def test_IEA37_ex16_windFarmModel(windFarmModel, aep_ref):
site = IEA37Site(16)
x, y = site.initial_position.T
windTurbines = IEA37_WindTurbines()
wf_model = windFarmModel(site,
windTurbines,
turbulenceModel=GCLTurbulence())
wf_model.superpositionModel = SquaredSum()
aep_ilk = wf_model(x, y, wd=np.arange(0, 360, 22.5),
ws=[9.8]).aep_ilk(normalize_probabilities=True)
aep_MW_l = aep_ilk.sum((0, 2)) * 1000
# check if ref is reasonable
aep_est = 16 * 3.35 * 24 * 365 * .8 # n_wt * P_rated * hours_pr_year - 20% wake loss = 375628.8
npt.assert_allclose(aep_ref[0], aep_est, rtol=.11)
npt.assert_allclose(aep_ref[1], [
9500, 8700, 11500, 14300, 21300, 25900, 39600, 44300, 23900, 13900,
15200, 33000, 72100, 18300, 12500, 8000
],
rtol=.15)
npt.assert_almost_equal(aep_MW_l.sum(), aep_ref[0], 5)
npt.assert_array_almost_equal(aep_MW_l, aep_ref[1], 5)
def test_interp(h, wd, ws, h_i, wd_l, ws_k):
ds = xr.Dataset({
'TI': 1,
'P': 1,
'XYHLK': (['x', 'y', 'h', 'wd', 'ws'], np.random.rand(10, 20, len(h), len(wd), len(ws))),
'XYHL': (['x', 'y', 'h', 'wd'], np.random.rand(10, 20, len(h), len(wd))),
'XYHK': (['x', 'y', 'h', 'ws'], np.random.rand(10, 20, len(h), len(ws))),
'K': (['ws'], np.random.rand(len(ws))),
'L': (['wd'], np.random.rand(len(wd))),
'KL': (['wd', 'ws'], np.random.rand(len(wd), len(ws))),
'XY': (['x', 'y'], np.random.rand(10, 20)),
'H': (['h'], np.random.rand(len(h))),
'XYH': (['x', 'y', 'h'], np.random.rand(10, 20, len(h))),
'XYL': (['x', 'y', 'wd'], np.random.rand(10, 20, len(wd))),
'XYK': (['x', 'y', 'ws'], np.random.rand(10, 20, len(ws))),
'I': (['i'], np.random.rand(2)),
'IL': (['i', 'wd'], np.random.rand(2, len(wd))),
'IK': (['i', 'ws'], np.random.rand(2, len(ws))),
'ILK': (['i', 'wd', 'ws'], np.random.rand(2, len(wd), len(ws))),
},
coords={'x': np.linspace(0, 100, 10),
'y': np.linspace(200, 300, 20),
'h': h,
'wd': wd,
'ws': ws,
'i': [0, 1]}
)
site = XRSite(ds)
lw = LocalWind(x_i=[25, 50], y_i=[225, 250], h_i=h_i, wd=wd_l, ws=ws_k, time=False, wd_bin_size=1)
for n in ['XYHLK', 'XYHL', 'XYHK', 'K', 'L', 'KL', 'XY', 'H', 'XYH', 'XYL', 'XYK', 'I', 'IL', 'IK', 'ILK']:
ip1 = site.interp(site.ds[n], lw.coords)
ip2 = ds[n].sel_interp_all(lw.coords)
npt.assert_array_equal(ip1.shape, ip2.shape)
if not np.isnan(ip2).sum():
npt.assert_array_almost_equal(ip1.data, ip2.data)
def test_flat_distances_src_neq_dst(distance):
x = [0, 50, 100]
y = [100, 100, 0]
h = [0, 10, 20]
wdirs = [0, 30]
site = FlatSite(distance=distance)
site.distance.setup(src_x_i=x, src_y_i=y, src_h_i=h, dst_xyh_j=(x, y, [1, 2, 3]))
dw_ijl, hcw_ijl, dh_ijl = site.distance(wd_il=np.array(wdirs)[na])
dw_indices_l = distance.dw_order_indices(wdirs)
if 0:
distance.plot(wd_il=np.array(wdirs)[na])
plt.show()
# check down wind distance wind from North and 30 deg
npt.assert_array_almost_equal(dw_ijl[:, :, 0], [[0, 0, 100],
[0, 0, 100],
[-100, -100, 0]])
npt.assert_array_almost_equal(dw_ijl[:, :, 1], [[0, -25, 36.60254038],
[25, 0, 61.60254038],
[-36.60254038, -61.60254038, 0]])
# check cross wind distance wind from North and 30 deg
npt.assert_array_almost_equal(hcw_ijl[:, :, 0], [[0, 50, 100],
[-50, 0, 50],
[-100, -50, 0]])
npt.assert_array_almost_equal(hcw_ijl[:, :, 1], [[0, 43.30127019, 136.60254038],
[-43.30127019, 0., 93.30127019],
[-136.60254038, -93.30127019, 0.]])
# check cross wind distance wind from North
npt.assert_array_almost_equal(dh_ijl[:, :, 0], [[1, 2, 3],
[-9, -8, -7],
[-19, -18, -17]])
# check dw indices
npt.assert_array_equal(dw_indices_l, [[1, 0, 2],
[1, 0, 2]])
def test_grid_interpolator_2d():
x = [5, 10, 15]
y = [200, 300, 400, 500]
v = np.arange(12).reshape(3, 4)
eq = GridInterpolator([x, y], v)
xp = [[i, 200] for i in np.arange(5, 16)]
npt.assert_array_almost_equal(eq(xp), np.linspace(0, 8, 11))
npt.assert_array_almost_equal(eq(xp, 'nearest'), np.round(np.linspace(0, 8, 11) / 4) * 4)
X, Y = np.meshgrid(x, y)
xp, yp = np.linspace(5, 15, 11), np.linspace(200, 500, 13)
Xp, Yp = np.meshgrid(xp, yp)
co = np.array([Xp, Yp]).T.reshape(-1, 2)
for method in ['nearest', 'linear']:
Z = eq(co, method).reshape(Xp.T.shape)
plt.figure()
c = plt.contourf(Xp, Yp, Z.T, np.arange(12))
plt.plot(X, Y, 'xw',)
plt.colorbar(c)
if 0:
plt.show()
plt.close()
def test_set_gradients():
wt = IEA37_WindTurbines()
wt.set_gradient_funcs(
lambda ws: np.where(
(ws > 4) & (ws <= 9.8),
100000 *
ws, # not the right gradient, but similar to the reference
0),
lambda ws: 0)
with use_autograd_in([WindTurbines, iea37_reader]):
ws_lst = np.arange(3, 25, .1)
plt.plot(ws_lst, wt.power(ws_lst))
ws_pts = np.array([3., 6., 9., 12.])
