The very first time I was taken aback when I typed in the following code I was surprised I got the following results in python inorder to solve the linear equation ax=b
#The code to solve a linear equation in python
import numpy as np
a=np.array([[1,1],[1.5,4])
b=np.array([2200,5050])
#Using the solve function in numpy
x=np.solve(a,b)
#Using the inverse of a
v=np.linalg.inv(a).dot(b)
#Now when you check both x and v values are same but when you perform x==v you will get an entirely different value
In [24]: v
Out[24]: array([ 1500., 700.])
In [25]: x
Out[25]: array([ 1500., 700.])
x==v
#The result is
array([ True, False], dtype=bool)
which is not expected as both values shown were same
what happened may be realised if you check the element values individually
In [31]: x[1]
Out[31]: 700.0
In [32]: v[1]
Out[32]: 699.99999999999977
i.e, the value of v[1] was actually only 699.99999999999977 no 700 and hence not equal. The correct answer corresponding to our linear equation is x and not v.
This is why built in functions are preferred most of the times over our own algorithms as appearances can be deceptive
#The code to solve a linear equation in python
import numpy as np
a=np.array([[1,1],[1.5,4])
b=np.array([2200,5050])
#Using the solve function in numpy
x=np.solve(a,b)
#Using the inverse of a
v=np.linalg.inv(a).dot(b)
#Now when you check both x and v values are same but when you perform x==v you will get an entirely different value
In [24]: v
Out[24]: array([ 1500., 700.])
In [25]: x
Out[25]: array([ 1500., 700.])
x==v
#The result is
array([ True, False], dtype=bool)
which is not expected as both values shown were same
what happened may be realised if you check the element values individually
In [31]: x[1]
Out[31]: 700.0
In [32]: v[1]
Out[32]: 699.99999999999977
i.e, the value of v[1] was actually only 699.99999999999977 no 700 and hence not equal. The correct answer corresponding to our linear equation is x and not v.
This is why built in functions are preferred most of the times over our own algorithms as appearances can be deceptive
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