def is_local_minimum(n):
variances = []
matrix = create_optimal_matrix(n)
v = compute_variance(np.array(matrix))
# variances.append(compute_variance(np.array(matrix)))
for i in range(n):
for j in range(n):
mat = np.array([row for row in matrix])
mat[i, j] = 1 - mat[i, j]
variances.append(compute_variance(mat))
print(v < min(variances))
return variances
def compute_variances(m, n):
variances = []
binary_matrices = compute_all_binary_matrices(m, n)
for matrix in binary_matrices:
model_variace = compute_variance(matrix)
variances.append(round(model_variace, 5))
return binary_matrices, variances
def compute_variances(number_of_rows, number_of_columns):
binary_matrices = compute_matrices(number_of_rows, number_of_columns)
variances = []
for matrix in binary_matrices:
model_variance = compute_variance(np.array(matrix))
variances.append(round(model_variance, 3))
return binary_matrices, variances
def compute_singular_designs(m, n):
singular_designs = []
binary_matrices = compute_all_binary_matrices(m, n)
for matrix in binary_matrices:
variance = compute_variance(matrix)
if variance == float('inf'):
singular_designs.append(matrix)
return singular_designs
def compute_up_to_dimension(n):
variances = []
for i in range(2, n):
mat = create_optimal_matrix(i)
mat = np.array(mat)
variance = compute_variance(mat)
variances.append(variance)
print('Dimension ' + str(i) + ': ' + str(round(variance, 3)))
plt.figure(figsize=(7, 2))
plt.plot(variances, 'rx')
def test_hypothesis(n):
for i in range(2, n):
dimension = 2 * i
print('Testing dimension ', dimension)
matrix = create_optimal_matrix(dimension)
M = compute_information_matrix(np.array(matrix))
hT = [0 for i in range(M.shape[0])]
hT[len(hT) - 2] = -0.5
hT[len(hT) - 1] = 0.5
hT = np.array(hT)
val = np.matmul(np.matmul(hT, M), np.transpose(hT))
print(1 / val)
print(np.matmul(hT, M))
print(compute_variance(np.array(matrix)))
hT[len(hT) - 1] = 0.5
hT = np.array(hT)
val = np.matmul(np.matmul(hT, M), np.transpose(hT))
print(1 / val)
print(np.matmul(hT, M))
print(compute_variance(np.array(matrix)))
# test_hypothesis(5)
s = ''
for i in range(2, 17):
matrix = create_optimal_matrix(i)
# print('Dimension ', 2*i)
d = compute_variance(np.array(matrix))
print((i, round(d, 4)))
s += str((i, round(d, 5)))
# F = compute_transformation_matrix(np.array(matrix))
# M = compute_information_matrix(np.array(matrix))
# print(F)
# print(M)
print(s)
# for i in range(20, 30):
# v = is_local_minimum(i)
# compute_up_to_dimension(10)
# plt.show()