dpdu_lst = np.diag(autograd(wt.power)(ws_pts))
if 0:
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), 100000 * ws_pts, 0)
npt.assert_array_almost_equal(dpdu_lst, dpdu_ref)
def test_YZGrid_variables():
site = IEA37Site(16)
x, y = [0], [0]
windTurbines = IEA37_WindTurbines()
wf_model = IEA37SimpleBastankhahGaussian(site, windTurbines)
sim_res = wf_model(x, y)
fm = sim_res.flow_map(grid=YZGrid(x=100, y=None, resolution=100,
extend=.1),
wd=270,
ws=None)
fm.WS_eff.plot()
plt.plot(fm.y[::10], fm.y[::10] * 0 + 110, '.')
if 0:
print(np.round(fm.WS_eff.interp(h=110)[::10].squeeze().values, 4))
plt.show()
plt.close()
npt.assert_array_almost_equal(
fm.WS_eff.interp(h=110)[::10].squeeze(), [
9.1461, 8.4157, 7.3239, 6.058, 5.022, 4.6455, 5.1019, 6.182, 7.446,
8.506
], 4)
def test_wake_map():
site = IEA37Site(16)
x, y = site.initial_position.T
windTurbines = IEA37_WindTurbines()
wake_model = NOJ(site, windTurbines)
aep = AEPCalculator(wake_model)
x_j = np.linspace(-1500, 1500, 200)
y_j = np.linspace(-1500, 1500, 100)
X, Y, Z = aep.wake_map(x_j, y_j, 110, x, y, wd=[0], ws=[9])
m = 49, slice(100, 133, 2)
# print(np.round(Z[m], 2).tolist()) # ref
if 0:
import matplotlib.pyplot as plt
c = plt.contourf(X, Y, Z) # , np.arange(2, 10, .01))
plt.colorbar(c)
windTurbines.plot(x, y)
plt.plot(X[m], Y[m], '.-r')
plt.show()
ref = [
3.27, 3.27, 9.0, 7.46, 7.46, 7.46, 7.46, 7.31, 7.31, 7.31, 7.31, 8.3,
8.3, 8.3, 8.3, 8.3, 8.3
]
npt.assert_array_almost_equal(Z[m], ref, 2)
def test_RotorGaussQuadratureGridAvgModel():
m = GQGridRotorAvg(4, 3)
npt.assert_array_almost_equal(m.nodes_x, [-0.34, 0.34, -0.86, -0.34, 0.34, 0.86, -0.34, 0.34], 2)
npt.assert_array_almost_equal(m.nodes_y, [-0.77, -0.77, 0.0, 0.0, 0.0, 0.0, 0.77, 0.77], 2)
npt.assert_array_almost_equal(m.nodes_weight, [0.11, 0.11, 0.1, 0.18, 0.18, 0.1, 0.11, 0.11], 2)
if 0:
for v in [m.nodes_x, m.nodes_y, m.nodes_weight]:
print(np.round(v, 2).tolist())
c = plt.scatter(m.nodes_x, m.nodes_y, c=m.nodes_weight)
plt.colorbar(c)
plt.axis('equal')
plt.gca().add_artist(plt.Circle((0, 0), 1, fill=False))
plt.ylim([-1, 1])
plt.show()
def test_grid_interpolator_non_regular():
x = [6, 10, 14]
y = [200, 300, 400, 500]
v = np.arange(12).reshape(3, 4)
eq = GridInterpolator([x, y], v)
xp = [[i, 200] for i in np.linspace(6, 14, 9)]
npt.assert_array_almost_equal(eq(xp), np.linspace(0, 8, 9))
x = [6, 12, 14]
y = [200, 300, 400, 500]
v = np.arange(12).reshape(3, 4)
v[1, 0] = 6
eq = GridInterpolator([x, y], v)
xp = [[i, 200] for i in np.linspace(6, 14, 9)]
npt.assert_array_almost_equal(eq(xp), np.linspace(0, 8, 9))
xp = [[i, 200] for i in np.linspace(6, 14, 10)]
npt.assert_array_almost_equal(eq(xp), np.linspace(0, 8, 10))
npt.assert_array_almost_equal(eq(xp, 'nearest'), [0., 0., 0., 0., 6., 6., 6., 6., 8., 8.])
