def test_position_second_derivatives(self):
"""
Performs finite difference testing of second derivatives of position
vector.
"""
[d2xdtheta2, d2xdzeta2, d2xdthetadzeta, d2ydtheta2, d2ydzeta2, \
d2ydthetadzeta, d2zdtheta2, d2zdzeta2, d2zdthetadzeta] = \
self.vmecOutput.position_second_derivatives()
for itheta in range(0, self.vmecOutput.ntheta, 5):
for izeta in range(0, self.vmecOutput.nzeta, 5):
this_zeta = self.vmecOutput.zetas[izeta]
this_theta = self.vmecOutput.thetas[itheta]
d2xdthetadzeta_fd = finiteDifferenceDerivative(this_zeta,\
lambda zeta : self.vmecOutput.position_first_derivatives(-1, \
this_theta,zeta)[0], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(d2xdthetadzeta_fd, \
d2xdthetadzeta[izeta,itheta], places=5)
d2ydthetadzeta_fd = finiteDifferenceDerivative(this_zeta,\
lambda zeta : self.vmecOutput.position_first_derivatives(-1, \
this_theta,zeta)[2], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(d2ydthetadzeta_fd, \
d2ydthetadzeta[izeta,itheta], places=5)
d2zdthetadzeta_fd = finiteDifferenceDerivative(this_zeta,\
lambda zeta : self.vmecOutput.position_first_derivatives(-1, \
this_theta,zeta)[4], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(d2zdthetadzeta_fd, \
d2zdthetadzeta[izeta,itheta], places=5)
d2xdtheta2_fd = finiteDifferenceDerivative(this_theta,\
lambda theta : self.vmecOutput.position_first_derivatives(-1, \
theta,this_zeta)[0], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(d2xdtheta2_fd, \
d2xdtheta2[izeta,itheta], places=5)
d2ydtheta2_fd = finiteDifferenceDerivative(this_theta,\
lambda theta : self.vmecOutput.position_first_derivatives(-1, \
theta,this_zeta)[2], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(d2ydtheta2_fd, \
d2ydtheta2[izeta,itheta], places=5)
d2zdtheta2_fd = finiteDifferenceDerivative(this_theta,\
lambda theta : self.vmecOutput.position_first_derivatives(-1, \
theta,this_zeta)[4], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(d2zdtheta2_fd, \
d2zdtheta2[izeta,itheta], places=5)
d2xdzeta2_fd = finiteDifferenceDerivative(this_zeta,\
lambda zeta : self.vmecOutput.position_first_derivatives(-1, \
this_theta,zeta)[1], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(d2xdzeta2_fd, \
d2xdzeta2[izeta,itheta], places=5)
d2ydzeta2_fd = finiteDifferenceDerivative(this_zeta,\
lambda zeta : self.vmecOutput.position_first_derivatives(-1, \
this_theta,zeta)[3], epsilon=1e-5, method='centered')
self.assertAlmostEqual(d2ydzeta2_fd, \
d2ydzeta2[izeta,itheta], places=5)
d2zdzeta2_fd = finiteDifferenceDerivative(this_zeta,\
lambda zeta : self.vmecOutput.position_first_derivatives(-1, \
this_theta,zeta)[5], epsilon=1e-5, method='centered')
self.assertAlmostEqual(d2zdzeta2_fd, \
d2zdzeta2[izeta,itheta], places=5)
def test_radius_derivatives(self):
"""
Performs finite difference testing of derivative of radius with
respect to boundary harmonics
"""
def temp_fun_rmnc(im, rmnc):
rmnc_init = self.vmecOutput.rmnc[-1, im]
self.vmecOutput.rmnc[-1, im] = rmnc
[X, Y, Z, R] = self.vmecOutput.compute_position()
self.vmecOutput.rmnc[-1, im] = rmnc_init
return R
# Check first 10 modes
xm_sensitivity = self.vmecOutput.xm[0:10]
xn_sensitivity = self.vmecOutput.xn[0:10] / self.vmecOutput.nfp
[dRdrmnc, dRdzmns] = self.vmecOutput.radius_derivatives(\
xm_sensitivity, xn_sensitivity)
for im in range(len(xm_sensitivity)):
this_rmnc = self.vmecOutput.rmnc[-1, im]
