def test_output_variance():
w = np.arange(0, 5, 0.5)
# Zero variance with zero transfer function
H = np.zeros((10, 3, 3)) # frequency, another parameter, xyz
S = np.ones(10)
assert_array_equal(utils.output_variance(w, H, S), np.zeros((3,3,3)))
# Zero variance with zero spectrum
H = np.ones((10, 3, 3)) # frequency, another parameter, xyz
S = np.zeros(10)
assert_array_equal(utils.output_variance(w, H, S), np.zeros((3,3,3)))
# White noise spectrum, single peak in transfer function
H = np.zeros((10, 3, 3))
S = np.ones(10)
# Put the peaks at various frequencies, amplitudes and coordinates
H[1,0,:] = 1.1
H[4,1,2] = 2.3
H[6,2,0] = 3.4
s1 = utils.output_variance(w, H, S)
# Expected:
dw = 0.5
s = np.zeros((3,3,3))
s[0,:,:] = 1.1**2 * dw
s[1,2,2] = 2.3**2 * dw
s[2,0,0] = 3.4**2 * dw
assert_allclose(s1[0], s[0])
assert_allclose(s1[1], s[1])
assert_allclose(s1[2], s[2])
def test_output_variance():
w = np.arange(0, 5, 0.5)
# Zero variance with zero transfer function
H = np.zeros((10, 3, 3)) # frequency, another parameter, xyz
S = np.ones(10)
assert_array_equal(utils.output_variance(w, H, S), np.zeros((3, 3, 3)))
# Zero variance with zero spectrum
H = np.ones((10, 3, 3)) # frequency, another parameter, xyz
S = np.zeros(10)
assert_array_equal(utils.output_variance(w, H, S), np.zeros((3, 3, 3)))
# White noise spectrum, single peak in transfer function
H = np.zeros((10, 3, 3))
S = np.ones(10)
# Put the peaks at various frequencies, amplitudes and coordinates
H[1, 0, :] = 1.1
H[4, 1, 2] = 2.3
H[6, 2, 0] = 3.4
s1 = utils.output_variance(w, H, S)
# Expected:
dw = 0.5
s = np.zeros((3, 3, 3))
s[0, :, :] = 1.1**2 * dw
s[1, 2, 2] = 2.3**2 * dw
s[2, 0, 0] = 3.4**2 * dw
assert_allclose(s1[0], s[0])
assert_allclose(s1[1], s[1])
assert_allclose(s1[2], s[2])
def linearised_drag_force(self, w, H_wave, S_wave, vc=None):
"""Calculate coefficients A & b so F = A w_v + b.
w_v is the local perpendicular varying relative velocity.
- w are the frequencies used to calculate H_wave and S_wave
- vc is the steady current velocity in global coordinates.
It can be given for all elements or else one value for all.
"""
# Calculate standard deviations of relative velocity
# Ref: Langley1984
H_rel = (self.wave_velocity_transfer_function(w) -
self.structural_velocity_transfer_function(w, H_wave))
H_rel_local = self.resolve_perpendicular_to_elements(H_rel)
wv_sigma = np.sqrt(output_variance(w, H_rel_local, S_wave))
# Assume current is equal everywhere unless specified otherwise
# Resolve into local perpendicular velocities
if vc is None:
vc = np.zeros(3)
wc = self.resolve_perpendicular_to_elements(vc)
# Calculate the local linearised drag force
A_local, b_local = self.local_linearised_drag_force(wc, wv_sigma)
# Transform results back to global coordinates
P = self.element_axes[:,:,0:2] # transformation matrix [n1 n2]
b = np.einsum('eip,ep->ei', P, b_local)
A = np.einsum('eip,epq,ejq->eij', P, A_local, P)
return A, b
