def to_sparse(self) -> _csr_matrix:
r"""Returns the sparse matrix representation of the operator. Note that,
in general, the size of the matrix is exponential in the number of quantum
numbers, and this operation should thus only be performed for
low-dimensional Hilbert spaces or sufficiently sparse operators.
This method requires an indexable Hilbert space.
Returns:
The sparse matrix representation of the operator.
"""
concrete_op = self.collect()
hilb = self.hilbert
x = hilb.all_states()
sections = np.empty(x.shape[0], dtype=np.int32)
x_prime, mels = concrete_op.get_conn_flattened(x, sections)
numbers = hilb.states_to_numbers(x_prime)
sections1 = np.empty(sections.size + 1, dtype=np.int32)
sections1[1:] = sections
sections1[0] = 0
## eliminate duplicates from numbers
# rows_indices = compute_row_indices(hilb.states_to_numbers(x), sections1)
return _csr_matrix(
(mels, numbers, sections1),
shape=(self.hilbert.n_states, self.hilbert.n_states),
)
def to_sparse(self):
r"""Returns the sparse matrix representation of the operator. Note that,
in general, the size of the matrix is exponential in the number of quantum
numbers, and this operation should thus only be performed for
low-dimensional Hilbert spaces or sufficiently sparse operators.
This method requires an indexable Hilbert space.
Returns:
scipy.sparse.csr_matrix: The sparse matrix representation of the operator.
"""
hilb = self.hilbert
x = hilb.all_states()
sections = _np.empty(x.shape[0], dtype=_np.int32)
x_prime, mels = self.get_conn_flattened(x, sections)
numbers = hilb.states_to_numbers(x_prime)
sections1 = _np.empty(sections.size + 1, dtype=_np.int32)
sections1[1:] = sections
sections1[0] = 0
return _csr_matrix((mels, numbers, sections1))
def _hadamard_mat(n: int, k: int, sparse: bool = False):
if n is None:
raise ValueError("Wire count cannot be `None`")
H = np.array([[1, 1], [1, -1]]) / np.sqrt(2)
acc = sp._csr_matrix([[1]])
for j in range(n):
acc = sp.kron(acc, H if j == k else sp.eye(2), format="csr")
return acc if sparse else acc.toarray()
def _phase_mat(n: int, k: int, theta: float, sparse: bool = False):
if n is None:
raise ValueError("Wire count cannot be `None`")
P = np.array([[1, 0], [0, np.exp(1j * theta)]])
acc = sp._csr_matrix([[1]])
for j in range(n):
acc = sp.kron(acc, P if j == k else sp.eye(2), format="csr")
return acc if sparse else acc.toarray()
def _cnot_mat(n: int, k1: int, k2: int, sparse: bool = False):
assert k1 != k2
if n is None:
raise ValueError("Wire count cannot be `None`")
X = sp._csr_matrix((2**n, 2**n), dtype=complex) if sparse \
else np.zeros((2**n, 2**n), dtype=complex)
for k in range(2**n):
B = int_to_bitlist(k, n)
B[k2] = (B[k1] + B[k2]) % 2
b = bitlist_to_int(B)
X[b, k] = 1
return X
def _sdf_to_csr(sdf, dtype=_np.float64):
cols, rows, datas = [], [], []
for col, name in enumerate(sdf):
s = sdf[name]
row = s.sp_index.to_int_index().indices
cols.append(_np.repeat(col, len(row)))
rows.append(row)
datas.append(s.sp_values.astype(dtype, copy=False))
cols = _np.concatenate(cols)
rows = _np.concatenate(rows)
datas = _np.concatenate(datas)
return _csr_matrix((datas, (rows, cols)), shape=sdf.shape)
def _xymodN_mat(n: int, k: int, q: int, x: int, N: int, sparse: bool = False):
assert 2**q >= N
assert k + q - 1 < n
X = sp._csr_matrix((2**n, 2**n), dtype=complex) if sparse \
else np.zeros((2**n, 2**n), dtype=complex)
for i in range(2**n):
I = i2b(i, n)
j = b2i(I[k:k + q])
if j < N:
J = (j * x) % N
else:
J = j
X[b2i(I[:k] + i2b(J, q) + I[k + q:]), i] = 1.0 + 0.0j
return X
def _multiple_regression_with_penalty(dep_var,
ind_vars,
data,
weights=None,
penalty=0.0,
constant=False,
use_sparse=True,
solver='auto'):
DS_FLAG = False
if isinstance(data, _Table):
DS_FLAG = True
data = data.to_df()
if isinstance(ind_vars, tuple):
ind_vars = list(ind_vars)
if not isinstance(ind_vars, list):
ind_vars = [ind_vars]
X = data[ind_vars].values
y = data[dep_var].values
if weights is not None:
w = data[weights].values.astype(float)
w /= w.sum()
X, y, w = X[w > 0], y[w > 0], w[w > 0]
else:
w = None
mask = ~_np.isnan(y)
X = X[mask, :]
y = y[mask]
if _np.min(w) == 0.:
raise ValueError("weight is 0")
if use_sparse:
X = _csr_matrix(X)
model = _linear_model.Ridge(alpha=penalty,
fit_intercept=constant,
copy_X=False,
solver=solver)
model.fit(X, y, sample_weight=w)
coefs = _pd.Series({var: coef for var, coef in zip(ind_vars, model.coef_)})
coefs['Intercept'] = model.intercept_
if DS_FLAG:
coefs = coefs.to_dict()
return coefs
def _cxymodN_mat(n: int,
k1: int,
k2: int,
q: int,
x: int,
N: int,
sparse: bool = False):
assert 2**q >= N
assert k2 + q - 1 < n
assert k1 < k2 or k1 >= k2 + q
X = sp._csr_matrix((2**n, 2**n), dtype=complex) if sparse \
else np.zeros((2**n, 2**n), dtype=complex)
for i in range(2**n):
I = i2b(i, n)
j = b2i(I[k2:k2 + q])
if j < N and I[k1] == "1":
J = (j * x) % N
else:
J = j
X[b2i(I[:k2] + i2b(J, q) + I[k2 + q:]), i] = 1.0 + 0.0j
return X
def _multiple_regression_with_penalty(dep_var,
ind_vars,
data,
weights=None,
penalty=0.,
constant=False,
use_sparse=True):
DS_FLAG = False
if isinstance(data, _ds.Table):
DS_FLAG = True
data = data.to_df()
if not isinstance(ind_vars, list):
ind_vars = [ind_vars]
if use_sparse:
data = data.to_sparse(fill_value=0)
X = data[ind_vars].values
y = data[dep_var].to_dense().values
m, n = X.shape
if weights is not None:
w = data[weights].to_dense().values.astype(float)
if use_sparse:
X = _csr_matrix(X)
model = _linear_model.Ridge(alpha=penalty,
fit_intercept=constant,
copy_X=False)
model.fit(X, y, sample_weight=w)
coefs = _pd.Series({var: coef for var, coef in zip(ind_vars, model.coef_)})
if DS_FLAG:
coefs = coefs.to_dict()
return coefs