from numpy import *
from numpy import linalg as l
from cmlib import showMatr
def make_ort(matr):
"""
:param matr: ndarray, rows - vectors to ort***
:return: nothing... it's just orthogonalizing
"""
for i in range(matr.shape[0]):
summ = matr[i]
for j in range(i):
summ -= dot(matr[i], matr[j]) / dot(matr[j], matr[j]) * matr[j]
matr[i] = summ
a = array([[1, 1, 1, 1],
[3, 3, -1, -1],
[-2, 0, 6, 8]], dtype='float64')
print(a)
make_ort(a)
# print(a)
showMatr(a)
from numpy import * from numpy import linalg as l from cmlib import showMatr A_e = array([[15, -11, 5], [20, -15, 8], [8, -7, 6]]) f_1 = array([2, 3, 1]) f_2 = array([3, 4, 1]) f_3 = array([1, 2, 2]) s_ef = vstack((f_1, f_2, f_3)).T A_f = dot(dot(l.inv(s_ef), A_e), s_ef) A_f = array([[int(round(elem)) for elem in row] for row in A_f]) showMatr(A_f)
from numpy import * from cmlib import showMatr A = matrix([[1, 1, 2], [1, -2, -1], [2, 1, 3], [-1, 2, 1]]) print(A.shape) showMatr(array(A)) print(linalg.matrix_rank(A) < A.shape[1])
from numpy import * from cmlib import showMatr A = matrix([[1, 2], [3, 4]], dtype='int') B = matrix([[3, 5], [5, 9]], dtype='int') res = linalg.solve(A, B) showMatr(array(res))
from numpy import * from numpy import linalg as l from fractions import Fraction from cmlib import showMatr a = array([1, 2, 0]) b = array([2, 0, -1]) ang = dot(a, b) / (l.norm(a) * l.norm(b)) print(Fraction(str(ang))) showMatr([[Fraction(str(ang))]])
from numpy import *
from numpy import random
from cmlib import showMatr
def is_upper_triangular(matr): # matrix as array with shape == (n, n)
for i in range(len(matr)):
for j in range(i):
if matr[i][j] != 0:
return False
return True
a = random.randint(1, 10, (10, 10))
b = eye(10, 10, dtype='int')
showMatr(a)
print(is_upper_triangular(a))
showMatr(b)
print(is_upper_triangular(b))
from numpy import *
from cmlib import showMatr
A = matrix([[1, 2, 0],
[0, 2, 2]])
B = matrix([[3, -1],
[-1, 3],
[1, 0]])
res = (A * B).T
showMatr(array(res))
from numpy import *
from cmlib import showMatr
A = matrix([[1, 1, 2],
[1, -2, -1],
[2, 1, 3],
[-1, 2, 1]])
print(A.shape)
showMatr(array(A))
print(linalg.matrix_rank(A) < A.shape[1])
from numpy import *
from numpy import linalg as l
from cmlib import showMatr
A_e = array([[15, -11, 5],
[20, -15, 8],
[8, - 7, 6]])
f_1 = array([2, 3, 1])
f_2 = array([3, 4, 1])
f_3 = array([1, 2, 2])
s_ef = vstack((f_1, f_2, f_3)).T
A_f = dot(dot(l.inv(s_ef), A_e), s_ef)
A_f = array([[int(round(elem)) for elem in row] for row in A_f])
showMatr(A_f)