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- Updated Perfomance recommendations, did some rewriting of parts of the text and removed more typos.
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@ -59,8 +59,8 @@ int main() {
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This value sets the lower bound for which the
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denominator $1+v_j^TS^{-1}u_j$ is considered to be too small and will most probably result in a singular matrix
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$S$, or at least in an inverse of $S$ of very poor numerical quality. Therefore, when $1+v_j^TS^{-1}u_j \geq \epsilon$,
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the update is applied as usual. If $1+v_j^TS^{-1}u_j \leq \epsilon$ the update is rejected and the kernel exits with
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return code \texttt{QMCKL_FAILURE}.
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the update is applied as usual and the kernel exits with return code \texttt{QMCKL_SUCCESS}.
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If $1+v_j^TS^{-1}u_j \leq \epsilon$ the update is rejected and the kernel exits with return code \texttt{QMCKL_FAILURE}.
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#+NAME: qmckl_sherman_morrison_args
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| qmckl_context | context | in | Global state |
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@ -176,8 +176,9 @@ qmckl_exit_code qmckl_sherman_morrison_c(const qmckl_context context,
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*** Performance
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This function performs better when there is only 1 rank-1 update in the update cycle and the fail-rate of rank-1 updates is high.
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This function performs best when there is only 1 rank-1 update in the update cycle. It is not useful to
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use Sherman-Morrison with update splitting for these cycles since splitting can never resolve a situation
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where applying the update causes singular behaviour.
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** C interface :noexport:
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@ -449,7 +450,8 @@ qmckl_exit_code qmckl_woodbury_2_c(const qmckl_context context,
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*** Performance
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This function is most efficient when used in cases where there are only 2 rank-1 updates.
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This function is most efficient when used in cases where there are only 2 rank-1 updates and
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it is sure they will not result in a singular matrix.
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** C interface :noexport:
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@ -689,8 +691,8 @@ qmckl_exit_code qmckl_woodbury_3_c(const qmckl_context context,
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*** Performance...
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This function is most efficient when used in cases where there are only 3 rank-1 updates.
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This function is most efficient when used in cases where there are only 3 rank-1 updates and
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it is sure they will not result in a singular matrix.
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** C interface :noexport:
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@ -780,11 +782,13 @@ assert(rc == QMCKL_SUCCESS);
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This is a variation on the 'Naive' Sherman-Morrison kernel. Whenever the denominator $1+v_j^T S^{-1} u_j$ in
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the Sherman-Morrison formula is deemed to be too close to zero, the update $u_j$ is split in half:
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$u_j \rightarrow \frac{1}{1} u_j$. One half is applied immediately --necessarily increasing the value of the
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$u_j \rightarrow \frac{1}{2} u_j$. One half is applied immediately --necessarily increasing the value of the
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denominator because of the split-- while the other halve is put in a queue that will be applied when all the
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remaining updates have been treated. The kernel is executed recursively until the queue is eiter empty and all
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remaining updates have been treated.
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The kernel is executed recursively until the queue is eiter empty and all
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updates are applied successfully, or the size of the queue equals the number of initial updates. In the last
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case the Slater-matrix that would have resulted from applying the updates is un-invertable and therefore the
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case the Slater-matrix that would have resulted from applying the updates is singular and therefore the
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kernel exits with an exit code.
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#+NAME: qmckl_sherman_morrison_splitting_args
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@ -877,7 +881,7 @@ qmckl_exit_code qmckl_sherman_morrison_splitting_c(const qmckl_context context,
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*** Performance...
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This kernel performs best when there are only 1 rank-1 update cycles and/or when the fail-rate is high.
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This kernel performs best when there are 2 or more rank-1 update cycles and fail-rate is high.
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** C interface :noexport:
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@ -1099,7 +1103,7 @@ qmckl_exit_code qmckl_sherman_morrison_smw32s_c(const qmckl_context context,
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*** Performance...
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This kernel performs best when the number of rank-1 updates is larger than 3 and fail-rates are low.
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This kernel performs best for update cycles with 2 or more rank-1 updates and the fail-rate is low.
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** C interface :noexport:
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@ -1191,7 +1195,7 @@ These functions can only be used internally by the kernels in this module.
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:END:
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~qmckl_slagel_splitting~ is the non-recursive, inner part of the 'Sherman-Morrison with update splitting'-kernel.
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It is used internally to apply a collection of $N$ of rank-1 updates to the inverse Slater-matrix $S^{-1}$ and
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It is used internally to apply a collection of $N$ rank-1 updates to the inverse Slater-matrix $S^{-1}$ and
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splitting an update in two equal pieces if necessary. In case of a split, it applies the first half of the update,
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while putting the second half in a waiting queue to be applied at the end.
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@ -1279,9 +1283,9 @@ qmckl_exit_code qmckl_slagel_splitting_c(uint64_t Dim,
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// Denominator
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double den = 1 + C[Updates_index[l] - 1];
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if (fabs(den) < breakdown) {
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if (fabs(den) < breakdown) { // Here is decided to split the update, or not.
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// U_l = U_l / 2 (do the split)
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// U_l = U_l / 2: split the update in 2 equal halves and save the second halve in later_updates
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for (uint64_t i = 0; i < Dim; i++) {
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later_updates[*later * Dim + i] = Updates[l * Dim + i] / 2.0;
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C[i] /= 2.0;
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@ -1290,7 +1294,7 @@ qmckl_exit_code qmckl_slagel_splitting_c(uint64_t Dim,
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(*later)++;
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den = 1 + C[Updates_index[l] - 1];
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}
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} // From here onwards we continue with applying the first havel of the update to Slater_inv
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double iden = 1 / den;
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// D = v^T x S^{-1}
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@ -1315,7 +1319,8 @@ qmckl_exit_code qmckl_slagel_splitting_c(uint64_t Dim,
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*** Performance
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This function performce better for cycles with 1 rank-1 update and with a high fail-rate.
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This function cannot be used by itself and is used in Sherman-Morrison with update splitting and Woodbury 3x3 and 2x2
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with Sherman-Morrison and update splitting. Please look at the performance reccomendations for those two kernels.
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** C interface :noexport:
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