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lab08.py
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lab08.py
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# import numpy as np
# # Printing matrices using NumPy:
# # Convert a list of lists into an array:
# M_listoflists = [[1,-2,3],[3,10,1],[1,5,3]]
# M = np.array(M_listoflists)
# # Now print it:
# print(M)
# #Compute M*x for matrix M and vector x by using
# #dot. To do that, we need to obtain arrays
# #M and x
# M = np.array([[1,-2,3],[3,10,1],[1,5,3]])
# x = np.array([75,10,-11])
# b = np.matmul(M,x)
# print(M)
# #[[ 1 -2 3]
# # [ 3 10 1]
# # [ 1 5 3]]
# # To obtain a list of lists from the array M, we use .tolist()
# M_listoflists = M.tolist()
# print(M_listoflists) #[[1, -2, 3], [3, 10, 1], [1, 5, 3]]
import numpy as np
def print_matrix(M_lol):
M = np.array(M_lol)
print(M)
def get_lead_ind(row):
for i in range(len(row)):
if (row[i] != 0):
return i
return len(row)
def get_row_to_swap(M, start_i):
max_row = start_i
for i in range(len(M) - start_i - 1): #4 - 0 - 1 = 3
if (get_lead_ind(M[start_i + 1 + i]) < get_lead_ind(M[max_row])):
max_row = start_i + 1 + i
return max_row
def add_rows_coefs(r1, c1, r2, c2):
M = [0]*len(r1)
for i in range(len(r1)):
M[i] = c1*r1[i] + c2*r2[i]
return M
def eliminate_forward(M, row_to_sub, best_lead_ind):
new = [0]*len(M[0])
coeff = 1
for i in range(len(M) - row_to_sub - 1):
coeff = -1*M[row_to_sub + i + 1][best_lead_ind]/M[row_to_sub][best_lead_ind]
new = add_rows_coefs(M[row_to_sub], coeff, M[row_to_sub + i + 1], 1)
M[row_to_sub + i + 1] = new
def eliminate_backward(M, row_to_sub, best_lead_ind):
new = [0]*len(M[0])
coeff = 1
for i in range(row_to_sub):
coeff = -1*M[row_to_sub - i - 1][best_lead_ind]/M[row_to_sub][best_lead_ind]
new = add_rows_coefs(M[row_to_sub], coeff, M[row_to_sub - i - 1], 1)
M[row_to_sub - i - 1] = new
def forward_step(M):
for i in range(len(M)):
swap = get_row_to_swap(M, i)
print("row to swap",swap)
M[swap], M[i] = M[i], M[swap] #this swaps the rows
print("after swap")
print_matrix(M)
eliminate_forward(M, i, get_lead_ind(M[i]))
print("after eliminate")
print_matrix(M)
def backward_step(M):
for i in range(len(M)):
eliminate_backward(M, len(M) - i - 1, get_lead_ind(M[len(M) - i - 1]))
print("after eliminate")
print_matrix(M)
for i in range(len(M)):
coeff = M[i][get_lead_ind(M[i])]
new = [0]*len(M[0])
for j in range(len(M[0])):
new[j] = M[i][j]/coeff
M[i] = new
print("divide leading coeff")
print_matrix(M)
def augment(M, b):
new = [[0 for x in range(len(M[0]) + 1)] for y in range(len(M))]
for i in range(len(M)):
for j in range(len(M[0])):
new[i][j] = M[i][j]
new[i][-1] = b[i][0]
return new
def solve(M, b): #make sure that b is 3 x 1
augmented = augment(M, b)
forward_step(augmented)
backward_step(augmented)
ans = [[0] for y in range(len(b))]
for i in range(len(b)):
ans[i] = augmented[i][-1]
return ans
def test(M, x):
array_M = np.array(M)
array_x = np.array(x)
return np.matmul(array_M, array_x)
if __name__ == "__main__":
# M = [[ 1, -2, 3, 22],
# [ 3, 10, 1, 314],
# [ 1, 5, 3, 92,]]
# print("forward")
# forward_step(M)
# print("backward")
# backward_step(M)
M = [[ 2, 3, -5],
[ 1, -1, 1],
[ 10, -8, 21]]
b = [[0], [1], [23]]
print_matrix(augment(M, b))
ans = solve (M, b)
print_matrix(ans)
print_matrix(test(M, ans))