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@ -27,7 +27,7 @@ int main() {
#+end_src
* Naïve Sherman-Morrison
** ~qmckl_sherman_morrison~
:PROPERTIES:
:Name: qmckl_sherman_morrison
@ -60,6 +60,9 @@ int main() {
the update is applied as usual and the kernel exits with return code \texttt{QMCKL_SUCCESS}.
If $1+v_j^TS^{-1}u_j \leq \epsilon$ the update is rejected and the kernel exits with return code \texttt{QMCKL_FAILURE}.
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
from applying the updates to the original matrix.
#+NAME: qmckl_sherman_morrison_args
| qmckl_context | context | in | Global state |
| uint64_t | Dim | in | Leading dimension of Slater_inv |
@ -68,6 +71,7 @@ int main() {
| uint64_t | Updates_index[N_updates] | in | Array containing the rank-1 updates |
| double | breakdown | in | Break-down parameter on which to fail or not |
| double | Slater_inv[Dim*Dim] | inout | Array containing the inverse of a Slater-matrix |
| double* | determinant | inout | Determinant of the Slater-matrix |
*** Requirements
@ -92,7 +96,8 @@ int main() {
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv);
double* Slater_inv,
double* determinant);
#+end_src
*** C source
@ -108,7 +113,8 @@ qmckl_exit_code qmckl_sherman_morrison(const qmckl_context context,
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv) {
double* Slater_inv,
double* determinant) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
@ -130,11 +136,16 @@ qmckl_exit_code qmckl_sherman_morrison(const qmckl_context context,
// Denominator
double den = 1 + C[Updates_index[l] - 1];
if (fabs(den) < breakdown) {
return QMCKL_FAILURE;
}
double iden = 1 / den;
// Update det(A)
if (determinant != NULL)
*determinant *= den;
// D = v^T x A^{-1}
for (uint64_t j = 0; j < Dim; j++) {
D[j] = Slater_inv[(Updates_index[l] - 1) * Dim + j];
@ -174,7 +185,7 @@ qmckl_exit_code qmckl_sherman_morrison(const qmckl_context context,
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_sherman_morrison &
(context, Dim, N_updates, Updates, Updates_index, breakdown, Slater_inv) &
(context, Dim, N_updates, Updates, Updates_index, breakdown, Slater_inv, determinant) &
bind(C)
use, intrinsic :: iso_c_binding
@ -188,6 +199,7 @@ qmckl_exit_code qmckl_sherman_morrison(const qmckl_context context,
integer (c_int64_t) , intent(in) :: Updates_index(N_updates)
real (c_double ) , intent(in) , value :: breakdown
real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
real (c_double ) , intent(inout) :: determinant
end function qmckl_sherman_morrison
end interface
@ -234,7 +246,14 @@ double Slater_inv5[441] = {-0.054189244668834902, -105.426713929607, -88.4584964
assert(Updates1 != NULL);
assert(Updates_index1 != NULL);
assert(Slater_inv1 != NULL);
rc = qmckl_sherman_morrison(context, Dim, N_updates1, Updates1, Updates_index1, breakdown, Slater_inv1);
// original determinant of Slater1 (before applying updates)
double det = 3.407025646103221e-10;
rc = qmckl_sherman_morrison(context, Dim, N_updates1, Updates1, Updates_index1, breakdown, Slater_inv1, &det);
// Check that the determinant is updated properly
assert(fabs(det + 4.120398385068217e-10) < 1e-15);
for (unsigned int i = 0; i < Dim; i++) {
for (unsigned int j = 0; j < Dim; j++) {
res[i * Dim + j] = 0;
@ -279,6 +298,10 @@ assert(rc == QMCKL_SUCCESS);
$B := 1 + VC$, the $2 \times 2$ matrix that is going to be inverted
$D := VS^{-1}$, a $2 \times Dim$ matrix
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
from applying the updates to the original matrix.