def test_CGIRotorAvg(n, x, y, w):
m = CGIRotorAvg(n)
if 0:
for v in [m.nodes_x, m.nodes_y, m.nodes_weight]:
print(np.round(v, 2).tolist())
plt.scatter(m.nodes_x, m.nodes_y, c=m.nodes_weight)
plt.axis('equal')
plt.gca().add_artist(plt.Circle((0, 0), 1, fill=False))
plt.ylim([-1, 1])
plt.show()
assert (len(m.nodes_weight) == len(m.nodes_x) == len(m.nodes_y) == n)
npt.assert_almost_equal(m.nodes_weight.sum(), 1)
npt.assert_array_almost_equal(m.nodes_x, x, 2)
npt.assert_array_almost_equal(m.nodes_y, y, 2)
npt.assert_array_almost_equal(m.nodes_weight, w, 2)
def test_polar_gauss_quadrature():
m = PolarGridRotorAvg(*polar_gauss_quadrature(4, 3))
if 0:
for v in [m.nodes_x, m.nodes_y, m.nodes_weight]:
print(np.round(v, 2).tolist())
plt.scatter(m.nodes_x, m.nodes_y, c=m.nodes_weight)
plt.axis('equal')
plt.gca().add_artist(plt.Circle((0, 0), 1, fill=False))
plt.ylim([-1, 1])
plt.show()
npt.assert_array_almost_equal(m.nodes_x, [-0.05, -0.21, -0.44, -0.61, -0.0, -0.0,
-0.0, -0.0, 0.05, 0.21, 0.44, 0.61], 2)
npt.assert_array_almost_equal(m.nodes_y, [-0.05, -0.25, -0.51, -0.71, 0.07, 0.33,
0.67, 0.93, -0.05, -0.25, -0.51, -0.71], 2)
npt.assert_array_almost_equal(m.nodes_weight, [0.05, 0.09, 0.09, 0.05, 0.08, 0.14, 0.14,
0.08, 0.05, 0.09, 0.09, 0.05], 2)
def test_superposition_model_indices():
class WTSite(UniformSite):
def local_wind(self, x_i=None, y_i=None, h_i=None, wd=None,
ws=None, time=False, wd_bin_size=None, ws_bins=None):
lw = UniformSite.local_wind(self, x_i=x_i, y_i=y_i, h_i=h_i, wd=wd, ws=ws,
wd_bin_size=wd_bin_size, ws_bins=ws_bins)
lw['TI'] = xr.DataArray(lw.TI_ilk + np.arange(len(x_i))[:, np.newaxis, np.newaxis] * .1,
[('wt', [0, 1, 2]), ('wd', np.atleast_1d(wd)), ('ws', np.atleast_1d(ws))])
return lw
site = WTSite([1], 0.1)
x_i = [0, 0, 0]
y_i = [0, -40, -100]
h_i = [50, 50, 50]
# WS_ilk different at each wt position
TI_ilk = site.local_wind(x_i, y_i, h_i, wd=0, ws=8.1).TI_ilk
npt.assert_array_almost_equal(TI_ilk, np.reshape([0.1, 0.2, 0.3], (3, 1, 1)), 10)
def get_wf_model(cls):
return cls(site, NibeA0, wake_deficitModel=NoWakeDeficit(),
superpositionModel=LinearSum(),
turbulenceModel=STF2017TurbulenceModel())
for wake_model in [get_wf_model(PropagateDownwind),
get_wf_model(All2AllIterative)]:
# No wake (ct = 0), i.e. WS_eff == WS
TI_eff_ilk = wake_model.calc_wt_interaction(x_i, y_i, h_i, [1, 1, 1], 0.0, 8.1)[1]
npt.assert_array_equal(TI_eff_ilk, TI_ilk)
# full wake (CT=8/9)
ref_TI_eff_ilk = TI_ilk + np.reshape([0, 0.33738364, np.sum([0.19369135, 0.21239116])], (3, 1, 1))
TI_eff_ilk = wake_model.calc_wt_interaction(x_i, y_i, h_i, [0, 0, 0], 0.0, 8.1)[1]
npt.assert_array_almost_equal(TI_eff_ilk, ref_TI_eff_ilk)
sim_res = wake_model(x_i, y_i, h_i, [0, 0, 0], 0.0, 8.1)
TI_eff_ilk = sim_res.flow_map(HorizontalGrid(x=[0], y=y_i, h=50)).TI_eff_xylk[:, 0]
npt.assert_array_almost_equal(TI_eff_ilk, ref_TI_eff_ilk)
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 test_MultiPowerCtCurve():
u_p, p, ct = v80_upct.copy()
curve = PowerCtFunctionList('mode', [
PowerCtTabular(ws=u_p, power=p, power_unit='w', ct=ct),
PowerCtTabular(ws=u_p, power=p * 1.1, power_unit='w', ct=ct + .1)
])
u = np.arange(0, 30, .1)
wfm = get_wfm(curve)
ri, oi = wfm.windTurbines.function_inputs
npt.assert_array_equal(ri, ['mode'])
npt.assert_array_equal(oi, ['Air_density', 'tilt', 'yaw'])
sim_res = wfm([0], [0], ws=u, wd=0, mode=0)
p0, ct0 = sim_res.Power.squeeze().values, sim_res.CT.squeeze().values,
sim_res = wfm([0], [0], ws=u, wd=0, mode=1)
p1, ct1 = sim_res.Power.squeeze().values, sim_res.CT.squeeze().values,
npt.assert_array_almost_equal(p0, p1 / 1.1)
npt.assert_array_almost_equal(ct0, ct1 - .1)
mode_16 = (np.arange(16) > 7)
mode_16_360 = np.broadcast_to(mode_16[:, na], (16, 360))
mode_16_360_23 = np.broadcast_to(mode_16[:, na, na], (16, 360, 23))
ref_p = np.array(
np.broadcast_to(hornsrev1.power_curve[:, 1][na, na], (16, 360, 23)))
ref_p[8:] *= 1.1
for m in [mode_16, mode_16_360, mode_16_360_23]:
sim_res = wfm(np.arange(16) * 1e3, [0] * 16,
wd=np.arange(360) % 5,
mode=m) # no wake effects
p = sim_res.Power.values
npt.assert_array_almost_equal(p, ref_p)
def test_plot_ws_distribution(site):
p = site.plot_ws_distribution(wd=[0, 90, 180, 270])
npt.assert_array_almost_equal(p.ws[p.argmax('ws')],
[7.35, 8.25, 7.95, 9.75])
npt.assert_array_almost_equal(
