## NIFTY (Numerical Information Field Theory) has been developed at the
## Max-Planck-Institute for Astrophysics.
##
## Copyright (C) 2013 Max-Planck-Society
##
## Author: Marco Selig
## Project homepage:
##
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
## See the GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program. If not, see .
##-----------------------------------------------------------------------------
import numpy as np
#from nifty.nifty_core import field
from nifty_about import about
def _math_helper(x, function):
try:
return x.apply_scalar_function(function)
except(AttributeError):
return function(np.array(x))
def cos(x):
"""
Returns the cos of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
cosx : {scalar, array, field}
Cosine of `x` to the specified base.
See Also
--------
sin
tan
Examples
--------
>>> cos([-1,1])
array([ 0.54030231, 0.54030231])
>>> cos(field(point_space(2), val=[10, 100])).val
array([ 0.54030231, 0.54030231])
"""
return _math_helper(x, np.cos)
def sin(x):
"""
Returns the sine of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
sinx : {scalar, array, field}
Sine of `x` to the specified base.
See Also
--------
cos
tan
Examples
--------
>>> sin([-1,1])
array([-0.84147098, 0.84147098])
>>> sin(field(point_space(2), val=[-1, 1])).val
array([-0.84147098, 0.84147098])
"""
return _math_helper(x, np.sin)
def cosh(x):
"""
Returns the hyperbolic cosine of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
coshx : {scalar, array, field}
cosh of `x` to the specified base.
See Also
--------
sinh
tanh
Examples
--------
>>> cosh([-1,1])
array([ 1.54308063, 1.54308063])
>>> cosh(field(point_space(2), val=[-1, 1])).val
array([ 1.54308063, 1.54308063])
"""
return _math_helper(x, np.cosh)
def sinh(x):
"""
Returns the hyperbolic sine of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
sinhx : {scalar, array, field}
sinh of `x` to the specified base.
See Also
--------
cosh
tanh
Examples
--------
>>> sinh([-1,1])
array([-1.17520119, 1.17520119])
>>> sinh(field(point_space(2), val=[-1, 1])).val
array([-1.17520119, 1.17520119])
"""
return _math_helper(x, np.sinh)
def tan(x):
"""
Returns the tangent of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
tanx : {scalar, array, field}
Tangent of `x` to the specified base.
See Also
--------
cos
sin
Examples
--------
>>> tan([10,100])
array([ 0.64836083, -0.58721392])
>>> tan(field(point_space(2), val=[10, 100])).val
array([ 0.64836083, -0.58721392])
"""
return _math_helper(x, np.tan)
def tanh(x):
"""
Returns the hyperbolic tangent of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
tanhx : {scalar, array, field}
tanh of `x` to the specified base.
See Also
--------
cosh
sinh
Examples
--------
>>> tanh([-1,1])
array([-0.76159416, 0.76159416])
>>> tanh(field(point_space(2), val=[-1, 1])).val
array([-0.76159416, 0.76159416])
"""
return _math_helper(x, np.tanh)
def arccos(x):
"""
Returns the arccosine of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
arccosx : {scalar, array, field}
arccos of `x` to the specified base.
See Also
--------
arcsin
arctan
Examples
--------
>>> arccos([-1,1])
array([ 3.14159265, 0. ])
>>> arccos(field(point_space(2), val=[-1, 1])).val
array([ 3.14159265, 0. ])
"""
return _math_helper(x, np.arccos)
def arcsin(x):
"""
Returns the arcsine of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
arcsinx : {scalar, array, field}
Logarithm of `x` to the specified base.
See Also
--------
arccos
arctan
Examples
--------
>>> arcsin([-1,1])
array([-1.57079633, 1.57079633])
>>> arcsin(field(point_space(2), val=[-1, 1])).val
array([-1.57079633, 1.57079633])
"""
return _math_helper(x, np.arcsin)
def arccosh(x):
"""
Returns the hyperbolic arccos of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
arccoshx : {scalar, array, field}
arccos of `x` to the specified base.
See Also
--------
arcsinh
arctanh
Examples
--------
>>> arcosh([1,10])
array([ 0. , 2.99322285])
>>> arccosh(field(point_space(2), val=[1, 10])).val
array([ 0. , 2.99322285])
"""
return _math_helper(x, np.arccosh)
def arcsinh(x):
"""
Returns the hypberbolic sin of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
arcsinhx : {scalar, array, field}
arcsinh of `x` to the specified base.
See Also
--------
arccosh
arctanh
Examples
--------
>>> arcsinh([1,10])
array([ 0.88137359, 2.99822295])
>>> arcsinh(field(point_space(2), val=[1, 10])).val
array([ 0.88137359, 2.99822295])
"""
return _math_helper(x, np.arcsinh)
def arctan(x):
"""
Returns the arctan of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
arctanx : {scalar, array, field}
arctan of `x` to the specified base.
See Also
--------
arccos
arcsin
Examples
--------
>>> arctan([1,10])
array([ 0.78539816, 1.47112767])
>>> arctan(field(point_space(2), val=[1, 10])).val
array([ 0.78539816, 1.47112767])
"""
return _math_helper(x, np.arctan)
def arctanh(x):
"""
Returns the hyperbolic arc tangent of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
arctanhx : {scalar, array, field}
arctanh of `x` to the specified base.
See Also
--------
arccosh
arcsinh
Examples
--------
>>> arctanh([0,0.5])
array([ 0. , 0.54930614])
>>> arctanh(field(point_space(2), val=[0, 0.5])).val
array([ 0. , 0.54930614])
"""
return _math_helper(x, np.arctanh)
def sqrt(x):
"""
Returns the square root of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
sqrtx : {scalar, array, field}
Square root of `x`.
Examples
--------
>>> sqrt([10,100])
array([ 10. , 31.6227766])
>>> sqrt(field(point_space(2), val=[10, 100])).val
array([ 10. , 31.6227766])
"""
return _math_helper(x, np.sqrt)
def exp(x):
"""
Returns the exponential of a given object.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
Returns
-------
expx : {scalar, array, field}
Exponential of `x` to the specified base.
See Also
--------
log
Examples
--------
>>> exp([10,100])
array([ 2.20264658e+04, 2.68811714e+43])
>>> exp(field(point_space(2), val=[10, 100])).val
array([ 2.20264658e+04, 2.68811714e+43])
"""
return _math_helper(x, np.exp)
def log(x,base=None):
"""
Returns the logarithm with respect to a specified base.
Parameters
----------
x : {scalar, list, array, field}
Input argument.
base : {scalar, list, array, field}, *optional*
Base of the logarithm (default: Euler's number).
Returns
-------
logx : {scalar, array, field}
Logarithm of `x` to the specified base.
See Also
--------
exp
Examples
--------
>>> log([100, 1000], base=10)
array([ 2., 3.])
>>> log(field(point_space(2), val=[100, 1000]), base=10).val
array([ 2., 3.])
"""
if(base is None):
return _math_helper(x, np.log)
base = np.array(base)
if(np.all(base>0)):
return _math_helper(x, np.log)/np.log(base)
else:
raise ValueError(about._errors.cstring("ERROR: invalid input basis."))
def conjugate(x):
"""
Computes the complex conjugate of a given object.
Parameters
----------
x : {ndarray, field}
The object to be complex conjugated.
Returns
-------
conjx : {ndarray,field}
The complex conjugated object.
"""
return _math_helper(x, np.conjugate)
##---------------------------------