def average_slope_intercept(lines):
left_lines = [] # (slope, intercept)
left_weights = [] # (length,)
right_lines = [] # (slope, intercept)
right_weights = [] # (length,)
for line in lines:
for x1, y1, x2, y2 in line:
if x2 == x1:
continue # ignore a vertical line
slope = (y2 - y1) / (x2 - x1)
intercept = y1 - slope * x1
length = np.sqrt((y2 - y1)**2 + (x2 - x1)**2)
if slope < 0: # y is reversed in image
left_lines.append((slope, intercept))
left_weights.append((length))
else:
right_lines.append((slope, intercept))
right_weights.append((length))
# add more weight to longer lines
left_lane = np.dot(left_weights, left_lines) / np.sum(left_weights) if len(
left_weights) > 0 else None
right_lane = np.dot(right_weights, right_lines) / np.sum(
right_weights) if len(right_weights) > 0 else None
return left_lane, right_lane # (slope, intercept), (slope, intercept)
def train(self, X, y, learning_rate = 0.01, update_size = None): assert len(np.shape(X)) == 2, "Invalid input shape. The input must be 2d (batch, input_dim)" batch_size, input_dim = np.shape(X) assert self.input_dim == input_dim, "Unmatch input_dim." X = np.column_stack((X, np.ones((batch_size, 1)))) y = y.reshape((-1, self.output_dim)) if self.updateMethod == "closed-form": # check whether the matrix can be inversed assert np.linalg.det(X) != 0, "This matrix cann't be inversed." # update the parameters self.w = np.linalg.inv(np.dot(X.T, X)) self.w = np.dot(self.w, X.T) self.w = np.dot(self.w, y) # predict under the train set Y_predict = np.dot(X, self.w) # calculate the absolute differences loss_train = np.average(np.abs(Y_predict - y)) return Y_predict, loss_train
def reflection_matrix(point, normal):
"""Return matrix to mirror at plane
defined by point and normal vector.
>>> v0 = np.random.random(4) - 0.5
>>> v0[3] = 1.
>>> v1 = np.random.random(3) - 0.5
>>> R = reflection_matrix(v0, v1)
>>> np.allclose(2, np.trace(R))
True
>>> np.allclose(v0, np.dot(R, v0))
True
>>> v2 = v0.copy()
>>> v2[:3] += v1
>>> v3 = v0.copy()
>>> v2[:3] -= v1
>>> np.allclose(v2, np.dot(R, v3))
True
"""
normal = unit_vector(normal[:3])
M = np.identity(4)
M[:3, :3] -= 2.0 * np.outer(normal, normal)
M[:3, 3] = (2.0 * np.dot(point[:3], normal)) * normal
return M
def train_weights(self):
self.patterns = 2 * self.patterns - 1
w_values = np.dot(self.patterns.T, self.patterns)
for i in range(w_values.shape[0]):
w_values[i,i] = 0
self.W = w_values
def computeCost(mytheta,X,y): #Cost function
"""
theta_start is an n- dimensional vector of initial theta guess
X is matrix with n- columns and m- rows
y is a matrix with m- rows and 1 column
"""
#note to self: *.shape is (rows, columns)
return float((1./(2*m)) * np.dot((h(mytheta,X)-y).T,(h(mytheta,X)-y)))
def predict(self, X): assert len(np.shape(X)) == 2, "Invalid input shape. The input must be 2d (batch, input_dim)" batch_size, input_dim = np.shape(X) assert self.input_dim == input_dim, "Unmatch input_dim." X = np.column_stack((X, np.ones((batch_size, 1)))) y_predict = np.dot(X, self.w) return y_predict
def updateLayer(layer, otherLayerValues, biases, weights, activationFun,
binary=False):
bias = biases[layer]
size = otherLayerValues.shape[0]
if layer == Layer.VISIBLE:
activation = np.dot(otherLayerValues, weights.T)
