def calculate_H_matrix(self):
""" unimodular completion of P(d/dt) with H = P1i * ... * P11 * P10
"""
pc.print_line()
print("Exit condition satisfied\n")
H_relevant_matrices, H_tilde_relevant_matrices = self._myStack.get_H_relevant_matrices()
H1 = self.multiply_matrices_in_list( H_relevant_matrices )
if not len(H_tilde_relevant_matrices)==0:
H2 = self.multiply_matrices_in_list( H_tilde_relevant_matrices )
else:
H2 = sp.Matrix([])
H = st.concat_rows(H1, H2)
m, n = H.shape
assert n==len(self._myStack.vec_x), "Dimensions of H-Matrix do not fit."
print "H-matrix = "
pc.print_nicely(H)
print "\n"
self.H = H
def calculate_H_matrix(self):
""" unimodular completion of P(d/dt) with H = P1i * ... * P11 * P10
"""
pc.print_line()
print("Exit condition satisfied\n")
H_relevant_matrices, H_tilde_relevant_matrices = self._myStack.get_H_relevant_matrices(
)
H1 = self.multiply_matrices_in_list(H_relevant_matrices)
if not len(H_tilde_relevant_matrices) == 0:
H2 = self.multiply_matrices_in_list(H_tilde_relevant_matrices)
else:
H2 = sp.Matrix([])
H = st.concat_rows(H1, H2)
m, n = H.shape
assert n == len(
self._myStack.vec_x), "Dimensions of H-Matrix do not fit."
print("H-matrix = ")
pc.print_nicely(H)
print("\n")
self.H = H
def calculate_G_matrix(self):
G = self.calculate_Gi_matrix(0)
for i in range(self._myStack.iteration_steps() - 1):
G = G * self.calculate_Gi_matrix(i + 1)
G_shifted = self.right_shift_all_in_matrix(G)
print("G-matrix = ")
pc.print_nicely(G_shifted)
self.G = G_shifted
def calculate_G_matrix(self):
G = self.calculate_Gi_matrix(0)
for i in xrange(self._myStack.iteration_steps()-1):
G = G*self.calculate_Gi_matrix(i+1)
G_shifted = self.right_shift_all_in_matrix(G)
print "G-matrix = "
pc.print_nicely(G_shifted)
self.G = G_shifted
def integrate_dwi(self, w, i):
print "------"
print "w[" + str(i) + "].d = 0"
print "------"
print "<-> Integrability condition satisfied for w[" + str(i) + "].\n\n"
print "Integrating w[" + str(i) + "]:"
y=0
for j in xrange(0,len(self._myStack.basis)):
y += sp.integrate(w[i].coeff[j], self._myStack.basis[j])
print "y[" + str(i) + "] ="
pc.print_nicely(y)
print "\n\n"
def tangent_system():
# exterior derivative of F_eq:
try:
P1i # in case the system is given by the matrices P1i and P0i
except NameError:
print "\n\n0 = F(x,xdot) ="; pc.print_nicely(example.F_eq)
P1i = example.F_eq.jacobian(myStack.vec_xdot)
P0i = example.F_eq.jacobian(myStack.vec_x)
print "\n\n"
return P1i, P0i
def tangent_system():
# exterior derivative of F_eq:
try:
P1i # in case the system is given by the matrices P1i and P0i
except NameError:
print("\n\n0 = F(x,xdot) =")
pc.print_nicely(example.F_eq)
P1i = example.F_eq.jacobian(myStack.vec_xdot)
P0i = example.F_eq.jacobian(myStack.vec_x)
print("\n\n")
return P1i, P0i
def integrate_dwi(self, w, i):
print("------")
print("w[" + str(i) + "].d = 0")
print("------")
print("<-> Integrability condition satisfied for w[" + str(i) +
"].\n\n")
print("Integrating w[" + str(i) + "]:")
y = 0
for j in range(0, len(self._myStack.basis)):
y += sp.integrate(w[i].coeff[j], self._myStack.basis[j])
print("y[" + str(i) + "] =")
pc.print_nicely(y)
print("\n\n")
diff_symbols = example.diff_symbols
else:
diff_symbols = sp.Matrix([])
mode = "auto" # "manual" or "auto"
calc_G = False # calculate G matrix
# raw_input() does not seem to handle empty strings, so this is a
# workaround to escape from the input
auto = None
myStack = sc.SystemStack(diff_symbols)
myStack.vec_x = example.vec_x
myStack.calc_G = calc_G
print "x ="; pc.print_nicely(myStack.vec_x)
print "\n\n","xdot ="; pc.print_nicely(myStack.vec_xdot)
def end_condition(Bi):
""" The algorithm ends if Bi has full row rank.
"""
n, p = Bi.shape
return True if (n == st.rnd_number_rank(Bi)) else False
def is_special_case(Bi):
""" Checks for special case
"""
n, p = Bi.shape
return True if (st.rnd_number_rank(Bi) < p) else False
def roc_hint(matrix_string, i, matrix):
else:
diff_symbols = sp.Matrix([])
mode = "auto" # "manual" or "auto"
calc_G = False # calculate G matrix
# raw_input() does not seem to handle empty strings, so this is a
# workaround to escape from the input
auto = None
myStack = sc.SystemStack(diff_symbols)
myStack.vec_x = example.vec_x
myStack.calc_G = calc_G
print("x =")
pc.print_nicely(myStack.vec_x)
print("\n\n", "xdot =")
pc.print_nicely(myStack.vec_xdot)
def end_condition(Bi):
""" The algorithm ends if Bi has full row rank.
"""
n, p = Bi.shape
return True if (n == st.rnd_number_rank(Bi)) else False
def is_special_case(Bi):
""" Checks for special case
"""
n, p = Bi.shape