def rotate(q, vec):
i = conjugate(q)
p = [0, vec[0], vec[1], vec[2]]
# [w, v] = [q] * [p] = [a, b] * [c, d]
a = q[0]
b = [q[1], q[2], q[3]]
c = p[0]
d = [p[1], p[2], p[3]]
w = a * c - matrix.innerProduct(b, d)
v = matrix.crossProduct(b, d)
v = matrix.add(v, matrix.scalarProduct(a, d))
v = matrix.add(v, matrix.scalarProduct(c, b))
# # [s, t] = [w, v] * [i[0], [i[1], i[2], i[3]]] = [w, v] * [j, k]
j = i[0]
k = [i[1], i[2], i[3]]
s = w * j - matrix.innerProduct(v, k)
t = matrix.crossProduct(v, k)
t = matrix.add(t, matrix.scalarProduct(w, k))
t = matrix.add(t, matrix.scalarProduct(j, v))
return [s, t[0], t[1], t[2]]
def solve(m, bs, p):
"""
Solve a triangularized linear system, writing the solutions to bs, p being the number of variables.
Returns False if there are no solutions.
"""
for i in range(len(m) - 1, -1, -1):
z = first_nonzero(m[i])
if z > p:
continue
elif z == p:
return False
bs[z][0] = m[i][p]
for j in range(z+1, p):
matrix.add(bs, z, -m[i][j], j)
matrix.mult(bs, z, 1.0/m[i][z])
return True
def main():
P = [[40], [40]]
V0 = [[30], [30]]
V1 = [[40], [70]]
V2 = [[50], [30]]
points = [V0, V1, V2]
aspect_correct = [[1, 0], [0, 4 / 7]]
home = "\N{escape}[H"
wakeup_time = time.time()
print(home + "\N{escape}[J\N{escape}[?25l")
t = 0
try:
while True:
kanvas = canvas.Canvas()
rot = matrix.rotate_2D(t * 0.5)
r_points = []
for point in points:
C = matrix.sub(point, P)
C = matrix.mult(rot, C)
C = matrix.add(P, C)
C = matrix.mult(aspect_correct, C)
r_points.append(C)
t += 1
kanvas.triangle(round(r_points[0][0][0]), round(r_points[0][1][0]),
round(r_points[1][0][0]), round(r_points[1][1][0]),
round(r_points[2][0][0]), round(r_points[2][1][0]))
image = home + kanvas.get_image()
print(image)
wakeup_time += 0.05
time.sleep(max(0, wakeup_time - time.time()))
finally:
print(home + "\N{escape}[J \N{escape}[?25h")
def draw_everything(self):
super(PygameInterpreter, self).draw_everything()
#~ if self.waiting and self.darkening < self.DARKENING_MAX:
#~ self.darkening += self.DARKENING_INC
#~
#~ # black filter behind text
#~ black = pygame.Surface(self.resolution)
#~ black.set_alpha(self.darkening)
#~ self._surface.blit( black, (0, 0) )
# text display
for topleft, s in self.text:
text_size = self.font.size(s)
text_area = pygame.Rect(topleft, text_size)
# once in black, to outline it
outline_topleft = matrix.add(topleft, [1, 1])
text = self.font.render(s, True, self.colors[OUTLINE_COLOR])
self._surface.blit( text, outline_topleft )
# and once normally
text = self.font.render(s, True, self.colors[TEXT_COLOR])
self._surface.blit( text, topleft )
def draw_offset_mult(offset, blend, mult, mask):
for y in range(min(f.height, pic.size[1])):
for x in range(min(f.width, pic.size[0])):
pix = matrix.add(
matrix.cmultiply(matrix.multiply(pic.getpixel((x + offset, y))[:3], mult * (1-blend)), mask),
matrix.cmultiply(matrix.multiply(pic.getpixel((x + offset + 1, y))[:3], mult * blend), mask)
)
f.point(x, y, pix)
def main():
P = [[40],
[40],
[0]]
Axis = [[10],
[5],
[3]]
# V0 = [[30],
# [30],
# [0]]
# V1 = [[40],
# [70],
# [0]]
# V2 = [[50],
# [30],
# [0]]
# points = [V0, V1, V2]
points = []
for i in range(15):