#+NAME: qmckl_woodbury_2_args
| qmckl_context | context | in | Global state |
@ -287,6 +310,7 @@ assert(rc == QMCKL_SUCCESS);
| uint64_t | Updates_index[2] | in | Array containing the rank-1 updates |
| double | breakdown | in | Break-down parameter on which to fail or not |
| double | Slater_inv[Dim*Dim] | inout | Array containing the inverse of a Slater-matrix |
| double* | determinant | inout | Determinant of Slater-matrix |
*** Requirements
@ -309,7 +333,8 @@ assert(rc == QMCKL_SUCCESS);
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv);
double* Slater_inv,
double* determinant);
#+end_src
*** C source
@ -324,7 +349,8 @@ qmckl_exit_code qmckl_woodbury_2(const qmckl_context context,
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv) {
double* Slater_inv,
double* determinant) {
/*
C := S^{-1} * U, dim x 2
B := 1 + V * C, 2 x 2
@ -362,6 +388,10 @@ qmckl_exit_code qmckl_woodbury_2(const qmckl_context context,
return QMCKL_FAILURE;
}
// Update det(S) when passed
if (determinant != NULL)
*determinant *= det;
// Compute B^{-1} with explicit formula for 2x2 inversion
double Binv[4], idet = 1.0 / det;
Binv[0] = idet * B3;
@ -408,7 +438,7 @@ qmckl_exit_code qmckl_woodbury_2(const qmckl_context context,
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_woodbury_2 &
(context, Dim, Updates, Updates_index, breakdown, Slater_inv) &
(context, Dim, Updates, Updates_index, breakdown, Slater_inv, determinant) &
bind(C)
use, intrinsic :: iso_c_binding
import
@ -420,6 +450,7 @@ qmckl_exit_code qmckl_woodbury_2(const qmckl_context context,
integer (c_int64_t) , intent(in) :: Updates_index(2)
real (c_double ) , intent(in) , value :: breakdown
real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
real (c_double ) , intent(inout) :: determinant
end function qmckl_woodbury_2
end interface
@ -431,7 +462,9 @@ qmckl_exit_code qmckl_woodbury_2(const qmckl_context context,
assert(Updates2 != NULL);
assert(Updates_index2 != NULL);
assert(Slater_inv2 != NULL);
rc = qmckl_woodbury_2(context, Dim, Updates2, Updates_index2, breakdown, Slater_inv2);
det = -1.4432116661319376e-11;
rc = qmckl_woodbury_2(context, Dim, Updates2, Updates_index2, breakdown, Slater_inv2, &det);
assert(fabs(det-2.367058141251457e-10) < 1e-15);
for (unsigned int i = 0; i < Dim; i++) {
for (unsigned int j = 0; j < Dim; j++) {
res[i * Dim + j] = 0;
@ -471,6 +504,11 @@ assert(rc == QMCKL_SUCCESS);
$B := 1 + VC$, the $3 \times 3$ matrix that is going to be inverted
$D := VS^{-1}$, a $3 \times Dim$ matrix
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
from applying the updates to the original matrix.
