I'm developing a scientific library where I would define vector functions in the time and frequency domain (linked by FFT). I created a class for vector formulas in the freq domain, and now I'd want to define an identical class for the time domain.
I want that in the time domain, the class functions - although being identical to their frequency-domain twin - have one parameter named t instead of omega. Is there an easier way of achieving this instead of repeated definition of every single method, while maintaining readibility?
My code:
(Note: my classes are much more complicated, and one can't just use the functions as formula.x_func(...) - some checking and etc are included. Also, there are actually 6 components.)
class VecFormula(object):
pass
class FreqFormula(VecFormula):
def __init__(self, x_func, y_func, z_func):
self.x_func = x_func
self.y_func = y_func
self.z_func = z_func
def x(self, x, y, z, omega, params):
return self.x_func(x, y, z, omega, params)
def y(self, x, y, z, omega, params):
return self.y_func(x, y, z, omega, params)
def z(self, x, y, z, omega, params):
return self.z_func(x, y, z, omega, params)
def component(self, comp, x, y, z, omega, params):
if comp == 'x':
return self.x(x, y, z, omega, params)
elif comp == 'y':
return self.y(x, y, z, omega, params)
elif comp == 'z':
return self.z(x, y, z, omega, params)
else:
raise ValueError(f'invalid component: {comp}')
class TimeFormula(FreqFormula):
"same as FreqFormula, but the omega parameter is renamed to t"
def x(self, x, y, z, t, params):
return super(TimeFormula, self).x(x, y, z, t, params)
def y(self, x, y, z, t, params):
return super(TimeFormula, self).y(x, y, z, t, params)
def z(self, x, y, z, t, params):
return super(TimeFormula, self).z(x, y, z, t, params)
def component(self, comp, x, y, z, t, params):
return super(TimeFormula, self).component(x, y, z, t, params)
It is easy to add methods to a class after creation they are just class attributes. The hard part here, is that you need to dynamically create new functions to clone the methods from the original class to be able to change their signature.
It is not the most clear part of Python, and dynamic function creation is not documented in the official reference documentations but can be found on SO: Python: dynamically create function at runtime
So here is a possible way:
# have the new class derive from the common base
class TimeFormula(VecFormula):
"same as FreqFormula, but the omega parameter is renamed to t"
pass
# loop over methods of origina class
for i,j in inspect.getmembers(FreqFormula, inspect.isfunction):
# copy the __init__ special method
if i == '__init__':
setattr(TimeFormula, i, j)
elif i.startswith('__'): continue # ignore all other special attributes
if not j.__qualname__.endswith('.'.join((FreqFormula.__name__, i))):
continue # ignore methods defined in parent classes
# clone the method from the original class
spec = inspect.getfullargspec(j)
newspec = inspect.FullArgSpec(['t' if i == 'omega' else i
for i in spec.args], *spec[1:])
f = types.FunctionType(j.__code__, j.__globals__, i, newspec, j.__closure__)
f.__qualname__ = '.'.join((TimeFormula.__qualname__, i))
# adjust the signature
sig = inspect.signature(j)
if ('omega' in sig.parameters):
f.__signature__ = sig.replace(
parameters = [p.replace(name='t') if name == 'omega' else p
for name, p in sig.parameters.items()])
# and finally insert the new method in the class
setattr(TimeFormula, i, f)
Sounds like you would achieve what you need through the use of class inheritance elegantly.
Please check out class inheritance python documentation or here.
Related
I've got a little project for my college and I need to write a method which fits an array to some function, here's it's part:
def Linear(self,x,a,b):
return a*x+b
def Quadratic(self, x, a,b,c):
return a*(x**2)+b*x+c
def Sinusoid(self,t, a, gam, omega, phi, offset):
return np.e ** (gam * t) * a * np.sin((2 * np.pi * omega * t) + phi) + offset
def Fit(self, name):
func= getattr(App, name)
self.fit_params, self.covariance_matrix = curve_fit(func, self.t, self.a, maxfev= 100000)
But it returns absolutely wrong values and also doesn't even work for Sinusoid function (ptimizeWarning: Covariance of the parameters could not be estimated warnings.warn('Covariance of the parameters could not be estimated'). I've already checked if it's not an issue with getattr function but it works correctly.
I'm running out of ideas where the issue is.
There are several problems here.
Linear, Quadratic and Sinusoid do not need self, you can define those as staticmethod:
#This is the decorator use to define staticmethod
#staticmethod
def Linear(x,a,b):
return a*x+b
The same applies to other methods (except Fit).
It will help when they are called in the future. When you call them with curve_fit(func,...), for example, if func is Sinusoid, what you are doing is
curve_fit(Sinusoid, ...) and not curve_fit(self.Sinusoid,...). When curve_fit use Sinusoid, the first argument may be understood as the self, therefore, you get and error.
