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| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/experimental/linalg/no_pivot_ldl.py#L53-L109) |

Non-pivoted batched LDL factorization.

    tfp.experimental.linalg.no_pivot_ldl(
        matrix, name='no_pivot_ldl'
    )

Performs the LDL factorization, using the outer product algorithm from \[1\]. No
pivoting (or block pivoting) is done, so this should be less stable than
e.g. Bunch-Kaufman sytrf. This is implemented as a tf.foldl, so should have
gradients and be accelerator-friendly, but is not particularly performant.

If compiling with XLA, make sure any surrounding GradientTape is also
XLA-compiled (b/193584244).

#### References

\[1\]: Gene H. Golub, Charles F. Van Loan. Matrix Computations, 4th ed., 2013.

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| ## Args ||
|---|---|
| `matrix` | A batch of symmetric square matrices, with shape `[..., n, n]`. |
| `name` | Python `str` name prefixed to Ops created by this function. Default value: 'no_pivot_ldl'. |

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| ## Returns ||
|---|---|
| `triangular_factor` | The unit lower triangular L factor of the LDL factorization of `matrix`, with the same shape `[..., n, n]`. Callers should check for `nans` and other indicators of instability. |
| `diag` | The diagonal from the LDL factorization, with shape `[..., n]`. |

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