else:
activation = np.dot(otherLayerValues, weights)
probs = activationFun(np.tile(bias, (size, 1)) + activation)
if binary:
# Sample from the distributions
return sampleAll(probs)
return probs
def modelAndDataSampleDiffs(batchData, biases, weights, activationFun,
dropout, cdSteps):
# Reconstruct the hidden weigs from the data
hidden = updateLayer(Layer.HIDDEN, batchData, biases, weights, activationFun,
binary=True)
# Chose the units to be active at this point
# different sets for each element in the mini batches
on = sample(dropout, hidden.shape)
dropoutHidden = on * hidden
hiddenReconstruction = dropoutHidden
for i in xrange(cdSteps - 1):
visibleReconstruction = updateLayer(Layer.VISIBLE, hiddenReconstruction,
biases, weights, activationFun,
binary=False)
hiddenReconstruction = updateLayer(Layer.HIDDEN, visibleReconstruction,
biases, weights, activationFun,
binary=True)
# sample the hidden units active (for dropout)
hiddenReconstruction = hiddenReconstruction * on
# Do the last reconstruction from the probabilities in the last phase
visibleReconstruction = updateLayer(Layer.VISIBLE, hiddenReconstruction,
biases, weights, activationFun,
binary=False)
hiddenReconstruction = updateLayer(Layer.HIDDEN, visibleReconstruction,
biases, weights, activationFun,
binary=False)
hiddenReconstruction = hiddenReconstruction * on
# here it should be hidden * on - hiddenreconstruction
# also below in the hidden bias
weightsDiff = np.dot(batchData.T, dropoutHidden) -\
np.dot(visibleReconstruction.T, hiddenReconstruction)
assert weightsDiff.shape == weights.shape
visibleBiasDiff = np.sum(batchData - visibleReconstruction, axis=0)
assert visibleBiasDiff.shape == biases[0].shape
hiddenBiasDiff = np.sum(dropoutHidden - hiddenReconstruction, axis=0)
assert hiddenBiasDiff.shape == biases[1].shape
return weightsDiff, visibleBiasDiff, hiddenBiasDiff
def modelAndDataSampleDiffsPCD(batchData, biases, weights, activationFun,
dropout, steps, fantasyParticles):
# Reconstruct the hidden weigs from the data
hidden = updateLayer(Layer.HIDDEN, batchData, biases, weights, activationFun,
binary=True)
# Chose the units to be active at this point
# different sets for each element in the mini batches
# on = sample(dropout, hidden.shape)
# dropoutHidden = on * hidden
# hiddenReconstruction = dropoutHidden
for i in xrange(steps):
visibleReconstruction = updateLayer(Layer.VISIBLE, fantasyParticles[1],
biases, weights, activationFun,
binary=False)
hiddenReconstruction = updateLayer(Layer.HIDDEN, visibleReconstruction,
biases, weights, activationFun,
binary=True)
# sample the hidden units active (for dropout)
# hiddenReconstruction = hiddenReconstruction * on
fantasyParticles = (visibleReconstruction, hiddenReconstruction)
# here it should be hidden * on - hiddenReconstruction
# also below in the hidden bias
weightsDiff = np.dot(batchData.T, hidden) -\
np.dot(visibleReconstruction.T, hiddenReconstruction)
assert weightsDiff.shape == weights.shape
visibleBiasDiff = np.sum(batchData - visibleReconstruction, axis=0)
assert visibleBiasDiff.shape == biases[0].shape
hiddenBiasDiff = np.sum(hidden - hiddenReconstruction, axis=0)
assert hiddenBiasDiff.shape == biases[1].shape
return weightsDiff, visibleBiasDiff, hiddenBiasDiff, fantasyParticles
