I've been trying to solve a nonlinear ordinary differential equation numerically by using Scipy, in particular by the scipy.integrate.RK23 command. It returns <scipy.integrate._ivp.rk.RK23 at 0x7f2b1a908390>. How can I plot the solution?
Thank you in advance for your help!
EDIT:
As a simple example for testing:
import numpy
import scipy.integrate
t0=0;
tf=1;
x0=numpy.array([0]);
def F(t,x): return t**2;
x=scipy.integrate.RK23(F,t0,x0,tf)
RK23 is a class that implements a way to solve an ODE, that is, it is an OdeSolver so it should not be used directly but in other functions like solve_ivp:
import numpy
from scipy.integrate import solve_ivp, RK23
import matplotlib.pyplot as plt
t0=0
tf=1
x0=numpy.array([0])
def F(t,x): return t**2
sol = solve_ivp(F, [t0, tf], x0, RK23)
print(sol)
plt.plot(sol.t, sol.y[0])
plt.show()
OdeSolver allows the developer to add custom methods without the need to rewrite scipy, but since RK23 is a classic method already implemented by scipy, you could pass just the name and scipy search for the appropriate class:
...
sol = solve_ivp(F, [t0, tf], x0, "RK23")
...
Related
I'm trying to edit a figure that was obtained using an external function.
For example, "nolds.lyap_r" function creates a figure. Let's say I want to add a title to it after it was plotted. How can I do it?
import nolds
import numpy as np
import matplotlib.pyplot as plt
nolds.lyap_r(y, debug_plot=True)
I guess I need to use plt.gca() or plt.gcf() but it didn't work for me:
ax=plt.gca()
ax.set_title("ABC")
pyplot.draw() is there to update the existing figure:
plt.title('A good title')
plt.draw()
I am using Numba to speed up a function and I bumped into the following problem.
When using the decorator #njit (or #jit) the behaviour of some numpy function is changed.
For example if I use the following function to calculate tanh
from numba import njit
import numpy as np
#njit
def check_tanh(z):
return np.tanh(z)
and I run it for real values of z I get the same as np.tanh(z) as it should be.
If I move instead parallel to the real axis but with an imaginary part, for example z = x+ 1.j, and increase x, the numpy tanh will converge to 1.+0.j, while check_tanh(z) will return a nan (on my computer this is happening when x>360).
Does anyone have an idea of what is going on and how can be fixed?
Thanks in advance!
Using tanh from cmath fixes the issue.
Seems that is still a problem in Numba
https://github.com/numba/numba/issues/2919
Let's say, I have the following code.
import numpy as np
import pandas as pd
x = pd.DataFrame(np.random.randn(100, 3)).rolling(window=10, center=True).cov()
For each index, I have a 3x3 matrix. I would like to calculate eigenvalues and then some function of those eigenvalues. Or, perhaps, I might want to compute some function of eigenvalues and eigenvectors. The point is that if I take x.loc[0] then I have no problem to compute anything from that matrix. How do I do it in a rolling fashion for all matrices?
Thanks!
You can use the analogous eigenvector/eigenvalue methods in spicy.sparse.linalg.
import numpy as np
import pandas as pd
from scipy import linalg as LA
x = pd.DataFrame(np.random.randn(100, 3)).rolling(window=10, center=True).cov()
for i in range(len(x)):
try:
e_vals,e_vec = LA.eig(x.loc[i])
print(e_vals,e_vec)
except:
continue
If there are no NaN values present then you need not use the try and except instead go for only for loop.
I am interested in using the interact function to use a slider to adjust the position of text in a matplotlib plot (you know, instead of adjusting the position, running the code, and repeating 1000 times).
Here's a simple example of a plot
import matplotlib.pyplot as plt
x=0.2
y=0.9
plt.text(x, y,'To move',size=19)
plt.show()
and some interact code
from __future__ import print_function
from ipywidgets import interact, interactive, fixed
import ipywidgets as widgets
def f(x):
return x
interact(f, cx=0.2)
I'm wondering how I can combine these to generate a plot with the text along with a slider that will interactively move the text based on the specified value for x. Is this possible? What if I want to do the same for y?
Thanks in advance!
Here you go:
%matplotlib inline
import matplotlib.pyplot as plt
from ipywidgets import interact
def do_plot(x=0.2, y=0.9):
plt.text(x, y,'To move',size=19)
plt.show()
interact(do_plot)
How can I fit my plots?
Up to now, I've got the following code, which plots a variety of graphs from an array (data from an experiment) as it is placed in a loop:
import matplotlib as plt
plt.figure(6)
plt.semilogx(Tau_Array, Correlation_Array, '+-')
plt.ylabel('Correlation')
plt.xlabel('Tau')
plt.title("APD" + str(detector) + "_Correlations_log_graph")
plt.savefig(DataFolder + "/APD" + str(detector) + "_Correlations_log_graph.png")
This works so far with a logarithmic plot, but I am wondering how the fitting process could work right here. In the end I would like to have some kind of a formula or/and a graph which best describes the data I measured.
I would be pleased if someone could help me!
You can use curve_fit from scipy.optimize for this. Here is an example
# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
def func(x,a):
return np.exp(a*x)
x,y,z = np.loadtxt("fit3.dat",unpack=True)
popt,pcov = curve_fit(func,x,y)
y_fit = np.exp(popt[0]*x)
plt.plot(x,y,'o')
plt.errorbar(x,y,yerr=z)
plt.plot(x,y_fit)
plt.savefig("fit3_plot.png")
plt.show()
In yourcase, you can define the func accordingly. popt is an array containing the value of your fitting parameters.