def ddu(self):
dudr_mat = self.dudrpol
dudphi_mat = self.dudphipol
dr_mat_r = self.dr_mat
dphi_mat_phi= np.delete(self.dphi_mat, -1, 1)
ddudrdr = (np.delete(dudr_mat, 0, 0) \
-np.delete(dudr_mat, -1, 0)) / np.delete(dr_mat_r, -1 ,0)
ddudrdphi = (np.delete(dudr_mat, 0, 1) \
-np.delete(dudr_mat, -1, 1)) / np.delete(dphi_mat_phi, -1 ,0)
ddudphidr = (np.delete(dudphi_mat, 0, 0) \
-np.delete(dudphi_mat, -1, 0)) / dr_mat_r
ddudphidphi = (np.delete(dudphi_mat, 0, 1) \
-np.delete(dudphi_mat, -1, 1)) / dphi_mat_phi
self.ddudrdr = ddudrdr
self.ddudrdphi = np.delete(make_periodic_der(ddudrdphi, -1), 0, 0)
self.ddudphidr = np.delete(ddudphidr, 0, 0)
self.ddudphidphi = np.delete(np.delete(make_periodic_der(ddudphidphi, -1), 0, 0), -1, 0)
self.ddudrdrcart = np.empty(self.phys_surf.shape, dtype = 'object')
self.ddudrdphicart = np.empty(self.phys_surf.shape, dtype = 'object')
self.ddudphidrcart = np.empty(self.phys_surf.shape, dtype = 'object')
self.ddudphidphicart= np.empty(self.phys_surf.shape, dtype = 'object')
dudr_mat, dudphi_mat = self.get_du()[:2]
for ir, rvec in np.ndenumerate(self.phys_surf):
r, phi = rvec[:2]
ur, uphi = self.phys_umat[ir][:2]
rp, phip = r + ur, phi + uphi
durdr, duphidr = dudr_mat[ir][0], dudr_mat[ir][1]
durdphi, duphidphi = dudphi_mat[ir][0], dudphi_mat[ir][1] #[:2] # self.get_du()[1][ir]
ddurdrdr, dduphidrdr, dduzdrdr = self.ddudrdr[ir]
ddurdphidr, dduphidphidr, dduzdphidr = self.ddudphidr[ir]
ddurdrdphi, dduphidrdphi, dduzdrdphi = self.ddudrdphi[ir]
ddurdphidphi, dduphidphidphi, dduzdphidphi = self.ddudphidphi[ir]
self.ddudrdrcart[ir] = np.zeros(3)
self.ddudphidrcart[ir] = np.zeros(3)
self.ddudrdphicart[ir] = np.zeros(3)
self.ddudphidphicart[ir] = np.zeros(3)
self.ddudrdrcart[ir][0] = ddurdrdr*np.cos(phip) - 2*(1 + durdr)*duphidr*np.sin(phip) \
- rp*(duphidr**2*np.cos(phip) + dduphidrdr*np.sin(phip))
self.ddudrdrcart[ir][1] = ddurdrdr*np.sin(phip) + 2*(1 + durdr)*duphidr*np.cos(phip) \
- rp*(duphidr**2*np.sin(phip) - dduphidrdr*np.cos(phip))
self.ddudrdrcart[ir][2] = dduzdrdr
self.ddudphidrcart[ir][0] = ddurdphidr*np.cos(phip) - (1 + durdr)*(1 + duphidphi) \
* np.sin(phip) - durdphi*duphidr*np.sin(phip) \
- rp*((1 + duphidphi)*duphidr*np.cos(phip) \
+ dduphidphidr*np.sin(phip)) + np.sin(phi)
self.ddudphidrcart[ir][1] = ddurdphidr*np.sin(phip) + (1 + durdr)*(1 + duphidphi) \
* np.cos(phip) + durdphi*duphidr*np.cos(phip) \
- rp*(duphidr*(1 + duphidphi)*np.sin(phip) \
- dduphidphidr*np.cos(phip)) - np.cos(phi)
self.ddudphidrcart[ir][2] = dduzdphidr
self.ddudrdphicart[ir][0] = ddurdrdphi*np.cos(phip) - (1 + durdr)*(1 + duphidphi) \
* np.sin(phip) - durdphi*duphidr*np.sin(phip) \
- rp*((1 + duphidphi)*duphidr*np.cos(phip) \
+ dduphidrdphi*np.sin(phip)) + np.sin(phi)