dRdrmnc_fd = finiteDifferenceDerivative(this_rmnc,\
lambda rmnc : temp_fun_rmnc(im, rmnc), epsilon=1e-5, \
method='centered')
for izeta in range(self.vmecOutput.nzeta):
for itheta in range(self.vmecOutput.ntheta):
self.assertAlmostEqual(dRdrmnc_fd[izeta, itheta], \
dRdrmnc[im, izeta, itheta], places=5)
self.assertEqual(0, dRdzmns[im, izeta, itheta])
def test_normalized_jacobian_derivatives(self):
"""
Performs finite difference testing of derivative of normalized
jacobian with respect to boundary harmonics
"""
def temp_fun_rmnc(im, rmnc):
rmnc_init = self.vmecOutput.rmnc[-1, im]
self.vmecOutput.rmnc[-1, im] = rmnc
normalized_jacobian = self.vmecOutput.normalized_jacobian()
self.vmecOutput.rmnc[-1, im] = rmnc_init
return normalized_jacobian
def temp_fun_zmns(im, zmns):
zmns_init = self.vmecOutput.zmns[-1, im]
self.vmecOutput.zmns[-1, im] = zmns
normalized_jacobian = self.vmecOutput.normalized_jacobian()
self.vmecOutput.zmns[-1, im] = zmns_init
return normalized_jacobian
# Check first 10 modes
xm_sensitivity = self.vmecOutput.xm[0:10]
xn_sensitivity = self.vmecOutput.xn[0:10] / self.vmecOutput.nfp
[dnormalized_jacobiandrmnc, dnormalized_jacobiandzmns] = \
self.vmecOutput.normalized_jacobian_derivatives(xm_sensitivity, \
xn_sensitivity)
for im in range(len(xm_sensitivity)):
this_rmnc = self.vmecOutput.rmnc[-1, im]
this_zmns = self.vmecOutput.zmns[-1, im]
dnormalized_jacobiandrmnc_fd = finiteDifferenceDerivative(this_rmnc,\
lambda rmnc : temp_fun_rmnc(im,rmnc), epsilon=1e-5, \
method='centered')
dnormalized_jacobiandzmns_fd = finiteDifferenceDerivative(this_zmns,\
lambda zmns : temp_fun_zmns(im,zmns), epsilon=1e-5, \
method='centered')
for izeta in range(self.vmecOutput.nzeta):
for itheta in range(self.vmecOutput.ntheta):
self.assertAlmostEqual(dnormalized_jacobiandrmnc_fd[izeta,itheta], \
dnormalized_jacobiandrmnc[im,izeta,itheta], places=5)
self.assertAlmostEqual(dnormalized_jacobiandzmns_fd[izeta,itheta], \
dnormalized_jacobiandzmns[im,izeta,itheta], places=5)
def area_derivatives(self):
"""
Performs finite difference testing of derivative of area with
respect to boundary harmonics
"""
def temp_fun_rmnc(im, rmnc):
rmnc_init = self.vmecOutput.rmnc[-1, im]
self.vmecOutput.rmnc[-1, im] = rmnc
area = self.vmecOutput.area()
self.vmecOutput.rmnc[-1, im] = rmnc_init
return area
def temp_fun_zmns(im, rmnc):
zmns_init = self.vmecOutput.zmns[-1, im]
self.vmecOutput.zmns[-1, im] = zmns
area = self.vmecOutput.area()
self.vmecOutput.zmns[-1, im] = zmns_init
return area
# Check first 10 modes
xm_sensitivity = self.vmecOutput.xm[0:10]
xn_sensitivity = self.vmecOutput.xn[0:10] / self.vmecOutput.nfp
[dareadrmnc, dareadzmns] = self.vmecOutput.area_derivatives(\
xm_sensitivity, xn_sensitivity)
for im in range(len(xm_sensitivity)):
this_rmnc = self.vmecOutput.rmnc[-1, im]
this_zmns = self.vmecOutput.zmns[-1, im]
dareadrmnc_fd = finiteDifferenceDerivative(this_rmnc,\
lambda rmnc : temp_fun_rmnc(im, rmnc), epsilon=1e-5, \
method='centered')
dareadzmns_fd = finiteDifferenceDerivative(this_zmns,\
lambda zmns : temp_fun_zmns(im, zmns), epsilon=1e-5, \
method='centered')
self.assertAlmostEqual(dareadrmnc_fd[izeta, itheta], \
dareadrmnc[im, izeta, itheta], places=5)
def test_position_first_derivatives(self):
"""
Checks that derivatives of position vector integrate to zero
over full grid and performs finite difference testing.
