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import sympy
import scipy.special
import scipy.sparse
import numpy as np
from polymatrix.polystruct import init_equation, init_poly_matrix, init_poly_vector
from polymatrix.sympyutils import poly_to_data_coord, poly_to_matrix
from polymatrix.utils import variable_to_index
binom = scipy.special.binom
def skew_symmetric(degree, p_row, p_col):
if p_col < p_row:
return p_col, p_row, -1
def zero_diagonal_for_uneven_degree(degree, p_row, p_col):
if degree % 2 == 1 and p_row == p_col:
return 0
def gradient(degree, v_row, monom):
if degree == 1:
factor = sum(v_row==e for e in monom) + 1
if monom[-1] < v_row:
n_v_row = monom[-1]
n_monom = sorted(monom + (v_row,), reverse=True)
if v_row <= monom[-1]:
n_v_row = v_row
n_monom = monom
return n_v_row, n_monom, factor
x = sympy.symbols('v_dc, i_d, i_q')
vdc, id, iq = x
g_dc = 3
wl = 106
jr_poly_list = [
g_dc, -1, g_dc*wl,
1, 0, wl,
-g_dc*wl, -wl, 0
]
jr_terms = poly_to_data_coord(list(sympy.poly(p, x) for p in jr_poly_list))
# print(jr_terms)
h = vdc**2/2 + id**2/2 + iq**2/2
dh_poly_list = [
sympy.diff(h, vdc), sympy.diff(h, id), sympy.diff(h, iq)
]
dh_terms = poly_to_data_coord(list(sympy.poly(p, x) for p in dh_poly_list))
# print(dh_terms)
mg_poly_list = [
g_dc-id, -iq,
vdc+1, 0,
0, vdc+1
]
mg_terms = poly_to_data_coord(list(sympy.poly(p, x) for p in mg_poly_list))
# print(mg_terms)
nabla_h = init_poly_vector(subs=dh_terms)
JR = init_poly_matrix(subs=jr_terms)
mg = init_poly_matrix(subs=mg_terms)
nabla_ha = init_poly_vector(
degrees=(1,),
re_index_func_2=gradient,
)
JRa = init_poly_matrix(
degrees=(0,1,2),
re_index_func=skew_symmetric,
subs_func=zero_diagonal_for_uneven_degree,
)
u = init_poly_vector(degrees=(1,2))
eq = init_equation(
terms = [(JR, nabla_ha), (JRa, nabla_ha), (JRa, nabla_h), (mg, u)],
n_var = 2,
# terms = [(JR, nabla_ha)],
# n_var = 2,
)
# n_var = 2
# n_param_nabla_ha = sum(n_var*binom(n_var+p-1, p) for p in nabla_ha.degrees)
# n_param_JRa = sum(n_var**2*binom(n_var+p-1, p) for p in JRa.non_zero_degrees)
# n_param_u = sum(n_var*binom(n_var+p-1, p) for p in u.non_zero_degrees)
# total = n_param_nabla_ha+n_param_JRa+n_param_u
# print(f'{n_param_nabla_ha=}')
# print(f'{n_param_JRa=}')
# print(f'{n_param_u=}')
# print(f'{total=}')
# print(binom(total+2-1, 2))
# mat = init_poly_matrix(
# degrees=(1,),
# re_index_func=skew_symmetric,
# subs_func=zero_diagonal_for_uneven_degree,
# )
# vec = init_poly_vector(
# subs={0: {(0, 0): 1, (1, 0): 1}},
# )
# # mat = init_poly_matrix(
# # subs={0: {(0, 0): 1, (1, 0): 1, (0, 1): 1, (1, 1): 1}},
# # )
# # vec = init_poly_vector(
# # degrees=(1,),
# # re_index_func_2=gradient,
# # )
# eq = init_equation(
# terms = [(mat, vec)],
# n_var = 2,
# )
eq_tuples, offset_dict, n_param = eq.create()
print(f'{list(offset_dict.values())=}')
print(f'{n_param=}')
# mapping from row index to entry in eq_tuples
rows_to_eq = list(set(key for eq_tuple_degree in eq_tuples.values() for key in eq_tuple_degree.keys()))
eq_to_rows = {eq: idx for idx, eq in enumerate(rows_to_eq)}
print(f'n_eq = {len(rows_to_eq)}')
# # mapping from col index to entry in eq_tuples
# cols_to_var = list(set(key for eq in eq_tuples[degree].values() for key in eq.keys()))
# var_to_cols = {var: idx for idx, var in enumerate(cols_to_var)}
def gen_matrix_per_degree():
for degree, eq_tuple_degree in eq_tuples.items():
if 0 < degree:
def gen_coords(eq_tuple_degree=eq_tuple_degree):
for eq, var_dict in eq_tuple_degree.items():
zero_degree_val = eq_tuples[0][eq][0]
row = eq_to_rows[eq]
for var, value in var_dict.items():
# col = variable_to_index(n_param, var)
# col = var_to_cols[var]
col = var
yield row, col, value / zero_degree_val
row, col, data = list(zip(*gen_coords()))
n_col = int(binom(n_param+degree-1, degree))
n_row = int(max(row) + 1)
sparse_matrix = scipy.sparse.coo_matrix((data, (row, col)), dtype=np.float64, shape=(n_row, n_col)).toarray()
yield degree, sparse_matrix
result = dict(gen_matrix_per_degree())
print(result[1].shape)
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