def deflated_power_iteration(
operator,
num_eigenthings=10,
power_iter_steps=20,
power_iter_err_threshold=1e-4,
momentum=0.0,
use_gpu=True,
to_numpy=True,
):
"""
Compute top k eigenvalues by repeatedly subtracting out dyads
operator: linear operator that gives us access to matrix vector product
num_eigenvals number of eigenvalues to compute
power_iter_steps: number of steps per run of power iteration
power_iter_err_threshold: early stopping threshold for power iteration
returns: np.ndarray of top eigenvalues, np.ndarray of top eigenvectors
"""
eigenvals = []
eigenvecs = []
current_op = operator
prev_vec = None
def _deflate(x, val, vec):
return val * vec.dot(x) * vec
log("beginning deflated power iteration")
for i in range(num_eigenthings):
log("computing eigenvalue/vector %d of %d" % (i + 1, num_eigenthings))
eigenval, eigenvec = power_iteration(
current_op,
power_iter_steps,
power_iter_err_threshold,
momentum=momentum,
use_gpu=use_gpu,
init_vec=prev_vec,
)
log("eigenvalue %d: %.4f" % (i + 1, eigenval))
def _new_op_fn(x, op=current_op, val=eigenval, vec=eigenvec):
return op.apply(x) - _deflate(x, val, vec)
current_op = LambdaOperator(_new_op_fn, operator.size)
prev_vec = eigenvec
eigenvals.append(eigenval)
eigenvec = eigenvec.cpu()
if to_numpy:
eigenvecs.append(eigenvec.numpy())
else:
eigenvecs.append(eigenvec)
eigenvals = np.array(eigenvals)
eigenvecs = np.array(eigenvecs)
# sort them in descending order
sorted_inds = np.argsort(eigenvals)
eigenvals = eigenvals[sorted_inds][::-1]
eigenvecs = eigenvecs[sorted_inds][::-1]
return eigenvals, eigenvecs
def deflated_power_iteration(
operator: Operator,
num_eigenthings: int = 10,
power_iter_steps: int = 20,
power_iter_err_threshold: float = 1e-4,
momentum: float = 0.0,
use_gpu: bool = True,
fp16: bool = False,
to_numpy: bool = True,
) -> Tuple[np.ndarray, np.ndarray]:
"""
Compute top k eigenvalues by repeatedly subtracting out dyads
operator: linear operator that gives us access to matrix vector product
num_eigenvals number of eigenvalues to compute
power_iter_steps: number of steps per run of power iteration
power_iter_err_threshold: early stopping threshold for power iteration
returns: np.ndarray of top eigenvalues, np.ndarray of top eigenvectors
"""
eigenvals = []
eigenvecs = []
current_op = operator
prev_vec = None
def _deflate(x, val, vec):
return val * vec.dot(x) * vec
utils.log("beginning deflated power iteration")
for i in range(num_eigenthings):
utils.log("computing eigenvalue/vector %d of %d" %
(i + 1, num_eigenthings))
eigenval, eigenvec = power_iteration(
current_op,
power_iter_steps,
power_iter_err_threshold,
momentum=momentum,
use_gpu=use_gpu,
fp16=fp16,
init_vec=prev_vec,
)
utils.log("eigenvalue %d: %.4f" % (i + 1, eigenval))
def _new_op_fn(x, op=current_op, val=eigenval, vec=eigenvec):
return utils.maybe_fp16(op.apply(x), fp16) - _deflate(x, val, vec)
current_op = LambdaOperator(_new_op_fn, operator.size)
prev_vec = eigenvec
eigenvals.append(eigenval)
eigenvec = eigenvec.cpu()
if to_numpy:
# Clone so that power_iteration can continue to use torch.
numpy_eigenvec = eigenvec.detach().clone().numpy()
eigenvecs.append(numpy_eigenvec)
else:
eigenvecs.append(eigenvec)
eigenvals = np.array(eigenvals)
eigenvecs = np.array(eigenvecs)
# sort them in descending order
sorted_inds = np.argsort(eigenvals)
eigenvals = eigenvals[sorted_inds][::-1]
eigenvecs = eigenvecs[sorted_inds][::-1]
return eigenvals, eigenvecs