cr.sparse.lop.identity

cr.sparse.lop.identity(in_dim, out_dim=None, axis=0)[source]

Returns an identity linear operator from model space to data space

Parameters

  • in_dim (int) – Dimension of the model space

  • out_dim (int) – Dimension of the data space

  • axis (int) – For multi-dimensional array input, the axis along which the linear operator will be applied

Returns

An identity linear operator

Return type

Operator

If out_dim is not specified, then we assume that both model space and data space have same dimension.

Example

A square identity operator:

>>> T = lop.identity(4)
>>> T.times(jnp.arange(4) + 0.)
DeviceArray([0., 1., 2., 3.], dtype=float32)
>>> T.trans(jnp.arange(4))
DeviceArray([0, 1, 2, 3], dtype=int32)

A tall identity operator (output has more dimensions):

>>> T = lop.identity(4, 6)
>>> T.times(jnp.arange(4) + 0.)
DeviceArray([0., 1., 2., 3., 0., 0.], dtype=float32)
>>> T.trans(T.times(jnp.arange(4) + 0.))
DeviceArray([0., 1., 2., 3.], dtype=float32)

A wide identity operator (output has less dimensions):

>>> T = lop.identity(4, 3)
>>> T.times(jnp.arange(4) + 0.)
DeviceArray([0., 1., 2.], dtype=float32)
>>> T.trans(T.times(jnp.arange(4) + 0.))
DeviceArray([0., 1., 2., 0.], dtype=float32)

By default T applies along columns of a matrix (axis=0):

>>> T.times(jnp.arange(20).reshape(4, 5))
DeviceArray([[ 0,  1,  2,  3,  4],
 [ 5,  6,  7,  8,  9],
 [10, 11, 12, 13, 14]], dtype=int32)

Identity operator applying along rows of a 2D matrix:

>>> T = lop.identity(4, 3, axis=1)
>>> T.times(jnp.arange(20).reshape(5, 4))
DeviceArray([[ 0,  1,  2],
 [ 4,  5,  6],
 [ 8,  9, 10],
 [12, 13, 14],
 [16, 17, 18]], dtype=int32)