#+NAME: qmckl_woodbury_3_args
| qmckl_context | context | in | Global state |
| uint64_t | Dim | in | Leading dimension of Slater_inv |
@ -478,6 +516,7 @@ assert(rc == QMCKL_SUCCESS);
| uint64_t | Updates_index[3] | in | Array containing the rank-1 updates |
| double | breakdown | in | Break-down parameter on which to fail or not |
| double | Slater_inv[Dim*Dim] | inout | Array containing the inverse of a Slater-matrix |
| double* | determinant | inout | Determinant of Slater-matrix |
*** Requirements
@ -500,7 +539,8 @@ assert(rc == QMCKL_SUCCESS);
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv);
double* Slater_inv,
double* determinant);
#+end_src
*** C source
@ -515,7 +555,8 @@ qmckl_exit_code qmckl_woodbury_3(const qmckl_context context,
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv) {
double* Slater_inv,
double* determinant) {
/*
C := S^{-1} * U, dim x 3
B := 1 + V * C, 3 x 3
@ -561,6 +602,10 @@ qmckl_exit_code qmckl_woodbury_3(const qmckl_context context,
return QMCKL_FAILURE;
}
// Update det(Slater) if passed
if (determinant != NULL)
*determinant *= det;
// Compute B^{-1} with explicit formula for 3x3 inversion
double Binv[9], idet = 1.0 / det;
Binv[0] = (B4 * B8 - B7 * B5) * idet;
@ -614,7 +659,7 @@ qmckl_exit_code qmckl_woodbury_3(const qmckl_context context,
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_woodbury_3 &
(context, Dim, Updates, Updates_index, breakdown, Slater_inv) &
(context, Dim, Updates, Updates_index, breakdown, Slater_inv, determinant) &
bind(C)
use, intrinsic :: iso_c_binding
import
@ -626,6 +671,7 @@ qmckl_exit_code qmckl_woodbury_3(const qmckl_context context,
integer (c_int64_t) , intent(in) :: Updates_index(3)
real (c_double ) , intent(in) , value :: breakdown
real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
real (c_double ) , intent(inout) :: determinant
end function qmckl_woodbury_3
end interface
@ -637,7 +683,9 @@ qmckl_exit_code qmckl_woodbury_3(const qmckl_context context,
assert(Updates3 != NULL);
assert(Updates_index3 != NULL);
assert(Slater_inv3_1 != NULL);
rc = qmckl_woodbury_3(context, Dim, Updates3, Updates_index3, breakdown, Slater_inv3_1);
det = -1.23743195512859e-09;
rc = qmckl_woodbury_3(context, Dim, Updates3, Updates_index3, breakdown, Slater_inv3_1, &det);
assert(fabs(det - 1.602708950725074e-10) < 1e-15);
for (unsigned int i = 0; i < Dim; i++) {
for (unsigned int j = 0; j < Dim; j++) {
res[i * Dim + j] = 0;
@ -680,6 +728,9 @@ assert(rc == QMCKL_SUCCESS);
case the Slater-matrix that would have resulted from applying the updates is singular and therefore the
kernel exits with an exit code.
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
from applying the updates to the original matrix.
#+NAME: qmckl_sherman_morrison_splitting_args
| qmckl_context | context | in | Global state |
| uint64_t | Dim | in | Leading dimension of Slater_inv |
@ -688,6 +739,10 @@ assert(rc == QMCKL_SUCCESS);
| uint64_t | Updates_index[N_updates] | in | Array containing the rank-1 updates |
| double | breakdown | in | Break-down parameter on which to fail or not |
| double | Slater_inv[Dim*Dim] | inout | Array containing the inverse of a Slater-matrix |
| double* | determinant | inout | Determinant of the Slater-matrix |
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
from applying the updates to the original matrix.
*** Requirements
@ -712,7 +767,8 @@ assert(rc == QMCKL_SUCCESS);
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv);
double* Slater_inv,
double* determinant);
#+end_src
*** C source
@ -727,7 +783,8 @@ qmckl_exit_code qmckl_sherman_morrison_splitting(const qmckl_context context,
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv) {
double* Slater_inv,
double* determinant) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
@ -738,11 +795,11 @@ qmckl_exit_code qmckl_sherman_morrison_splitting(const qmckl_context context,
uint64_t later = 0;
(void) qmckl_slagel_splitting(Dim, N_updates, Updates, Updates_index,