If you define
#staticmethod
def Sinusoid(t, a, gam, omega, phi, offset):
return np.e ** (gam * t) * a * np.sin((2 * np.pi * omega * t) + phi) + offset
a, gam, omega, phi and offset are constants to fit. Therefore, when you call curve_fit, you need to pass this constants as params:
scipy.optimize.curve_fit(f, xdata, ydata, p0=None, sigma=None, absolute_sigma=False, check_finite=True, bounds=- inf, inf, method=None, jac=None, **kwargs)
To clarify: The first argument is the func, the second is your experimental data for x, and the third, is the data for y. And after that all the others kwargs, like maxfev. I don't know if self.a is the data for y, or if you want to set an initial value for a. I'm going to guess you want to set the initial value of a. You need to do it like this: p0=[x1,x2,x3,x4,..., xn] where xi is the initial value of the i-th constant. If you don't pass p0 as an argument to curve_fit, the default value for each constant is going to be 1. But here it comes the last problem:
The diferent functions use a diferent number arguments, so for the first one, Linear, you need to do p0 = [a,1]. For the second, p0 = [a, 1, 1]. And for the last one, the Sinusoid one, p0 = [a, 1, 1, 1, 1]
I don't really know if you can pass p0 = [a] to all of the functions and curve_fit will magically understand. But try so and if curve_fit doesn't let you, use condictionals:
def Fit(self, name):
if func = Linear:
p0 = [a,1]
elif func = Quadratic:
p0 = [a,1,1]
elif func = Sinusoid:
p0 = [a,1,1,1,1]
self.fit_params, self.covariance_matrix = curve_fit(func, self.t, self.y_values, p0=p0, maxfev= 100000)
Where self.y_values is the experimental data as an array-like element.
If self.a is the data for y you can cut all of this mambojambo and let Fit define as it currently is. But don't forguet the #staticmethod in the other functions.
Hope this solves your problem.
In the case shown below I have a function titled func1() that resides in func3(), where func3() is solving for the value of an ODE using the Euler method.
def func1(x, y):
return y * np.log(y) / x
def func3(x, y, step_size, func):
dydx = func(x, y)
new_x = x + step_size
new_y = y _ step_size * dydx
return new_x, new_y
step_size - 0.1
lower = 2.0
upper = 3.0
e = 2.7182828284
x_val = [2.0]
y_val = [e]
for i in range(10):
x, y = func3(x_val[i], y_val[i], step_size, func1)
x_val.append(x)
y_val.append(y)
The code is passing func1 to func3 as a decorator and writing the output to a list as it iterates over the range of 0 to 10. However, the code inside func3() is hardcoded to the exact input of func1(), which is x and y. I would like to write func3() to be generic enough that you can pass any function to it as long as its first two inputs are x and y, but it should be cabaple of taking more inputs. So assume that all the code shown above was identical, but instead of passing func1(), I passed func2() to func3(), with the structure whown below.
def func2(x, y, z):
return z * y * np.log(y) / (x*z)
How could I write func3() to be generic enough that it could take either of the two functions and understand that their are more arguments to pass to func1(), which would also have to be passed into func3()?
You can use Python's variable-length argument syntax to await any extra arguments, and pass them on. If there are none, it works anyway: The starred variable will receive the empty list as its value, and will disappear when expanded in the fall to func.
def func1(x, y):
return x+y
def func2(x, y, z):
return (x+y)*z
def caller(func, x, y, other, other2, *args):
return func(x, y, *args)
Use *args and **kwargs to collect arguments (in addition to x and y intended for your callback):
def func3(x, y, step_size, func, *args, **kwargs):
dydx = func(x, y, *args, **kwargs)
...
However, consider if it's really necessary for func3 to call func itself; have the caller do it instead.
def func3(x, y, step_size, dydx):
new_x = x + step_size
new_y = y - step_size * dydx
return new_x, new_y
for old_x, old_y in zip(x_val, y_val):
x, y = func3(old_x, old_y, step_size, func1(x, y))
...
It would be better to use *args and **kargs (**kwargs in function definitions in python is used to pass a keyworded, variable-length argument list. We use the name kwargs with the double star. The reason is because the double star allows us to pass through keyword arguments and any number of them).
For Example:
def myFun(arg1, arg2, arg3):
print("arg1:", arg1)
print("arg2:", arg2)
print("arg3:", arg3)
args = ("Hey", "hi", "bye")
myFun(*args)
kwargs = {"arg1" : "Geek", "arg2" : "Nerd", "arg3" : "Noob" }
myFun(**kwargs)
Output:
Hey
hi
bye
Geek
Nerd
Noob
I don’t think that you really need to accept other arguments except x and y or change func3.
Let’s assume you want to pass z to inner function. And you need to pass it to func3 as well. Since z will not change during func3 call you can just do something like func3(x, y, lambda x, y : your_func (x, y , z), step) and use functions with any number of arguments through lambda which accepts x and y.
