import numpy as np@Pyodide.eval
See on LiaScript:
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NumPy means numerical python. It is made to work with multidimensional array objects, such as matrices and vectors. And there is a collection of operations for working with these objects. When you use NumPy together with the packages SciPy (which means scientific python) and Matplotlib, you get a functional opportunity to replace MATLAB.
- NumPy = numerical Python (working with multidimensional array objects)
- NumPy + SciPy + Matplotlib = replacement for MATLAB
Remark: Referring to array objects Python doesn't distinguish between vectors and matrices. They both are just arrays having different dimensions.
# Create a simple vector
a = np.array([1,0,2])
print (a)
a.dtype@Pyodide.eval
=> Data types are chosen automatically except you chose yourself.
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The data type is chosen automatically. But sometimes that will not be what you need, so you can do this yourself. See below.
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# Create another vector
C = np.array([1,2,0], dtype=complex )
print (C)
C.dtype@Pyodide.eval
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You can choose between all Python data types, such as integer, float, boolean, single characters, complex numbers or others (see Python documentation for this).
If all elements known, use following implementation:
# Create matrix like vector, both are arrays
B = np.array([[1,2,0],[2,0,1],[0,1,2]])
print (B)
B.dtype@Pyodide.eval
Remark: Normally Python does print the arrays with ordered rows and columns. This line style is also a little problem of LiaScript.
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What if you just know the dimension but not all entries? That is also possible! For example in the following ways.
D = np.zeros((2,3), dtype=np.int16 )
print ("D=\n",D)
E = np.zeros((2,3))
print ("E=\n",E)@Pyodide.eval
Remark: You can also create arrays of higher dimensions if needed.
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Let's imagine you have to plot a function f depending on x. To plot that Python needs points. So first we create an array consisting of x.
#np.arange(startpoint, endpoint, stepsize)
x1 = np.arange( 0, 2.1, 0.1 )
print (x1)
#np.linspace(startpoint, endpoint, number of points in between -> useful for many entries)
from numpy import pi
x2 = np.linspace( 0, 2*pi, 100 )
#print (x2)@Pyodide.eval
f1 = np.sin(x2)
print ("f1", f1)
f2 = x1**2
print ("f2", f2)@Pyodide.eval
Remark: You can always check your results by simply printing them.
import matplotlib.pyplot as plt@Pyodide.eval
Normally you would use this code:
plt.plot(x2,f1)
plt.show()But that doesn't work in LiaScript, so we do the following:
fig, ax = plt.subplots()
plt.plot(x2,f1)
plt.show()
plot(fig)@Pyodide.eval
fig2, ax = plt.subplots()
plt.plot(x1,f2)
plt.show()
plot(fig2)@Pyodide.eval
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It is also possible to combine different commands. For example you can create a matrix out of a set of ordered numbers.
F = np.arange(20).reshape(5,4)
print (F)@Pyodide.eval
=> Indeces beginning with zero. Don't want? Try this:
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Here you see that Python is indexed beginning with zero. If you don't want this you have to consider it in the command line. For example change the one above to the following.
F2 = np.arange(1,21,1).reshape(5,4)
print (F2)@Pyodide.eval
F2.sum(axis=0) # sum of each column@Pyodide.eval
F2.sum(axis=1) # sum of each row@Pyodide.eval
A = np.arange(3)
print (A)
expA = np.exp(A)
print (expA)
sqrtA = np.sqrt(A)
print (sqrtA)
B = np.array([2., 0., -1.])
AplusB = np.add(A, B)
print (AplusB)@Pyodide.eval
Again we take our matrix F.
print (F)@Pyodide.eval
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Iterating in a multidimensional array is always done with respect to the first axis.
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for row in F:
print (row)@Pyodide.eval
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If you want to iterate somehow else, it is a bit more complicated. Just be creative or look it up. Python is that popular that there is nearly always someone who already found a solution for your problem. For example let's do an iteration over the columns of the matrix.
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for column in F.T: # iterating over rows in transposed matrix
print (column)@Pyodide.eval
Remark: It doesn't make any difference whether you call those indices
row,columnor justi,j,indexor somehow else. They are just indices, variables if you want.
A = np.array([[1,2],[0,-1]], dtype=np.float)
B = np.array([[3,-2],[1,-1]], dtype=np.float)
AdotB = A.dot(B) # the "common" matrix product
print (AdotB)@Pyodide.eval
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This is just one of many ready implemented functions. You will find a suitable one for any problem.
There is also a cross product that could be suitable for physics:
np.cross(A,B). Further we also do have np.tensordot(A,B) with optional
argument axis=1. It doesn't matter what you need, just look into the Python
ducomentation and be sure you will find something useful.
Aditionally we need another module for this.
import scipy.linalg as la@Pyodide.eval
print (B)@Pyodide.eval
Binv = la.inv(B)
print (Binv)@Pyodide.eval
#Do only load modul if you haven't done already.
import scipy.linalg as la@Pyodide.eval
print (AdotB)@Pyodide.eval
vec_b = np.array([1,-2.5], dtype = np.float)
print (vec_b)@Pyodide.eval
x = la.solve(AdotB,vec_b)
print (x)@Pyodide.eval
There are far more possibilities with NumPy, SciPy, Pandas and other modules. Feel free to check out things in this basic script and have a look into the Python documentation. There is nearly always a solution for any problem.