def test_dot_mat_vect(self):
self.mat.shape = (5, 4, 2, 3)
self.mat.cols = (0, 2, 3)
self.mat.axes = ('freq', 'mode', 'a', 'b')
prod = algebra.dot(self.mat, self.vect)
self.assertEqual(prod.mat_shape(), (20, ))
self.assertEqual(prod.shape, (5, 4))
self.assertEqual(prod.info['axes'], ('freq', 'mode'))
self.assertTrue(
sp.allclose(prod.flatten(),
sp.dot(self.mat.expand(), self.vect.flatten())))
# Make sure it checks that the inner axis names match.
self.mat.axes = ('freq', 'mode', 'c', 'b')
algebra.dot(self.mat, self.vect, check_inner_axes=False)
self.assertRaises(ce.DataError, algebra.dot, self.mat, self.vect)
# Make sure that is checks that the inner axes lengths match.
self.mat.shape = (5, 4, 6)
self.mat.cols = (0, 2)
self.mat.axes = ('freq', 'mode', 'a')
algebra.dot(self.mat, self.vect, check_inner_axes=False)
self.assertRaises(ce.DataError, algebra.dot, self.mat, self.vect)
def luna(light=(0, 0, 1), bary=(1, 1, 1), vnormals=(), bcolor=(1, 1, 1)):
# coordenadas barycentricas
w, v, u = bary
# vectores normales
nA, nB, nC = vnormals
light = (0, 1, -2)
iA, iB, iC = [algebra.dot(n, light) for n in (nA, nB, nC)]
# Calculamos la intensidad de la luz
intensity = w * iA + v * iB + u * iC
return objetos.glColor(bcolor[2] * intensity, bcolor[1] * intensity,
bcolor[0] * intensity)
def test_dot_mat_vect(self) :
self.mat.shape = (5, 4, 2, 3)
self.mat.cols = (0, 2, 3)
self.mat.axes = ('freq', 'mode', 'a', 'b')
prod = algebra.dot(self.mat, self.vect)
self.assertEqual(prod.mat_shape(), (20,))
self.assertEqual(prod.shape, (5, 4))
self.assertEqual(prod.info['axes'], ('freq', 'mode'))
self.assertTrue(sp.allclose(prod.flatten(),
sp.dot(self.mat.expand(),
self.vect.flatten())))
# Make sure it checks that the inner axis names match.
self.mat.axes = ('freq', 'mode', 'c', 'b')
algebra.dot(self.mat, self.vect, check_inner_axes=False)
self.assertRaises(ce.DataError, algebra.dot, self.mat, self.vect)
# Make sure that is checks that the inner axes lengths match.
self.mat.shape = (5, 4, 6)
self.mat.cols = (0, 2)
self.mat.axes = ('freq', 'mode', 'a')
algebra.dot(self.mat, self.vect, check_inner_axes=False)
self.assertRaises(ce.DataError, algebra.dot, self.mat, self.vect)
def backpropogate(network, input_vector, target):
hidden_outputs, outputs = feed_forward(network, input_vector)
# the output * (1 - output) is from the derivative of sigmoid
output_deltas = [output * (1 - output) * (output - target[i])
for i, output in enumerate(outputs)]
# adjust weights for output layer (network[-1])
for i, output_neuron in enumerate(network[-1]):
for j, hidden_output in enumerate(hidden_outputs + [1]):
output_neuron[j] -= output_deltas[i] * hidden_output
hidden_deltas = [hidden_output * (1 - hidden_output) *
algebra.dot(output_deltas, [n[i] for n in network[1]])
for i, hidden_output in enumerate(hidden_outputs)]
for i, hidden_neuron in enumerate(network[0]):
for j, input in enumerate(input_vector + 1):
hidden_neuron[j] -= hidden_deltas[i] * input
def backpropogate(network, input_vector, target):
hidden_outputs, outputs = feed_forward(network, input_vector)
# the output * (1 - output) is from the derivative of sigmoid
output_deltas = [
output * (1 - output) * (output - target[i])
for i, output in enumerate(outputs)
]
