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Finished first draft of the documentation

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Francois Coppens 2021-09-02 17:56:42 +02:00
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org/qmckl_sherman_morrison_woodbury.org
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@ -26,7 +26,7 @@ int main() {
qmckl_exit_code rc;
#+end_src
* Helper Functions
Helper functions that are used by the Sherman-Morrison-Woodbury kernels.
@ -39,10 +39,11 @@ These functions can only be used internally by higher level functions.
:FRetType: double precision
:END:
~qmckl_slagel_splitting~ is used internally to perform a J.~Slagel style split of rank-1 updates.
~qmckl_slagel_splitting~ is used internally to apply a list of rank-1 updates while splitting an update if necessary.
In case of a split it applies the first half of the update while putting the second half in waiting queue to be applied at the end.
For a given $u_j$ we define a threshold $\epsilon_j$, which is the minimum value of
$1+v_j^TS^{-1}u_j$ for the matrix to be considered nonsingular. If $1+v_j^TS^{-1}u_j \geq \epsilon_j$,
For a given update $u_j$ we define a threshold value $\epsilon_j$, which is the minimum value of
$1+v_j^TS^{-1}u_j$ for a non-singular matrix $S$. If $1+v_j^TS^{-1}u_j \geq \epsilon_j$,
the update is applied as usual. Otherwise, $u_j$ will be redefined as $\frac{u_j}{2}$, and the other half
(to be applied at the end) will be defined using vectors $\frac{u_{j'}}{2}$ and $v_{j'}^T=v_{j'}^T$.
@ -69,7 +70,7 @@ These functions can only be used internally by higher level functions.
- ~later_updates~ is allocated with at least $1 \times 2 \times 8$ bytes
- ~later_index~ is allocated with at least $1 \times 8$ bytes
- ~later >= 0~
*** C header
#+CALL: generate_c_header(table=qmckl_slagel_splitting_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
@ -337,8 +338,6 @@ qmckl_exit_code qmckl_sherman_morrison_c(const qmckl_context context,
#+end_src
*** Performance
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.
@ -567,7 +566,6 @@ qmckl_exit_code qmckl_woodbury_2_c(const qmckl_context context,
#+end_src
*** Performance
This function is most efficient when used in cases where there are only 2 rank-1 updates.
@ -640,7 +638,7 @@ rc = qmckl_woodbury_2_c(context, woodbury_Dim, woodbury_Updates, woodbury_Update
assert(rc == QMCKL_SUCCESS);
#+end_src
* Woodbury 3x3
** ~qmckl_woodbury_3~
@ -651,7 +649,8 @@ assert(rc == QMCKL_SUCCESS);
:END:
The 3x3 version of the Woodbury 2x2 kernel. It is used to apply three
rank-1 updates at once. The formula used in this kernel is the same as for Woodbury 2x2, with the exception of
rank-1 updates at once. The formula used in this kernel is the same as for Woodbury 2x2,
except for the sizes of the following matrices:
$C:= S^{-1}U$, a Dim $\times 3$ matrix
$B := 1 + VC$, the $3 \times 3$ matrix that is going to be inverted
@ -875,17 +874,6 @@ assert(rc == QMCKL_SUCCESS);
* Sherman-Morrison with update splitting
This is like naïve Sherman-Morrising, but whenever a denominator is
found that is too close to zero the update is split in half. Then one
half is applied immediately and the other have is ket for later. When
all the updates have been processed, the list of split updates that
have been kept for later are processed. If again applying an update
results in a denominator that is too close to zero, it is split in
half again. One half is applied immediately and one half is kept for
later. The algorithm is done when no more updates have been kept for
later. This recursion will always end in a finite number of steps,
unless the last original update causes a singular Slater-matrix.
** ~qmckl_sherman_morrison_splitting~
:PROPERTIES:
:Name: qmckl_sherman_morrison_splitting
@ -893,11 +881,14 @@ unless the last original update causes a singular Slater-matrix.
:FRetType: qmckl_exit_code
:END:
This is the simplest of the available Sherman-Morrison-Woodbury
kernels in QMCkl. It applies rank-1 updates one by one in the order
that is given. It only checks if the denominator in the
Sherman-Morrison formula is not too close to zero (and exit with an
error if it does) during the application of an update.
