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#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
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from ..arithmetic.utils import arithmetic_operator
from ..utils import implement_scipy, infer_scipy_dtype
from .core import (
TensorSpecialMultiOp,
TensorSpecialUnaryOp,
TensorSpecialUnaryTupleOp,
_register_special_op,
)
@_register_special_op
@arithmetic_operator(sparse_mode="unary")
class TensorErf(TensorSpecialUnaryOp):
_func_name = "erf"
@_register_special_op
@arithmetic_operator(sparse_mode="unary")
class TensorErfc(TensorSpecialUnaryOp):
_func_name = "erfc"
@_register_special_op
@arithmetic_operator(sparse_mode="unary")
class TensorErfcx(TensorSpecialUnaryOp):
_func_name = "erfcx"
@_register_special_op
@arithmetic_operator(sparse_mode="unary")
class TensorErfi(TensorSpecialUnaryOp):
_func_name = "erfi"
@_register_special_op
@arithmetic_operator(sparse_mode="unary")
class TensorErfinv(TensorSpecialUnaryOp):
_func_name = "erfinv"
@_register_special_op
@arithmetic_operator(sparse_mode="unary")
class TensorErfcinv(TensorSpecialUnaryOp):
_func_name = "erfcinv"
@_register_special_op
@arithmetic_operator(sparse_mode="unary")
class TensorWofz(TensorSpecialUnaryOp):
_func_name = "wofz"
@_register_special_op
@arithmetic_operator(sparse_mode="unary")
class TensorDawsn(TensorSpecialUnaryOp):
_func_name = "dawsn"
@_register_special_op
class TensorFresnel(TensorSpecialUnaryTupleOp):
_func_name = "fresnel"
_n_outputs = 2
@_register_special_op
class TensorModFresnelP(TensorSpecialUnaryTupleOp):
_func_name = "modfresnelp"
_n_outputs = 2
@_register_special_op
class TensorModFresnelM(TensorSpecialUnaryTupleOp):
_func_name = "modfresnelm"
_n_outputs = 2
@_register_special_op
class TensorVoigtProfile(TensorSpecialMultiOp):
_ARG_COUNT = 3
_func_name = "voigt_profile"
[docs]
@implement_scipy("scipy.special.erf")
@infer_scipy_dtype("scipy.special.erf")
def erf(x, out=None, where=None, **kwargs):
"""
Returns the error function of complex argument.
It is defined as ``2/sqrt(pi)*integral(exp(-t**2), t=0..z)``.
Parameters
----------
x : Tensor
Input tensor.
Returns
-------
res : Tensor
The values of the error function at the given points `x`.
See Also
--------
erfc, erfinv, erfcinv, wofz, erfcx, erfi
Notes
-----
The cumulative of the unit normal distribution is given by
``Phi(z) = 1/2[1 + erf(z/sqrt(2))]``.
References
----------
.. [1] https://en.wikipedia.org/wiki/Error_function
.. [2] Milton Abramowitz and Irene A. Stegun, eds.
Handbook of Mathematical Functions with Formulas,
Graphs, and Mathematical Tables. New York: Dover,
1972. http://www.math.sfu.ca/~cbm/aands/page_297.htm
.. [3] Steven G. Johnson, Faddeeva W function implementation.
http://ab-initio.mit.edu/Faddeeva
Examples
--------
>>> import maxframe.tensor as mt
>>> from maxframe.tensor import special
>>> import matplotlib.pyplot as plt
>>> x = mt.linspace(-3, 3)
>>> plt.plot(x, special.erf(x))
>>> plt.xlabel('$x$')
>>> plt.ylabel('$erf(x)$')
>>> plt.show()
"""
op = TensorErf(**kwargs)
return op(x, out=out, where=where)
[docs]
@implement_scipy("scipy.special.erfc")
@infer_scipy_dtype("scipy.special.erfc")
def erfc(x, out=None, where=None, **kwargs):
op = TensorErfc(**kwargs)
return op(x, out=out, where=where)
[docs]
@implement_scipy("scipy.special.erfcx")
@infer_scipy_dtype("scipy.special.erfcx")
def erfcx(x, out=None, where=None, **kwargs):
op = TensorErfcx(**kwargs)
return op(x, out=out, where=where)
[docs]
@implement_scipy("scipy.special.erfi")
@infer_scipy_dtype("scipy.special.erfi")
def erfi(x, out=None, where=None, **kwargs):
op = TensorErfi(**kwargs)
return op(x, out=out, where=where)
[docs]
@implement_scipy("scipy.special.erfinv")
@infer_scipy_dtype("scipy.special.erfinv")
def erfinv(x, out=None, where=None, **kwargs):
op = TensorErfinv(**kwargs)
return op(x, out=out, where=where)
[docs]
@implement_scipy("scipy.special.erfcinv")
@infer_scipy_dtype("scipy.special.erfcinv")
def erfcinv(x, out=None, where=None, **kwargs):
op = TensorErfcinv(**kwargs)
return op(x, out=out, where=where)
[docs]
@implement_scipy("scipy.special.wofz")
@infer_scipy_dtype("scipy.special.wofz")
def wofz(x, out=None, where=None, **kwargs):
op = TensorWofz(**kwargs)
return op(x, out=out, where=where)
[docs]
@implement_scipy("scipy.special.dawsn")
@infer_scipy_dtype("scipy.special.dawsn")
def dawsn(x, out=None, where=None, **kwargs):
op = TensorDawsn(**kwargs)
return op(x, out=out, where=where)
[docs]
@implement_scipy("scipy.special.fresnel")
@infer_scipy_dtype("scipy.special.fresnel", multi_outputs=True)
def fresnel(x, out=None, **kwargs):
op = TensorFresnel(**kwargs)
return op(x, out=out)
[docs]
@implement_scipy("scipy.special.modfresnelp")
@infer_scipy_dtype("scipy.special.modfresnelp", multi_outputs=True)
def modfresnelp(x, out=None, **kwargs):
op = TensorModFresnelP(**kwargs)
return op(x, out=out)
[docs]
@implement_scipy("scipy.special.modfresnelm")
@infer_scipy_dtype("scipy.special.modfresnelm", multi_outputs=True)
def modfresnelm(x, out=None, **kwargs):
op = TensorModFresnelM(**kwargs)
return op(x, out=out)
@implement_scipy("scipy.special.voigt_profile")
@infer_scipy_dtype("scipy.special.voigt_profile")
def voigt_profile(x, sigma, gamma, **kwargs):
op = TensorVoigtProfile(**kwargs)
return op(x, sigma, gamma)