def _get_piecewise_mean_price_vs_size_from_orderbook_entry(orders):
""" orders is just asks or just orders """
cm = [0] + [x['cm'] for x in orders]
# integral (price times qty) d_qty / qty
# represent this as integral of piecewise polynomial with coeff [0, price]
price = np.zeros((2, len(cm) - 1))
price[1, :] = [x['price'] for x in orders]
f = PPoly(price, cm, extrapolate=False)
F = f.antiderivative()
return lambda x: F(x) / x
def test_antiderivative_simple(self):
np.random.seed(1234)
# [ p1(x) = 3*x**2 + 2*x + 1,
# p2(x) = 1.6875]
c = np.array([[3, 2, 1], [0, 0, 1.6875]]).T
# [ pp1(x) = x**3 + x**2 + x,
# pp2(x) = 1.6875*(x - 0.25) + pp1(0.25)]
ic = np.array([[1, 1, 1, 0], [0, 0, 1.6875, 0.328125]]).T
# [ ppp1(x) = (1/4)*x**4 + (1/3)*x**3 + (1/2)*x**2,
# ppp2(x) = (1.6875/2)*(x - 0.25)**2 + pp1(0.25)*x + ppp1(0.25)]
iic = np.array([[1 / 4, 1 / 3, 1 / 2, 0, 0],
[0, 0, 1.6875 / 2, 0.328125, 0.037434895833333336]]).T
x = np.array([0, 0.25, 1])
pp = PPoly(c, x)
ipp = pp.antiderivative()
iipp = pp.antiderivative(2)
iipp2 = ipp.antiderivative()
assert_allclose(ipp.x, x)
assert_allclose(ipp.c.T, ic.T)
assert_allclose(iipp.c.T, iic.T)
assert_allclose(iipp2.c.T, iic.T)
def test_multi_shape(self):
c = np.random.rand(6, 2, 1, 2, 3)
x = np.array([0, 0.5, 1])
p = PPoly(c, x)
assert_equal(p.x.shape, x.shape)
assert_equal(p.c.shape, c.shape)
assert_equal(p(0.3).shape, c.shape[2:])
assert_equal(p(np.random.rand(5, 6)).shape, (5, 6) + c.shape[2:])
dp = p.derivative()
assert_equal(dp.c.shape, (5, 2, 1, 2, 3))
ip = p.antiderivative()
assert_equal(ip.c.shape, (7, 2, 1, 2, 3))
def test_antiderivative_simple(self):
np.random.seed(1234)
# [ p1(x) = 3*x**2 + 2*x + 1,
# p2(x) = 1.6875]
c = np.array([[3, 2, 1], [0, 0, 1.6875]]).T
# [ pp1(x) = x**3 + x**2 + x,
# pp2(x) = 1.6875*(x - 0.25) + pp1(0.25)]
ic = np.array([[1, 1, 1, 0], [0, 0, 1.6875, 0.328125]]).T
# [ ppp1(x) = (1/4)*x**4 + (1/3)*x**3 + (1/2)*x**2,
# ppp2(x) = (1.6875/2)*(x - 0.25)**2 + pp1(0.25)*x + ppp1(0.25)]
iic = np.array([[1/4, 1/3, 1/2, 0, 0],
[0, 0, 1.6875/2, 0.328125, 0.037434895833333336]]).T
x = np.array([0, 0.25, 1])
pp = PPoly(c, x)
ipp = pp.antiderivative()
iipp = pp.antiderivative(2)
iipp2 = ipp.antiderivative()
assert_allclose(ipp.x, x)
assert_allclose(ipp.c.T, ic.T)
assert_allclose(iipp.c.T, iic.T)
assert_allclose(iipp2.c.T, iic.T)
def test_multi_shape(self):
c = np.random.rand(6, 2, 1, 2, 3)
x = np.array([0, 0.5, 1])
p = PPoly(c, x)
assert_equal(p.x.shape, x.shape)
assert_equal(p.c.shape, c.shape)
assert_equal(p(0.3).shape, c.shape[2:])
assert_equal(p(np.random.rand(5,6)).shape,
(5,6) + c.shape[2:])
dp = p.derivative()
assert_equal(dp.c.shape, (5, 2, 1, 2, 3))
ip = p.antiderivative()
assert_equal(ip.c.shape, (7, 2, 1, 2, 3))
def get_piecewise_price_vs_size_from_orderbook_entry(orders, mean=True):
""" orders is just asks or just orders. takes maybe 300 micros though timeit reports much less """
if not orders:
return None
cm = [0] + [x['cm'] for x in orders]
# integral (price times qty) d_qty / qty
# represent this as integral of piecewise polynomial with coeff [0, price]
price = np.zeros((2, len(cm)-1))
price[1,:] = [x['price'] for x in orders]
f = PPoly(price, cm, extrapolate=False)
F = f.antiderivative()
if mean:
# generally you want mean price if you took out the stack up to some size
return lambda x: F(x) / x
else:
return F
def test_extrapolate_attr(self):
# [ 1 - x**2 ]
c = np.array([[-1, 0, 1]]).T
x = np.array([0, 1])
for extrapolate in [True, False, None]:
pp = PPoly(c, x, extrapolate=extrapolate)
pp_d = pp.derivative()
pp_i = pp.antiderivative()
if extrapolate is False:
assert_(np.isnan(pp([-0.1, 1.1])).all())
assert_(np.isnan(pp_i([-0.1, 1.1])).all())
assert_(np.isnan(pp_d([-0.1, 1.1])).all())
assert_equal(pp.roots(), [1])
else:
assert_allclose(pp([-0.1, 1.1]), [1 - 0.1**2, 1 - 1.1**2])
assert_(not np.isnan(pp_i([-0.1, 1.1])).any())
assert_(not np.isnan(pp_d([-0.1, 1.1])).any())
assert_allclose(pp.roots(), [1, -1])
def test_extrapolate_attr(self):
# [ 1 - x**2 ]
c = np.array([[-1, 0, 1]]).T
x = np.array([0, 1])
for extrapolate in [True, False, None]:
pp = PPoly(c, x, extrapolate=extrapolate)
pp_d = pp.derivative()
pp_i = pp.antiderivative()
if extrapolate is False:
assert_(np.isnan(pp([-0.1, 1.1])).all())
assert_(np.isnan(pp_i([-0.1, 1.1])).all())
assert_(np.isnan(pp_d([-0.1, 1.1])).all())
assert_equal(pp.roots(), [1])
else:
assert_allclose(pp([-0.1, 1.1]), [1-0.1**2, 1-1.1**2])
assert_(not np.isnan(pp_i([-0.1, 1.1])).any())
assert_(not np.isnan(pp_d([-0.1, 1.1])).any())
assert_allclose(pp.roots(), [1, -1])