tfp.math.low_rank_cholesky | TensorFlow Probability (original) (raw)
tfp.math.low_rank_cholesky
Computes a low-rank approximation to the Cholesky decomposition.
tfp.math.low_rank_cholesky(
matrix, max_rank, trace_atol=0, trace_rtol=0, name=None
)
This routine is similar to pivoted_cholesky, but works under JAX, at the cost of being slightly less numerically stable.
| Args | |
|---|---|
| matrix | Floating point Tensor batch of symmetric, positive definite matrices, or a tf.linalg.LinearOperator. |
| max_rank | Scalar int Tensor, the rank at which to truncate the approximation. |
| trace_atol | Scalar floating point Tensor (same dtype as matrix). If trace_atol > 0 and trace(matrix - LR * LR^t) < trace_atol, the output LR matrix is allowed to be of rank less than max_rank. |
| trace_rtol | Scalar floating point Tensor (same dtype as matrix). If trace_rtol > 0 and trace(matrix - LR * LR^t) < trace_rtol * trace(matrix), the output LR matrix is allowed to be of rank less than max_rank. |
| name | Optional name for the op. |
| Returns | |
|---|---|
| A triplet (LR, r, residual_diag) of | |
| LR | a matrix such that LR * LR^t is approximately the input matrix. If matrix is of shape (b1, ..., bn, m, m), then LR will be of shape (b1, ..., bn, m, r) where r <= max_rank. |
| r | the rank of LR. If r is < max_rank, then trace(matrix - LR * LR^t) < trace_atol, and |
| residual_diag | The diagonal entries of matrix - LR * LR^t. This is returned because together with LR, it is useful for preconditioning the input matrix. |
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Last updated 2023-11-21 UTC.