# tf.linalg.lu_solve

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| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linalg_impl.py#L937-L1032) |

Solves systems of linear eqns `A X = RHS`, given LU factorizations.

#### View aliases


**Compat aliases for migration**

See
[Migration guide](https://www.tensorflow.org/guide/migrate) for
more details.

[`tf.compat.v1.linalg.lu_solve`](https://www.tensorflow.org/api_docs/python/tf/linalg/lu_solve)

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    tf.linalg.lu_solve(
        lower_upper, perm, rhs, validate_args=False, name=None
    )

> [!NOTE]
> **Note:** this function does not verify the implied matrix is actually invertible nor is this condition checked even when `validate_args=True`.

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| ## Args ||
|---|---|
| `lower_upper` | `lu` as returned by [`tf.linalg.lu`](https://www.tensorflow.org/versions/r2.14/api_docs/python/tf/linalg/lu), i.e., if `matmul(P, matmul(L, U)) = X` then `lower_upper = L + U - eye`. |
| `perm` | `p` as returned by `tf.linag.lu`, i.e., if `matmul(P, matmul(L, U)) = X` then `perm = argmax(P)`. |
| `rhs` | Matrix-shaped float `Tensor` representing targets for which to solve; `A X = RHS`. To handle vector cases, use: `lu_solve(..., rhs[..., tf.newaxis])[..., 0]`. |
| `validate_args` | Python `bool` indicating whether arguments should be checked for correctness. Note: this function does not verify the implied matrix is actually invertible, even when `validate_args=True`. Default value: `False` (i.e., don't validate arguments). |
| `name` | Python `str` name given to ops managed by this object. Default value: `None` (i.e., 'lu_solve'). |

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| ## Returns ||
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| `x` | The `X` in `A @ X = RHS`. |

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#### Examples

    import numpy as np
    import tensorflow as tf
    import tensorflow_probability as tfp

    x = [[[1., 2],
          [3, 4]],
         [[7, 8],
          [3, 4]]]
    inv_x = tf.linalg.lu_solve(*tf.linalg.lu(x), rhs=tf.eye(2))
    tf.assert_near(tf.matrix_inverse(x), inv_x)
    # ==> True