self.ddudrdphicart[ir][1] = ddurdrdphi*np.sin(phip) + (1 + durdr)*(1 + duphidphi) \
* np.cos(phip) + durdphi*duphidr*np.cos(phip) \
- rp*(duphidr*(1 + duphidphi)*np.sin(phip) \
- dduphidrdphi*np.cos(phip)) - np.cos(phi)
self.ddudrdphicart[ir][2] = dduzdrdphi
self.ddudphidphicart[ir][0] = ddurdphidphi*np.cos(phip) - durdphi*(1 + duphidphi) \
* np.sin(phip) - durdphi*(1 + duphidphi)*np.sin(phip) \
- rp*(dduphidphidphi*np.sin(phip) \
+ (1 + duphidphi)**2*np.cos(phip)) + r*np.cos(phi)
self.ddudphidphicart[ir][1] = ddurdphidphi*np.sin(phip) + durdphi*(1 + duphidphi) \
* np.cos(phip) + durdphi*(1 + duphidphi)*np.cos(phip) \
+ rp*(dduphidphidphi*np.cos(phip) \
- (1 + duphidphi)**2*np.sin(phip)) + r*np.sin(phi)
self.ddudphidphicart[ir][2] = dduzdphidphi
def du(self):
# r_mat = make_periodic_surf(self.ext_surf, self.phi_period)
r_mat = make_periodic(self.ext_surf, 'surf', phi_period = self.phi_period)
u_mat_pol = make_periodic(self.ext_umat, 'umat', sym_op = self.sym_op)
dr_mat = np.delete(r_mat, 0, 0) - np.delete(r_mat, -1, 0)
dphi_mat = np.delete(r_mat, 0, 1) - np.delete(r_mat, -1, 1)
dr_mat_r = np.empty(dr_mat.shape)
dphi_mat_phi = np.empty(dphi_mat.shape)
for ir,dr in np.ndenumerate(dr_mat):
dr_mat_r[ir] = dr[0]
for iphi, dphi in np.ndenumerate(dphi_mat):
dphi_mat_phi[iphi] = dphi[1]
dudrpol = (np.delete(u_mat_pol, 0, 0) \
-np.delete(u_mat_pol, -1, 0)) / dr_mat_r
dudphipol = (np.delete(u_mat_pol, 0, 1) \
-np.delete(u_mat_pol, -1, 1)) / dphi_mat_phi
self.dr_mat = dr_mat_r
self.dphi_mat = make_periodic_der(dphi_mat_phi, 1, nums = True)
self.dudrpol = dudrpol
self.dudphipol = make_periodic_der(dudphipol)
# testi
dudrcart = np.empty(self.dr_mat.shape, dtype = 'object')
dudphicart = np.empty(self.dphi_mat.shape, dtype = 'object')
for ind, vec in np.ndenumerate(self.dr_mat):
dudrcart[ind] = np.zeros(3)
r, phi = r_mat[ind][:2] #self.ext_surf[ind][:2]
#rp, phip = r + self.ext_umat[ind][0], phi + self.ext_umat[ind][1]
rp, phip = r + u_mat_pol[ind][0], phi + u_mat_pol[ind][1]
durdr, duphidr, duzdr = self.dudrpol[ind]
dudrcart[ind][0] = -np.cos(phi) - rp*duphidr*np.sin(phip) \
+(1 + durdr)*np.cos(phip)
dudrcart[ind][1] = -np.sin(phi) + rp*duphidr*np.cos(phip) \
+(1 + durdr)*np.sin(phip)
dudrcart[ind][2] = duzdr
for ind, vec in np.ndenumerate(self.dphi_mat):
dudphicart[ind] = np.zeros(3)
r, phi = r_mat[ind][:2] #self.ext_surf[ind][:2]
#rp, phip = r + self.ext_umat[ind][0], phi + self.ext_umat[ind][1]
rp, phip = r + u_mat_pol[ind][0], phi + u_mat_pol[ind][1]
durdphi, duphidphi, duzdphi \
= self.dudphipol[ind]
dudphicart[ind][0] = r*np.sin(phi) + np.cos(phip)*durdphi \
-rp*(1 + duphidphi)*np.sin(phip)
dudphicart[ind][1] = -r*np.cos(phi) + np.sin(phip)*durdphi \
+rp*(1 + duphidphi)*np.cos(phip)
dudphicart[ind][2] = duzdphi
self.dudrcart = dudrcart
self.dudphicart = dudphicart