This is a variation on the 'Naive' Sherman-Morrison kernel. Whenever the denominator $1+v_j^T S^{-1} u_j$ in
the Sherman-Morrison formula is deemed to be too close to zero, the update $u_j$ is split in half:
$u_j \rightarrow \frac{1}{1} u_j$. One half is applied immediately --necessarily increasing the value of the
denominator because of the split-- while the other halve is put in a queue that will be applied when all the
remaining updates have been treated. The kernel is executed recursively until the queue is eiter empty and all
updates are applied successfully, or the size of the queue equals the number of initial updates. In the last
case the Slater-matrix that would have resulted from applying the updates is un-invertable and therefore the
kernel exits with an exit code.
#+NAME: qmckl_sherman_morrison_splitting_args
| qmckl_context | context | in | Global state |
@ -910,8 +901,14 @@ unless the last original update causes a singular Slater-matrix.
*** Requirements
Add description of the input variables. (see for e.g. qmckl_distance.org)
- ~context~ is not ~QMCKL_NULL_CONTEXT~
- ~Dim >= 2~
- ~N_updates >= 1~
- ~Updates~ is allocated with at least $1 \times 2 \times 8$ bytes
- ~Updates_index~ is allocated with at least $1 \times 8$ bytes
- ~breakdown~ is a small number such that $0 < breakdown << 1$
- ~Slater_inv~ is allocated with at least $Dim \times Dim \times 8$ bytes
*** C header
#+CALL: generate_c_header(table=qmckl_sherman_morrison_splitting_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
@ -945,7 +942,6 @@ integer function qmckl_sherman_morrison_splitting_f(context, Dim, N_updates,
end function qmckl_sherman_morrison_splitting_f
#+end_src
*** Source C
#+begin_src c :tangle (eval c) :comments org
@ -984,6 +980,8 @@ qmckl_exit_code qmckl_sherman_morrison_splitting_c(const qmckl_context context,
*** Performance...
This kernel performs best when there are only 1 rank-1 update cycles and/or when the fail-rate is high.
** C interface :noexport:
#+CALL: generate_c_interface(table=qmckl_sherman_morrison_splitting_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
@ -1059,17 +1057,6 @@ assert(rc == QMCKL_SUCCESS);
* Woodbury 2x2 with Sherman-Morrison and update splitting
This is like naïve Sherman-Morrising, but whenever a denominator is
found that is too close to zero the update is split in half. Then one
half is applied immediately and the other have is ket for later. When
all the updates have been processed, the list of split updates that
have been kept for later are processed. If again applying an update
results in a denominator that is too close to zero, it is split in
half again. One half is applied immediately and one half is kept for
later. The algorithm is done when no more updates have been kept for
later. This recursion will always end in a finite number of steps,
unless the last original update causes a singular Slater-matrix.
** ~qmckl_sherman_morrison_smw2s~
:PROPERTIES:
:Name: qmckl_sherman_morrison_smw2s
@ -1077,11 +1064,17 @@ unless the last original update causes a singular Slater-matrix.
:FRetType: qmckl_exit_code
:END:
This is the simplest of the available Sherman-Morrison-Woodbury
kernels in QMCkl. It applies rank-1 updates one by one in the order
that is given. It only checks if the denominator in the
Sherman-Morrison formula is not too close to zero (and exit with an
error if it does) during the application of an update.
The Woodbury 2x2 kernel with Sherman-Morrison and update splitting combines the low-level Woodbury 2x2 kernel
and Sherman-Morrison with update splitting. For a given number of updates $N$ it splits the number of updates
in blocks of two updates. The blocks of two updates are then applied one by one using Woodbury 2x2. If a block
of updates fails, both updates in the block are applied with Sherman-Morrison instead, split if necessary and
with their second half put in a queue. After all blocks are processed the remaining one update --in case there
was an odd number of updates to begin with-- is also aplpied with Sherman-Morrison and split if necessary.
