Develop Reference

Why does nothing showing up on my plot even with defined variables

So i made this code to create a plot that should look like this[This image was done in Mathematica] 1 but for some reason nothing shows up on the plot plot i made.does it have to something with the gam(x_2) or gam itself because i tried defining that as a range but still nothing. please teach me. From the plot made in matematica it seems like he set both the x and y ranges all the way up to 10,000.
import matplotlib.pyplot as plt
import numpy as np
import math
import pylab
%matplotlib inline
gam0 = 72.8
temp = 293.15
def gam(x_2):
return gam0 - 0.0187 * temp * math.log10(1+628.14*55.556*x_2)
x = range(0, 10000)
x_2= x
plt.plot('gam(x_2), x_2')
plt.xlabel('Log_10x_2')
plt.ylabel('gamma (erg cm^2)')

A few fixes needed; defining your function, there's an indent missing, also multiplying the whole array with ' * ' isn't working, so you can save up the values in a separate array through a for loop:
EDIT: Oh, and also while plotting, you don't put the variable names as strings, you just call them as they are.
import matplotlib.pyplot as plt
import numpy as np
import math
import pylab
%matplotlib inline
gam0 = 72.8
temp = 293.15
x = range(0, 10000)
x_2= x
def gam(x_2):
returns = []
for x_i in x_2:
returns.append(gam0 - 0.0187 * temp * math.log10(1+628.14*55.556*x_i))
return returns
plt.plot(gam(x_2), x_2)
plt.xlabel('Log_10x_2')
plt.ylabel('gamma (erg cm^2)')
plt.show()

Indent your function
def gam(x_2):
return gam0 - 0.0187 * temp * math.log10(1+628.14*55.556*x_2)
Find gam(x_2) for each item(x_2) in list x
gam_x = [gam(x_2) for x_2 in x]
Finally, plot and show.
plt.plot(gam_x, x)
plt.xlabel('Log_10x_2')
plt.ylabel('gamma (erg cm^2)')
plt.show()

Explicitly calculate convolution in Python

I want to calculate a convolution in Python by explicitly evaluating the integral
and comparing the result with what I get from fftconvolve. The integral would be calculated using quad:
import numpy as np
from scipy.integrate import quad
from scipy.signal import fftconvolve
import matplotlib.pyplot as plt
from sympy import symbols
def f(x,a,b):
return np.exp(-(x-a)**2/b)
def g(x,a,b):
return np.exp(-(x-np.pi*a)**2/(2.9*b))
x = symbols('x')
a = 1.2
b = 4.7
t = np.linspace(-100,100,int(1e4))
dt = t[1] - t[0]
h1 = fftconvolve(f(t,a,b),g(t,a,b),mode='same')*dt
h2,_ = quad(f(t,a,b)*g(x-t,a,b),-np.inf,np.inf,epsabs=0,epsrel=1e-6,args=(a,b))
x = np.linspace(-100,100,int(1e4))
plt.figure()
plt.plot(t,h1,label='fftconvolve')
plt.plot(x,h2,label='brute force')
plt.legend()
plt.show()
I keep getting the error AttributeError: 'Mul' object has no attribute 'exp' which refers to the line h2,_ = quad(... when it is called by quad.
What does this error mean and is this an appropriate way to use quad to evaluate the integral?

Solving nonlinear differential first order equations using Python

I would like to solve a nonlinear first order differential equation using Python.
For instance,
df/dt = f**4
I wrote the following program, but I have an issue with matplotlib, so I don't know if the method I used with scipy is correct.
from scipy.integrate import odeint
import numpy as np
import matplotlib.pyplot as plt
derivate=lambda f,t: f**4
f0=10
t=np.linspace(0,2,100)
f_numeric=scipy.integrate.odeint(derivate,f0,t)
print(f_numeric)
plt.plot(t,f_numeric)
plt.show()
Which results in the following error:
AttributeError: 'float' object has no attribute 'rint'