# adjust weights for output layer (network[-1])
for i, output_neuron in enumerate(network[-1]):
for j, hidden_output in enumerate(hidden_outputs + [1]):
output_neuron[j] -= output_deltas[i] * hidden_output
hidden_deltas = [
hidden_output * (1 - hidden_output) *
algebra.dot(output_deltas, [n[i] for n in network[1]])
for i, hidden_output in enumerate(hidden_outputs)
]
for i, hidden_neuron in enumerate(network[0]):
for j, input in enumerate(input_vector + 1):
hidden_neuron[j] -= hidden_deltas[i] * input
def directional_variance_gradient_i(x_i, w):
"""the contribution of row x_i
to the gradient of the direction-w variance"""
projection_length = algebra.dot(x_i, direction(w))
return [2 * projection_length * x_ij for x_ij in x_i]
def covariance(x, y):
"""how variables vary in tandem from their means"""
n = len(x)
return algebra.dot(de_mean(x), de_mean(y)) / (n - 1)
def directional_variance_i(x_i, w):
"""the variance of the row x_i in the direction determined by w"""
return algebra.dot(x_i, direction(w)) ** 2
def logistic_log_partial_ij(x_i, y_i, beta, j):
"""i is the index of the data point, j is the index
of the derivative"""
return (y_i - logistic(algebra.dot(x_i, beta))) * x_i[j]
def logistic_log_likelihood_i(x_i, y_i, beta):
if y_i == 1:
return math.log(logistic(algebra.dot(x_i, beta)))
else:
return math.log(1 - logistic(algebra.dot(x_i, beta)))
def logistic_log_partial_ij(x_i, y_i, beta, j):
"""i is the index of the data point, j is the index
of the derivative"""
return (y_i - logistic(algebra.dot(x_i, beta))) * x_i[j]
def logistic_log_likelihood_i(x_i, y_i, beta):
if y_i == 1:
return math.log(logistic(algebra.dot(x_i, beta)))
else:
return math.log(1 - logistic(algebra.dot(x_i, beta)))
def perceptron_output(weights, bias, x):
"""returns 1 if the perceptron 'fires'; 0 if not"""
return step_function(algebra.dot(weights, x) + bias)
def directional_variance_i(x_i, w):
"""the variance of the row x_i in the direction determined by w"""
return algebra.dot(x_i, direction(w)) ** 2
def neuron_output(weights, inputs):
return sigmoid(algebra.dot(weights, inputs))
def predict(x_i, beta):
"""assumes that the first element of each x_i is 1"""
return dot(x_i, beta)
def predict(x_i, beta):
"""assumes that the first element of each x_i is 1"""
return dot(x_i, beta)
def ridge_penalty(beta, alpha):
"""alpha is a hyper-parameter controlling how harsh the penalty
is; sometimes called 'lambda' but that is already a Python keyword"""
return alpha * algebra.dot(beta[1:], beta[1:])
def perceptron_output(weights, bias, x):
"""returns 1 if the perceptron 'fires'; 0 if not"""
return step_function(algebra.dot(weights, x) + bias)
def covariance(xs: List[float], ys: List[float]) -> float:
assert len(xs) == len(ys)
return dot((de_mean(xs), de_mean(ys) / (len(xs) - 1)))
def directional_variance_gradient_i(x_i, w):
"""the contribution of row x_i
to the gradient of the direction-w variance"""
projection_length = algebra.dot(x_i, direction(w))
return [2 * projection_length * x_ij for x_ij in x_i]
def ridge_penalty(beta, alpha):
"""alpha is a hyper-parameter controlling how harsh the penalty
is; sometimes called 'lambda' but that is already a Python keyword"""
return alpha * algebra.dot(beta[1:], beta[1:])
def neuron_output(weights, inputs):
return sigmoid(algebra.dot(weights, inputs))
