def main():
g = Graph()
v1 = Matrix([[3, 0]]).T
v2 = Matrix([[1, 2]]).T
g.add_vector(v1, color='tab:green')
g.add_vector(v2, color='tab:red')
p1 = v1.copy()
p2 = orthogonal(p1, v2)
pprint([p1, p2])
g.add_vector(p1, color='tab:blue') # same as v1 (green) so it hides it
g.add_vector(p2, color='tab:orange')
g.show()
def main():
g = Graph()
v1 = Matrix([[2, 1]]).T
v2 = Matrix([[1, 1]]).T
g.add_vector(v1)
g.add_vector(v2)
p1 = v1.copy()
p2 = orthogonal(p1, v2)
g.add_vector(p1, color='tab:blue')
g.add_vector(p2, color='tab:blue')
n1 = normalize(p1)
n2 = normalize(p2)
g.add_vector(n1, color='tab:green')
g.add_vector(n2, color='tab:green')
g.show()
import numpy as np from util.graph import Graph from sympy import Matrix u = np.array([-1, 1]) v = np.array([2, 3]) # Solve Ax=0 where A = (u v) A = np.array([u, v, [0, 0]]).T A, _ = Matrix(A).rref() A = np.array(A) print(A) # u and v are linearly independent because scalars k and c = zero g = Graph() g.add_vector(u, color='b') g.add_vector(v, color='g') g.show()
x, y = symbols('x y')
eq1 = Eq(2 * x - y, 0)
eq2 = Eq(-x + 2 * y, 3)
pprint(eq1)
pprint(eq2)
result = linsolve([eq1, eq2], [x, y])
print('x, y:', pretty(result))
# row "picture"
# See an intersection at [1, 2]
g_row = plot(solve(eq1, y)[0],
show=False,
line_color='tab:blue',
xlim=[-5, 5],
ylim=[-5, 5])
g_row.append(plot(solve(eq2, y)[0], show=False, line_color='tab:blue')[0])
g_row.show()
# col "picture"
g_col = Graph()
M, b = linear_eq_to_matrix([eq1, eq2], x, y)
# Show the columns vectors in green
u = np.array(M.col(0)).T[0]
v = np.array(M.col(1)).T[0]
g_col.add_vector(u, color='tab:green')
g_col.add_vector(v, color='tab:green')
# Show [0, 3] in orange (2x the second column, added to the first)
w = 2 * v
g_col.add_vector(w, start=u, color='tab:orange')
g_col.show()