"""
[dxdtheta, dxdzeta, dydtheta, dydzeta, dzdtheta, dzdzeta] = \
self.vmecOutput.position_first_derivatives(\
theta=self.vmecOutput.thetas_2d_full,
zeta=self.vmecOutput.zetas_2d_full)
dxdtheta_sum = np.sum(dxdtheta) * self.vmecOutput.dtheta \
* self.vmecOutput.dzeta * self.vmecOutput.nfp
dxdzeta_sum = np.sum(dxdzeta) * self.vmecOutput.dtheta \
* self.vmecOutput.dzeta * self.vmecOutput.nfp
dydtheta_sum = np.sum(dydtheta) * self.vmecOutput.dtheta \
* self.vmecOutput.dzeta * self.vmecOutput.nfp
dydzeta_sum = np.sum(dydzeta) * self.vmecOutput.dtheta \
* self.vmecOutput.dzeta * self.vmecOutput.nfp
dzdtheta_sum = np.sum(dzdtheta) * self.vmecOutput.dtheta \
* self.vmecOutput.dzeta * self.vmecOutput.nfp
dzdzeta_sum = np.sum(dzdzeta) * self.vmecOutput.dtheta \
* self.vmecOutput.dzeta * self.vmecOutput.nfp
self.assertAlmostEqual(dxdtheta_sum, 0)
self.assertAlmostEqual(dxdzeta_sum, 0)
self.assertAlmostEqual(dydtheta_sum, 0)
self.assertAlmostEqual(dydzeta_sum, 0)
self.assertAlmostEqual(dzdtheta_sum, 0)
self.assertAlmostEqual(dzdzeta_sum, 0)
for itheta in range(0, self.vmecOutput.ntheta, 5):
for izeta in range(0, self.vmecOutput.nzeta, 5):
this_zeta = self.vmecOutput.zetas[izeta]
this_theta = self.vmecOutput.thetas[itheta]
dxdzeta_fd = finiteDifferenceDerivative(this_zeta,\
lambda zeta : self.vmecOutput.compute_position(-1, \
this_theta,zeta)[0], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(dxdzeta_fd,
dxdzeta[izeta, itheta],
places=5)
dydzeta_fd = finiteDifferenceDerivative(this_zeta,\
lambda zeta : self.vmecOutput.compute_position(-1, \
this_theta,zeta)[1], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(dydzeta_fd,
dydzeta[izeta, itheta],
places=5)
dzdzeta_fd = finiteDifferenceDerivative(this_zeta,\
lambda zeta : self.vmecOutput.compute_position(-1, \
this_theta,zeta)[2], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(dzdzeta_fd,
dzdzeta[izeta, itheta],
places=5)
dxdtheta_fd = finiteDifferenceDerivative(this_theta,\
lambda theta : self.vmecOutput.compute_position(-1, \
theta,this_zeta,)[0], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(dxdtheta_fd,
dxdtheta[izeta, itheta],
places=5)
dydtheta_fd = finiteDifferenceDerivative(this_theta,\
lambda theta : self.vmecOutput.compute_position(-1, \
theta,this_zeta)[1], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(dydtheta_fd,
dydtheta[izeta, itheta],
places=5)
dzdtheta_fd = finiteDifferenceDerivative(this_theta,\
lambda theta : self.vmecOutput.compute_position(-1, \
theta,this_zeta)[2], epsilon=1e-5 ,method='centered')
self.assertAlmostEqual(dzdtheta_fd,
dzdtheta[izeta, itheta],
places=5)