def fourseven(iter_stack):
# load matrices
Ai = iter_stack.A
Bi = iter_stack.B
P1i_roc = iter_stack.P1_roc
P1i_rpinv = iter_stack.P1_rpinv
K2 = roc_hint("B", iter_stack.i, Bi) if mode=="manual" else al.right_ortho_complement(Bi)
K1 = al.regular_completion(K2)
K = st.concat_cols(K1, K2)
assert al.is_regular_matrix(K), "K is not a regular matrix."
Bi_tilde = al.custom_simplify(Bi*K1) # unit matrix
if myStack.calc_G:
Bi_tilde_lpinv = al.left_pseudo_inverse(Bi_tilde)
else:
Bi_tilde_lpinv = None
P1i_tilde_roc = al.custom_simplify( P1i_roc*K1 )
Zi = al.custom_simplify( P1i_roc*K2 )
Zi_lpinv = al.Zi_left_pinv_with_restrictions(P1i_rpinv, P1i_tilde_roc, Zi)
assert al.is_unit_matrix( Zi_lpinv*Zi ), "Zi_lpinv seems to be wrong."
# store
iter_stack.store_special_case_matrices( Zi, Zi_lpinv, Bi_tilde, Bi_tilde_lpinv, P1i_tilde_roc )
return Bi_tilde
def reduction(iter_stack):
P1i = iter_stack.P1
P0i = iter_stack.P0
P1i_roc = roc_hint(
"P1", iter_stack.i,
P1i) if mode == "manual" else al.right_ortho_complement(P1i)
P1i_rpinv = rpinv_hint(
"P1", iter_stack.i,
P1i) if mode == "manual" else al.right_pseudo_inverse(P1i)
P1i_dot = st.time_deriv(P1i, myStack.diffvec_x)
Ai = al.custom_simplify((P0i - P1i_dot) * P1i_rpinv)
Bi = al.custom_simplify((P0i - P1i_dot) * P1i_roc)
if myStack.calc_G:
Bi_lpinv = al.left_pseudo_inverse(Bi)
else:
Bi_lpinv = None
# store
iter_stack.store_reduction_matrices(Ai, Bi, Bi_lpinv, P1i_roc, P1i_rpinv,
P1i_dot)
return Bi
def mul_rs_and_simplify_nc(self, A, B):
""" multiplies nc matrices A and B, right shifts s, converts
the result to commutative and simplifies it
"""
AB_nc = A * B
AB_nc_shifted = self.right_shift_all_in_matrix(AB_nc)
AB_shifted_c = self.make_symbols_commutative(AB_nc_shifted)
extr_result = list(AB_shifted_c)[0]
result = al.custom_simplify(extr_result)
return result
def mul_rs_and_simplify_nc(self, A, B):
""" multiplies nc matrices A and B, right shifts s, converts
the result to commutative and simplifies it
"""
AB_nc = A*B
AB_nc_shifted = self.right_shift_all_in_matrix(AB_nc)
AB_shifted_c = self.make_symbols_commutative(AB_nc_shifted)
extr_result = list(AB_shifted_c)[0]
result = al.custom_simplify(extr_result)
return result
def reduction(iter_stack):
P1i = iter_stack.P1
P0i = iter_stack.P0
P1i_roc = roc_hint("P1", iter_stack.i, P1i) if mode=="manual" else al.right_ortho_complement(P1i)
P1i_rpinv = rpinv_hint("P1", iter_stack.i, P1i) if mode=="manual" else al.right_pseudo_inverse(P1i)
P1i_dot = st.time_deriv(P1i, myStack.diffvec_x)
Ai = al.custom_simplify( (P0i - P1i_dot)*P1i_rpinv )
Bi = al.custom_simplify( (P0i - P1i_dot)*P1i_roc )
if myStack.calc_G:
Bi_lpinv = al.left_pseudo_inverse(Bi)
else:
Bi_lpinv = None
# store
iter_stack.store_reduction_matrices( Ai, Bi, Bi_lpinv, P1i_roc, P1i_rpinv, P1i_dot )
return Bi
def fourseven(iter_stack):
# load matrices
Ai = iter_stack.A
Bi = iter_stack.B
P1i_roc = iter_stack.P1_roc
P1i_rpinv = iter_stack.P1_rpinv
K2 = roc_hint("B", iter_stack.i,
Bi) if mode == "manual" else al.right_ortho_complement(Bi)
K1 = al.regular_completion(K2)
K = st.concat_cols(K1, K2)
assert al.is_regular_matrix(K), "K is not a regular matrix."
Bi_tilde = al.custom_simplify(Bi * K1) # unit matrix
if myStack.calc_G:
Bi_tilde_lpinv = al.left_pseudo_inverse(Bi_tilde)
else:
Bi_tilde_lpinv = None
P1i_tilde_roc = al.custom_simplify(P1i_roc * K1)
Zi = al.custom_simplify(P1i_roc * K2)
Zi_lpinv = al.Zi_left_pinv_with_restrictions(P1i_rpinv, P1i_tilde_roc, Zi)
assert al.is_unit_matrix(Zi_lpinv * Zi), "Zi_lpinv seems to be wrong."
# store
iter_stack.store_special_case_matrices(Zi, Zi_lpinv, Bi_tilde,
Bi_tilde_lpinv, P1i_tilde_roc)
return Bi_tilde