In your case call will look like:
x, y = func3(x_val[i], y_val[i], step_size, lambda x, y: func2(x, y, 111))
I am doing a multi integral with 4 variables, among them 2 have limits as functions. However the error appears on one of my constant-limit variable. Really cannot figure our why. Many thanks for your advice!
from numpy import sqrt, sin, cos, pi, arcsin, maximum
from sympy.functions.special.delta_functions import Heaviside
from scipy.integrate import nquad
def bmax(x):
return 1.14*10**9/sin(x/2)**(9/7)
def thetal(x,y,z):
return arcsin(3.7*10**15*sqrt(cos(x/2)**2/10**6-1.23*10**10/z+0.003*sin(x/2)**2*(2.51*10**63/sin(x/2)**9/y**7-1))/(z*sin(x/2)**2*cos(x/2)*(2.51*10**63/sin(x/2)**9/y**7-1)))
def rt(x,y):
return 3.69*10**12/(2.5*10**63/sin(x/2)**7*y**7-sin(x/2)**2)
def rd(x,y):
return maximum(1.23*10**10,rt(x,y))
def rl(x,y):
return rd(x,y)*(sqrt(1+5.04*10**16/(rd(x,y)*cos(x/2)**2))-1)/2
def wbound():
return [1.23*10**10,3.1*10**16]
def zbound():
return [10**(-10),pi-10**(-10)]
def ybound(z):
return [0,bmax(z)-10**(-10)]
def xbound(z,y,w):
return [thetal(z,y,w),pi-thetal(z,y,w)]
def f(x,y,z,w):
return [5.77/10**30*sin(z)*sin(z/2)*y*sin(x)*Heaviside(w-rl(z,y))*Heaviside(w-rd(z,y))/w**2]
result = nquad(f, [xbound, ybound,zbound,wbound])
The reason for that error is that although you don't want these bounds to depend on the variables, nquad still passes the variables to the functions you provide to it. So the bound functions have to take the right number of variables:
def wbound():
return [1.23*10**10,3.1*10**16]
def zbound(w_foo):
return [10**(-10),pi-10**(-10)]
def ybound(z, w_foo):
return [0,bmax(z)-10**(-10)]
def xbound(z,y,w):
return [thetal(z,y,w),pi-thetal(z,y,w)]
Now the functions zbound and ybound accept the extra variables but simply ignore them.
I'm not sure about the last bound, xbound(...): Do you want the variables y and z to be flipped? The supposedly correct ordering according to the definition of scipy.integrate.nquad would be
def xbound(y,z,w):
...
Edit: As kazemakase pointed out, the function f should return a float instead of a list so the brackets [...] in the return statement should be removed.
nquad expects a sequence of bounds for its second argument, with a rather stringent syntax.
If the integrand f depends on x, y, z, w and this is the order of definition, the terms in bounds must be, in sequence, xb, yb, zb and wb, where each of the bounds can be either a 2-tuple, e.g., xb = (xmin, xmax)
or a function that returns a 2-tuple.
The critical point is, the arguments of those functions... when we perform the inner integration, in dx, we have available y, z and w for computing the bounds in x, so that it must be
def xb(y,z,w): return(..., ...) — likewise
def yb(z,w): return (..., ...) and
def zb(w): return (..., ...).
The bounds with respect to the last variable of integration must be constant.
To summarize
# DEFINITIONS
def f(x, y, z, w): return .. . # x inner integration, ..., w outer integration
def xb(y,z,w): return (...,...) # or simply xb=(...,...) if it's a constant
def yb(z,w): return (...,...) # or yb=(...,...)
def zb(w): return (...,...) # or zb=(...,...)
wb = (...,...)
# INTEGRATION
result, _ = nquad(f, [xb, yb, zb, wb])
Let us take an example. In certain libraries like "scipy.integrate" calling a function like "odeint" (integrating functions) has to be expressed as "odeint(func, y0, T, ...)" where "func" is a name of a function that has to be predefined with two parameters (y,t0), y vector and t0 a scalar.
The question is how to use "odeint" if the already defined function "func" is specified with two parameters but in the inverse order "(t0, y)".
Best regards.
You can use a lambda function to reorder the arguments like so:
odeint(lambda p, q: func(q, p), y0, T, ...)
Alternatively, you can supposedly swap the orders in the main call if all odeint does is call func on the arguments and does interact directly with the arguments:
odeint(func, T, y0, ...)
You can explicitly call parameters in arbitrary sequence:
def func(a, b, c):
print('a = {}'.format(a))
print('b = {}'.format(b))
print('c = {}'.format(c))
x = 1
y = 2
z = 3
func(a = x, b = y, c = z)
func(c = z, b = y, a = x)
func(b = y, c = z, a = x)
P.S. I'm not on 100% sure, but try odeint(func, y0 = y0, T = T, ...)
or odeint(func, T = T, y0 = y0, ...).
I have the following function
def fun(X, alpha, y):
#some stuff
return J, gradient
And I am trying to minimze alpha with this, but nothing happens.
optimized_alpha = sp.optimize.minimize(lambda t: fun(X, t, y), alpha, method="Newton-CG", jac=True)
You can use functools.partial to turn your function to partial function with only one argument. In order to make it work with scipy.optimize.minimize you will need to keep the variable argument at the last position:
def fun(X, y, alpha):
#some stuff
return J, gradient
then:
from functools import partial
optfunc = partial(func, X, y)
optimized_alpha = sp.optimize.minimize(optfunc, alpha, method="Newton-CG", jac=True)