def P(self, zval):
# choose between identity and fancy projection
if zval[self.si] > 0:
return zval
else:
expr = self._P
vals = zval
params = self.z
return tn.eval(expr, params, vals)
def P(self, zval):
# choose between identity and fancy projection
if zval[self.si] > 0:
return zval
else:
expr = self._P
vals = zval
params = self.z
return tn.eval(expr, params, vals)
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 dP(self, zval):
# for debug purposes
return tn.eval(self._dP, self.z, zval)
def __init__(self, si=0, **kwargs):
# this is the special index: z[si] = phi(z)
self.si = si
self.t = S('t')
n = self.dim
self.qtoz = zip(self.q, self._Ohm)
self.alltoz = self.qtoz + zip(self.x, self.z)
self.ztoq = zip(self.z, self._Psi)
self.alltoq = self.ztoq + zip(self.x, self._Psi)
self.ztox = zip(self.z, self.x)
# dOhm/dz, dPhi/dq, assuming the pieces are already defined
self._dOhm = tn.diff(self._Ohm, self.z)
self._dPsi = tn.diff(self._Psi, self.q)
self.Mz = matmult(self._dOhm.T, self.Mq, self._dOhm)
self.Mzi = self._Mzi()
self.dMq = tn.diff(self.Mq, self.q)
self.dMz = tn.diff(self.Mz, self.z)
self.delta = self.Mzi[:, self.si] / self.Mzi[self.si, self.si]
# self.ddelta = tn.diff(self.delta, self.z)
self.Vz = self.Vq.subs(self.alltoz, simultaneous=True)
self.dVz = tn.diff(self.Vz, self.z)
self._P = self._makeP(self.k)
self._dP = tn.diff(self._P, self.z)
self._dPi = np.array(sym.Matrix(self._dP).inv())
self.ztozz = {self.z[i]: self._P[i] for i in range(self.dim)}
self.Mzzi = tn.subs(self.Mzi, self.ztozz)
self.dMzz = tn.subs(self.dMz, self.ztozz)
self.dVzz = tn.subs(self.dVz, self.ztozz)
self.dPzz = tn.subs(self._dP, self.ztozz)
params = [self.t, self.x, self.u]
self._fplus = self._makefp(params)
self._fmins = self._makefm(params)
self._dfxp = tn.SymExpr(self._fplus.diff(self.x))
self._dfxp.callable(*params)
self._dfxm = tn.SymExpr(self._fmins.diff(self.x))
self._dfxm.callable(*params)
self._dfup = tn.SymExpr(self._fplus.diff(self.u))
self._dfup.callable(*params)
self._dfum = tn.SymExpr(self._fmins.diff(self.u))
self._dfum.callable(*params)
self._ohm = tn.lambdify(self.z, self._Ohm)
self._psi = tn.lambdify(self.q, self._Psi)
# make the jump term generator callable
# and a bunch of other stuff as well
self.delf = lambda t, x, u: self._delf(t, x, u)
self.Ohm = lambda z: tn.eval(self._Ohm, self.z, z)
self.dOhm = lambda z: tn.eval(self._dOhm, self.z, z)
self.Psi = lambda q: tn.eval(self._Psi, self.q, q)
self.dPsi = lambda q: tn.eval(self._dPsi, self.q, q)
def dP(self, zval):
# for debug purposes
return tn.eval(self._dP, self.z, zval)
def __init__(self, si=0, **kwargs):
# this is the special index: z[si] = phi(z)
self.si = si
self.t = S('t')
n = self.dim
self.qtoz = zip(self.q, self._Ohm)
self.alltoz = self.qtoz + zip(self.x, self.z)
self.ztoq = zip(self.z, self._Psi)
self.alltoq = self.ztoq + zip(self.x, self._Psi)
self.ztox = zip(self.z, self.x)
# dOhm/dz, dPhi/dq, assuming the pieces are already defined
self._dOhm = tn.diff(self._Ohm, self.z)
self._dPsi = tn.diff(self._Psi, self.q)
self.Mz = matmult(self._dOhm.T, self.Mq, self._dOhm)
self.Mzi = self._Mzi()
self.dMq = tn.diff(self.Mq, self.q)
self.dMz = tn.diff(self.Mz, self.z)
self.delta = self.Mzi[:, self.si] / self.Mzi[self.si, self.si]
# self.ddelta = tn.diff(self.delta, self.z)
self.Vz = self.Vq.subs(self.alltoz, simultaneous=True)
self.dVz = tn.diff(self.Vz, self.z)
self._P = self._makeP(self.k)
self._dP = tn.diff(self._P, self.z)
self._dPi = np.array(sym.Matrix(self._dP).inv())
self.ztozz = {self.z[i]: self._P[i] for i in range(self.dim)}
self.Mzzi = tn.subs(self.Mzi, self.ztozz)
self.dMzz = tn.subs(self.dMz, self.ztozz)
self.dVzz = tn.subs(self.dVz, self.ztozz)
self.dPzz = tn.subs(self._dP, self.ztozz)
params = [self.t, self.x, self.u]
self._fplus = self._makefp(params)
self._fmins = self._makefm(params)
self._dfxp = tn.SymExpr(self._fplus.diff(self.x))
self._dfxp.callable(*params)
self._dfxm = tn.SymExpr(self._fmins.diff(self.x))
self._dfxm.callable(*params)
self._dfup = tn.SymExpr(self._fplus.diff(self.u))
self._dfup.callable(*params)
self._dfum = tn.SymExpr(self._fmins.diff(self.u))
self._dfum.callable(*params)
self._ohm = tn.lambdify(self.z, self._Ohm)
self._psi = tn.lambdify(self.q, self._Psi)
# make the jump term generator callable
# and a bunch of other stuff as well
self.delf = lambda t, x, u: self._delf(t, x, u)
self.Ohm = lambda z: tn.eval(self._Ohm, self.z, z)
self.dOhm = lambda z: tn.eval(self._dOhm, self.z, z)
self.Psi = lambda q: tn.eval(self._Psi, self.q, q)
self.dPsi = lambda q: tn.eval(self._dPsi, self.q, q)