def train(training_inputs, yd, training_iterations):
w = np.random.randn(2, 1)
# w = np.array([[3.0],[1.0]])
for iteration in range(training_iterations):
# 得到輸出
y = sigmoid(np.dot(training_inputs, w))
# 計算誤差
error = yd - y
# 微調權重( x 與 e*sigmoid_derivative )
adjustments = np.dot(training_inputs.T, error * sigmoid_derivative(y))
w += learning_rate * adjustments
fig = plt.figure()
ax = plt.subplot()
# ax=fig.add_axes([0, 0, 5, 5])
plt.figure(figsize=(10, 7))
# plt.plot(x_train.data.numpy(),y_train.data.numpy(),'*')
plt.scatter(x[:, 0], yd, s=100, alpha=0.3)
xs = np.linspace(0, 70, 200)
ys2 = w[1] + w[0] * xs
plt.plot(xs, ys2, 'g', linewidth=1)
plt.show()
return w
def forward_kinematics(l1, l2, l3, q1, q2, q3, q4):
# create inital transformation matricies relateing each joint position to the global fram
# global frame is the center of the robot
# T is a 4x4 transformation matrix
# T(1:3,1:3) is a rotation matrix
# T(1:3,4) is the x,y,z position of the frame
# i.e if i want the x position of the second joint it is T(1,4), y position is T(2,4)
# T(4,:) is used for scaleing and remains at 0 0 0 1 for no scaleing
T10 = dh(q1, 0, 0, pi / 2) # Base rotation relative to global frame
T21 = dh(
q2, 0, l1,
0) # frame of reference at the end of the first link, relative to Base
T32 = dh(q3, 0, l2, 0) # second link end relative to first link
T43 = dh(
q4, 0, l3, 0
) # end effector relative to second link, ca nbe considered a third link
T20 = np.dot(T10, T21)
T30 = np.dot(T20, T32)
T40 = np.dot(T30, T43)
# Create matrix where each row is a joint position, i.e
# joint positions = [x1 y1 z1
# x2 y2 z2]
# assume 0 index notation
# T10=numpy.transpose(T10)
# print(T10)
# print(T20)
p_joints = [T10[0:3, 3], T20[0:3, 3], T30[0:3, 3], T40[0:3, 3]]
p_joints = np.transpose(p_joints)
return p_joints
def recall(self, input, update_order):
self.no_nodes = self.W.shape[0]
no_stable_nodes = 0
for i in update_order:
if no_stable_nodes == self.no_nodes:
break
else:
new_node = step(np.dot(self.W[:,i], input))
if input[i] == new_node:
no_stable_nodes += 1
else:
no_stable_nodes = 0
input[i] = new_node
return input
def unit_vector(data, axis=None, out=None):
"""Return ndarray normalized by length,
i.e. Euclidean norm, along axis.
>>> v0 = np.random.random(3)
>>> v1 = unit_vector(v0)
>>> np.allclose(v1, v0 / np.linalg.norm(v0))
True
>>> v0 = np.random.rand(5, 4, 3)
>>> v1 = unit_vector(v0, axis=-1)
>>> v2 = v0 / np.expand_dims(np.sqrt(np.sum(v0*v0, axis=2)), 2)
>>> np.allclose(v1, v2)
True
>>> v1 = unit_vector(v0, axis=1)
>>> v2 = v0 / np.expand_dims(np.sqrt(np.sum(v0*v0, axis=1)), 1)
>>> np.allclose(v1, v2)
True
>>> v1 = np.empty((5, 4, 3))
>>> unit_vector(v0, axis=1, out=v1)
>>> np.allclose(v1, v2)
True
>>> list(unit_vector([]))
[]
>>> list(unit_vector([1]))
[1.0]
"""
if out is None:
data = np.array(data, dtype=np.float64, copy=True)
if data.ndim == 1:
data /= np.sqrt(np.dot(data, data))
return data
else:
if out is not data:
out[:] = np.array(data, copy=False)
data = out
length = np.atleast_1d(np.sum(data * data, axis))
np.sqrt(length, length)
if axis is not None:
length = np.expand_dims(length, axis)
data /= length
if out is None:
return data
