def random_cov(d, diff=None):
"""Generate random covariance matrix.
Generates a random covariance matrix, or two dependent covariance matrices
if the argument `diff` is given.
"""
S = 0.8*np.random.randn(d,d)
copy_triu_to_tril(S)
np.fill_diagonal(S,0)
mineig = linalg.eigvalsh(S, eigvals=(0,0))[0]
drand = 0.8*np.random.randn(d)
if mineig < 0:
S += np.diag(np.exp(drand)-mineig)
else:
S += np.diag(np.exp(drand))
if not diff:
return S.T
S2 = S * np.random.randint(2, size=(d,d))*np.exp(diff*np.random.randn(d,d))
copy_triu_to_tril(S2)
np.fill_diagonal(S2,0)
mineig = linalg.eigvalsh(S2, eigvals=(0,0))[0]
drand += diff*np.random.randn(d)
if mineig < 0:
S2 += np.diag(np.exp(drand)-mineig)
else:
S2 += np.diag(np.exp(drand))
return S.T, S2.T
def random_cov(d, diff=None):
"""Generate random covariance matrix.
Generates a random covariance matrix, or two dependent covariance matrices
if the argument `diff` is given.
"""
S = 0.8 * np.random.randn(d, d)
copy_triu_to_tril(S)
np.fill_diagonal(S, 0)
mineig = linalg.eigvalsh(S, eigvals=(0, 0))[0]
drand = 0.8 * np.random.randn(d)
if mineig < 0:
S += np.diag(np.exp(drand) - mineig)
else:
S += np.diag(np.exp(drand))
if not diff:
return S.T
S2 = S * np.random.randint(2, size=(d, d)) * np.exp(
diff * np.random.randn(d, d))
copy_triu_to_tril(S2)
np.fill_diagonal(S2, 0)
mineig = linalg.eigvalsh(S2, eigvals=(0, 0))[0]
drand += diff * np.random.randn(d)
if mineig < 0:
S2 += np.diag(np.exp(drand) - mineig)
else:
S2 += np.diag(np.exp(drand))
return S.T, S2.T
def invert_normal_params(A, b=None, out_A=None, out_b=None, cho_form=False):
"""Invert moment parameters into natural parameters or vice versa.
Switch between moment parameters (S,m) and natural parameters (Q,r) of
a multivariate normal distribution. Providing (S,m) yields (Q,r) and vice
versa.
Parameters
----------
A : ndarray
A symmetric positive-definite matrix to be inverted. Either the
covariance matrix S or the precision matrix Q.
b : {None, ndarray}, optional
The mean vector m, the natural parameter vector r, or None (default)
if `out_b` is not requested.
out_A, out_b : {None, ndarray, 'in-place'}, optional
Spesifies where the output is calculate into; None (default) indicates
that a new array is created, providing a string 'in-place' overwrites
the corresponding input array.
cho_form : bool
If True, `A` is assumed to be the upper Cholesky of the real S or Q.
Returns
-------
out_A, out_b : ndarray
The corresponding output arrays (`out_A` in F-order). If `b` was not
provided, `out_b` is None.
Raises
------
LinAlgError
If the provided array A is not positive definite.
"""
# Process parameters
if not isinstance(out_A, np.ndarray) and out_A == 'in-place':
out_A = A
elif out_A is None:
out_A = A.copy(order='F')
else:
np.copyto(out_A, A)
if not out_A.flags['FARRAY']:
# Convert from C-order to F-order by transposing (note symmetric)
out_A = out_A.T
if not out_A.flags['FARRAY'] and out_A.shape[0] > 1:
raise ValueError('Provided array A is inappropriate')
if not b is None:
if not isinstance(out_b, np.ndarray) and out_b == 'in-place':
out_b = b
elif out_b is None:
out_b = b.copy()
else:
np.copyto(out_b, b)
else:
out_b = None
# Invert
if not cho_form:
cho = linalg.cho_factor(out_A, overwrite_a=True)
else:
# Already in upper Cholesky form
cho = (out_A, False)
if not out_b is None:
linalg.cho_solve(cho, out_b, overwrite_b=True)
_, info = dpotri_routine(out_A, overwrite_c=True)
if info:
# This should never occour if cho_factor was succesful ... I think
raise linalg.LinAlgError(
"dpotri LAPACK routine failed with error code {}".format(info))
# Copy the upper triangular into the bottom
copy_triu_to_tril(out_A)
return out_A, out_b
def invert_normal_params(A, b=None, out_A=None, out_b=None, cho_form=False):
"""Invert moment parameters into natural parameters or vice versa.
Switch between moment parameters (S,m) and natural parameters (Q,r) of
a multivariate normal distribution. Providing (S,m) yields (Q,r) and vice
versa.
Parameters
----------
A : ndarray
A symmetric positive-definite matrix to be inverted. Either the
covariance matrix S or the precision matrix Q.
b : {None, ndarray}, optional
The mean vector m, the natural parameter vector r, or None (default)
if `out_b` is not requested.
out_A, out_b : {None, ndarray, 'in_place'}, optional
Spesifies where the output is calculate into; None (default) indicates
that a new array is created, providing a string 'in_place' overwrites
the corresponding input array.
cho_form : bool
If True, `A` is assumed to be the upper Cholesky of the real S or Q.
Returns
-------
out_A, out_b : ndarray
The corresponding output arrays (`out_A` in F-order). If `b` was not
provided, `out_b` is None.
Raises
------
LinAlgError
If the provided array A is not positive definite.
"""
# Process parameters
if out_A == 'in_place':
out_A = A
elif out_A is None:
out_A = A.copy(order='F')
else:
np.copyto(out_A, A)
if not out_A.flags['FARRAY']:
# Convert from C-order to F-order by transposing (note symmetric)
out_A = out_A.T
if not out_A.flags['FARRAY'] and out_A.shape[0] > 1:
raise ValueError('Provided array A is inappropriate')
if not b is None:
if out_b == 'in_place':
out_b = b
elif out_b is None:
out_b = b.copy()
else:
np.copyto(out_b, b)
else:
out_b = None
# Invert
if not cho_form:
cho = linalg.cho_factor(out_A, overwrite_a=True)
else:
# Already in upper Cholesky form
cho = (out_A, False)
if not out_b is None:
linalg.cho_solve(cho, out_b, overwrite_b=True)
_, info = dpotri_routine(out_A, overwrite_c=True)
if info:
# This should never occour if cho_factor was succesful ... I think
raise linalg.LinAlgError(
"dpotri LAPACK routine failed with error code {}".format(info))
# Copy the upper triangular into the bottom
copy_triu_to_tril(out_A)
return out_A, out_b