In this case, you might be better of using Sympy, which allows you to obtain the closed form solutions:
from IPython.display import display
import sympy as sy
from sympy.solvers.ode import dsolve
import matplotlib.pyplot as plt
import numpy as np
sy.init_printing() # LaTeX like pretty printing for IPython
t = sy.symbols("t", real=True)
f = sy.symbols("f", function=True)
eq1 = sy.Eq(f(t).diff(t), f(t)**4) # the equation
sls = dsolve(eq1) # solvde ODE
# print solutions:
print("For ode")
display(eq1)
print("the solutions are:")
for s in sls:
display(s)
# plot solutions:
x = np.linspace(0, 2, 100)
fg, axx = plt.subplots(2, 1)
axx[0].set_title("Real part of solution of $\\frac{d}{dt}f(t)= (f(t))^4$")
axx[1].set_title("Imag. part of solution of $\\frac{d}{dt}f(t)= (f(t))^4$")
fg.suptitle("$C_1=0.1$")
for i, s in enumerate(sls, start=1):
fn1 = s.rhs.subs("C1", .1) # C_1 -> 1
fn2 = sy.lambdify(t, fn1, modules="numpy") # make numpy function
y = fn2(x+0j) # needs to be called with complex number
axx[0].plot(x, np.real(y), label="Sol. %d" % i)
axx[1].plot(x, np.imag(y), label="Sol. %d" % i)
for ax in axx:
ax.legend(loc="best")
ax.grid(True)
axx[0].set_ylabel("Re$\\{f(t)\\}$")
axx[1].set_ylabel("Im$\\{f(t)\\}$")
axx[-1].set_xlabel("$t$")
fg.canvas.draw()
plt.show()
In an IPython shell, you should see the following:

Numpy roots function and pyplot plot

I want to plot the two solutions of quadratic equation as a function of a parameter ( function coeff(t) ). I am using function numpy.roots (I am sure that all roots are real in this case), and I am trying to invoke it from within pyplot.plot as below:
import numpy as np
import matplotlib.pyplot as plt
r = 3.74
def coeff(pp):
return np.array([pp-1,r+1-0.5*pp,-r])
def sroot(t):
return np.roots(coeff(t))
a = np.linspace(0,0.9,100)
fig = plt.figure()
plt.plot(a,sroot(a)[0,:])
plt.plot(a,sroot(a)[1,:])
plt.show()
I get error message:
File "quest.py", line 18, in <module>
plt.plot(a,sroot(a)[0,:])
File "quest.py", line 10, in sroot
return np.roots(coeff(t))
File "/usr/lib64/python2.7/site-packages/numpy/lib/polynomial.py", line 218, in roots
p = p.astype(float)
I understand that the numpy.roots takes only list of parameters and is unable to recognize a row in array 3xlen(a). Is there a way to do it in one line, preferably inside the pyplot.plot? I would like to avoid using loop.

This is because you transform all of your coefficient at once and try to call the numpy roots solver on all of them. np.roots only accept 1-d array and solves a single polynomial. Here is a script that does what you want:
import numpy as np
import matplotlib.pyplot as plt
# Parameters
r = 3.74
T = np.linspace(0.0,0.9,100)
# Coefficients
C = np.zeros((len(T),3))
C[:,0] = T-1
C[:,1] = r + 1 - 0.5*T
C[:,2] = r
# Roots
R = np.zeros((len(T),2))
for i in range(len(T)):
R[i] = np.roots(C[i])
# Plot
fig = plt.figure()
plt.plot(T,R[:,0])
plt.plot(T,R[:,1])
plt.show()

scipy.optimze curve_fit return wrong value

I was trying to fit a specific function with scipy and I got weird results. I decided to test something I know the answer to so I created this:
from scipy.optimize import curve_fit as cf
import numpy as np
import random
def func(x,a):
return a+X
X =[]
for i in range (10):
V = random.random()
X.append(i+3 + V/10)
print cf(func, np.array(range(10)),np.array(X))
I expected to get something around 3, nevertheless, here the output:
(array([ -2.18158824e-12]), inf)
As a side note, I tried to see what I send something to func and I got this:
print func(np.array(range(10)),3)
Traceback (most recent call last):
File "/tmp/py1759O-P", line 16, in <module>
print func(np.array(range(10)),3)
File "/tmp/py1759O-P", line 6, in func
return a+X
TypeError: unsupported operand type(s) for +: 'int' and 'list
What am I doing wrong?

Don't use x and X as variable names when they carry such different meanings (or perhaps you didn't know Python is case sensitive?):
def func(x,a):
return a+X
X =[]
x is a numpy array, X is a list, and a is a scalar parameter value.
a+X results in an error since you can not add a scalar to a list.

In func, the argument is x, but X is used in the body of the function.
Here's a modified version of your code. It uses a few more features of numpy (e.g. np.random.random() instead of random.random()).
from scipy.optimize import curve_fit as cf
import numpy as np
def func(x, a):
return a + x
n = 10
xdata = np.arange(n)
ydata = func(xdata, 3) + np.random.random(n) / 10
print cf(func, xdata, ydata)
The output is
(array([ 3.04734293]), array([[ 8.19208558e-05]]))