Beispiel #1
0
 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)
Beispiel #2
0
 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)
Beispiel #3
0
    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
Beispiel #4
0
 def dP(self, zval):
     # for debug purposes
     return tn.eval(self._dP, self.z, zval)
Beispiel #5
0
    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)
Beispiel #6
0
 def dP(self, zval):
     # for debug purposes
     return tn.eval(self._dP, self.z, zval)
Beispiel #7
0
    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)