points.append([[random.randint(20, 60)],
[random.randint(30, 60)],
[random.randint(-20, 20)]])
aspect_correct = [[1, 0, 0],
[0, 4/7, 0],
[0, 0, 1]]
home = "\N{escape}[H"
wakeup_time = time.time()
print(home + "\N{escape}[J\N{escape}[?25l")
t = 0
try:
while True:
kanvas = canvas.Canvas()
rot = matrix.rotate_3D(t * 0.1, Axis)
r_points = []
for point in points:
C = matrix.sub(point, P)
C = matrix.mult(rot, C)
C = matrix.add(P, C)
C = matrix.mult(aspect_correct, C)
r_points.append(C)
t += 1
for r_point in r_points:
kanvas.dab(round(r_point[0][0]),
round(r_point[1][0]))
# kanvas.triangle(round(r_points[0][0][0]),
# round(r_points[0][1][0]),
# round(r_points[1][0][0]),
# round(r_points[1][1][0]),
# round(r_points[2][0][0]),
# round(r_points[2][1][0]))
image = home + kanvas.get_image()
print(image)
wakeup_time += 0.05
time.sleep(max(0, wakeup_time - time.time()))
finally:
print(home + "\N{escape}[J \N{escape}[?25h")
def remove(m, x, y):
"""
Remove the x-eme element in lines ]y,end[
Returns false if it was already removed
"""
piv = None
for j in range(y, len(m)):
if is_zero(m[j][x]):
continue
if not piv:
piv = m[j][x]
if j != y:
matrix.swap(m, j, y)
continue
matrix.add(m, j, -m[j][x]/piv, y)
if piv:
return True
else:
return False
def add_word(self, s):
needed = self.font.size(s)[0]
if needed > self.remaining_row:
self._next_line()
topleft = self.get_pixelpos(self.linenumber, self.remaining_row)
topleft = matrix.add(topleft, self.text_topleft)
self.text.append( (topleft, s) )
self.remaining_row -= needed
def add_word(self, s):
needed = self.font.size(s)[0]
if needed > self.remaining_row:
self._next_line()
topleft = self.get_pixelpos(self.linenumber, self.remaining_row)
topleft = matrix.add(topleft, self.text_topleft)
self.text.append((topleft, s))
self.remaining_row -= needed
def draw_everything(self):
super(PygameInterpreter, self).draw_everything()
#~ if self.waiting and self.darkening < self.DARKENING_MAX:
#~ self.darkening += self.DARKENING_INC
#~
#~ # black filter behind text
#~ black = pygame.Surface(self.resolution)
#~ black.set_alpha(self.darkening)
#~ self._surface.blit( black, (0, 0) )
# text display
for topleft, s in self.text:
text_size = self.font.size(s)
text_area = pygame.Rect(topleft, text_size)
# once in black, to outline it
outline_topleft = matrix.add(topleft, [1, 1])
text = self.font.render(s, True, self.colors[OUTLINE_COLOR])
self._surface.blit(text, outline_topleft)
# and once normally
text = self.font.render(s, True, self.colors[TEXT_COLOR])
self._surface.blit(text, topleft)
def main(x, hidden, b, learning, test, w, g, n_d):
random.seed(1)
training_data = x[:]
noise_data = n_d[:]
# Adding bias to training data
training_data.append([])
noise_data.append([])
for _ in x[0]:
training_data[1].append(b)
noise_data[1].append(b)
# Random weights for synapses
synapses0 = []
synapses1 = []
for _ in range(hidden):
synapses0.append([random.uniform(w, -w), random.uniform(w, -w)]) # second rand for bias synapses
for j in range(hidden + 1): # +1 for bias
synapses1.append([random.uniform(w, -w)])
sig_layer2 = []
global loading_message
global loading_progress
