def _maximal_eigenvector_power_method(matrix,
epsilon=1e-6,
maximum_iterations=100):
"""Returns the maximal right-eigenvector of `matrix` using the power method.
Args:
matrix: 2D Tensor, the matrix of which we will find the maximal
right-eigenvector.
epsilon: nonnegative float, if two iterations of the power method differ (in
L2 norm) by no more than epsilon, we will terminate.
maximum_iterations: nonnegative int, if we perform this many iterations, we
will terminate.
Result:
The maximal right-eigenvector of `matrix`.
Raises:
ValueError: If the `matrix` tensor is not floating-point, or if the
`epsilon` or `maximum_iterations` parameters violate their bounds.
"""
if not matrix.dtype.is_floating:
raise ValueError("multipliers must have a floating-point dtype")
if epsilon <= 0.0:
raise ValueError("epsilon must be strictly positive")
if maximum_iterations <= 0:
raise ValueError("maximum_iterations must be strictly positive")
def while_loop_condition(iteration, eigenvector, old_eigenvector):
"""Returns false if the while loop should terminate."""
not_done = (iteration < maximum_iterations)
not_converged = (standard_ops.norm(eigenvector - old_eigenvector) > epsilon)
return standard_ops.logical_and(not_done, not_converged)
def while_loop_body(iteration, eigenvector, old_eigenvector):
"""Performs one iteration of the power method."""
del old_eigenvector # Needed by the condition, but not the body.
iteration += 1
# We need to use tf.matmul() and tf.expand_dims(), instead of
# tf.tensordot(), since the former will infer the shape of the result, while
# the latter will not (tf.while_loop() needs the shapes).
new_eigenvector = standard_ops.matmul(
matrix, standard_ops.expand_dims(eigenvector, 1))[:, 0]
new_eigenvector /= standard_ops.norm(new_eigenvector)
return (iteration, new_eigenvector, eigenvector)
iteration = standard_ops.constant(0)
eigenvector = standard_ops.ones_like(matrix[:, 0])
eigenvector /= standard_ops.norm(eigenvector)
# We actually want a do-while loop, so we explicitly call while_loop_body()
# once before tf.while_loop().
iteration, eigenvector, old_eigenvector = while_loop_body(
iteration, eigenvector, eigenvector)
iteration, eigenvector, old_eigenvector = control_flow_ops.while_loop(
while_loop_condition,
while_loop_body,
loop_vars=(iteration, eigenvector, old_eigenvector),
name="power_method")
return eigenvector
def _maximal_eigenvector_power_method(matrix,
epsilon=1e-6,
maximum_iterations=100):
"""Returns the maximal right-eigenvector of `matrix` using the power method.
Args:
matrix: 2D Tensor, the matrix of which we will find the maximal
right-eigenvector.
epsilon: nonnegative float, if two iterations of the power method differ (in
L2 norm) by no more than epsilon, we will terminate.
maximum_iterations: nonnegative int, if we perform this many iterations, we
will terminate.
Result: The maximal right-eigenvector of `matrix`.
Raises:
ValueError: If the `matrix` tensor is not floating-point, or if the
`epsilon` or `maximum_iterations` parameters violate their bounds.
"""
if not matrix.dtype.is_floating:
raise ValueError("multipliers must have a floating-point dtype")
if epsilon <= 0.0:
raise ValueError("epsilon must be strictly positive")
if maximum_iterations <= 0:
raise ValueError("maximum_iterations must be strictly positive")
def while_loop_condition(iteration, eigenvector, old_eigenvector):
"""Returns false if the while loop should terminate."""
not_done = (iteration < maximum_iterations)
not_converged = (standard_ops.norm(eigenvector - old_eigenvector) >
epsilon)
return standard_ops.logical_and(not_done, not_converged)
def while_loop_body(iteration, eigenvector, old_eigenvector):
"""Performs one iteration of the power method."""
del old_eigenvector # Needed by the condition, but not the body.
iteration += 1
# We need to use tf.matmul() and tf.expand_dims(), instead of
# tf.tensordot(), since the former will infer the shape of the result, while
# the latter will not (tf.while_loop() needs the shapes).
new_eigenvector = standard_ops.matmul(
matrix, standard_ops.expand_dims(eigenvector, 1))[:, 0]
new_eigenvector /= standard_ops.norm(new_eigenvector)
return (iteration, new_eigenvector, eigenvector)
iteration = standard_ops.constant(0)
eigenvector = standard_ops.ones_like(matrix[:, 0])
eigenvector /= standard_ops.norm(eigenvector)
# We actually want a do-while loop, so we explicitly call while_loop_body()
# once before tf.while_loop().
iteration, eigenvector, old_eigenvector = while_loop_body(
iteration, eigenvector, eigenvector)
iteration, eigenvector, old_eigenvector = control_flow_ops.while_loop(
while_loop_condition,
while_loop_body,
loop_vars=(iteration, eigenvector, old_eigenvector),
name="power_method")
return eigenvector
def while_loop_body(iteration, eigenvector, old_eigenvector):
"""Performs one iteration of the power method."""
del old_eigenvector # Needed by the condition, but not the body.
iteration += 1
# We need to use tf.matmul() and tf.expand_dims(), instead of
# tf.tensordot(), since the former will infer the shape of the result, while
# the latter will not (tf.while_loop() needs the shapes).
new_eigenvector = standard_ops.matmul(
matrix, standard_ops.expand_dims(eigenvector, 1))[:, 0]
new_eigenvector /= standard_ops.norm(new_eigenvector)
return (iteration, new_eigenvector, eigenvector)
def while_loop_body(iteration, eigenvector, old_eigenvector):
"""Performs one iteration of the power method."""
del old_eigenvector # Needed by the condition, but not the body.
iteration += 1
# We need to use tf.matmul() and tf.expand_dims(), instead of
# tf.tensordot(), since the former will infer the shape of the result, while
# the latter will not (tf.while_loop() needs the shapes).
new_eigenvector = standard_ops.matmul(
matrix, standard_ops.expand_dims(eigenvector, 1))[:, 0]
new_eigenvector /= standard_ops.norm(new_eigenvector)
return (iteration, new_eigenvector, eigenvector)
def while_loop_condition(iteration, eigenvector, old_eigenvector): """Returns false if the while loop should terminate.""" not_done = (iteration < maximum_iterations) not_converged = (standard_ops.norm(eigenvector - old_eigenvector) > epsilon) return standard_ops.logical_and(not_done, not_converged)
def while_loop_condition(iteration, eigenvector, old_eigenvector): """Returns false if the while loop should terminate.""" not_done = (iteration < maximum_iterations) not_converged = (standard_ops.norm(eigenvector - old_eigenvector) > epsilon) return standard_ops.logical_and(not_done, not_converged)