p.max('ws'), [0.01063067, 0.01048959, 0.01081972, 0.00893762])
plt.figure()
p = site.plot_ws_distribution(wd=[0, 90, 180, 270],
include_wd_distribution=True)
npt.assert_array_almost_equal(p.ws[p.argmax('ws')],
[7.75, 8.25, 8.15, 9.55])
npt.assert_array_almost_equal(p.max('ws'),
[0.001269, 0.002169, 0.002771, 0.003548])
with pytest.raises(AssertionError,
match="Wind directions must be equidistant"):
p = site.plot_ws_distribution(wd=[0, 180, 270],
include_wd_distribution=True)
plt.figure()
p = site.plot_ws_distribution(wd=[90, 180, 270, 0],
include_wd_distribution=True)
npt.assert_array_almost_equal(p.ws[p.argmax('ws')], [
8.25,
8.15,
9.55,
7.75,
])
npt.assert_array_almost_equal(p.max('ws'),
[0.002182, 0.002771, 0.003548, 0.001257])
if 0:
plt.show()
plt.close('all')
def test_fuga():
# move turbine 1 600 300
wt_x = [-250, 600, -500, 0, 500, -250, 250]
wt_y = [433, 300, 0, 0, 0, -433, -433]
wts = HornsrevV80()
path = tfp + 'fuga/2MW/Z0=0.03000000Zi=00401Zeta0=0.00E+00/'
site = UniformSite([1, 0, 0, 0], ti=0.075)
wake_model = Fuga(path, site, wts)
res, _ = timeit(wake_model.__call__,
verbose=0,
line_profile=0,
profile_funcs=[
FugaDeficit.interpolate, LUTInterpolator.__call__,
GridInterpolator.__call__
])(x=wt_x, y=wt_y, wd=[30], ws=[10])
npt.assert_array_almost_equal(res.WS_eff_ilk.flatten(), [
10.00669629, 10., 8.47606501, 10.03143097, 9.37288077, 8.49301941,
8.07462708
], 8)
npt.assert_array_almost_equal(res.ct_ilk.flatten(), [
0.7926384, 0.793, 0.80647607, 0.79130273, 0.80177967, 0.80649302,
0.80607463
], 8)
x_j = np.linspace(-1500, 1500, 500)
y_j = np.linspace(-1500, 1500, 300)
wake_model = Fuga(path, site, wts)
sim_res = wake_model(wt_x, wt_y, wd=[30], ws=[10])
flow_map70 = sim_res.flow_map(HorizontalGrid(x_j, y_j, h=70))
flow_map73 = sim_res.flow_map(HorizontalGrid(x_j, y_j, h=73))
X, Y = flow_map70.XY
Z70 = flow_map70.WS_eff_xylk[:, :, 0, 0]
Z73 = flow_map73.WS_eff_xylk[:, :, 0, 0]
if 0:
flow_map70.plot_wake_map(levels=np.arange(6, 10.5, .1))
plt.plot(X[0], Y[140])
plt.figure()
plt.plot(X[0], Z70[140, :], label="Z=70m")
plt.plot(X[0], Z73[140, :], label="Z=73m")
plt.plot(X[0, 100:400:10], Z70[140, 100:400:10], '.')
print(list(np.round(Z70.data[140, 100:400:10], 4)))
print(list(np.round(Z73.data[140, 100:400:10], 4)))
plt.legend()
plt.show()
npt.assert_array_almost_equal(Z70[140, 100:400:10], [
10.0407, 10.0438, 10.0438, 10.013, 9.6847, 7.8787, 6.9561, 9.2251,
9.9686, 10.0382, 10.0498, 10.0569, 10.0325, 9.1787, 7.4004, 9.1384,
10.0329, 10.0297, 10.0232, 9.9265, 9.3163, 8.0768, 6.8858, 8.3754,
9.9592, 10.0197, 10.0118, 10.0141, 10.0118, 10.0095
], 4)
npt.assert_array_almost_equal(Z73[140, 100:400:10], [
10.0404, 10.0435, 10.0433, 10.0113, 9.6836, 7.9206, 7.0218, 9.2326,
9.9665, 10.0376, 10.0494, 10.0563, 10.0304, 9.1896, 7.4515, 9.15,
10.0317, 10.0294, 10.0226, 9.9245, 9.3252, 8.1192, 6.9462, 8.3988,
9.9574, 10.0194, 10.0117, 10.014, 10.0117, 10.0094
], 4)
def test_fuga():
# move turbine 1 600 300
wt_x = [-250, 600, -500, 0, 500, -250, 250]
wt_y = [433, 300, 0, 0, 0, -433, -433]
wts = HornsrevV80()
path = tfp + 'fuga/2MW/Z0=0.03000000Zi=00401Zeta0=0.00E+0/'
site = UniformSite([1, 0, 0, 0], ti=0.075)
wake_model = Fuga(path, site, wts)
res, _ = timeit(wake_model.__call__,
verbose=0,
line_profile=0,
profile_funcs=[
FugaDeficit.interpolate, LUTInterpolator.__call__,
GridInterpolator.__call__
])(x=wt_x, y=wt_y, wd=[30], ws=[10])
npt.assert_array_almost_equal(res.WS_eff_ilk.flatten(), [
10.002683492812844, 10.0, 8.413483643142389, 10.036952526815286,
9.371203842245153, 8.437429367715435, 8.012759083790058
], 8)
npt.assert_array_almost_equal(res.ct_ilk.flatten(), [
0.79285509, 0.793, 0.80641348, 0.79100456, 0.80180315, 0.80643743,
0.80601276
], 8)
x_j = np.linspace(-1500, 1500, 500)
y_j = np.linspace(-1500, 1500, 300)
wake_model = Fuga(path, site, wts)
sim_res = wake_model(wt_x, wt_y, wd=[30], ws=[10])
flow_map70 = sim_res.flow_map(HorizontalGrid(x_j, y_j, h=70))
flow_map73 = sim_res.flow_map(HorizontalGrid(x_j, y_j, h=73))
X, Y = flow_map70.XY
Z70 = flow_map70.WS_eff_xylk[:, :, 0, 0]
Z73 = flow_map73.WS_eff_xylk[:, :, 0, 0]
if 0:
flow_map70.plot_wake_map(levels=np.arange(6, 10.5, .1))
plt.plot(X[0], Y[140])
plt.figure()
plt.plot(X[0], Z70[140, :], label="Z=70m")
plt.plot(X[0], Z73[140, :], label="Z=73m")
plt.plot(X[0, 100:400:10], Z70[140, 100:400:10], '.')
