
'''simple docstring'''







import math

import tensorflow as tf
from packaging import version







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			Optional[Any]:
	_snake_case     		=	tf.convert_to_tensor(__A			)
	_snake_case     		=	0.5 * (1.0 + tf.math.erf(x / tf.cast(tf.sqrt(2.0			)    ,       x.dtype			)			))

	return x * cdf







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			str:
	_snake_case     		=	tf.convert_to_tensor(__A			)
	_snake_case     		=	tf.cast(math.pi    ,       x.dtype			)
	_snake_case     		=	tf.cast(0.0_4_4_7_1_5    ,       x.dtype			)
	_snake_case     		=	0.5 * (1.0 + tf.tanh(tf.sqrt(2.0 / pi			) * (x + coeff * tf.pow(__A    ,       3			))			))

	return x * cdf







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			Union[str, Any]:
	_snake_case     		=	tf.convert_to_tensor(__A			)

	return x * tf.tanh(tf.math.softplus(__A			)			)







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			Dict:
	_snake_case     		=	tf.convert_to_tensor(__A			)
	_snake_case     		=	tf.cast(0.0_4_4_7_1_5    ,       x.dtype			)
	_snake_case     		=	tf.cast(0.7_9_7_8_8_4_5_6_0_8    ,       x.dtype			)

	return 0.5 * x * (1.0 + tf.tanh(x * coeffa * (1.0 + coeffa * x * x)			))







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			Union[str, Any]:
	_snake_case     		=	tf.convert_to_tensor(__A			)
	_snake_case     		=	tf.cast(1.7_0_2    ,       x.dtype			)
	return x * tf.math.sigmoid(coeff * x			)







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			Any:
	return tf.clip_by_value(_gelu(__A			)    ,       -10    ,       10			)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A=-1			) ->			Any:
	_snake_case		,				_snake_case     		=	tf.split(__A    ,       2    ,       axis=__A			)
	return a * tf.math.sigmoid(__A			)


if version.parse(tf.version.VERSION) >= version.parse("2.4"):







					def        SCREAMING_SNAKE_CASE__			(     __A			) ->			str:
						return tf.keras.activations.gelu(__A    ,       approximate=__A			)

					lowercase					:							Dict   =      tf.keras.activations.gelu





					lowercase					:							List[Any]   =      approximate_gelu_wrap
else:
					lowercase					:							str   =      _gelu
					lowercase					:							int   =      _gelu_new


lowercase					:							List[str]   =      {
    "gelu": gelu,
    "gelu_10": gelu_aa,
    "gelu_fast": gelu_fast,
    "gelu_new": gelu_new,
    "glu": glu,
    "mish": mish,
    "quick_gelu": quick_gelu,
    "relu": tf.keras.activations.relu,
    "sigmoid": tf.keras.activations.sigmoid,
    "silu": tf.keras.activations.swish,
    "swish": tf.keras.activations.swish,
    "tanh": tf.keras.activations.tanh,
}







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			Optional[Any]:
	if activation_string in ACTaFN:
		return ACTaFN[activation_string]
	else:
		raise KeyError(F'function {activation_string} not found in ACT2FN mapping {list(ACTaFN.keys()			)}'			)



'''simple docstring'''







from typing import Any

import numpy as np







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			bool:
	return np.array_equal(__A    ,       matrix.conjugate().T			)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			Any:
	_snake_case     		=	v.conjugate().T
	_snake_case     		=	v_star.dot(__A			)
	assert isinstance(__A    ,       np.ndarray			)
	return (v_star_dot.dot(__A			)) / (v_star.dot(__A			))







def        SCREAMING_SNAKE_CASE__			(     ) ->			None:
	_snake_case     		=	np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]			)
	_snake_case     		=	np.array([[1], [2], [3]]			)
	assert is_hermitian(__A			), F'{a} is not hermitian.'
	print(rayleigh_quotient(__A    ,       __A			)			)

	_snake_case     		=	np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]			)
	assert is_hermitian(__A			), F'{a} is not hermitian.'
	assert rayleigh_quotient(__A    ,       __A			) == float(3			)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					tests()