breakdown, Slater_inv, later_updates, later_index, &later);
breakdown, Slater_inv, later_updates, later_index, &later, determinant);
if (later > 0) {
(void) qmckl_sherman_morrison_splitting(context, Dim, later,
later_updates, later_index, breakdown, Slater_inv);
later_updates, later_index, breakdown, Slater_inv, determinant);
}
return QMCKL_SUCCESS;
@ -767,7 +824,7 @@ qmckl_exit_code qmckl_sherman_morrison_splitting(const qmckl_context context,
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_sherman_morrison_splitting &
(context, Dim, N_updates, Updates, Updates_index, breakdown, Slater_inv) &
(context, Dim, N_updates, Updates, Updates_index, breakdown, Slater_inv, determinant) &
bind(C)
use, intrinsic :: iso_c_binding
import
@ -780,6 +837,7 @@ qmckl_exit_code qmckl_sherman_morrison_splitting(const qmckl_context context,
integer (c_int64_t) , intent(in) :: Updates_index(N_updates)
real (c_double ) , intent(in) , value :: breakdown
real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
real (c_double ) , intent(inout) :: determinant
end function qmckl_sherman_morrison_splitting
end interface
@ -791,7 +849,9 @@ qmckl_exit_code qmckl_sherman_morrison_splitting(const qmckl_context context,
assert(Updates3 != NULL);
assert(Updates_index3 != NULL);
assert(Slater_inv3_2 != NULL);
rc = qmckl_sherman_morrison_splitting(context, Dim, N_updates3, Updates3, Updates_index3, breakdown, Slater_inv3_2);
det = -1.23743195512859e-09;
rc = qmckl_sherman_morrison_splitting(context, Dim, N_updates3, Updates3, Updates_index3, breakdown, Slater_inv3_2, &det);
assert(fabs(det - 1.602708950725074e-10) < 1e-15);
for (unsigned int i = 0; i < Dim; i++) {
for (unsigned int j = 0; j < Dim; j++) {
res[i * Dim + j] = 0;
@ -829,6 +889,9 @@ assert(rc == QMCKL_SUCCESS);
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.
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
from applying the updates to the original matrix.
#+NAME: qmckl_sherman_morrison_smw32s_args
| qmckl_context | context | in | Global state |
| uint64_t | Dim | in | Leading dimension of Slater_inv |
@ -837,6 +900,8 @@ assert(rc == QMCKL_SUCCESS);
| uint64_t | Updates_index[N_updates] | in | Array containing the rank-1 updates |
| double | breakdown | in | Break-down parameter on which to fail or not |
| double | Slater_inv[Dim*Dim] | inout | Array containing the inverse of a Slater-matrix |
| double* | determinant | inout | Determinant of the Slater-matrix |
*** Requirements
@ -861,7 +926,8 @@ assert(rc == QMCKL_SUCCESS);
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv);
double* Slater_inv,
double* determinant);
#+end_src
*** C source
@ -876,7 +942,8 @@ qmckl_exit_code qmckl_sherman_morrison_smw32s(const qmckl_context context,
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv) {
double* Slater_inv,
double* determinant) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
@ -897,11 +964,11 @@ qmckl_exit_code qmckl_sherman_morrison_smw32s(const qmckl_context context,
for (uint64_t i = 0; i < n_of_3blocks; i++) {
const double *Updates_3block = &Updates[i * length_3block];
const uint64_t *Updates_index_3block = &Updates_index[i * 3];
rc = qmckl_woodbury_3(context, Dim, Updates_3block, Updates_index_3block, breakdown, Slater_inv);
rc = qmckl_woodbury_3(context, Dim, Updates_3block, Updates_index_3block, breakdown, Slater_inv, determinant);
if (rc != 0) { // Send the entire block to slagel_splitting
uint64_t l = 0;
rc = qmckl_slagel_splitting(Dim, 3, Updates_3block, Updates_index_3block,
breakdown, Slater_inv, later_updates + (Dim * later), later_index + later, &l);
breakdown, Slater_inv, later_updates + (Dim * later), later_index + later, &l, determinant);
later = later + l;
}
}
@ -911,11 +978,11 @@ qmckl_exit_code qmckl_sherman_morrison_smw32s(const qmckl_context context,
if (remainder == 2) {
const double *Updates_2block = &Updates[n_of_3blocks * length_3block];
