def linearize_vector_valued_state_function(
vector_valued_function: sym.MatrixBase,
state_vector_symbols: tp.Tuple[sym.Symbol, ...]) \
-> tp.Tuple[sym.MatrixBase, sym.MatrixBase]:
"""
This function takes a vector involving state variables and computed the
coefficients of a first order Taylor expansion around zero.
Args:
vector_valued_function: a column vector depending on the state
state_vector_symbols: state vector as a tuple of symbols
Returns: a tuple consisting of the constant and the linear coefficient in
that order
"""
# construct dictionary mapping state variables to zero:
zero_state_dict = {state_variable: sym.core.numbers.Zero()
for state_variable
in state_vector_symbols}
# generate constant coefficient
constant_coefficient = vector_valued_function.subs(zero_state_dict)
# generate linear coefficient
linear_coefficient = sym.zeros(len(vector_valued_function),
len(state_vector_symbols))
for i in range(len(vector_valued_function)):
for j, state_vector_symbol in enumerate(state_vector_symbols):
matrix_element = \
(vector_valued_function[i]
.diff(state_vector_symbol)
.subs(zero_state_dict))
linear_coefficient[i, j] = matrix_element
return constant_coefficient, linear_coefficient
def numpy_to_sympy(m, **options):
"""Convert a numpy matrix to a sympy matrix."""
return MatrixBase(m)
def scipy_sparse_to_sympy(m, **options):
"""Convert a scipy.sparse matrix to a sympy matrix."""
return MatrixBase(m.todense())