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import numpy as np
# Model A only.
# Uses least squares regression to find the solution
# when there is one unknown variable.
def lstsq_solution(A, B):
A_inv = np.linalg.pinv(A)
x = np.matmul(A_inv, B)
return x[0][0]
# Model B only.
# Uses the pseudoinverse matrix to find the solution
# when there are two unknown variables.
def pinv_solution(A, mv, B):
new_A = np.concatenate((A, mv), axis=1)
new_A_inv = np.linalg.pinv(new_A)
new_x = np.matmul(new_A_inv, B)
print("pinv solution:", new_x[0][0], new_x[1][0])
return (new_x[0][0], new_x[1][0])
# Model A only.
# Finds the coefficient to multiply A by to minimize
# the percentage error between A and B.
def minimize_percentage_error_model_a(A, B):
R = np.divide(A, B)
num = 0
den = 0
best_x = 0
best_error = 100
for r_i in R:
num += r_i
den += r_i**2
if den == 0:
return 0
return (num/den)[0]
# Model B only.
# Finds the coefficients to multiply to the frame bitrate
# and the motion vector bitrate to minimize the percent error.
def minimize_percentage_error_model_b(r_e, r_m, r_f):
r_ef = np.divide(r_e, r_f)
r_mf = np.divide(r_m, r_f)
sum_ef = np.sum(r_ef)
sum_ef_sq = np.sum(np.square(r_ef))
sum_mf = np.sum(r_mf)
sum_mf_sq = np.sum(np.square(r_mf))
sum_ef_mf = np.sum(np.multiply(r_ef, r_mf))
# Divides x by y. If y is zero, returns 0.
divide = lambda x, y : 0 if y == 0 else x / y
# Set up and solve the matrix equation
A = np.array([[1, divide(sum_ef_mf, sum_ef_sq)],[divide(sum_ef_mf, sum_mf_sq), 1]])
B = np.array([divide(sum_ef, sum_ef_sq), divide(sum_mf, sum_mf_sq)])
A_inv = np.linalg.pinv(A)
x = np.matmul(A_inv, B)
return x
# Model A only.
# Calculates the least squares error between A and B
# using coefficients in X.
def average_lstsq_error(A, B, x):
error = 0
n = 0
for i, a in enumerate(A):
a = a[0]
b = B[i][0]
if b == 0:
continue
n += 1
error += (b - x*a)**2
if n == 0:
return None
error /= n
return error
# Model A only.
# Calculates the average percentage error between A and B.
def average_percent_error_model_a(A, B, x):
error = 0
n = 0
for i, a in enumerate(A):
a = a[0]
b = B[i][0]
if b == 0:
continue
n += 1
error_i = (abs(x*a-b)/b)*100
error += error_i
error /= n
return error
# Model B only.
# Calculates the average percentage error between A and B.
def average_percent_error_model_b(A, M, B, x):
error = 0
for i, a in enumerate(A):
a = a[0]
mv = M[i]
b = B[i][0]
if b == 0:
continue
estimate = x[0]*a
estimate += x[1]*mv
error += abs(estimate - b) / b
error *= 100
error /= A.shape[0]
return error
def average_squared_error_model_a(A, B, x):
error = 0
n = 0
for i, a in enumerate(A):
a = a[0]
b = B[i][0]
if b == 0:
continue
n += 1
error_i = (1 - x*(a/b))**2
error += error_i
error /= n
error = error**0.5
return error * 100
def average_squared_error_model_b(A, M, B, x):
error = 0
n = 0
for i, a in enumerate(A):
a = a[0]
b = B[i][0]
mv = M[i]
if b == 0:
continue
n += 1
error_i = 1 - ((x[0]*a + x[1]*mv)/b)
error_i = error_i**2
error += error_i
error /= n
error = error**0.5
return error * 100
# Traverses the data and prints out one value for
# each update type.
def print_solutions(file_path):
data = np.genfromtxt(file_path, delimiter="\t")
prev_update = 0
split_list_indices = list()
for i, val in enumerate(data):
if prev_update != val[3]:
split_list_indices.append(i)
prev_update = val[3]
split = np.split(data, split_list_indices)
for array in split:
A, mv, B, update = np.hsplit(array, 4)
z = np.where(B == 0)[0]
r_e = np.delete(A, z, axis=0)
r_m = np.delete(mv, z, axis=0)
r_f = np.delete(B, z, axis=0)
A = r_e
mv = r_m
B = r_f
all_zeros = not A.any()
if all_zeros:
continue
print("update type:", update[0][0])
x_ls = lstsq_solution(A, B)
x_a = minimize_percentage_error_model_a(A, B)
x_b = minimize_percentage_error_model_b(A, mv, B)
percent_error_a = average_percent_error_model_a(A, B, x_a)
percent_error_b = average_percent_error_model_b(A, mv, B, x_b)[0]
baseline_percent_error_a = average_percent_error_model_a(A, B, 1)
baseline_percent_error_b = average_percent_error_model_b(A, mv, B, [1, 1])[0]
squared_error_a = average_squared_error_model_a(A, B, x_a)
squared_error_b = average_squared_error_model_b(A, mv, B, x_b)[0]
baseline_squared_error_a = average_squared_error_model_a(A, B, 1)
baseline_squared_error_b = average_squared_error_model_b(A, mv, B, [1, 1])[0]
print("model,\tframe_coeff,\tmv_coeff,\terror,\tbaseline_error")
print("Model A %_error,\t" + str(x_a) + ",\t" + str(0) + ",\t" + str(percent_error_a) + ",\t" + str(baseline_percent_error_a))
print("Model A sq_error,\t" + str(x_a) + ",\t" + str(0) + ",\t" + str(squared_error_a) + ",\t" + str(baseline_squared_error_a))
print("Model B %_error,\t" + str(x_b[0]) + ",\t" + str(x_b[1]) + ",\t" + str(percent_error_b) + ",\t" + str(baseline_percent_error_b))
print("Model B sq_error,\t" + str(x_b[0]) + ",\t" + str(x_b[1]) + ",\t" + str(squared_error_b) + ",\t" + str(baseline_squared_error_b))
print()
if __name__ == "__main__":
print_solutions("data2/all_lowres_target_lt600_data.txt")
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