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Compute the Moore-Penrose pseudo-inverse of one or more matrices.
tf.linalg.pinv(
a, rcond=None, validate_args=False, name=None
)
Calculate the generalized inverse of a matrix using its singular-value decomposition (SVD) and including all large singular values.
The pseudo-inverse of a matrix A
, is defined as: 'the matrix that 'solves'
[the least-squares problem] A @ x = b
,' i.e., if x_hat
is a solution, then
A_pinv
is the matrix such that x_hat = A_pinv @ b
. It can be shown that if
U @ Sigma @ V.T = A
is the singular value decomposition of A
, then
A_pinv = V @ inv(Sigma) U^T
. [(Strang, 1980)][1]
This function is analogous to numpy.linalg.pinv
.
It differs only in default value of rcond
. In numpy.linalg.pinv
, the
default rcond
is 1e-15
. Here the default is
10. * max(num_rows, num_cols) * np.finfo(dtype).eps
.
Returns | |
---|---|
a_pinv
|
(Batch of) pseudo-inverse of input a . Has same shape as a except
rightmost two dimensions are transposed.
|
Raises | |
---|---|
TypeError
|
if input a does not have float -like dtype .
|
ValueError
|
if input a has fewer than 2 dimensions.
|
Examples
import tensorflow as tf
import tensorflow_probability as tfp
a = tf.constant([[1., 0.4, 0.5],
[0.4, 0.2, 0.25],
[0.5, 0.25, 0.35]])
tf.matmul(tf.linalg.pinv(a), a)
# ==> array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]], dtype=float32)
a = tf.constant([[1., 0.4, 0.5, 1.],
[0.4, 0.2, 0.25, 2.],
[0.5, 0.25, 0.35, 3.]])
tf.matmul(tf.linalg.pinv(a), a)
# ==> array([[ 0.76, 0.37, 0.21, -0.02],
[ 0.37, 0.43, -0.33, 0.02],
[ 0.21, -0.33, 0.81, 0.01],
[-0.02, 0.02, 0.01, 1. ]], dtype=float32)
References
[1]: G. Strang. 'Linear Algebra and Its Applications, 2nd Ed.' Academic Press, Inc., 1980, pp. 139-142.