def test_steepest_descent_armijo():
"""Should trigger the line search
"""
initial_guess = Array([Number(2), Number(1)])
_, xstar, _, _ = optimizations.steepest_descent(rosenbrock,
initial_guess,
iterations=50)
def test_steepest_descent():
initial_guess = Array([Number(1.1), Number(1.1)])
_, xstar, _, _ = optimizations.steepest_descent(bowl,
initial_guess,
iterations=400)
# print(xstar)
assert xstar[0].val == pytest.approx(1, abs=1e-3)
assert xstar[1].val == pytest.approx(1, abs=1e-3)
def inner_func(*args, **kwargs):
# Check if args[0] has len. If so, apply the function elementwise and return an array
# rather than a Number
try:
value = func(*args, **kwargs)
deriv = deriv_func(*args, **kwargs)
return Number(value, deriv)
except AttributeError:
vals = [func(element, *args[1:], **kwargs) for element in args[0]]
derivs = [deriv_func(element, *args[1:], **kwargs) for element in args[0]]
numbers = [Number(val, deriv) for val, deriv in zip(vals, derivs)]
return Array(numbers)
def test_steepest_descent_scalar():
initial_guess = Number(1.1)
xstar, _, _ = optimizations.steepest_descent(quadratic,
initial_guess,
iterations=400)
print(xstar)
assert xstar.val == pytest.approx(1, abs=1e-3)
def test_dot():
q = Array((Number(0), 0))
assert q.dot(q).val == 0
def test_neq():
q = Array((Number(0), 0))
w = Array((Number(0), 1))
assert q != w
def test_neq_mixed():
q = Array((Number(0), 0))
assert q != 'a'
assert q != 1
def test_eq():
q = Array((Number(0), 0))
assert q == q
def test_array_converts_to_number():
q = Array((Number(0), 0))
assert q[0].val == 0
assert q[1].val == 0
def test_array_func():
q = Array((Number(0), Number(1)))
w = operations.exp(q)
assert w[0].val == pytest.approx(1)
assert w[1].val == pytest.approx(np.exp(1))
"""Tests for the Array class
"""
import sys
import pytest
sys.path.append('..')
import autodiff.operations as operations
from autodiff.structures import Number
from autodiff.structures import Array
import numpy as np
num2 = Number(2)
num3 = Number(3)
def test_len():
q = Array((num2, num3))
assert len(q) == 2
def test_repr():
q = Array((num2, num3))
assert repr(q) == 'Array([Number(val=2) Number(val=3)])'
def test_str():
q = Array((num2, num3))
assert str(q) == '[Number(val=2) Number(val=3)]'
def test_bfgs_scalar_verbose():
initial_guess = Number(2)
xstar, _, _ = optimizations.bfgs(quadratic, initial_guess, verbose=True)
assert xstar.val == pytest.approx(1)
def test_bfgs_verbose():
initial_guess = Array([Number(2), Number(1)])
xstar, _, _ = optimizations.bfgs(rosenbrock, initial_guess, verbose=True)
assert xstar[0].val == pytest.approx(1)
assert xstar[1].val == pytest.approx(1)
def test_bfgs_scalar_correct_start():
initial_guess = Number(1)
xstar, _, _ = optimizations.bfgs(quadratic, initial_guess)
assert xstar.val == pytest.approx(1)
def test_bfgs_correct_start():
initial_guess = Array([Number(1), Number(1)])
xstar, _, _ = optimizations.bfgs(rosenbrock, initial_guess)
assert xstar[0].val == pytest.approx(1)
assert xstar[1].val == pytest.approx(1)
jacobians = []
x0 = initial_guess
fxn = func(initial_guess)
fpxn = fxn.jacobian(initial_guess)
x1 = x0 - fxn / fpxn
jacobians.append(fpxn)
while fxn.val > 1e-7:
x0 = x1
fxn = func(x0)
fpxn = fxn.jacobian(x0)
jacobians.append(fpxn)
x1 = x0 - fxn / fpxn
return x1, jacobians
if __name__ == '__main__':
x0 = Number(5)
xstar, jacobians = newtons_method(func, x0)
print(xstar, jacobians[-1])