from numpy import *
import matplotlib.pyplot as plt

# Definere matriser
A = array([[1,-2,1],[2,-3,4],[3,-8,0]])
B = array([[1,2,0],[3,4,1],[5,6,3]])

# Summere, subtrahere, gange, potens
print(A+B)
print(A-B)
print(A@B)
print(3*A)
print(matrix(A)**3)

# Transponering, invers, determinant
print(A.T)
print(linalg.inv(A))
print(linalg.det(A))

# Radvektor, s?ylevektor
a = array([[1,2,3]])
b = array([[4],[5],[6]])

# skalarprodukt p? to forskjellige m?ter
print(a@b)
print(dot(a,b))

# Matrise-vektor multiplikasjon
print(A@b)

# Komponentvise operasjoner
A = array([[1,2],[3,4]])
B = array([[0,pi/2],[pi,3*pi/2]])
print(A**2)
print(A*B)
print(sin(B))
print(B/A)
print(exp(A*B**2))

# min, max, sum, prod
print(a.min())
print(a.max())
print(b.max())
print(A.max(0))
print(sum(a))
print(prod(a))

# lengde av vektor p? to forskjellige m?ter
print(sqrt(sum(a**2)))
print(linalg.norm(a))

# plotting
x = linspace(-1,1,100)
plt.plot(x,x**2)
plt.plot(x,x**4)
plt.axis('equal')
plt.show()

# Sette sammen matriser
A = array([[1,2,3],[1,2,3],[1,2,3]])
B = array([[4,5,6],[4,5,6],[4,5,6]])
C = array([[7,8,9],[7,8,9],[7,8,9]])
D = array([[10,11,12],[10,11,12],[10,11,12]])
print(block([[A,B]]))
print(block([[A],[B]]))
print(block([[A,B],[C,D]]))


# Trekke ut en del av matrisen
print(A[1:3,1:3])

# Definere nyttige matriser
print(eye(3))
print(zeros((3,3)))
print(ones((3,3)))