def _delf(self, t, xval, uval):
# calculates the jump term assuming the field switches
# between fplus and fminus at (t, x)
params = np.concatenate(([t], xval, uval))
dphi = self.dphi(xval)
# determine if going from f- to f+
# or vice-versa
if matmult(dphi[:self.dim],xval[-self.dim:]) > 0:
fp = self._fplus.func(*params)
fm = self._fmins.func(*params)
else:
fp = self._fmins.func(*params)
fm = self._fplus.func(*params)
#out = 2*np.outer(fp-fm, dphi)/np.abs(matmult(fm+fp, dphi))
#out = np.outer(fp-fm, dphi)/np.abs(matmult(fm, dphi))
out = np.outer(fp, dphi)/matmult(dphi, fm) \
#+ np.eye(len(fp)) - np.outer(dphi, dphi)/np.dot(dphi,dphi)
#Tracer()()
#out = np.zeros((2*self.dim, 2*self.dim))
#for i in range(self.dim):
# out[self.si, i] = -M[self.si, i]
return out
def _delf(self, t, xval, uval):
# calculates the jump term assuming the field switches
# between fplus and fminus at (t, x)
params = np.concatenate(([t], xval, uval))
dphi = self.dphi(xval)
# determine if going from f- to f+
# or vice-versa
if matmult(dphi[:self.dim], xval[-self.dim:]) > 0:
fp = self._fplus.func(*params)
fm = self._fmins.func(*params)
else:
fp = self._fmins.func(*params)
fm = self._fplus.func(*params)
#out = 2*np.outer(fp-fm, dphi)/np.abs(matmult(fm+fp, dphi))
#out = np.outer(fp-fm, dphi)/np.abs(matmult(fm, dphi))
out = np.outer(fp, dphi)/matmult(dphi, fm) \
#+ np.eye(len(fp)) - np.outer(dphi, dphi)/np.dot(dphi,dphi)
#Tracer()()
#out = np.zeros((2*self.dim, 2*self.dim))
#for i in range(self.dim):
# out[self.si, i] = -M[self.si, i]
return out
def dfdu(self, t, xval, uval=[0, 0]):
# choose between dfxm and dfxp
if xval[self.si] > 0:
func = self._dfup.func
else:
func = self._dfum.func
vals = np.concatenate([[t], xval, uval])
return func(*vals)
def dfdu(self, t, xval, uval=[0, 0]):
# choose between dfxm and dfxp
if xval[self.si] > 0:
func = self._dfup.func
else:
func = self._dfum.func
vals = np.concatenate([[t], xval, uval])
return func(*vals)
def f(self, t, xval, uval=[0, 0], ctrl=None):
# choose between _fplus and _fmins
# depending on the configuration
# assume that ctrl is a rule for substituting u
if xval[self.si] >= 0:
func = self._fplus.func
else:
func = self._fmins.func
vals = np.concatenate([[t], xval, uval])
return func(*vals)
def f(self, t, xval, uval=[0, 0], ctrl=None):
# choose between _fplus and _fmins
# depending on the configuration
# assume that ctrl is a rule for substituting u
if xval[self.si] >= 0:
func = self._fplus.func
else:
func = self._fmins.func
vals = np.concatenate([[t], xval, uval])
return func(*vals)
def _makefp(self, params):
zdot = self.x[self.dim:]
out = np.concatenate((
zdot,
np.dot(
self.Mzi, -tn.einsum('i,ijk,k', zdot, self.dMz, zdot) +
tn.einsum('i,ikl,k', zdot, self.dMz, zdot) / 2 + self.dVz) +
matmult(
tn.subs(self._dPsi, self.qtoz),
self.Mqi, # here we might need subs
self.u)))
out = tn.SymExpr(tn.subs(out, self.ztox))
out.callable(*params)
return out
def _makefp(self, params):
zdot = self.x[self.dim:]
out = np.concatenate((zdot,
np.dot(self.Mzi,
- tn.einsum(
'i,ijk,k', zdot, self.dMz, zdot)
+ tn.einsum(
'i,ikl,k', zdot, self.dMz, zdot) / 2
+ self.dVz)
+ matmult(
tn.subs(self._dPsi, self.qtoz),
self.Mqi, # here we might need subs
self.u)
))
out = tn.SymExpr(tn.subs(out, self.ztox))
out.callable(*params)
return out
def _delf(self, t, xval, uval):
# calculates the jump term assuming the field switches
# between fplus and fminus at (t, x)
params = np.concatenate(([t], xval, uval))
fp = self._fplus.func(*params)
fm = self._fmins.func(*params)
dphi = self.dphi(xval)
# this assumes x = [z, zdot]
M = tn.eval(self.Mz, self.z, xval[:self.dim])
M = scipy.linalg.block_diag(M, np.eye(self.dim))
#dphi = matmult(M, dphi)
out = -np.outer(fp-fm, dphi)/np.abs(np.inner(fp, dphi))
#Tracer()()
#out = np.zeros((2*self.dim, 2*self.dim))
#for i in range(self.dim):
# out[self.si, i] = -M[self.si, i]
return out
def _makefm(self, params):
zdot = self.x[self.dim:]
OhmP = tn.subs(self._Ohm, zip(self.z, self._P))
OhmI = tn.subs(self._dPsi, zip(self.q, OhmP))
zz = self._P
zzdot = np.dot(self._dP, zdot)
out = -tn.einsum('i,ijk,k', zzdot, self.dMzz, zzdot) \
+ tn.einsum('i,ikj,k', zzdot, self.dMzz, zzdot) / 2
out = np.dot(self.Mzzi, out + self.dVzz)
out = out - tn.einsum('ijk,j,k', tn.diff(self._dP, self.z), zdot, zdot)
out = out + matmult(OhmI, self.Mqi, self.u)
# in general, there should be a subs here
out = matmult(self._dPi, out)
out = np.concatenate((zdot, out))
out = tn.SymExpr(tn.subs(out, self.ztox))
out.callable(*params)
return out
def _makefm(self, params):
zdot = self.x[self.dim:]
OhmP = tn.subs(self._Ohm, zip(self.z, self._P))
OhmI = tn.subs(self._dPsi, zip(self.q, OhmP))
zz = self._P
zzdot = np.dot(self._dP, zdot)
out = -tn.einsum('i,ijk,k', zzdot, self.dMzz, zzdot) \
+ tn.einsum('i,ikj,k', zzdot, self.dMzz, zzdot) / 2
out = np.dot(self.Mzzi, out + self.dVzz)
out = out - tn.einsum('ijk,j,k',
tn.diff(self._dP, self.z), zdot, zdot)
out = out + matmult(OhmI, self.Mqi, self.u)
# in general, there should be a subs here
out = matmult(self._dPi, out)
out = np.concatenate((zdot, out))
out = tn.SymExpr(tn.subs(out, self.ztox))
out.callable(*params)
return out
