def extract_quadratic_coeffs(self, affine_expr, quad_forms):
""" Assumes quadratic forms all have variable arguments.
Affine expressions can be anything.
"""
assert affine_expr.is_dpp()
# Here we take the problem objective, replace all the SymbolicQuadForm
# atoms with variables of the same dimensions.
# We then apply the canonInterface to reduce the "affine head"
# of the expression tree to a coefficient vector c and constant offset d.
# Because the expression is parameterized, we extend that to a matrix
# [c1 c2 ...]
# [d1 d2 ...]
# where ci,di are the vector and constant for the ith parameter.
affine_id_map, affine_offsets, x_length, affine_var_shapes = \
InverseData.get_var_offsets(affine_expr.variables())
op_list = [affine_expr.canonical_form[0]]
param_coeffs = canonInterface.get_problem_matrix(
op_list, x_length, affine_offsets, self.param_to_size,
self.param_id_map, affine_expr.size)
# Iterates over every entry of the parameters vector,
# and obtains the Pi and qi for that entry i.
# These are then combined into matrices [P1.flatten(), P2.flatten(), ...]
# and [q1, q2, ...]
constant = param_coeffs[-1, :]
c = param_coeffs[:-1, :].A
# coeffs stores the P and q for each quad_form,
# as well as for true variable nodes in the objective.
coeffs = {}
# The goal of this loop is to appropriately multiply
# the matrix P of each quadratic term by the coefficients
# in param_coeffs. Later we combine all the quadratic terms
# to form a single matrix P.
for var in affine_expr.variables():
# quad_forms maps the ids of the SymbolicQuadForm atoms
# in the objective to (modified parent node of quad form,
# argument index of quad form,
# quad form atom)
if var.id in quad_forms:
var_id = var.id
orig_id = quad_forms[var_id][2].args[0].id
var_offset = affine_id_map[var_id][0]
var_size = affine_id_map[var_id][1]
c_part = c[var_offset:var_offset + var_size, :]
if quad_forms[var_id][2].P.value is not None:
# Convert to sparse matrix.
P = quad_forms[var_id][2].P.value
if sp.issparse(P) and not isinstance(P, sp.coo_matrix):
P = P.tocoo()
else:
P = sp.coo_matrix(P)
if var_size == 1:
c_part = np.ones((P.shape[0], 1)) * c_part
else:
P = sp.eye(var_size, format='coo')
# We multiply the columns of P, by c_part
# by operating directly on the data.
data = P.data[:, None] * c_part[P.col]
P_tup = (data, (P.row, P.col), P.shape)
# Conceptually similar to
# P = P[:, :, None] * c_part[None, :, :]
if orig_id in coeffs:
if 'P' in coeffs[orig_id]:
# Concatenation becomes addition when constructing
# COO matrix because repeated indices are summed.
# Conceptually equivalent to
# coeffs[orig_id]['P'] += P_tup
acc_data, (acc_row, acc_col), _ = coeffs[orig_id]['P']
acc_data = np.concatenate([acc_data, data], axis=0)
acc_row = np.concatenate([acc_row, P.row], axis=0)
acc_col = np.concatenate([acc_col, P.col], axis=0)
P_tup = (acc_data, (acc_row, acc_col), P.shape)
coeffs[orig_id]['P'] = P_tup
else:
coeffs[orig_id]['P'] = P_tup
else:
coeffs[orig_id] = dict()
coeffs[orig_id]['P'] = P_tup
coeffs[orig_id]['q'] = np.zeros((P.shape[0], c.shape[1]))
else:
var_offset = affine_id_map[var.id][0]
var_size = np.prod(affine_var_shapes[var.id], dtype=int)
if var.id in coeffs:
coeffs[var.id]['q'] += c[var_offset:var_offset +
var_size, :]
else:
coeffs[var.id] = dict()
coeffs[var.id]['q'] = c[var_offset:var_offset +
var_size, :]
return coeffs, constant
def extract_quadratic_coeffs(self, affine_expr, quad_forms):
""" Assumes quadratic forms all have variable arguments.
Affine expressions can be anything.
"""
assert affine_expr.is_dpp()
# Here we take the problem objective, replace all the SymbolicQuadForm
# atoms with variables of the same dimensions.
# We then apply the canonInterface to reduce the "affine head"
# of the expression tree to a coefficient vector c and constant offset d.
# Because the expression is parameterized, we extend that to a matrix
# [c1 c2 ...]
# [d1 d2 ...]
# where ci,di are the vector and constant for the ith parameter.
affine_id_map, affine_offsets, x_length, affine_var_shapes = \
InverseData.get_var_offsets(affine_expr.variables())
op_list = [affine_expr.canonical_form[0]]
param_coeffs = canonInterface.get_problem_matrix(
op_list, x_length, affine_offsets, self.param_to_size,
self.param_id_map, affine_expr.size)
# TODO vectorize this code.
# Iterates over every entry of the parameters vector,
# and obtains the Pi and qi for that entry i.
# These are then combined into matrices [P1.flatten(), P2.flatten(), ...]
# and [q1, q2, ...]
coeff_list = []
constant = param_coeffs[-1, :]
for p in range(param_coeffs.shape[1]):
c = param_coeffs[:-1, p].A.flatten()
# coeffs stores the P and q for each quad_form,
# as well as for true variable nodes in the objective.
coeffs = {}
# The goal of this loop is to appropriately multiply
# the matrix P of each quadratic term by the coefficients
# in param_coeffs. Later we combine all the quadratic terms
# to form a single matrix P.
for var in affine_expr.variables():
# quad_forms maps the ids of the SymbolicQuadForm atoms
# in the objective to (modified parent node of quad form,
# argument index of quad form,
# quad form atom)
if var.id in quad_forms:
var_id = var.id
orig_id = quad_forms[var_id][2].args[0].id
var_offset = affine_id_map[var_id][0]
var_size = affine_id_map[var_id][1]
c_part = c[var_offset:var_offset + var_size]
if quad_forms[var_id][2].P.value is not None:
P = quad_forms[var_id][2].P.value
if c_part.size == 1:
P = c_part[0] * P
else:
P = P @ sp.diags(c_part)
else:
P = sp.diags(c_part)
if orig_id in coeffs:
coeffs[orig_id]['P'] += P
else:
coeffs[orig_id] = dict()
coeffs[orig_id]['P'] = P
coeffs[orig_id]['q'] = np.zeros(P.shape[0])
else:
var_offset = affine_id_map[var.id][0]
var_size = np.prod(affine_var_shapes[var.id], dtype=int)
if var.id in coeffs:
coeffs[var.id]['P'] += sp.csr_matrix(
(var_size, var_size))
coeffs[var.id]['q'] += c[var_offset:var_offset +
var_size]
else:
coeffs[var.id] = dict()
coeffs[var.id]['P'] = sp.csr_matrix(
(var_size, var_size))
coeffs[var.id]['q'] = c[var_offset:var_offset +
var_size]
coeff_list.append(coeffs)
return coeff_list, constant