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149 lines
4.0 KiB
Org Mode
149 lines
4.0 KiB
Org Mode
#+TITLE: Sherman-Morrison-Woodbury
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#+SETUPFILE: ../tools/theme.setup
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#+INCLUDE: ../tools/lib.org
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Low- and high-level functions that use the Sherman-Morrison and Woodbury matrix inversion formulas to update the
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inverse of a non-singualr matrix
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* Headers
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#+begin_src elisp :noexport :results none
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(org-babel-lob-ingest "../tools/lib.org")
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#+end_src
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#+begin_src c :comments link :tangle (eval c_test) :noweb yes
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#include "qmckl.h"
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#include "assert.h"
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#ifdef HAVE_CONFIG_H
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#include "config.h"
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#endif
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#include <cmath>
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#ifndef THRESHOLD
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#define THRESHOLD 1e-3
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#endif
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int main() {
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qmckl_context context;
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context = qmckl_context_create();
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#+end_src
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* Naïve Sherman-Morrison
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** ~qmckl_sherman_morrison~
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:PROPERTIES:
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:Name: qmckl_sherman_morrison
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:CRetType: qmckl_exit_code
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:FRetType: qmckl_exit_code
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:END:
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The Sherman-Morrison formula
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\begin{align}
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S_k^{-1} &= (S_l + U_k)^-1 \\
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&= S_l^{-1} - \frac{S_l^{-1}U_kS_l}{1+\underline{v}_k^tS_l^{-1}\underline{u}_k}
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\end{align}
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#+NAME: qmckl_sherman_morrison_args
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| qmckl_context | context | in | Global state |
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| double | Slater_inv[Dim*Dim] | inout | Array containing the inverse of a Slater-matrix |
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| uint | Dim | in | Leading dimension of Slater_inv |
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| uint | N_updates | in | Number of rank-1 updates to be applied to Slater_inv |
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| double | Updates[N_updates*Dim] | in | Array containing the updates |
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| double | Updates_index | in | Array containing the rank-1 updates |
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*** Requirements
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Add description of the input variables. (see for e.g. qmckl_distance.org)
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*** C header
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#+CALL: generate_c_header(table=qmckl_sherman_morrison_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
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#+RESULTS:
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#+begin_src c :tangle (eval h_func) :comments org
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qmckl_exit_code qmckl_sherman_morrison (
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const qmckl_context context,
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double *Slater_inv,
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unsigned int Dim,
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unsigned int N_updates,
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double *Updates,
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unsigned int *Updates_index );
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#+end_src
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*** Source
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#+begin_src c :tangle (eval c_func) :comments org
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bool qmckl_sherman_morrison(double *Slater_inv, unsigned int Dim, unsigned int N_updates,
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double *Updates, unsigned int *Updates_index) {
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#ifdef DEBUG
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std::cerr << "Called qmckl_sherman_morrison with " << N_updates << " updates" << std::endl;
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#endif
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double C[Dim];
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double D[Dim];
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unsigned int l = 0;
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// For each update
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while (l < N_updates) {
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// C = A^{-1} x U_l
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for (unsigned int i = 0; i < Dim; i++) {
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C[i] = 0;
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for (unsigned int j = 0; j < Dim; j++) {
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C[i] += Slater_inv[i * Dim + j] * Updates[l * Dim + j];
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}
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}
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// Denominator
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double den = 1 + C[Updates_index[l] - 1];
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if (std::fabs(den) < threshold()) {
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return false;
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}
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double iden = 1 / den;
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// D = v^T x A^{-1}
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for (unsigned int j = 0; j < Dim; j++) {
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D[j] = Slater_inv[(Updates_index[l] - 1) * Dim + j];
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}
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// A^{-1} = A^{-1} - C x D / den
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for (unsigned int i = 0; i < Dim; i++) {
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for (unsigned int j = 0; j < Dim; j++) {
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double update = C[i] * D[j] * iden;
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Slater_inv[i * Dim + j] -= update;
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}
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}
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l += 1;
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}
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return true;
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}
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#+end_src
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*** Performance
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** C interface :noexport:
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#+CALL: generate_c_interface(table=qmckl_sherman_morrison_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
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#+CALL: generate_f_interface(table=qmckl_sherman_morrison_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
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*** Test :noexport:
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[TODO: FMJC] Write tests for the Sherman-Morrison part.
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* End of files
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#+begin_src c :comments link :tangle (eval c_test)
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assert (qmckl_context_destroy(context) == QMCKL_SUCCESS);
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return 0;
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}
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#+end_src
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# -*- mode: org -*-
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# vim: syntax=c
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