The queue containing the collected second halves of all the processed updates is processed at the very end to
avoid having many intermediate queues containing only a few updates that risks an increased probability
of artificially created non-singular intermediate matrices, resulting from division up the total number of
updates in blocks of three.
#+NAME: qmckl_sherman_morrison_smw2s_args
| qmckl_context | context | in | Global state |
@ -1094,7 +1087,13 @@ unless the last original update causes a singular Slater-matrix.
*** Requirements
Add description of the input variables. (see for e.g. qmckl_distance.org)
- ~context~ is not ~QMCKL_NULL_CONTEXT~
- ~Dim >= 2~
- ~N_updates >= 1~
- ~Updates~ is allocated with at least $1 \times 2 \times 8$ bytes
- ~Updates_index~ is allocated with at least $1 \times 8$ bytes
- ~breakdown~ is a small number such that $0 < breakdown << 1$
- ~Slater_inv~ is allocated with at least $Dim \times Dim \times 8$ bytes
*** C header
@ -1112,7 +1111,6 @@ unless the last original update causes a singular Slater-matrix.
double* Slater_inv );
#+end_src
*** Source Fortran
#+begin_src f90 :tangle (eval f)
@ -1129,7 +1127,6 @@ integer function qmckl_sherman_morrison_smw2s_f(context, Slater_inv, Dim, N_upda
end function qmckl_sherman_morrison_smw2s_f
#+end_src
*** Source C
#+begin_src c :tangle (eval c) :comments org
@ -1192,6 +1189,8 @@ qmckl_exit_code qmckl_sherman_morrison_smw2s_c(const qmckl_context context,
*** Performance...
This kernel performs best for the case of two rank-1 update and a low fail-rate.
** C interface :noexport:
#+CALL: generate_c_interface(table=qmckl_sherman_morrison_smw2s_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
@ -1265,17 +1264,6 @@ assert(rc == QMCKL_SUCCESS);
* Woodbury 3x3 with Sherman-Morrison and update splitting
This is like naïve Sherman-Morrising, but whenever a denominator is
found that is too close to zero the update is split in half. Then one
half is applied immediately and the other have is ket for later. When
all the updates have been processed, the list of split updates that
have been kept for later are processed. If again applying an update
results in a denominator that is too close to zero, it is split in
half again. One half is applied immediately and one half is kept for
later. The algorithm is done when no more updates have been kept for
later. This recursion will always end in a finite number of steps,
unless the last original update causes a singular Slater-matrix.
** ~qmckl_sherman_morrison_smw3s~
:PROPERTIES:
:Name: qmckl_sherman_morrison_smw3s
@ -1283,11 +1271,10 @@ unless the last original update causes a singular Slater-matrix.
:FRetType: qmckl_exit_code
:END:
This is the simplest of the available Sherman-Morrison-Woodbury
kernels in QMCkl. It applies rank-1 updates one by one in the order
that is given. It only checks if the denominator in the
Sherman-Morrison formula is not too close to zero (and exit with an
error if it does) during the application of an update.
The Woodbury 3x3 kernel with Sherman-Morrison and update splitting combines the low-level Woodbury 3x3 kernel
and Sherman-Morrison with update splitting. It works the same as Woodbury 2x2 with Sherman-Morrison and update
splitting, except that the updates are divided in blocks of three rank-1 updates instead of blocks of two
rank-1 updates.
#+NAME: qmckl_sherman_morrison_smw3s_args
| qmckl_context | context | in | Global state |
@ -1300,7 +1287,13 @@ unless the last original update causes a singular Slater-matrix.
*** Requirements
Add description of the input variables. (see for e.g. qmckl_distance.org)
- ~context~ is not ~QMCKL_NULL_CONTEXT~
- ~Dim >= 2~
- ~N_updates >= 1~
- ~Updates~ is allocated with at least $1 \times 2 \times 8$ bytes
- ~Updates_index~ is allocated with at least $1 \times 8$ bytes
- ~breakdown~ is a small number such that $0 < breakdown << 1$
- ~Slater_inv~ is allocated with at least $Dim \times Dim \times 8$ bytes
*** C header
@ -1318,7 +1311,6 @@ unless the last original update causes a singular Slater-matrix.