print(list(np.round(Z70.data[140, 100:400:10], 4)))
print(list(np.round(Z73.data[140, 100:400:10], 4)))
plt.legend()
plt.show()
npt.assert_array_almost_equal(Z70[140, 100:400:10], [
10.0467, 10.0473, 10.0699, 10.0093, 9.6786, 7.8589, 6.8539, 9.2199,
9.9837, 10.036, 10.0796, 10.0469, 10.0439, 9.1866, 7.2552, 9.1518,
10.0449, 10.0261, 10.0353, 9.9256, 9.319, 8.0062, 6.789, 8.3578,
9.9393, 10.0332, 10.0183, 10.0186, 10.0191, 10.0139
], 4)
npt.assert_array_almost_equal(Z73[140, 100:400:10], [
10.0463, 10.0468, 10.0688, 10.0075, 9.6778, 7.9006, 6.9218, 9.228,
9.9808, 10.0354, 10.0786, 10.0464, 10.0414, 9.1973, 7.3099, 9.1629,
10.0432, 10.0257, 10.0344, 9.9236, 9.3274, 8.0502, 6.8512, 8.3813,
9.9379, 10.0325, 10.018, 10.0183, 10.019, 10.0138
], 4)
def test_superposition_model_indices(superpositionModel, sum_func):
class WTSite(UniformSite):
def local_wind(self,
x_i=None,
y_i=None,
h_i=None,
wd=None,
ws=None,
wd_bin_size=None,
ws_bins=None):
lw = UniformSite.local_wind(self,
x_i=x_i,
y_i=y_i,
h_i=h_i,
wd=wd,
ws=ws,
wd_bin_size=wd_bin_size,
ws_bins=ws_bins)
lw['WS'] = xr.DataArray(
lw.WS_ilk + np.arange(len(x_i))[:, np.newaxis, np.newaxis],
[('wt', [0, 1, 2]), ('wd', np.atleast_1d(wd)),
('ws', np.atleast_1d(ws))])
return lw
site = WTSite([1], 0.1)
x_i = [0, 0, 0]
y_i = [0, -40, -100]
h_i = [50, 50, 50]
# WS_ilk different at each wt position
WS_ilk = site.local_wind(x_i, y_i, h_i, wd=0, ws=8.1).WS_ilk
npt.assert_array_equal(WS_ilk, np.reshape([8.1, 9.1, 10.1], (3, 1, 1)))
for wake_model in [
PropagateDownwind(site,
NibeA0,
wake_deficitModel=NOJDeficit(),
superpositionModel=superpositionModel),
All2AllIterative(site,
NibeA0,
wake_deficitModel=NOJDeficit(),
superpositionModel=superpositionModel)
]:
# No wake (ct = 0), i.e. WS_eff == WS
WS_eff_ilk = wake_model.calc_wt_interaction(x_i, y_i, h_i, [1, 1, 1],
0.0, 8.1)[0]
npt.assert_array_equal(WS_eff_ilk, WS_ilk)
ref = WS_ilk - np.reshape(
[0, 3.75, sum_func([2.4, 3.58974359])], (3, 1, 1))
# full wake (CT=8/9)
WS_eff_ilk = wake_model.calc_wt_interaction(x_i, y_i, h_i, [0, 0, 0],
0.0, 8.1)[0]
npt.assert_array_almost_equal(WS_eff_ilk, ref)
sim_res = wake_model(x_i, y_i, h_i, [0, 0, 0], 0.0, 8.1)
WS_eff_ilk = sim_res.flow_map(HorizontalGrid(x=[0], y=y_i,
h=50)).WS_eff_xylk[:, 0]
npt.assert_array_almost_equal(WS_eff_ilk, ref)
def test_wasp_resources_grid_point(site):
# x = np.array([l.split() for l in """0.6010665 -10.02692 32.71442 -6.746912
# 0.5007213 -4.591617 37.10247 -11.0699
# 0.3104101 -1.821247 59.18301 -12.56743
# 0.4674515 16.14293 44.84665 -9.693183
# 0.8710347 5.291974 26.01634 -6.154611
# 0.9998786 -2.777032 15.72486 1.029988
# 0.9079611 -7.882853 16.33216 6.42329
# 0.759553 -5.082487 17.23354 10.18187
# 0.7221162 4.606324 17.96417 11.45838
# 0.8088576 8.196074 16.16308 9.277925
# 0.8800673 3.932325 14.82337 5.380589
# 0.8726974 -3.199536 19.99724 -1.433086""".split("\n")], dtype=np.float)
# for x_ in x.T:
# print(list(x_))
x = [262978]
y = [6504814]
npt.assert_almost_equal(site.elevation(x, y), 227.8, 1)
# Data from WAsP:
# - add turbine (262878,6504814,30)
# - Turbine (right click) - reports - Turbine Site Report full precision
wasp_A = [
2.197305, 1.664085, 1.353185, 2.651781, 5.28438, 5.038289, 4.174325,
4.604496, 5.043066, 6.108261, 6.082033, 3.659798
]
wasp_k = [
1.771484, 2.103516, 2.642578, 2.400391, 2.357422, 2.306641, 2.232422,
2.357422, 2.400391, 2.177734, 1.845703, 1.513672
]
wasp_f = [
5.188083, 2.509297, 2.869334, 4.966141, 13.16969, 9.514355, 4.80275,
6.038354, 9.828702, 14.44174, 16.60567, 10.0659
]
wasp_spd = [
0.6010665, 0.5007213, 0.3104101, 0.4674515, 0.8710347, 0.9998786,
0.9079611, 0.759553, 0.7221162, 0.8088576, 0.8800673, 0.8726974
]
wasp_trn = [
-10.02692, -4.591617, -1.821247, 16.14293, 5.291974, -2.777032,
-7.882853, -5.082487, 4.606324, 8.196074, 3.932325, -3.199536
]
wasp_inc = [
-6.746912, -11.0699, -12.56743, -9.693183, -6.154611, 1.029988,
6.42329, 10.18187, 11.45838, 9.277925, 5.380589, -1.433086
]
wasp_ti = [
32.71442, 37.10247, 59.18301, 44.84665, 26.01634, 15.72486, 16.33216,
17.23354, 17.96417, 16.16308, 14.82337, 19.99724
]
rho = 1.179558
wasp_u_mean = [
1.955629, 1.473854, 1.202513, 2.350761, 4.683075, 4.463644, 3.697135,
4.080554, 4.470596, 5.409509, 5.402648, 3.300305
]
wasp_p_air = [
9.615095, 3.434769, 1.556282, 12.45899, 99.90289, 88.03519, 51.41135,
66.09097, 85.69466, 164.5592, 193.3779, 56.86945
]
# wasp_aep = np.array([3725293.0, 33722.71, 0.3093564, 3577990.0, 302099600.0, 188784100.0,
# 48915640.0, 84636210.0, 189009800.0, 549195100.0, 691258600.0, 120013000.0]) / 1000
wasp_aep_no_density_correction = np.array([
3937022.0, 36046.93, 0.33592, 3796496.0, 314595600.0, 196765700.0,
51195440.0, 88451200.0, 197132700.0, 568584400.0, 712938400.0,
124804600.0
]) / 1000
# wasp_aep_total = 2.181249024
wasp_aep_no_density_correction_total = 2.26224
wt_u = np.array([
3.99, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25
])
wt_p = np.array([
0, 55., 185., 369., 619., 941., 1326., 1741., 2133., 2436., 2617.,
2702., 2734., 2744., 2747., 2748., 2748., 2750., 2750., 2750., 2750.,
2750., 2750.