const uint64_t *Updates_index_2block = &Updates_index[3 * n_of_3blocks];
rc = qmckl_woodbury_2(context, Dim, Updates_2block, Updates_index_2block, breakdown, Slater_inv);
rc = qmckl_woodbury_2(context, Dim, Updates_2block, Updates_index_2block, breakdown, Slater_inv, determinant);
if (rc != 0) { // Send the entire block to slagel_splitting
uint64_t l = 0;
(void) qmckl_slagel_splitting(Dim, 2, Updates_2block, Updates_index_2block,
breakdown, Slater_inv, later_updates + (Dim * later), later_index + later, &l);
breakdown, Slater_inv, later_updates + (Dim * later), later_index + later, &l, determinant);
later = later + l;
}
}
@ -925,12 +992,12 @@ qmckl_exit_code qmckl_sherman_morrison_smw32s(const qmckl_context context,
const uint64_t *Updates_index_1block = &Updates_index[3 * n_of_3blocks];
uint64_t l = 0;
(void) qmckl_slagel_splitting(Dim, 1, Updates_1block, Updates_index_1block,
breakdown, Slater_inv, later_updates + (Dim * later), later_index + later, &l);
breakdown, Slater_inv, later_updates + (Dim * later), later_index + later, &l, determinant);
later = later + l;
}
if (later > 0) {
(void) qmckl_sherman_morrison_splitting(context, Dim, later, later_updates, later_index, breakdown, Slater_inv);
(void) qmckl_sherman_morrison_splitting(context, Dim, later, later_updates, later_index, breakdown, Slater_inv, determinant);
}
return QMCKL_SUCCESS;
}
@ -978,7 +1045,10 @@ qmckl_exit_code qmckl_sherman_morrison_smw32s(const qmckl_context context,
assert(Updates5 != NULL);
assert(Updates_index5 != NULL);
assert(Slater_inv5 != NULL);
rc = qmckl_sherman_morrison_smw32s(context, Dim, N_updates5, Updates5, Updates_index5, breakdown, Slater_inv5);
det = -3.186005284713128e-10;
rc = qmckl_sherman_morrison_smw32s(context, Dim, N_updates5, Updates5, Updates_index5, breakdown, Slater_inv5, &det);
assert(fabs(det + 5.260200118412903e-10) < 1e-15);
for (unsigned int i = 0; i < Dim; i++) {
for (unsigned int j = 0; j < Dim; j++) {
res[i * Dim + j] = 0;
@ -1022,6 +1092,9 @@ These functions can only be used internally by the kernels in this module.
as $\frac{1}{2}u_j$. One half is applied immediately, the other half will be applied at the end of the algorithm, using vectors
$u_{j'}=\frac{1}{2}u_j$ and $v_{j'}^T=v_{j}^T$, which are stored in the array \texttt{later_updates}.
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
from applying the updates to the original matrix.
#+NAME: qmckl_slagel_splitting_args
| uint64_t | Dim | in | Leading dimension of Slater_inv |
| uint64_t | N_updates | in | Number of rank-1 updates to be applied to Slater_inv |
@ -1032,6 +1105,7 @@ These functions can only be used internally by the kernels in this module.
| double | later_updates[Dim * N_updates] | inout | Array containing the split updates for later |
| uint64_t | later_index[N_updates] | inout | Array containing the positions of the split updates for later |
| uint64_t | later | inout | Number of split updates for later |
| double* | determinant | inout | Determinant of the Slater-matrix |
*** Requirements
@ -1061,7 +1135,8 @@ These functions can only be used internally by the kernels in this module.
double* Slater_inv,
double* later_updates,
uint64_t* later_index,
uint64_t* later );
uint64_t* later,
double* determinant);
#+end_src
*** C source
@ -1079,7 +1154,8 @@ qmckl_exit_code qmckl_slagel_splitting(uint64_t Dim,
double *Slater_inv,
double *later_updates,
uint64_t *later_index,
uint64_t *later) {
uint64_t *later,
double *determinant) {
// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
// std::cerr << "Called slagel_splitting with " << N_updates << " updates" << std::endl;
// #endif
@ -1114,6 +1190,9 @@ qmckl_exit_code qmckl_slagel_splitting(uint64_t Dim,
} // From here onwards we continue with applying the first havel of the update to Slater_inv
double iden = 1 / den;
if (determinant != NULL)
*determinant *= den;
// D = v^T x S^{-1}
for (uint64_t j = 0; j < Dim; j++) {
D[j] = Slater_inv[(Updates_index[l] - 1) * Dim + j];