# learning loop (learning = iterations)
for i in xrange(learning):
temp = i+1
loading_progress = round((float(temp) / float(iterations)) * 100, 1)
# loading_progress = (temp / learning) * 100
# # # Forward pass
# # Input Layer
layer1 = matrix.multiply(synapses0, training_data)
# Activation level
sig_layer1 = matrix.sig(layer1)
# # Hidden Layer
# Adding bias to layer1
b_sig_layer1 = sig_layer1[:]
b_sig_layer1.append([])
for _ in b_sig_layer1[0]:
b_sig_layer1[len(b_sig_layer1) - 1].append(b)
layer2 = matrix.multiply(matrix.transpose(synapses1), b_sig_layer1)
sig_layer2 = matrix.sig(layer2)
# Calculate net error
error = [matrix.subtract(test, matrix.transpose(sig_layer2))]
# if i % 25000 == 0:
# temp = 0
# for j in range(len(error)):
# temp += temp + error[0][j]
# print i, temp
# Delta for neuron in output layer (1 for each training data)
deriv_sig_layer2 = matrix.derivative(sig_layer2)
delta_layer2 = [[]]
for j in range(len(error[0])):
delta_layer2[0].append(deriv_sig_layer2[0][j] * error[0][j] * g)
# Delta for neurons in hidden layer
deriv_sig_layer1 = matrix.derivative(sig_layer1)
delta_layer1 = []
delta_weight_sum = []
for k in range(len(synapses1)):
delta_weight_sum.append([])
for j in range(len(delta_layer2[0])):
delta_weight_sum[k].append(synapses1[k][0] * delta_layer2[0][j])
for k in range(len(deriv_sig_layer1)):
delta_layer1.append([])
for j in range(len(deriv_sig_layer1[0])):
delta_layer1[k].append(deriv_sig_layer1[k][j] * delta_weight_sum[k][j] * g)
delta_w_oh = matrix.multiply(delta_layer2, matrix.transpose(b_sig_layer1))
delta_w_hi = matrix.multiply(delta_layer1, matrix.transpose(training_data))
# # Update weights
synapses1 = matrix.add(synapses1, matrix.transpose(delta_w_oh))
synapses0 = matrix.add(synapses0, delta_w_hi)
if i > learning * 0.5:
if i > learning * 0.95:
loading_message = "I'm nearly done, good training."
else:
loading_message = "Well, I'm halfway through."
# Testing net with noised data
sig_noise = []
if len(n_d) > 0:
# print "testing with noise data"
l1 = matrix.multiply(synapses0, noise_data)
sig_l1 = matrix.sig(l1)
b_sig_l1 = sig_l1[:]
b_sig_l1.append([])
for _ in b_sig_l1[0]:
b_sig_l1[len(b_sig_l1) - 1].append(b)
l2 = matrix.multiply(matrix.transpose(synapses1), b_sig_l1)
sig_noise = matrix.sig(l2)
# formatting net output for plot
result1 = [] # training data
result2 = [] # noised data
for i in range(len(sig_layer2[0])):
result1.append(sig_layer2[0][i] * 2 - 1)
result2.append(sig_noise[0][i] * 2 - 1)
# Plot
# Some code lines from: https://matplotlib.org/users/legend_guide.html
neuron_patch = mpatches.Patch(label='Neurons: ' + str(hidden))
bias_patch = mpatches.Patch(label='Bias: ' + str(b))
iteration_patch = mpatches.Patch(label='Iterations: ' + str(learning))
epsilon_patch = mpatches.Patch(label='Epsilon: ' + str(g))
weight_patch = mpatches.Patch(label='Weight range (0 +/-): ' + str(w))
time_patch = mpatches.Patch(label=str(round((time.time() - start_time) / 60, 2)) + " min")
first_legend = plt.legend(
handles=[bias_patch, time_patch, epsilon_patch, neuron_patch, iteration_patch, weight_patch],
bbox_to_anchor=(0., 1.02, 1., .102), loc=3,
ncol=3, mode="expand", borderaxespad=0.)