])
wt_ct = np.array([
0, 0.871, 0.853, 0.841, 0.841, 0.833, 0.797, 0.743, 0.635, 0.543,
0.424, 0.324, 0.258, 0.21, 0.175, 0.147, 0.126, 0.109, 0.095, 0.083,
0.074, 0.065, 0.059
])
wt = OneTypeWindTurbines.from_tabular(name="NEG-Micon 2750/92 (2750 kW)",
diameter=92,
hub_height=70,
ws=wt_u,
ct=wt_ct,
power=wt_p,
power_unit='kw')
A_lst, k_lst, f_lst, spd_lst, orog_trn_lst, flow_inc_lst, tke_lst = [
site.interp_funcs[n]((x, y, 30, range(0, 360, 30)))
for n in ['A', 'k', 'f', 'spd', 'orog_trn', 'flow_inc', 'tke']
]
f_lst = f_lst * 360 / 12
pdf_lst = [
lambda x, A=A, k=k: k / A * (x / A)**(k - 1) * np.exp(-(x / A)**k) *
(x[1] - x[0]) for A, k in zip(A_lst, k_lst)
]
# cdf_lst = [lambda x, A=A, k=k: 1 - np.exp(-(x / A) ** k) for A, k in zip(A_lst, k_lst)]
dx = .1
ws = np.arange(dx / 2, 35, dx)
# compare to wasp data
npt.assert_array_equal(A_lst, wasp_A)
npt.assert_array_equal(k_lst, wasp_k)
npt.assert_array_almost_equal(f_lst, np.array(wasp_f) / 100)
npt.assert_array_almost_equal(spd_lst, wasp_spd)
npt.assert_array_almost_equal(orog_trn_lst, wasp_trn)
npt.assert_array_almost_equal(flow_inc_lst, wasp_inc)
npt.assert_array_almost_equal(tke_lst, np.array(wasp_ti) / 100)
# compare pdf, u_mean and aep to wasp
lw = site.local_wind(x,
np.array(y) + 1e-6,
30,
wd=np.arange(0, 360, 30),
ws=ws)
P = lw.P_ilk / lw.P_ilk.sum(2)[:, :,
na] # only wind speed probablity (not wdir)
# pdf
for l in range(12):
npt.assert_array_almost_equal(
np.interp(ws, lw.WS_ilk[0, l], np.cumsum(P[0, l])),
np.cumsum(pdf_lst[l](ws)), 1)
# u_mean
npt.assert_almost_equal(
[A * math.gamma(1 + 1 / k) for A, k in zip(A_lst, k_lst)], wasp_u_mean,
5)
npt.assert_almost_equal([(pdf(ws) * ws).sum() for pdf in pdf_lst],
wasp_u_mean, 5)
npt.assert_almost_equal((P * lw.WS_ilk).sum((0, 2)), wasp_u_mean, 5)
# air power
p_air = [(pdf(ws) * 1 / 2 * rho * ws**3).sum() for pdf in pdf_lst]
npt.assert_array_almost_equal(p_air, wasp_p_air, 3)
npt.assert_array_almost_equal((P * 1 / 2 * rho * lw.WS_ilk**3).sum((0, 2)),
wasp_p_air, 2)
# AEP
AEP_ilk = NOJ(site, wt)(x, y, h=30, wd=np.arange(0, 360, 30),
ws=ws).aep_ilk(with_wake_loss=False,
normalize_probabilities=True)
if 0:
plt.plot(wasp_aep_no_density_correction / 1000, '.-', label='WAsP')
plt.plot(AEP_ilk.sum((0, 2)) * 1e3, label='PyWake')
plt.xlabel('Sector')
plt.ylabel('AEP [MWh]')
plt.legend()
plt.show()
npt.assert_array_less(
np.abs(wasp_aep_no_density_correction - AEP_ilk.sum((0, 2)) * 1e6),
300)
npt.assert_almost_equal(AEP_ilk.sum(),
wasp_aep_no_density_correction_total, 3)
def test_mirror():
path = tfp + 'fuga/2MW/Z0=0.03000000Zi=00401Zeta0=0.00E+0/'
fuga_utils = FugaUtils(path, on_mismatch='input_par')
npt.assert_array_almost_equal(fuga_utils.mirror([0, 1, 3]), [3, 1, 0, 1, 3])
npt.assert_array_almost_equal(fuga_utils.mirror([0, 1, 3], anti_symmetric=True), [-3, -1, 0, 1, 3])
def test_selfsimilarity_reference_figures(setup):
ss = setup[2]
ss20 = setup[3]
ws = 10
D = 80
R = D / 2
WS_ilk = np.array([[[ws]]])
D_src_il = np.array([[D]])
ct_ilk = np.array([[[.8]]])
x1, y1 = -np.arange(200), np.array([0])
deficit_centerline = ss.calc_deficit(WS_ilk=WS_ilk, D_src_il=D_src_il,
dw_ijlk=x1.reshape((1, len(x1), 1, 1)),
cw_ijlk=y1.reshape((1, len(y1), 1, 1)), ct_ilk=ct_ilk)[0, :, 0, 0]
deficit20_centerline = ss20.calc_deficit(WS_ilk=WS_ilk, D_src_il=D_src_il,
dw_ijlk=x1.reshape((1, len(x1), 1, 1)),
cw_ijlk=y1.reshape((1, len(y1), 1, 1)), ct_ilk=ct_ilk)[0, :, 0, 0]
x2, y2 = np.array([-2 * R]), np.arange(200)
