� � � Z e e� � d� � � Z dS )a� 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. Functions --------- .. autosummary:: :toctree: generated/ sqrt log log2 logn log10 power arccos arcsin arctanh � N)�asarray�any)�array_function_dispatch)�isreal) �sqrt�log�log2�logn�log10�power�arccos�arcsin�arctanhg @c �6 � t | j j t j t j t j t j t j t j f� � r | � t j � � S | � t j � � S )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) ) � issubclass�dtype�type�nt�single�byte�short�ubyte�ushort�csingle�astype�cdouble)�arrs �H/opt/cloudlinux/venv/lib64/python3.11/site-packages/numpy/lib/scimath.py� _tocomplexr 1 sc � �p �#�)�.�2�9�b�g�r�x���#%�9�b�j�#:� ;� ;� &��z�z�"�*�%�%�%��z�z�"�*�%�%�%� c � � t | � � } t t | � � | dk z � � rt | � � } | 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 ��xs r �_fix_real_lt_zeror$ p s> � �, �� � �A� �6�!�9�9��A�� � � � � �q�M�M�� �Hr c �t � 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 -------- >>> 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& � s< � �* �� � �A� �6�!�9�9��A�� � � � � ��G�� �Hr c � � t | � � } t t | � � t | � � dk z � � rt | � � } | 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" s r �_fix_real_abs_gt_1r* � sD � �* �� � �A� �6�!�9�9��A���� � #�$�$� � �q�M�M�� �Hr c � � | fS �N� r" s r �_unary_dispatcherr. � s � � �4�Kr c �H � 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`: >>> 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 � �b �!� � �A� �7�1�:�:�r c �H � 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 -------- >>> 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$ r0 r r" s r r r � s � �X �!� � �A� �6�!�9�9�r c �H � 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 -------- (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$ r0 r r" s r r r + s � �\ �!� � �A� �8�A�;�;�r c � � | |fS r, r- ��nr# s r �_logn_dispatcherr7 ] s � � �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 -------- >>> 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 ]) r2 r5 s r r r a s9 � �> �!� � �A��!� � �A� �6�!�9�9�R�V�A�Y�Y� � r c �H � 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$ r0 r r" s r r r � s � �X �!� � �A� �7�1�:�:�r c � � | |fS r, r- �r# �ps r �_power_dispatcherr= � s � � �q�6�Mr c �h � 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 -------- >>> np.set_printoptions(precision=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]) )r$ r& r0 r r; s r r r � s/ � �P �!� � �A�����A� �8�A�q�>�>�r c �H � 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 -------- >>> 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* r0 r r" s r r r � s � �R �1� � �A� �9�Q�<�<�r c �H � 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 -------- >>> np.set_printoptions(precision=4) >>> np.emath.arcsin(0) 0.0 >>> np.emath.arcsin([0,1]) array([0. , 1.5708]) )r* r0 r r" s r r r s � �T �1� � �A� �9�Q�<�<�r c �H � 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 -------- >>> 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* r0 r r" s r r r A s � �^ �1� � �A� �:�a�=�=�r ) �__doc__�numpy.core.numeric�core�numericr0 �numpy.core.numerictypes� numerictypesr r r �numpy.core.overridesr �numpy.lib.type_checkr �__all__r �_ln2r r$ r& r* r. r r r7 r r r= r r r r r- r r �<module>rL s� �� � �@ � � � � � � � � � $� $� $� $� $� $� $� $� $� +� +� +� +� +� +� +� +� 8� 8� 8� 8� 8� 8� '� '� '� '� '� '� � � �� �r�v�c�{�{��<&� <&� <&�~ � � �8 � � �6 � � �6� � � ��*�+�+�1� 1� ,�+�1�h ��*�+�+�,� ,� ,�+�,�^ ��*�+�+�.� .� ,�+�.�b� � � ��)�*�*� � � +�*� �F ��*�+�+�,� ,� ,�+�,�^� � � ��*�+�+�)� )� ,�+�)�X ��*�+�+�)� )� ,�+�)�X ��*�+�+�*� *� ,�+�*�Z ��*�+�+�/� /� ,�+�/� /� /r