def loss(y_pred,
y_true,
metric=SO3.bi_invariant_metric,
representation="vector"):
"""Loss function given by a Riemannian metric on a Lie group.
Parameters
----------
y_pred : array-like
Prediction on SO(3).
y_true : array-like
Ground-truth on SO(3).
metric : RiemannianMetric
Metric used to compute the loss and gradient.
representation : str, {'vector', 'matrix'}
Representation chosen for points in SO(3).
Returns
-------
lie_loss : array-like
Loss using the Riemannian metric.
"""
if representation == "quaternion":
y_pred = SO3.rotation_vector_from_quaternion(y_pred)
y_true = SO3.rotation_vector_from_quaternion(y_true)
lie_loss = lie_group.loss(y_pred, y_true, SO3, metric)
return lie_loss
def loss(y_pred, y_true,
metric=SO3.bi_invariant_metric,
representation='vector'):
if representation == 'quaternion':
y_pred = SO3.rotation_vector_from_quaternion(y_pred)
y_true = SO3.rotation_vector_from_quaternion(y_true)
loss = lie_group.loss(y_pred, y_true, SO3, metric)
return loss
def loss(y_pred, y_true,
metric=SE3.left_canonical_metric,
representation='vector'):
"""
Loss function given by a riemannian metric on a Lie group,
by default the left-invariant canonical metric.
"""
if gs.ndim(y_pred) == 1:
y_pred = gs.expand_dims(y_pred, axis=0)
if gs.ndim(y_true) == 1:
y_true = gs.expand_dims(y_true, axis=0)
if representation == 'quaternion':
y_pred_rot_vec = SO3.rotation_vector_from_quaternion(y_pred[:, :4])
y_pred = gs.hstack([y_pred_rot_vec, y_pred[:, 4:]])
y_true_rot_vec = SO3.rotation_vector_from_quaternion(y_true[:, :4])
y_true = gs.hstack([y_true_rot_vec, y_true[:, 4:]])
loss = lie_group.loss(y_pred, y_true, SE3, metric)
return loss
def loss(y_pred,
y_true,
metric=SE3.left_canonical_metric,
representation='vector'):
"""Loss function given by a Riemannian metric on a Lie group.
Parameters
----------
y_pred : array-like
Prediction on SE(3).
y_true : array-like
Ground-truth on SE(3).
metric : RiemannianMetric
Metric used to compute the loss and gradient.
representation : str, {'vector', 'matrix'}
Representation chosen for points in SE(3).
Returns
-------
lie_loss : array-like
Loss using the Riemannian metric.
"""
if gs.ndim(y_pred) == 1:
y_pred = gs.expand_dims(y_pred, axis=0)
if gs.ndim(y_true) == 1:
y_true = gs.expand_dims(y_true, axis=0)
if representation == 'quaternion':
y_pred_rot_vec = SO3.rotation_vector_from_quaternion(y_pred[:, :4])
y_pred = gs.hstack([y_pred_rot_vec, y_pred[:, 4:]])
y_true_rot_vec = SO3.rotation_vector_from_quaternion(y_true[:, :4])
y_true = gs.hstack([y_true_rot_vec, y_true[:, 4:]])
lie_loss = lie_group.loss(y_pred, y_true, SE3, metric)
if gs.ndim(lie_loss) == 2:
lie_loss = gs.squeeze(lie_loss, axis=1)
if gs.ndim(lie_loss) == 1 and gs.shape(lie_loss)[0] == 1:
lie_loss = gs.squeeze(lie_loss, axis=0)
return lie_loss