class Linear_Regression(Model): def __init__(self, arg): self.input_dim = arg["input_dim"] self.output_dim = arg["output_dim"] self.w = np.random.normal(1, 1, size=(self.input_dim + 1, self.output_dim)) self.updateMethod = arg["update"].lower() if "update" in arg else "sgd" def train(self, X, y, learning_rate = 0.01, update_size = None): assert len(np.shape(X)) == 2, "Invalid input shape. The input must be 2d (batch, input_dim)" batch_size, input_dim = np.shape(X) assert self.input_dim == input_dim, "Unmatch input_dim." X = np.column_stack((X, np.ones((batch_size, 1)))) y = y.reshape((-1, self.output_dim)) if self.updateMethod == "closed-form": # check whether the matrix can be inversed assert np.linalg.det(X) != 0, "This matrix cann't be inversed." # update the parameters self.w = np.linalg.inv(np.dot(X.T, X)) self.w = np.dot(self.w, X.T) self.w = np.dot(self.w, y) # predict under the train set Y_predict = np.dot(X, self.w) # calculate the absolute differences loss_train = np.average(np.abs(Y_predict - y)) return Y_predict, loss_train elif self.updateMethod.lower == "sgd": if update_size == None: update_size = batch_size assert update_size <= batch_size, "Update size lager than batch size!" y_predict = np.dot(X, self.w) diff = y_predict - y
Y_predict = np.dot(X, self.w) # calculate the absolute differences loss_train = np.average(np.abs(Y_predict - y)) return Y_predict, loss_train elif self.updateMethod.lower == "sgd": if update_size == None: update_size = batch_size assert update_size <= batch_size, "Update size lager than batch size!" y_predict = np.dot(X, self.w) diff = y_predict - y randind = np.random.randint(0,X.shape[0]-1, size=update_size) # calculate the gradient G = -np.dot(X[randind].T.reshape(-1, update_size), y[randind].reshape(update_size, -1)) G += np.dot(X[randind].T.reshape(-1, update_size), X[randind].reshape(update_size, -1)).dot(self.w) G = -G # update the parameters self.w += learning_rate * G y_predict_selected = np.dot(X[randind], self.w) loss_train = np.average(np.abs(y_predict_selected - y[randind])) return y_predict, loss_train def predict(self, X): assert len(np.shape(X)) == 2, "Invalid input shape. The input must be 2d (batch, input_dim)" batch_size, input_dim = np.shape(X) assert self.input_dim == input_dim, "Unmatch input_dim."
def my_action(self, img):
img_np = np.array(img)
b = np.dot(img_np, 0.5, np=int)
# cv.imshow('original', img)
return b
def fabrik(l1, l2, l3, x_prev, y_prev, z_prev, x_command, y_command, z_command,
tol_limit, max_iterations):
# Base rotation is simply based on angle made within the x-y plane
q1_prev = np.arctan2(y_prev[3], x_prev[3])
q1 = np.arctan2(y_command, x_command)
base_rotation = q1 - q1_prev # this is the rotation the base must make to get from initial position to the commanded position
# Base rotation matrix about z
R_z = np.array([[np.cos(base_rotation), -np.sin(base_rotation), 0.0],
[np.sin(base_rotation),
np.cos(base_rotation), 0.0], [0.0, 0.0, 1.0]])
# Rotate the location of each joint by the base rotation
# This will force the FABRIK algorithim to only solve
# in two dimensions, else each joint will move as if it has
# a 3 DOF range of motion
# print 'inside the fabrik method and x_joints is'
# print x_joints
p4 = np.dot(R_z, [x_prev[3], y_prev[3], z_prev[3]])
