def find_eigenvector(A, tolerance=0.00001):
guess = [1 for __ in A]
while True:
result = matrix_operate(A, guess)
length = magnitude(result)
next_guess = scalarMultiply(1 / length, result)
if distance(guess, next_guess) < tolerance:
return next_guess, length # eigenvector, eigenvalue
guess = next_guess
def find_eigenvector(A, tolerance=0.00001):
guess = [1 for __ in A]
while True:
result = matrix_operate(A, guess)
length = magnitude(result)
next_guess = scalarMultiply(1/length, result)
if distance(guess, next_guess) < tolerance:
return next_guess, length # eigenvector, eigenvalue
guess = next_guess
def minimizeStochastic(targetFn, gradientFn, x, y, theta0, alpha0=0.01):
data = zip(x, y)
theta = theta0
alpha = alpha0
minTheta, minValue = None, float("inf")
iterationsWithNoMovement = 0
while iterationsWithNoMovement < 100:
value = sum([targetFn(xi, yi, theta) for xi, yi in data])
if value < minValue:
minTheta, minValue = theta, value
iterationsWithNoMovement = 0
alpha = alpha0
else:
iterationsWithNoMovement += 1
alpha *= 0.9
for xi, yi in inRandomOrder(x, y):
gradientI = gradientFn(xi, yi, theta)
theta = vectorSubtract(theta, scalarMultiply(alpha, gradientI))
return minTheta
def minimizeStochastic(targetFn, gradientFn, x, y, theta0, alpha0=0.01):
data = zip(x, y)
theta = theta0
alpha = alpha0
minTheta, minValue = None, float("inf")
iterationsWithNoMovement = 0
while iterationsWithNoMovement < 100:
value = sum([targetFn(xi, yi, theta) for xi, yi in data])
if value < minValue:
minTheta, minValue = theta, value
iterationsWithNoMovement = 0
alpha = alpha0
else:
iterationsWithNoMovement += 1
alpha *= 0.9
for xi, yi in inRandomOrder(x, y):
gradientI = gradientFn(xi, yi, theta)
theta = vectorSubtract(theta, scalarMultiply(alpha, gradientI))
return minTheta
def project(v, w):
projectionLength = dotProduct(v, w)
return scalarMultiply(projectionLength, w)
def project(v, w):
projectionLength = dotProduct(v, w)
return scalarMultiply(projectionLength, w)