Recursive cholesky #710
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Recursive cholesky #710
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EdDAzevedo
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tfalders,
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qjojo and
jmachado-amd
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I have opened a PR on your local fork with my suggested changes. Please have a look when you have a chance. |
* Cleanup for recursive Cholesky * Added ROCBLAS_CHECK to all nested calls in potrf * Removed unused variables * Add back offset variables * Reintroduce row_offset * Added row_offset to the log
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Implement recursive formulation of Cholesky factorization for n by n symmetric positive definite matrix A.
Let the following be a block partitioning of matrix A.
Here submatrix L22 is n/2 by n/2, L11 is n1 by n1, where n1 = n - n/2, or partition matrix at mid-point
[L11 0 ] * [ L11' L21'] = [A11 A21' ]
[L21 L22] [ L22'] [A21 A22 ]
(1) L11 * L11' = A11 , recursive Cholesky factorization
(2) L21 * L11' = A21 or
L21 = A21 / L11' triangular solve (TRSM)
(3) L21 * L21' + L22 * L22' = A22
or
(3a) A22 <- A22 - L21 * L21', symmetric rank-k update (SYRK)
(3b) L22 * L22' = A22, recursive Cholesky factorization
Note C++ recursion is performed on CPU host and the recursion depth is O( log2( n ) ).