deficit_radial = ss.calc_deficit(WS_ilk=WS_ilk, D_src_il=D_src_il,
dw_ijlk=x2.reshape((1, len(x2), 1, 1)),
cw_ijlk=y2.reshape((1, len(y2), 1, 1)), ct_ilk=ct_ilk)[0, :, 0, 0]
deficit20_radial = ss20.calc_deficit(WS_ilk=WS_ilk, D_src_il=D_src_il,
dw_ijlk=x2.reshape((1, len(x2), 1, 1)),
cw_ijlk=y2.reshape((1, len(y2), 1, 1)), ct_ilk=ct_ilk)[0, :, 0, 0]
# r12 = np.sqrt(ss.lambda_ * (ss.eta + (x2 / R) ** 2)) # Eq. (13) from [1]
r12 = ss.r12(x2 / R)
r12_20 = ss20.r12(x2 / R)
if debug:
plt.title('Fig 11 from [1]')
plt.xlabel('x/R')
plt.ylabel('a')
plt.plot(x1 / R, deficit_centerline / ws)
plt.plot(x1 / R, deficit20_centerline / ws, '--')
print(list(np.round(deficit_centerline[::20], 6)))
print(list(np.round(deficit20_centerline[::20], 6)))
plt.figure()
plt.title('Fig 10 from [1]')
print(list(np.round(deficit_radial[::20] / deficit_radial[0], 6)))
print(list(np.round(deficit20_radial[::20] / deficit20_radial[0], 6)))
plt.xlabel('y/R12 (epsilon)')
plt.ylabel('f')
plt.plot((y2 / R) / r12, deficit_radial / deficit_radial[0])
plt.plot((y2 / R) / r12_20, deficit20_radial / deficit20_radial[0], '--')
plt.show()
fig11_ref = np.array([[-0.025, -1, -2, -3, -4, -5], [0.318, 0.096, 0.035, 0.017, 0.010, 0.0071]]).T
npt.assert_array_almost_equal(np.interp(-fig11_ref[:, 0], -x1 / R, deficit_centerline / ws), fig11_ref[:, 1], 1)
npt.assert_array_almost_equal(deficit_centerline[::20], [0.0, 1.780159, 0.943215, 0.540855, 0.33998, 0.230329,
0.165257, 0.123906, 0.096151, 0.076686])
npt.assert_array_almost_equal(deficit20_centerline[::20],
[0.0,
1.758202,
0.931581,
0.562763,
0.362938,
0.249322,
0.180358,
0.135934,
0.105854,
0.08463])
fig10_ref = np.array([[0, 1, 2, 3], [1, .5, .15, .045]]).T
npt.assert_array_almost_equal(np.interp(fig10_ref[:, 0], (y2 / R) / r12, deficit_radial / deficit_radial[0]),
fig10_ref[:, 1], 1)
npt.assert_array_almost_equal(deficit_radial[::20] / deficit_radial[0],
[1.0, 0.933011, 0.772123, 0.589765, 0.430823, 0.307779,
0.217575, 0.153065, 0.107446, 0.075348])
npt.assert_array_almost_equal(deficit20_radial[::20] / deficit20_radial[0],
[1.0, 0.937523, 0.78531, 0.608956, 0.451715, 0.32748, 0.23477, 0.167415, 0.119088, 0.084613])
def test_grid_interpolator_2d_plus_2d():
eq = GridInterpolator([[5, 10, 15], [200, 300, 400, 500]], np.arange(12).repeat(10).reshape(3, 4, 2, 5))
x = [[i, 200] for i in np.arange(5, 16)]
npt.assert_array_almost_equal(eq(x).sum((1, 2)), np.linspace(0, 8, 11) * 10)
npt.assert_array_equal(eq(x).shape, (11, 2, 5))
def test_wec():
# move turbine 1 600 300
wt_x = [-250, 600, -500, 0, 500, -250, 250]
wt_y = [433, 300, 0, 0, 0, -433, -433]
wts = HornsrevV80()
site = UniformSite([1, 0, 0, 0], ti=0.075)
wake_model = Fuga(LUT_path_2MW_z0_0_03, site, wts)
aep = AEPCalculator(wake_model)
x_j = np.linspace(-1500, 1500, 500)
y_j = np.linspace(-1500, 1500, 300)
_, _, Z_wec1 = aep.wake_map(x_j,
y_j,
70,
wt_x,
wt_y,
wt_height=70,
wd=[30],
ws=[10])
aep.wake_model.wec = 2
X, Y, Z_wec2 = aep.wake_map(x_j,
y_j,
70,
wt_x,
wt_y,
wt_height=70,
wd=[30],
ws=[10])
if 0:
import matplotlib.pyplot as plt
c = plt.contourf(X, Y, Z_wec1, np.arange(6, 10.5, .1))
plt.colorbar(c)
plt.plot(X[0], Y[140])
wts.plot(wt_x, wt_y)
plt.figure()
c = plt.contourf(X, Y, Z_wec2, np.arange(6, 10.5, .1))
plt.colorbar(c)
plt.plot(X[0], Y[140])
wts.plot(wt_x, wt_y)
plt.figure()
plt.plot(X[0], Z_wec1[140, :], label="Z=70m")
plt.plot(X[0], Z_wec2[140, :], label="Z=70m")
plt.plot(X[0, 100:400:10], Z_wec1[140, 100:400:10], '.')
plt.plot(X[0, 100:400:10], Z_wec2[140, 100:400:10], '.')
