def rejection_sampling_z(N, y, W1, W2):
"""
A rejection sampling method for sampling the inactive variables from a
polytope.
**See Also**
domains.sample_z
"""
m, n = W1.shape
s = np.dot(W1, y).reshape((m, 1))
# Build a box around z for uniform sampling
qps = QPSolver()
A = np.vstack((W2, -W2))
b = np.vstack((-1-s, -1+s)).reshape((2*m, 1))
lbox, ubox = np.zeros((1,m-n)), np.zeros((1,m-n))
for i in range(m-n):
clb = np.zeros((m-n,1))
clb[i,0] = 1.0
lbox[0,i] = qps.linear_program_ineq(clb, A, b)[i,0]
cub = np.zeros((m-n,1))
cub[i,0] = -1.0
ubox[0,i] = qps.linear_program_ineq(cub, A, b)[i,0]
bn = BoundedNormalizer(lbox, ubox)
Zbox = bn.unnormalize(np.random.uniform(-1.0,1.0,size=(50*N,m-n)))
ind = np.all(np.dot(A, Zbox.T) >= b, axis=0)
if np.sum(ind) >= N:
Z = Zbox[ind,:]
return Z[:N,:].reshape((N,m-n))
else:
return None
def rejection_sampling_z(N, y, W1, W2):
"""A rejection sampling method for sampling the from a polytope.
Parameters
----------
N : int
the number of inactive variable samples
y : ndarray
the value of the active variables
W1 : ndarray
m-by-n matrix that contains the eigenvector bases of the n-dimensional
active subspace
W2 : ndarray
m-by-(m-n) matrix that contains the eigenvector bases of the
(m-n)-dimensional inactive subspace
Returns
-------
Z : ndarray
N-by-(m-n) matrix that contains values of the inactive variable that
correspond to the given `y`
See Also
--------
domains.sample_z
Notes
-----
The interface for this implementation is written specifically for
`domains.sample_z`.
"""
m, n = W1.shape
s = np.dot(W1, y).reshape((m, 1))
# Build a box around z for uniform sampling
qps = QPSolver()
A = np.vstack((W2, -W2))
b = np.vstack((-1 - s, -1 + s)).reshape((2 * m, 1))
lbox, ubox = np.zeros((1, m - n)), np.zeros((1, m - n))
for i in range(m - n):
clb = np.zeros((m - n, 1))
clb[i, 0] = 1.0
lbox[0, i] = qps.linear_program_ineq(clb, A, b)[i, 0]
cub = np.zeros((m - n, 1))
cub[i, 0] = -1.0
ubox[0, i] = qps.linear_program_ineq(cub, A, b)[i, 0]
bn = BoundedNormalizer(lbox, ubox)
Zbox = bn.unnormalize(np.random.uniform(-1.0, 1.0, size=(50 * N, m - n)))
ind = np.all(np.dot(A, Zbox.T) >= b, axis=0)
if np.sum(ind) >= N:
Z = Zbox[ind, :]
return Z[:N, :].reshape((N, m - n))
else:
return None
def rejection_sampling_z(N, y, W1, W2):
"""A rejection sampling method for sampling the from a polytope.
Parameters
----------
N : int
the number of inactive variable samples
y : ndarray
the value of the active variables
W1 : ndarray
m-by-n matrix that contains the eigenvector bases of the n-dimensional
active subspace
W2 : ndarray
m-by-(m-n) matrix that contains the eigenvector bases of the
(m-n)-dimensional inactive subspace
Returns
-------
Z : ndarray
N-by-(m-n) matrix that contains values of the inactive variable that
correspond to the given `y`
See Also
--------
domains.sample_z
Notes
-----
The interface for this implementation is written specifically for
`domains.sample_z`.
"""
m, n = W1.shape
s = np.dot(W1, y).reshape((m, 1))
# Build a box around z for uniform sampling
qps = QPSolver()
A = np.vstack((W2, -W2))
b = np.vstack((-1-s, -1+s)).reshape((2*m, 1))
lbox, ubox = np.zeros((1,m-n)), np.zeros((1,m-n))
for i in range(m-n):
clb = np.zeros((m-n,1))
clb[i,0] = 1.0
lbox[0,i] = qps.linear_program_ineq(clb, A, b)[i,0]
cub = np.zeros((m-n,1))
cub[i,0] = -1.0
ubox[0,i] = qps.linear_program_ineq(cub, A, b)[i,0]
bn = BoundedNormalizer(lbox, ubox)
Zbox = bn.unnormalize(np.random.uniform(-1.0,1.0,size=(50*N,m-n)))
ind = np.all(np.dot(A, Zbox.T) >= b, axis=0)
if np.sum(ind) >= N:
Z = Zbox[ind,:]
return Z[:N,:].reshape((N,m-n))
else:
return None