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Started integration of naive Sherman-Morrison in the org-mode file. #25

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Francois Coppens 2021-07-19 17:38:53 +02:00
parent 81f5696950
commit 7849f510f4
1 changed files with 82 additions and 6 deletions
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88
org/qmckl_sherman_morrison_woodbury.org
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@ -2,7 +2,8 @@
#+SETUPFILE: ../tools/theme.setup
#+INCLUDE: ../tools/lib.org
[TODO: FMJC] Please add some intro.
Low- and high-level functions that use the Sherman-Morrison and Woodbury matrix inversion formulas to update the
inverse of a non-singualr matrix
* Headers
#+begin_src elisp :noexport :results none
@ -15,15 +16,18 @@
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <cmath>
#ifndef THRESHOLD
#define THRESHOLD 1e-3
#endif
int main() {
qmckl_context context;
context = qmckl_context_create();
#+end_src
* Sherman Morrison
[TODO: FMJC] Add general doc for Naive SM.
* Naïve Sherman-Morrison
** ~qmckl_sherman_morrison~
:PROPERTIES:
@ -32,20 +36,92 @@ int main() {
:FRetType: qmckl_exit_code
:END:
[TODO: FMJC] Add some detailed description. Including formulae etc.
The Sherman-Morrison formula
\begin{align}
S_k^{-1} &= (S_l + U_k)^-1 \\
&= S_l^{-1} - \frac{S_l^{-1}U_kS_l}{1+\underline{v}_k^tS_l^{-1}\underline{u}_k}
\end{align}
#+NAME: qmckl_sherman_morrison_args
| qmckl_context | context | in | Global state |
| double | Slater_inv[Dim*Dim] | inout | Array containing the inverse of a Slater-matrix |
| uint | Dim | in | Leading dimension of Slater_inv |
| uint | N_updates | in | Number of rank-1 updates to be applied to Slater_inv |
| double | Updates[N_updates*Dim] | in | Array containing the updates |
| double | Updates_index | in | Array containing the rank-1 updates |
*** Requirements
[TODO: FMJC] Add description of the input variables. (see for e.g. qmckl_distance.org)
Add description of the input variables. (see for e.g. qmckl_distance.org)
*** C header
#+CALL: generate_c_header(table=qmckl_sherman_morrison_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_sherman_morrison (
const qmckl_context context,
double *Slater_inv,
unsigned int Dim,
unsigned int N_updates,
double *Updates,
unsigned int *Updates_index );
#+end_src
*** Source
#+begin_src c :tangle (eval c_func) :comments org
bool qmckl_sherman_morrison(double *Slater_inv, unsigned int Dim, unsigned int N_updates,
double *Updates, unsigned int *Updates_index) {
#ifdef DEBUG
std::cerr << "Called qmckl_sherman_morrison with " << N_updates << " updates" << std::endl;
#endif
double C[Dim];
double D[Dim];
unsigned int l = 0;
// For each update
while (l < N_updates) {
// C = A^{-1} x U_l
for (unsigned int i = 0; i < Dim; i++) {
C[i] = 0;
for (unsigned int j = 0; j < Dim; j++) {
C[i] += Slater_inv[i * Dim + j] * Updates[l * Dim + j];
}
}
// Denominator
double den = 1 + C[Updates_index[l] - 1];
if (std::fabs(den) < threshold()) {
return false;
}
double iden = 1 / den;
// D = v^T x A^{-1}
for (unsigned int j = 0; j < Dim; j++) {
D[j] = Slater_inv[(Updates_index[l] - 1) * Dim + j];
}
// A^{-1} = A^{-1} - C x D / den
for (unsigned int i = 0; i < Dim; i++) {
for (unsigned int j = 0; j < Dim; j++) {
double update = C[i] * D[j] * iden;
Slater_inv[i * Dim + j] -= update;
}
}
l += 1;
}
return true;
}
#+end_src
*** Performance
** C interface :noexport: