def test_multivector2vector_independent():
def f(x, y):
return x**2 + 2 * y**3 + 1
def dfdx(x, y):
return 2 * x
def dfdy(x, y):
return 6 * y**2
x = np.array([2, 3, 4])
y = np.array([1, 2, 3])
ref_x = [4, 6, 8]
ref_y = [6, 24, 54]
npt.assert_array_almost_equal(fd(f, False)(x, y), ref_x, 5)
npt.assert_array_almost_equal(fd(f, False, 1)(x, y), ref_y, 4)
npt.assert_array_almost_equal_nulp(cs(f, False)(x, y), ref_x)
npt.assert_array_almost_equal_nulp(cs(f, False, 1)(x, y), ref_y)
npt.assert_array_equal(autograd(f, False)(x, y), ref_x)
npt.assert_array_equal(autograd(f, False, 1)(x, y), ref_y)
pf = primitive(f)
defvjp(pf, lambda ans, x, y: lambda g: g * dfdx(x, y),
lambda ans, x, y: lambda g: g * dfdy(x, y))
npt.assert_array_equal(autograd(pf, False)(x, y), ref_x)
npt.assert_array_equal(autograd(pf, False, 1)(x, y), ref_y)
def test_spline():
wt_tab = V80()
wt_spline = V80()
wt_spline.spline_ct_power(err_tol_factor=1e-2)
ws_lst = np.arange(3, 25, .001)
# mean and max error
assert (wt_tab.power(ws_lst) - wt_spline.power(ws_lst)).mean() < 1
assert ((wt_tab.power(ws_lst) - wt_spline.power(ws_lst)).max()) < 1400
# max change of gradient 80 times lower
assert np.diff(np.diff(wt_spline.power(ws_lst))).max() * 80 < np.diff(np.diff(wt_tab.power(ws_lst))).max()
ws_pts = [6.99, 7.01]
dpdu_tab_pts = np.diag(fd(wt_tab.power)(np.array(ws_pts)))
with use_autograd_in():
dpdu_spline_pts = np.diag(autograd(wt_spline.power)(np.array(ws_pts)))
npt.assert_array_almost_equal(dpdu_spline_pts, [205555.17794162, 211859.45965873])
if 0:
plt.plot(ws_lst, wt_tab.power(ws_lst))
plt.plot(ws_lst, wt_spline.power(ws_lst))
for wt, dpdu_pts, label in [(wt_tab, dpdu_tab_pts, 'V80 tabular'),
(wt_spline, dpdu_spline_pts, 'V80 spline')]:
for ws, dpdu in zip(ws_pts, dpdu_pts):
plot_gradients(wt.power(ws), dpdu, ws, label, 1)
ax = plt.gca().twinx()
ax.plot(ws_lst, wt.power(ws_lst) - wt_spline.power(ws_lst))
plt.figure()
plt.plot(np.diff(np.diff(wt_tab.power(ws_lst))))
plt.plot(np.diff(np.diff(wt_spline.power(ws_lst))))
plt.show()
def test_scalar2scalar():
def f(x):
return x**2 + 1
x = np.array([3])
npt.assert_equal(cs(f)(x), 6)
npt.assert_almost_equal(fd(f)(x), 6, 5)
npt.assert_equal(autograd(f)(x), 6)
pf = primitive(f)
defvjp(pf, lambda ans, x: lambda g: g * 2 * x)
npt.assert_array_equal(autograd(pf, False)(x), 6)
def test_vector2vector_dependent():
def f(x):
return x**2 + x[::-1]
def df(x):
return np.diag(2 * x) + np.diag(np.ones(3))[::-1]
x = np.array([2., 3, 4])
ref = [[4., 0., 1.], [0., 7., 0.], [1., 0., 8.]]
npt.assert_array_almost_equal(fd(f, True)(x), ref, 5)
npt.assert_array_almost_equal_nulp(cs(f, True)(x), ref)
npt.assert_array_equal(autograd(f, True)(x), ref)
pf = primitive(f)
defvjp(pf, lambda ans, x: lambda g: np.dot(g, df(x)))
npt.assert_array_equal(autograd(pf, True)(x), ref)
def test_vector2vector_independent():
def f(x):
return x**2 + 1
def df(x):
return 2 * x
x = np.array([2, 3, 4])
ref = [4, 6, 8]
npt.assert_array_almost_equal(fd(f, False)(x), ref, 5)
npt.assert_array_equal(cs(f, False)(x), ref)
npt.assert_array_equal(autograd(f, False)(x), ref)
pf = primitive(f)
defvjp(pf, lambda ans, x: lambda g: g * df(x))
npt.assert_array_equal(autograd(pf, False)(x), ref)
def test_scalar2multi_scalar():
def fxy(x):
return x**2 + 1, 2 * x + 1
def f(x):
fx, fy = fxy(x)
return fx + fy
x = 3.
ref = 8
npt.assert_equal(cs(f)(x), ref)
npt.assert_almost_equal(fd(f)(x), ref, 5)
npt.assert_equal(autograd(f)(x), ref)
pf = primitive(f)
defvjp(pf, lambda ans, x: lambda g: g * (2 * x + 2))
npt.assert_array_equal(autograd(pf, False)(x), ref)
pf = primitive(fxy)
defvjp(pf, lambda ans, x: lambda g: (g[0] * 2 * x, g[1] * 2))
npt.assert_array_equal(autograd(f, False)(x), ref)
def test_gradients():
wt = IEA37_WindTurbines()
wt.enable_autograd()
ws_lst = np.arange(3, 25, .1)
ws_pts = np.array([3., 6., 9., 12.])
dpdu_lst = autograd(wt.power)(ws_pts)
if 0:
plt.plot(ws_lst, wt.power(ws_lst))
for dpdu, ws in zip(dpdu_lst, ws_pts):
plot_gradients(wt.power(ws), dpdu, ws, "", 1)
plt.show()
dpdu_ref = np.where((ws_pts > 4) & (ws_pts <= 9.8),
3 * 3350000 * (ws_pts - 4)**2 / (9.8 - 4)**3, 0)
npt.assert_array_almost_equal(dpdu_lst, dpdu_ref)
fd_dpdu_lst = fd(wt.power)(ws_pts)
npt.assert_array_almost_equal(fd_dpdu_lst, dpdu_ref, 0)
cs_dpdu_lst = cs(wt.power)(ws_pts)
npt.assert_array_almost_equal(cs_dpdu_lst, dpdu_ref)
def power_ct_grad_func(ws, run_only):
# fd is fine for linear interpolation
return fd(lambda ws, run_only=run_only, self=self: self.
np_interp(ws, run_only))(ws)
def test_vector2multi_vector():
def fxy(x):
return x**2 + 1, 2 * x + 1
def f0(x):
return fxy(x)[0]
def fsum(x):
fx, fy = fxy(x)
return fx + fy
x = np.array([1., 2, 3])
ref0 = [2, 4, 6]
refsum = [4, 6, 8]
npt.assert_equal(cs(f0)(x), ref0)
npt.assert_almost_equal(fd(f0)(x), ref0, 5)
npt.assert_equal(autograd(f0)(x), ref0)
pf0 = primitive(f0)
defvjp(pf0, lambda ans, x: lambda g: g * (2 * x))
npt.assert_array_equal(autograd(pf0, False)(x), ref0)
npt.assert_equal(cs(fsum)(x), refsum)
npt.assert_almost_equal(fd(fsum)(x), refsum, 5)
npt.assert_equal(autograd(fsum)(x), refsum)
pfsum = primitive(fsum)
defvjp(pfsum, lambda ans, x: lambda g: g * (2 * x + 2))
npt.assert_array_equal(autograd(pfsum, False)(x), refsum)
pfxy = primitive(fxy)
def dfxy(x):
return 2 * x, np.full(x.shape, 2)
def gsum(x):
fx, fy = pfxy(x)
return fx + fy
def g0(x):
return pfxy(x)[0]
pgsum = primitive(gsum)
pg0 = primitive(g0)
defvjp(pgsum, lambda ans, x: lambda g: g * np.sum(dfxy(x), 0))
defvjp(pg0, lambda ans, x: lambda g: g * dfxy(x)[0])
npt.assert_array_equal(autograd(pgsum, False)(x), refsum)
npt.assert_array_equal(autograd(pg0, False)(x), ref0)
defvjp(pfxy, lambda ans, x: lambda g: dfxy(x)[0])
def h0(x):
return pfxy(x)[0]
npt.assert_array_equal(autograd(h0, False)(x), ref0)
defvjp(pfxy, lambda ans, x: lambda g: np.sum(g * np.asarray(dfxy(x)), 0))
def hsum(x):
fx, fy = pfxy(x)
return fx + fy
npt.assert_array_equal(autograd(hsum, False)(x), refsum)
