tf.linalg.pinv
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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.
Args |
|---|
a
|
(Batch of) float-like matrix-shaped Tensor(s) which are to be
pseudo-inverted.
|
rcond
|
Tensor of small singular value cutoffs. Singular values smaller
(in modulus) than rcond * largest_singular_value (again, in modulus) are
set to zero. Must broadcast against tf.shape(a)[:-2].
Default value: 10. * max(num_rows, num_cols) * np.finfo(a.dtype).eps.
|
validate_args
|
When True, additional assertions might be embedded in the
graph.
Default value: False (i.e., no graph assertions are added).
|
name
|
Python str prefixed to ops created by this function.
Default value: 'pinv'.
|
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.
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Last updated 2024-04-26 UTC.
[[["Easy to understand","easyToUnderstand","thumb-up"],["Solved my problem","solvedMyProblem","thumb-up"],["Other","otherUp","thumb-up"]],[["Missing the information I need","missingTheInformationINeed","thumb-down"],["Too complicated / too many steps","tooComplicatedTooManySteps","thumb-down"],["Out of date","outOfDate","thumb-down"],["Samples / code issue","samplesCodeIssue","thumb-down"],["Other","otherDown","thumb-down"]],["Last updated 2024-04-26 UTC."],[],[],null,["# tf.linalg.pinv\n\n\u003cbr /\u003e\n\n|--------------------------------------------------------------------------------------------------------------------------------------|\n| [View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v2.16.1/tensorflow/python/ops/linalg/linalg_impl.py#L807-L934) |\n\nCompute the Moore-Penrose pseudo-inverse of one or more matrices.\n\n#### View aliases\n\n\n**Compat aliases for migration**\n\nSee\n[Migration guide](https://www.tensorflow.org/guide/migrate) for\nmore details.\n\n[`tf.compat.v1.linalg.pinv`](https://www.tensorflow.org/api_docs/python/tf/linalg/pinv)\n\n\u003cbr /\u003e\n\n tf.linalg.pinv(\n a, rcond=None, validate_args=False, name=None\n )\n\nCalculate the [generalized inverse of a matrix](https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse) using its\nsingular-value decomposition (SVD) and including all large singular values.\n\nThe pseudo-inverse of a matrix `A`, is defined as: 'the matrix that 'solves'\n\\[the least-squares problem\\] `A @ x = b`,' i.e., if `x_hat` is a solution, then\n`A_pinv` is the matrix such that `x_hat = A_pinv @ b`. It can be shown that if\n`U @ Sigma @ V.T = A` is the singular value decomposition of `A`, then\n`A_pinv = V @ inv(Sigma) U^T`. \\[(Strang, 1980)\\]\\[1\\]\n\nThis function is analogous to [`numpy.linalg.pinv`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.pinv.html).\nIt differs only in default value of `rcond`. In `numpy.linalg.pinv`, the\ndefault `rcond` is `1e-15`. Here the default is\n`10. * max(num_rows, num_cols) * np.finfo(dtype).eps`.\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Args ---- ||\n|-----------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| `a` | (Batch of) `float`-like matrix-shaped `Tensor`(s) which are to be pseudo-inverted. |\n| `rcond` | `Tensor` of small singular value cutoffs. Singular values smaller (in modulus) than `rcond` \\* largest_singular_value (again, in modulus) are set to zero. Must broadcast against `tf.shape(a)[:-2]`. Default value: `10. * max(num_rows, num_cols) * np.finfo(a.dtype).eps`. |\n| `validate_args` | When `True`, additional assertions might be embedded in the graph. Default value: `False` (i.e., no graph assertions are added). |\n| `name` | Python `str` prefixed to ops created by this function. Default value: 'pinv'. |\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Returns ------- ||\n|----------|---------------------------------------------------------------------------------------------------------------|\n| `a_pinv` | (Batch of) pseudo-inverse of input `a`. Has same shape as `a` except rightmost two dimensions are transposed. |\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Raises ------ ||\n|--------------|--------------------------------------------------|\n| `TypeError` | if input `a` does not have `float`-like `dtype`. |\n| `ValueError` | if input `a` has fewer than 2 dimensions. |\n\n\u003cbr /\u003e\n\n#### Examples\n\n import tensorflow as tf\n import tensorflow_probability as tfp\n\n a = tf.constant([[1., 0.4, 0.5],\n [0.4, 0.2, 0.25],\n [0.5, 0.25, 0.35]])\n tf.matmul(tf.linalg.pinv(a), a)\n # ==\u003e array([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]], dtype=float32)\n\n a = tf.constant([[1., 0.4, 0.5, 1.],\n [0.4, 0.2, 0.25, 2.],\n [0.5, 0.25, 0.35, 3.]])\n tf.matmul(tf.linalg.pinv(a), a)\n # ==\u003e array([[ 0.76, 0.37, 0.21, -0.02],\n [ 0.37, 0.43, -0.33, 0.02],\n [ 0.21, -0.33, 0.81, 0.01],\n [-0.02, 0.02, 0.01, 1. ]], dtype=float32)\n\n#### References\n\n\\[1\\]: G. Strang. 'Linear Algebra and Its Applications, 2nd Ed.' Academic Press,\nInc., 1980, pp. 139-142."]]
View source on GitHub