def _fidfi(y):
# fi first
f = self._model(tnext, y)
fi = deepcopy(f)
beta = deepcopy(fi)
for n in self._sequence:
fi[n] = 137.0*y[n] - 300.0*s[n] + \
300.0*self.__prev[3][n] - \
200.0*self.__prev[2][n] + \
75.0*self.__prev[1][n] - \
12.0*self.__prev[0][n] - 60.0*h*f[n]
beta[n] = - fi[n]
# then fid = dfi[n]/dy[m] = 137*dy[n]/dy[m] - 60*h*df[n]/dy[m],
# or - 60*h*df[n]/dy[m]; n != m, and
# 137 - 60*h*df[n]/dy[m]; n == m
jacob = self._jake3(tnext, y, hf, ha)
fid = Matrix()
for n in self._sequence:
derivs = array('d', [])
for m in self._sequence:
deriv = 137.0*krond(n, m) - 60.0*h*jacob[n][m]
derivs.append(deriv)
fid.append(derivs)
alpha = Matrix(fid)
return alpha, beta
def _fidfi(y):
# fi first
f = self._model(tnext, y)
fi = deepcopy(f)
beta = deepcopy(fi)
for n in self._sequence:
fi[n] = y[n] - s[n] - h*f[n]
beta[n] = - fi[n]
# then fid = dfi[n]/dy[m] = dy[n]/dy[m] - h*df[n]/dy[m], or
# - h*df[n]/dy[m]; n != m, and
# 1.0 - h*df[n]/dy[m]; n == m
jacob = self._jake3(tnext, y, hf, ha)
fid = Matrix()
for n in self._sequence:
derivs = array('d', [])
for m in self._sequence:
deriv = 1.0*krond(n, m) - h*jacob[n][m]
derivs.append(deriv)
fid.append(derivs)
alpha = Matrix(fid)
return alpha, beta
def _fidfi(y):
# fi first
f = self._model(tnext, y)
fi = deepcopy(f)
beta = deepcopy(fi)
for n in self._sequence:
fi[n] = 25.0*y[n] - 48.0*s[n] + 36.0*self.__prev[2][n] - \
16.0*self.__prev[1][n] + \
3.0*self.__prev[0][n] - 12.0*h*f[n]
beta[n] = - fi[n]
# then fid = dfi[n]/dy[m] = 3*dy[n]/dy[m] - 2*h*df[n]/dy[m], or
# - 12*h*df[n]/dy[m]; n != m, and
# 25 - 12*h*df[n]/dy[m]; n == m
jacob = self._jake3(tnext, y, hf, ha)
fid = Matrix()
for n in self._sequence:
derivs = array('d', [])
for m in self._sequence:
deriv = 25.0*krond(n, m) - 12.0*h*jacob[n][m]
derivs.append(deriv)
fid.append(derivs)
alpha = Matrix(fid)
return alpha, beta