def test_dbiot_segment_mid(self):
if self.print_info:
print(
'\n------------------------- Testing dbiot.eval_seg at mid-point'
)
gamma = 2.4
zetaA = self.zeta1
zetaB = self.zeta2
zetaP = .3 * zetaA + 0.7 * zetaB
Q0 = uvlmutils.biot_segment(zetaP, zetaA, zetaB, vortex_radius, gamma)
### compare different analytical derivative
DerP_an, DerA_an, DerB_an = dbiot.eval_seg_exp(zetaP, zetaA, zetaB,
vortex_radius, gamma)
DerP_an2, DerA_an2, DerB_an2 = dbiot.eval_seg_comp(
zetaP, zetaA, zetaB, gamma)
er_max = max(np.max(np.abs(DerP_an2 - DerP_an)),
np.max(np.abs(DerA_an2 - DerA_an)),
np.max(np.abs(DerB_an2 - DerB_an)))
assert er_max < 1e-16, 'Analytical models not matching'
### compare vs numerical derivative
# first step must be smaller than vortex radius
Steps = np.linspace(vortex_radius * 0.99, vortex_radius * 1e-2, 4)
Er_max = 0.0 * Steps
for ss in range(len(Steps)):
step = Steps[ss]
DerP_num = 0.0 * DerP_an
DerA_num = 0.0 * DerA_an
DerB_num = 0.0 * DerB_an
for cc_zeta in range(3):
dzeta = np.zeros((3, ))
dzeta[cc_zeta] = step
DerP_num[:, cc_zeta] = (uvlmutils.biot_segment(
zetaP + dzeta, zetaA, zetaB, vortex_radius, gamma) -
Q0) / step
DerA_num[:, cc_zeta] = (uvlmutils.biot_segment(
zetaP, zetaA + dzeta, zetaB, vortex_radius, gamma) -
Q0) / step
DerB_num[:, cc_zeta] = (uvlmutils.biot_segment(
zetaP, zetaA, zetaB + dzeta, vortex_radius, gamma) -
Q0) / step
er_max = max(np.max(np.abs(DerP_num - DerP_an)),
np.max(np.abs(DerA_num - DerA_an)),
np.max(np.abs(DerB_num - DerB_an)))
if self.print_info:
print('FD step: %.2e ---> Max error: %.2e' % (step, er_max))
assert er_max < 5e1 * step, 'Error larger than 50 times step size'
Er_max[ss] = er_max
def test_dbiot_segment(self):
print('\n-------------------------------------- Testing dbiot.eval_seg')
gamma = 2.4
zetaP = self.zetaP
zetaA = self.zeta1
zetaB = self.zeta2
Q0 = uvlmutils.biot_segment(zetaP, zetaA, zetaB, gamma)
### compare different analytical derivative
DerP_an, DerA_an, DerB_an = dbiot.eval_seg_exp(zetaP, zetaA, zetaB, gamma)
DerP_an2, DerA_an2, DerB_an2 = dbiot.eval_seg_comp(zetaP, zetaA, zetaB, gamma)
er_max = max(np.max(np.abs(DerP_an2 - DerP_an)),
np.max(np.abs(DerA_an2 - DerA_an)),
np.max(np.abs(DerB_an2 - DerB_an)))
assert er_max < 1e-16, 'Analytical models not matching'
### compare vs numerical derivative
Steps = np.linspace(uvlmutils.VORTEX_RADIUS * 0.99, uvlmutils.VORTEX_RADIUS * 1e-2, 4)
Er_max = 0.0 * Steps
for ss in range(len(Steps)):
step = Steps[ss]
DerP_num = 0.0 * DerP_an
DerA_num = 0.0 * DerA_an
DerB_num = 0.0 * DerB_an
for cc_zeta in range(3):
dzeta = np.zeros((3,))
dzeta[cc_zeta] = step
DerP_num[:, cc_zeta] = (
uvlmutils.biot_segment(zetaP + dzeta, zetaA, zetaB, gamma) - Q0) / step
DerA_num[:, cc_zeta] = (
uvlmutils.biot_segment(zetaP, zetaA + dzeta, zetaB, gamma) - Q0) / step
DerB_num[:, cc_zeta] = (
uvlmutils.biot_segment(zetaP, zetaA, zetaB + dzeta, gamma) - Q0) / step
er_max = max(np.max(np.abs(DerP_num - DerP_an)),
np.max(np.abs(DerA_num - DerA_an)),
np.max(np.abs(DerB_num - DerB_an)))
print('FD step: %.2e ---> Max error: %.2e' % (step, er_max))
assert er_max < 5e1 * step, 'Error larger than 50 times step size'
Er_max[ss] = er_max