line1, = plt.plot(inputData[0], result1, label="Training Data", linewidth=0.75)
line2, = plt.plot(inputData[0], result2, label="Test Data", linestyle=':', linewidth=0.75)
line3, = plt.plot(x_data, y_data, label="sin(x)", linestyle='--', linewidth=0.75)
ax = plt.gca().add_artist(first_legend)
plt.legend(handles=[line1, line2, line3])
plt.savefig('./plots/plot' + str(time.time())[2:10] + '.png')
plt.clf()
plt.cla()
plt.close()
def main(x, hidden, b, epochs, test, w, g, n_d, m, p_m):
random.seed(1)
training_data = x[:]
noise_data = n_d[:]
# Adding bias to training data
training_data.append([])
noise_data.append([])
for _ in x[0]:
training_data[len(training_data)-1].append(b)
noise_data[len(noise_data)-1].append(b)
# Random weights for synapses
synapses0 = []
synapses1 = []
for f in range(hidden):
synapses0.append([])
for _ in range(len(training_data)):
synapses0[f].append(random.uniform(w, -w)) # second rand for bias synapses
for j in range(hidden + 1): # +1 for bias
synapses1.append([random.uniform(w, -w)])
sig_layer2 = []
error_log = []
error_log2 = []
gamma_log = []
global loading_message
global loading_progress
# learning loop (learning = iterations)
for i in xrange(epochs):
loading_progress = round((float(i) / float(iterations)) * 100, 1)
# # # Forward pass
# # Input Layer
layer1 = matrix.multiply(synapses0, training_data)
# Activation level
sig_layer1 = matrix.sig(layer1)
# # Hidden Layer
# Adding bias to layer1
b_sig_layer1 = sig_layer1[:]
b_sig_layer1.append([])
for _ in b_sig_layer1[0]:
b_sig_layer1[len(b_sig_layer1) - 1].append(b)
layer2 = matrix.multiply(matrix.transpose(synapses1), b_sig_layer1)
sig_layer2 = matrix.sig(layer2)
# # # ----------------
# # Calculate net error
error = [matrix.subtract(test, matrix.transpose(sig_layer2))]
# error = [matrix.error(test, matrix.transpose(sig_layer2))]
# if i % 5000 == 0:
# print(error)
temp = 0
for j in range(len(error)):
temp += temp + error[0][j]
error_log.append(temp/len(error))
# Test with test data
sig_noise = []
l1 = matrix.multiply(synapses0, noise_data)
sig_l1 = matrix.sig(l1)
b_sig_l1 = sig_l1[:]
b_sig_l1.append([])
for _ in b_sig_l1[0]:
b_sig_l1[len(b_sig_l1) - 1].append(b)
l2 = matrix.multiply(matrix.transpose(synapses1), b_sig_l1)
sig_noise = matrix.sig(l2)
error2 = [matrix.subtract(test, matrix.transpose(sig_noise))]
temp2 = 0
for j in range(len(error2)):
temp2 += temp2 + error2[0][j]
error_log2.append(temp2 / len(error2))
# # # ----------------
# # Calculating weight updates
# Delta for neuron in output layer (1 for each training data)
deriv_sig_layer2 = matrix.derivative(sig_layer2)
delta_layer2 = [[]]
# temp_g = (g/(i+1))
# gamma_log.append(temp_g)
for j in range(len(error[0])):
delta_layer2[0].append(deriv_sig_layer2[0][j] * error[0][j] * g)
# Delta for neurons in hidden layer
deriv_sig_layer1 = matrix.derivative(sig_layer1)
delta_layer1 = []
delta_weight_sum = []
for k in range(len(synapses1)):
delta_weight_sum.append([])
for j in range(len(delta_layer2[0])):
delta_weight_sum[k].append(synapses1[k][0] * delta_layer2[0][j])
for k in range(len(deriv_sig_layer1)):
delta_layer1.append([])
for j in range(len(deriv_sig_layer1[0])):
delta_layer1[k].append(deriv_sig_layer1[k][j] * delta_weight_sum[k][j] * g)
delta_w_oh = matrix.multiply(delta_layer2, matrix.transpose(b_sig_layer1))
delta_w_hi = matrix.multiply(delta_layer1, matrix.transpose(training_data))
# # # Backwards pass
# # Update weights
synapses1 = matrix.add(synapses1, matrix.transpose(delta_w_oh))
synapses0 = matrix.add(synapses0, delta_w_hi)
if i > epochs * 0.5:
if i > epochs * 0.95:
loading_message = "I'm nearly done, good training."
else:
loading_message = "Well, I'm halfway through."