double* Slater_inv );
#+end_src
*** Source Fortran
#+begin_src f90 :tangle (eval f)
@ -1336,7 +1328,6 @@ integer function qmckl_sherman_morrison_smw3s_f(context, Slater_inv, Dim, N_upda
end function qmckl_sherman_morrison_smw3s_f
#+end_src
*** Source C
#+begin_src c :tangle (eval c) :comments org
@ -1399,6 +1390,9 @@ qmckl_exit_code qmckl_sherman_morrison_smw3s_c(const qmckl_context context,
*** Performance...
This kernel performs best for the case of three rank-1 update and a low fail-rate.
** C interface :noexport:
#+CALL: generate_c_interface(table=qmckl_sherman_morrison_smw3s_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
@ -1471,17 +1465,6 @@ assert(rc == QMCKL_SUCCESS);
* Woodbury 3x3 and 2x2 with Sherman-Morrison and update splitting
This is like naïve Sherman-Morrising, but whenever a denominator is
found that is too close to zero the update is split in half. Then one
half is applied immediately and the other have is ket for later. When
all the updates have been processed, the list of split updates that
have been kept for later are processed. If again applying an update
results in a denominator that is too close to zero, it is split in
half again. One half is applied immediately and one half is kept for
later. The algorithm is done when no more updates have been kept for
later. This recursion will always end in a finite number of steps,
unless the last original update causes a singular Slater-matrix.
** ~qmckl_sherman_morrison_smw32s~
:PROPERTIES:
@ -1490,11 +1473,11 @@ unless the last original update causes a singular Slater-matrix.
:FRetType: qmckl_exit_code
:END:
This is the simplest of the available Sherman-Morrison-Woodbury
kernels in QMCkl. It applies rank-1 updates one by one in the order
that is given. It only checks if the denominator in the
Sherman-Morrison formula is not too close to zero (and exit with an
error if it does) during the application of an update.
The Woodbury 3x3 and 2x2 kernel with Sherman-Morrison and update splitting combines the low-level Woodbury 3x3 kernel,
the Woobury 2x2 kernel and Sherman-Morrison with update splitting. It works the almost the same as Woodbury 3x3 with
Sherman-Morrison and update splitting, except that when there is a remainder of two rank-1 updates, it is first tried
with Woodbury 2x2 instead of sending them all to Sherman-Morrison with update splitting. For example, in the case of
5 updates the updates are applied in 1 block of 3 updates end 1 block of 2 updates.
#+NAME: qmckl_sherman_morrison_smw32s_args
| qmckl_context | context | in | Global state |
@ -1507,7 +1490,13 @@ unless the last original update causes a singular Slater-matrix.
*** Requirements
Add description of the input variables. (see for e.g. qmckl_distance.org)
- ~context~ is not ~QMCKL_NULL_CONTEXT~
- ~Dim >= 2~
- ~N_updates >= 1~
- ~Updates~ is allocated with at least $1 \times 2 \times 8$ bytes
- ~Updates_index~ is allocated with at least $1 \times 8$ bytes
- ~breakdown~ is a small number such that $0 < breakdown << 1$
- ~Slater_inv~ is allocated with at least $Dim \times Dim \times 8$ bytes
*** C header
@ -1525,7 +1514,6 @@ unless the last original update causes a singular Slater-matrix.
double* Slater_inv );
#+end_src
*** Source Fortran
#+begin_src f90 :tangle (eval f)
@ -1543,7 +1531,6 @@ integer function qmckl_sherman_morrison_smw32s_f(context, Slater_inv, Dim, N_upd
end function qmckl_sherman_morrison_smw32s_f
#+end_src
*** Source C
#+begin_src c :tangle (eval c) :comments org
@ -1617,6 +1604,8 @@ qmckl_exit_code qmckl_sherman_morrison_smw32s_c(const qmckl_context context,
*** Performance...
This kernel performs best when the number of rank-1 updates is larger than 3 and fail-rates are low.
** C interface :noexport:
#+CALL: generate_c_interface(table=qmckl_sherman_morrison_smw32s_args,rettyp=get_value("FRetType"),fname=get_value("Name"))