def residuals(f, g, s, x, dr, nodes, weights, p, diff=True):
N, n_x = x.shape
dr.set_values(x)
output = numpy.zeros((N, n_x))
if not diff:
for i in range(nodes.shape[0]):
E = nodes[i, :][None, :].repeat(N, axis=0)
S = g(s, x, E, p)
X = dr.interpolate(S)
t = f(s, x, E, S, X, p)
output += weights[i]*t
return output
if diff:
output_x = scipy.sparse.csr_matrix((N*n_x, N*n_x))
for i in range(nodes.shape[0]):
E = nodes[i, :][None, :].repeat(N, axis=0)
S, S_s, S_x, S_E = g(s, x, E, p, diff=True)
X, X_S, X_x = dr.interpolate(S, deriv=True, deriv_X=True)
R, R_s, R_x, R_E, R_S, R_X = f(s, x, E, S, X, p, diff=True)
output += weights[i]*R
t1 = weights[i]*(R_x + smult(R_S, S_x) + smult(R_X, smult(X_S, S_x))) # N.n_x.n_x
t1 = serial_to_full(t1)
t2 = weights[i] * serial_to_full(R_X) @ diag_to_full(X_x)
output_x += t1 + t2
return output, output_x
def g(self, s, x, e, p, derivs=True):
if not derivs:
a = self.__a(s, x, p, derivs=False)[0]
return self.__g(s, x, a, e, p, derivs=False)
else:
[a, a_s, a_x] = self.__a(s, x, p, derivs=True)
[g, g_s, g_x, g_a, g_e] = self.__g(s, x, a, e, p, derivs=True)
G = g
G_s = g_s + smult(g_a, a_s)
G_x = g_x + smult(g_a, a_x)
G_e = g_e
return [G, G_s, G_x, G_e]
def g(self,s,x,e,p,derivs=True):
if not derivs:
a = self.__a(s,x,p,derivs=False)[0]
return self.__g(s,x,a,e,p,derivs=False)
else:
[a,a_s,a_x] = self.__a(s,x,p,derivs=True)
[g,g_s,g_x,g_a,g_e] = self.__g(s,x,a,e,p,derivs=True)
G = g
G_s = g_s + smult(g_a,a_s)
G_x = g_x + smult(g_a,a_x)
G_e = g_e
return [G,G_s,G_x,G_e]
def f(self, s, x, snext, xnext, e, p, derivs=True):
if not derivs:
a = self.__a(s,x,p,derivs=False)[0]
anext = self.__a(snext,xnext,p,derivs=False)[0]
return self.__f(s,x,snext,xnext,a,anext,e,p,derivs=False)
else:
[a,a_s,a_x] = self.__a(s,x,p,derivs=True)
[A,A_S,A_X] = self.__a(snext,xnext,p,derivs=True)
[f,f_s,f_x,f_S,f_X,f_a,f_A] = self.__f(s,x,snext,xnext,a,A,e,p)
F = f
F_s = f_s + smult(f_a,a_s)
F_x = f_x + smult(f_a,a_x)
F_S = f_S + smult(f_A,A_S)
F_X = f_X + smult(f_A,A_X)
return [F,F_s,F_x,F_S,F_X]
def f(self, s, x, snext, xnext, e, p, derivs=True):
if not derivs:
a = self.__a(s, x, p, derivs=False)[0]
anext = self.__a(snext, xnext, p, derivs=False)[0]
return self.__f(s, x, snext, xnext, a, anext, e, p, derivs=False)
else:
[a, a_s, a_x] = self.__a(s, x, p, derivs=True)
[A, A_S, A_X] = self.__a(snext, xnext, p, derivs=True)
[f, f_s, f_x, f_S, f_X, f_a,
f_A] = self.__f(s, x, snext, xnext, a, A, e, p)
F = f
F_s = f_s + smult(f_a, a_s)
F_x = f_x + smult(f_a, a_x)
F_S = f_S + smult(f_A, A_S)
F_X = f_X + smult(f_A, A_X)
return [F, F_s, F_x, F_S, F_X]