plt.legend()
plt.show()
npt.assert_array_almost_equal(Z_wec1[140, 100:400:10], [
10.0547, 10.0519, 10.0718, 10.0093, 9.6786, 7.8589, 6.8539, 9.2199,
9.9837, 10.036, 10.0796, 10.0469, 10.0439, 9.1866, 7.2552, 9.1518,
10.0449, 10.0261, 10.0353, 9.9256, 9.319, 8.0062, 6.789, 8.3578,
9.9393, 10.0332, 10.0191, 10.0186, 10.0191, 10.0139
], 4)
npt.assert_array_almost_equal(Z_wec2[140, 100:400:10], [
10.0297, 9.9626, 9.7579, 9.2434, 8.2318, 7.008, 6.7039, 7.7303, 9.0101,
9.6877, 9.9068, 9.7497, 9.1127, 7.9505, 7.26, 7.9551, 9.2104, 9.7458,
9.6637, 9.1425, 8.2403, 7.1034, 6.5109, 7.2764, 8.7653, 9.7139, 9.9718,
10.01, 10.0252, 10.0357
], 4)
kwargs = {k: 1 for k in wt.function_inputs[0]}
dpdu_lst = grad_method(wt.power)(ws_pts, **kwargs)
dctdu_lst = grad_method(wt.ct)(ws_pts, **kwargs)
if 0:
gradients.color_dict = {'power': 'b', 'ct': 'r'}
plt.plot(ws_lst, wt.power(ws_lst, **kwargs), label='power')
c = plt.plot([], label='ct')[0].get_color()
for dpdu, ws in zip(dpdu_lst, ws_pts):
plot_gradients(wt.power(ws, **kwargs), dpdu, ws, "power", 1)
ax = plt.twinx()
ax.plot(ws_lst, wt.ct(ws_lst, **kwargs), color=c)
for dctdu, ws in zip(dctdu_lst, ws_pts):
plot_gradients(wt.ct(ws, **kwargs), dctdu, ws, "ct", 1, ax=ax)
plt.title(case)
plt.show()
npt.assert_array_almost_equal(dpdu_lst, dpdu_ref,
(0, 4)[grad_method == autograd])
npt.assert_array_almost_equal(dctdu_lst, dctdu_ref,
(4, 6)[grad_method == autograd])
if __name__ == '__main__':
x = np.linspace(0, 2 * np.pi, 100)
import matplotlib.pyplot as plt
import numpy as np
plt.plot(x, np.sin(x) / x)
plt.plot(x, np.sin(x))
plt.show()
def test_get_model_input():
site, windTurbines = IEA37Site(16), IEA37_WindTurbines()
wfm = IEA37SimpleBastankhahGaussian(site, windTurbines)
args = get_model_input(wfm, [1000], [0], ws=10, wd=270)
npt.assert_array_almost_equal(args['dw_ijl'], [[[1000]]])
npt.assert_array_almost_equal(args['hcw_ijl'], [[[0]]])
npt.assert_array_almost_equal(args['dh_ijl'], [[[0]]])
npt.assert_array_almost_equal(args['yaw_ilk'], [[[0]]])
npt.assert_array_almost_equal(args['WS_ilk'], [[[10]]])
npt.assert_array_almost_equal(args['ct_ilk'], [[[8 / 9]]])
def test_fuga():
# move turbine 1 600 300
wt_x = [-250, 600, -500, 0, 500, -250, 250]
wt_y = [433, 300, 0, 0, 0, -433, -433]
wts = HornsrevV80()
path = tfp + 'fuga/2MW/Z0=0.03000000Zi=00401Zeta0=0.00E+0/'
site = UniformSite([1, 0, 0, 0], ti=0.075)
wake_model = Fuga(path, site, wts)
res = wake_model(x=wt_x, y=wt_y, wd=[30], ws=[10])
npt.assert_array_almost_equal(res.WS_eff_ilk.flatten(), [
10.002683492812844, 10.0, 8.413483643142389, 10.036952526815286,
9.371203842245153, 8.437429367715435, 8.012759083790058
], 8)
npt.assert_array_almost_equal(res.ct_ilk.flatten(), [
0.79285509, 0.793, 0.80641348, 0.79100456, 0.80180315, 0.80643743,
0.80601276
], 8)
x_j = np.linspace(-1500, 1500, 500)
y_j = np.linspace(-1500, 1500, 300)
wake_model = Fuga(path, site, wts)
sim_res = wake_model(wt_x, wt_y, wd=[30], ws=[10])
flow_map70 = sim_res.flow_map(HorizontalGrid(x_j, y_j, h=70))
flow_map73 = sim_res.flow_map(HorizontalGrid(x_j, y_j, h=73))
X, Y = flow_map70.XY
Z70 = flow_map70.WS_eff_xylk[:, :, 0, 0]
Z73 = flow_map73.WS_eff_xylk[:, :, 0, 0]
if 0:
import matplotlib.pyplot as plt
flow_map70.plot_wake_map(levels=np.arange(6, 10.5, .1))
plt.plot(X[0], Y[140])
plt.figure()
plt.plot(X[0], Z70[140, :], label="Z=70m")
plt.plot(X[0], Z73[140, :], label="Z=73m")
plt.plot(X[0, 100:400:10], Z70[140, 100:400:10], '.')
print(list(np.round(Z70[140, 100:400:10], 4)))
print(list(np.round(Z73[140, 100:400:10], 4)))
plt.legend()
plt.show()
# npt.assert_array_almost_equal(
# Z70[140, 100:400:10],
# [10.0547, 10.0519, 10.0741, 10.0099, 9.6774, 7.8538, 6.8484, 9.2134, 9.9749, 10.0232, 10.0658, 10.0189, 10.0187,
# 9.1496, 7.2077, 9.1154, 10.0183, 10.0008, 10.0146, 9.8838, 9.2848, 7.9681, 6.7412, 8.3149, 9.9114, 10.0119,
# 10.0011, 9.9979, 10.0002, 9.9981], 4)
npt.assert_array_almost_equal(Z70[140, 100:400:10], [
10.0547, 10.0519, 10.0718, 10.0093, 9.6786, 7.8589, 6.8539, 9.2199,
9.9837, 10.036, 10.0796, 10.0469, 10.0439, 9.1866, 7.2552, 9.1518,
10.0449, 10.0261, 10.0353, 9.9256, 9.319, 8.0062, 6.789, 8.3578,
9.9393, 10.0332, 10.0191, 10.0186, 10.0191, 10.0139
], 4)
npt.assert_array_almost_equal(Z73[140, 100:400:10], [
10.0542, 10.0514, 10.0706, 10.0075, 9.6778, 7.9006, 6.9218, 9.228,
9.9808, 10.0354, 10.0786, 10.0464, 10.0414, 9.1973, 7.3099, 9.1629,
10.0432, 10.0257, 10.0344, 9.9236, 9.3274, 8.0502, 6.8512, 8.3813,
9.9379, 10.0325, 10.0188, 10.0183, 10.019, 10.0138
], 4)
def test_gauss_quadrature():
x, _, w = gauss_quadrature(4, 1)
npt.assert_array_almost_equal(x, [-0.861136, -0.339981, 0.339981, 0.861136])
npt.assert_array_almost_equal(w, np.array([0.347855, 0.652145, 0.652145, 0.347855]) / 2)