p3 = np.dot(R_z, [x_prev[2], y_prev[2], z_prev[2]])
p2 = np.dot(R_z, [x_prev[1], y_prev[1], z_prev[1]])
p1 = np.dot(R_z, [x_prev[0], y_prev[0], z_prev[0]])
# Store the (x,y,z) position of each joint
p4x = p4[0]
p4y = p4[1]
p4z = p4[2]
p3x = p3[0]
p3y = p3[1]
p3z = p3[2]
p2x = p2[0]
p2y = p2[1]
p2z = p2[2]
p1x = p1[0]
p1y = p1[1]
p1z = p1[2]
# Starting point of each joint
p1x_o = p1x
p1y_o = p1y
p1z_o = p1z
iterations = 0
for j in range(1, max_iterations + 1):
if np.sqrt(
np.power(x_command, 2) + np.power(y_command, 2) +
np.power(z_command, 2)) > (l1 + l2 + l3):
print(' desired point is likely out of reach')
[p3x, p3y, p3z] = project_along_vector(x_command, y_command, z_command,
p3x, p3y, p3z, l3)
[p2x, p2y, p2z] = project_along_vector(p3x, p3y, p3z, p2x, p2y, p2z,
l2)
[p1x, p1y, p1z] = project_along_vector(p2x, p2y, p2z, p1x, p1y, p1z,
l1)
[p2x, p2y, p2z] = project_along_vector(p1x_o, p1y_o, p1z_o, p2x, p2y,
p2z, l1)
[p3x, p3y, p3z] = project_along_vector(p2x, p2y, p2z, p3x, p3y, p3z,
l2)
[p4x, p4y, p4z] = project_along_vector(p3x, p3y, p3z, x_command,
y_command, z_command, l3)
# check how close FABRIK position is to command position
tolx = p4x - x_command
toly = p4y - y_command
tolz = p4z - z_command
tol = np.sqrt(
np.power(tolx, 2) + np.power(toly, 2) + np.power(tolz, 2))
iterations = iterations + 1
# Check if tolerance is within the specefied limit
# Re-organize points into a big matrix for plotting elsewhere
p_joints = np.array([[p1x, p2x, p3x, p4x], [p1y, p2y, p3y, p4y],
[p1z, p2z, p3z, p4z]])
v21 = np.array([p2x - p1x, p2y - p1y, p2z - p1z])
v32 = np.array([p3x - p2x, p3y - p2y, p3z - p2z])
v43 = np.array([p4x - p3x, p4y - p3y, p4z - p3z])
q2 = np.arctan2(
(p2z - p1z),
np.sqrt(np.power(p2x - p1x, 2) + np.power(p2y - p1y, 2)))
q3 = -1 * angle_from_dot_product(v21, v32)
q4 = -1 * angle_from_dot_product(v32, v43)
q_joints = np.array([q1, q2, q3, q4])
return q_joints
import np as np
import numpy as np
from numpy.linalg import inv
# 1 Write a NumPy program to compute the multiplication of two given matrixes
x = [[1, 2], [5, 6]]
y = [[4, 5], [9, 5]]
print("original:")
print(x)
print(y)
result = np.dot(x, y)
print("Multiplication:")
print(result, "\n")
# 2Write a NumPy program to compute the determinant of an array
x = np.array([[1, 2], [3, 4]])
print("original arr:")
print(x)
result = np.linalg.det(x)
print("determinant:")
print(result, '\n')
# 3 Write a NumPy program to compute the sum of the diagonal element of a given array
x = np.array([[2, 4, 5], [8, 9, 10], [12, 15, 16]])
print(x, "matrix:")
diag = np.diagonal(x)
print("\nDiagonal matrix:")
print(diag)
print("\nSum of diagonal matrix:")
print(sum(diag))
from django.test import TestCase
import np
# Create your tests here.
X = np.array([[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1]])
y = np.array([[0, 1, 1, 0]]).T
syn0 = 2 * np.random.random((3, 4)) - 1
syn1 = 2 * np.random.random((4, 1)) - 1
for j in xrange(60000):
l1 = 1 / (1 + np.exp(-(np.dot(X, syn0))))
l2 = 1 / (1 + np.exp(-(np.dot(l1, syn1))))
l2_delta = (y - l2) * (l2 * (1 - l2))
l1_delta = l2_delta.dot(syn1.T) * (l1 * (1 - l1))
syn1 += l1.T.dot(l2_delta)
syn0 += X.T.dot(l1_delta)
def h(theta,X): #Linear hypothesis function
return np.dot(X,theta)
