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bleasdale.py
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bleasdale.py
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# -*- coding: utf-8 -*-
# Copyright 2007-2021 The HyperSpy developers
#
# This file is part of HyperSpy.
#
# HyperSpy 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.
#
# HyperSpy 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 HyperSpy. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
from hyperspy._components.expression import Expression
class Bleasdale(Expression):
r"""Bleasdale function component.
Also called the Bleasdale-Nelder function. Originates from the description of the yield-density relationship in crop growth.
.. math::
f(x) = \left(a+b\cdot x\right)^{-1/c}
Parameters
-----------
a : Float
b : Float
c : Float
**kwargs
Extra keyword arguments are passed to the ``Expression`` component.
For :math:`(a+b\cdot x)\leq0`, the component will be set to 0.
"""
def __init__(self, a=1., b=1., c=1., module="numexpr", **kwargs):
super(Bleasdale, self).__init__(
expression="where((a + b * x) > 0, (a + b * x) ** (-1 / c), 0)",
name="Bleasdale",
a=a,
b=b,
c=c,
module=module,
autodoc=False,
compute_gradients=False,
**kwargs)
def grad_a(self, x):
"""
Returns d(function)/d(parameter_1)
"""
a = self.a.value
b = self.b.value
c = self.c.value
return np.where((a + b * x) > 0, -(a + b * x) ** (-1 / c - 1) / c, 0)
def grad_b(self, x):
"""
Returns d(function)/d(parameter_1)
"""
a = self.a.value
b = self.b.value
c = self.c.value
return np.where((a + b * x) > 0, -x * (a + b * x) ** (-1 / c - 1) / c
, 0)
def grad_c(self, x):
"""
Returns d(function)/d(parameter_1)
"""
a = self.a.value
b = self.b.value
c = self.c.value
return np.where((a + b * x) > 0, np.log(a + b * x) / (c ** 2. *
(b * x + a) ** (1. / c)), 0)