# # # End of learning
# Testing net with noised/test data
sig_noise = []
l1 = matrix.multiply(synapses0, noise_data)
sig_l1 = matrix.sig(l1)
b_sig_l1 = sig_l1[:]
b_sig_l1.append([])
for _ in b_sig_l1[0]:
b_sig_l1[len(b_sig_l1) - 1].append(b)
l2 = matrix.multiply(matrix.transpose(synapses1), b_sig_l1)
sig_noise = matrix.sig(l2)
# formatting net output for plot
result1 = [] # training data
result2 = [] # noised data
for i in range(len(sig_layer2[0])):
result1.append(sig_layer2[0][i] * 2 - 1)
result2.append(sig_noise[0][i] * 2 - 1)
if m == "sin":
# Plot
# Some code lines from: https://matplotlib.org/users/legend_guide.html
neuron_patch = mpatches.Patch(label='Neurons: ' + str(hidden))
bias_patch = mpatches.Patch(label='Bias: ' + str(b))
iteration_patch = mpatches.Patch(label='Iterations: ' + str(epochs))
epsilon_patch = mpatches.Patch(label='Gamma: ' + str(g))
weight_patch = mpatches.Patch(label='Weight range: +/- ' + str(w))
time_patch = mpatches.Patch(label=str(round((time.time() - start_time) / 60, 2)) + " min")
first_legend = plt.legend(
handles=[bias_patch, time_patch, epsilon_patch, neuron_patch, iteration_patch, weight_patch],
bbox_to_anchor=(0., 1.02, 1., .102), loc=3,
ncol=3, mode="expand", borderaxespad=0.)
line4, = plt.plot(error_axis[0], error_log, label="Error", linewidth=0.5)
line6, = plt.plot(error_axis[0], error_log2, label="Error2", linewidth=0.5)
line1, = plt.plot(inputData[0], result1, label="Training Data", linewidth=0.75)
line2, = plt.plot(inputData[0], result2, label="Test Data", linestyle=':', linewidth=0.75)
line3, = plt.plot(x_data, y_data, label="sin(x)", linestyle='--', linewidth=0.75)
line5, = plt.plot(x_axis, y_axis, label="Axis", linewidth=0.5)
ax = plt.gca().add_artist(first_legend)
plt.legend(handles=[line4, line1, line2, line3, line5, line6])
if p_m:
plt.savefig('./plots/' + str(time.time())[2:10] + '.png')
else:
plt.show()
plt.clf()
plt.cla()
plt.close()
elif m == "xor":
print("-----")
for i in range(len(sig_noise[0])):
print "Input: " + str(round(noise_data[0][i], 0)) + " & " \
+ str(round(noise_data[1][i], 0)) + " = " + str(round(sig_noise[0][i], 0)) + " (" \
+ str(round(sig_noise[0][i] * 100, 4)) + "% for True)"
latex_line(mat)
# Eliminating
for i in range(len(mat)):
if is_zero(mat[i][i]):
print("Can't invert the matrix.")
latex.output("\\end{array}")
latex.enq()
latex.output("\\\\Can't invert the matrix.\n")
latex.end("Inverting the matrix")
exit()
matrix.mult(mat, i, 1/mat[i][i])
for j in range(len(mat)):
if j == i:
continue
matrix.add(mat, j, -mat[j][i], i)
latex_line(mat)
# Output
invert = []
for i in range(len(mat)):
invert += [[0] * size]
for j in range(size):
invert[i][j] = mat[i][j + size]
matrix.output(invert)
# LaTeX output
latex.output("\\end{array}")
latex.enq()
latex.output("\\\\Inverse :\n")
latex.beq()
# Если это цифра - добавить в список вызываемых функций
if param.isdigit():
calls.append(param)
# Иначе - это путь к файлу со входными данными
else:
path = param
# Чтение JSON со входными данными
with open(path) as f:
data = json.load(f)
# Словарь функций
dictionary = {
'1':
matrix.add(data['first_matrix_dimensions'],
data['second_matrix_dimensions'], data['first_matrix'],
data['second_matrix']),
'2':
matrix.sub(data['first_matrix_dimensions'],
data['second_matrix_dimensions'], data['first_matrix'],
data['second_matrix']),
'3':
matrix.mult(data['first_matrix_dimensions'],
data['second_matrix_dimensions'], data['first_matrix'],
data['second_matrix']),
'4':
matrix.det(data['number'], data['first_matrix'])
}
# Вызов функции из словоря по списку входных данных
for param in calls:
def global_rect(topleft, width):
# They have to be global positions
return pygame.Rect( matrix.add(self.text_topleft, topleft), width )
def global_rect(topleft, width):
# They have to be global positions
return pygame.Rect(matrix.add(self.text_topleft, topleft), width)
def write_new(self, location):
return matrix.add(location)