 # multivariate root finding in python

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• Techknowledgy :
```>>> def f(x):
...
return x * 14.80461 + x * (-4.9233) + x * (10 * 0.4803) >>>
def vf(x):
...
return [f(x), 0, 0] >>
xx = fsolve(vf, x0 = [0, 0, 1]) >>>
>>>
f(xx)
8.8817841970012523e-16```

Suggestion : 2

As you may think, Python has the existing root-finding functions for us to use to make things easy. The function we will use to find the root is f_solve from the scipy.optimize.,The f_solve function takes in many arguments that you can find in the documentation, but the most important two is the function you want to find the root, and the initial guess.,We know that this function has two roots \(x = 1\) and \(x = 100\), therefore, we can get the two roots out fairly simple using the f_solve function.,The copyright of the book belongs to Elsevier. We also have this interactive book online for a better learning experience. The code is released under the MIT license. If you find this content useful, please consider supporting the work on Elsevier or Amazon!

```from scipy.optimize
import fsolve```
```f = lambda x: x ** 3 - 100 * x ** 2 - x + 100

fsolve(f, [2, 80])```
`array([1., 100.])`

Suggestion : 3

11.4.4. Multivariate Root-Finding , 11.5.1. Multivariate Optimization , 11.5. Optimization 11.5.1. Multivariate Optimization , 11.4. Roots and Fixed Points 11.4.1. Bisection 11.4.2. The Newton-Raphson Method 11.4.3. Hybrid Methods 11.4.4. Multivariate Root-Finding 11.4.5. Fixed Points

```# Import numpy symbols to scipy namespace
from numpy
import *
from numpy.random
import rand, randn
from numpy.fft
import fft, ifft
from numpy.lib.scimath
import *```
```import numpy as np

a = np.identity(3)```
`np.random.beta(5, 5, size = 3)`
`array([0.25649238, 0.49605511, 0.50187648])`
```% matplotlib inline
from scipy.stats
import beta
import matplotlib.pyplot as plt
plt.rcParams['figure.figsize'] = (10, 6)

q = beta(5, 5) # Beta(a, b), with a = b = 5
obs = q.rvs(2000) # 2000 observations
grid = np.linspace(0.01, 0.99, 100)

fig, ax = plt.subplots()
ax.hist(obs, bins = 40, density = True)
ax.plot(grid, q.pdf(grid), 'k-', linewidth = 2)
plt.show()```
```q.cdf(0.4) # Cumulative distribution
function```