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- Added Woodbury 2x2 to org-mode file. QMCkl compiles but the testsuite fails with a segementation fault. #25
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Francois Coppens
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04d2ec2d70
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11eee81f84
@ -143,7 +143,7 @@ return QMCKL_SUCCESS;
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* Naïve Sherman-Morrison
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* Naïve Sherman-Morrison
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** ~qmckl_sherman_morrison~
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:PROPERTIES:
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@ -152,13 +152,7 @@ return QMCKL_SUCCESS;
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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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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.
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#+NAME: qmckl_sherman_morrison_args
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| qmckl_context | context | in | Global state |
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@ -336,6 +330,207 @@ rc = qmckl_sherman_morrison_c(context, Dim, N_updates, Updates, Updates_index, S
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assert(rc == QMCKL_SUCCESS);
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#+end_src
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* Woodbury 2x2
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** ~qmckl_woodbury_2~
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:PROPERTIES:
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:Name: qmckl_woodbury_2
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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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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.
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#+NAME: qmckl_woodbury_2_args
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| qmckl_context | context | in | Global state |
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| uint64_t | Dim | in | Leading dimension of Slater_inv |
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| double | Updates[2*Dim] | in | Array containing the updates |
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| uint64_t | Updates_index[2] | in | Array containing the rank-1 updates |
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| double | Slater_inv[Dim*Dim] | inout | Array containing the inverse of a Slater-matrix |
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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_woodbury_2_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_woodbury_2_c (
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const qmckl_context context,
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const uint64_t Dim,
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const double* Updates,
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const uint64_t* Updates_index,
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double* Slater_inv );
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#+end_src
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*** Source Fortran
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#+begin_src f90 :tangle (eval f)
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integer function qmckl_woodbury_2_f(context, Slater_inv, Dim, &
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Updates, Updates_index) result(info)
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use qmckl
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implicit none
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integer(qmckl_context) , intent(in) :: context
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integer*8 , intent(in), value :: Dim
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integer*8 , intent(in) :: Updates_index(2)
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real*8 , intent(in) :: Updates(2*Dim)
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real*8 , intent(inout) :: Slater_inv(Dim*Dim)
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!logical, external :: qmckl_woodbury_2_f
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info = qmckl_woodbury_2(context, Dim, Updates, Updates_index, Slater_inv)
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end function qmckl_woodbury_2_f
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#+end_src
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*** Source C
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#+begin_src c :tangle (eval c) :comments org
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#include <stdbool.h>
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#include "qmckl.h"
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qmckl_exit_code qmckl_woodbury_2_c(const qmckl_context context,
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const uint64_t Dim,
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const double* Updates,
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const uint64_t* Updates_index,
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double * Slater_inv) {
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/*
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C := S^{-1} * U, dim x 2
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B := 1 + V * C, 2 x 2
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D := V * S^{-1}, 2 x dim
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*/
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// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
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// std::cerr << "Called Woodbury 2x2 kernel" << std::endl;
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// #endif
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const unsigned int row1 = (Updates_index[0] - 1);
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const unsigned int row2 = (Updates_index[1] - 1);
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// Compute C = S_inv * U !! NON-STANDARD MATRIX MULTIPLICATION BECAUSE
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// OF LAYOUT OF 'Updates' !!
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double C[2 * Dim];
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for (unsigned int i = 0; i < Dim; i++) {
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for (unsigned int j = 0; j < 2; j++) {
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C[i * 2 + j] = 0;
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for (unsigned int k = 0; k < Dim; k++) {
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C[i * 2 + j] += Slater_inv[i * Dim + k] * Updates[Dim * j + k];
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}
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}
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}
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// Compute B = 1 + V * C
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const double B0 = C[row1 * 2] + 1;
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const double B1 = C[row1 * 2 + 1];
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const double B2 = C[row2 * 2];
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const double B3 = C[row2 * 2 + 1] + 1;
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// Check if determinant of inverted matrix is not zero
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double det = B0 * B3 - B1 * B2;
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double thresh = 0.0;
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qmckl_exit_code rc = qmckl_sherman_morrison_threshold_c(&thresh);
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if (fabs(det) < thresh) {
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return QMCKL_FAILURE;
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}
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// Compute B^{-1} with explicit formula for 2x2 inversion
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double Binv[4], idet = 1.0 / det;
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Binv[0] = idet * B3;
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Binv[1] = -1.0 * idet * B1;
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Binv[2] = -1.0 * idet * B2;
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Binv[3] = idet * B0;
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// Compute tmp = B^{-1} x (V.S^{-1})
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double tmp[2 * Dim];
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for (unsigned int i = 0; i < 2; i++) {
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for (unsigned int j = 0; j < Dim; j++) {
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tmp[i * Dim + j] = Binv[i * 2] * Slater_inv[row1 * Dim + j];
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tmp[i * Dim + j] += Binv[i * 2 + 1] * Slater_inv[row2 * Dim + j];
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}
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}
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// Compute (S + U V)^{-1} = S^{-1} - C x tmp
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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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Slater_inv[i * Dim + j] -= C[i * 2] * tmp[j];
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Slater_inv[i * Dim + j] -= C[i * 2 + 1] * tmp[Dim + j];
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}
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}
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return QMCKL_SUCCESS;
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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_woodbury_2_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
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#+RESULTS:
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#+begin_src f90 :tangle (eval f) :comments org :exports none
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integer(c_int32_t) function qmckl_woodbury_2 &
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(context, Dim, Updates, Updates_index, Slater_inv) &
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bind(C) result(info)
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use, intrinsic :: iso_c_binding
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implicit none
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integer (c_int64_t) , intent(in) , value :: context
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integer (c_int64_t) , intent(in) , value :: Dim
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real (c_double ) , intent(in) :: Updates(2*Dim)
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integer (c_int64_t) , intent(in) :: Updates_index(2)
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real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
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integer(c_int32_t), external :: qmckl_woodbury_2_c
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info = qmckl_woodbury_2_c &
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(context, Dim, Updates, Updates_index, Slater_inv)
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end function qmckl_woodbury_2
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#+end_src
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#+CALL: generate_f_interface(table=qmckl_woodbury_2_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
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#+RESULTS:
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#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
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interface
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integer(c_int32_t) function qmckl_woodbury_2 &
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(context, Dim, Updates, Updates_index, Slater_inv) &
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bind(C)
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use, intrinsic :: iso_c_binding
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import
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implicit none
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integer (c_int64_t) , intent(in) , value :: context
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integer (c_int64_t) , intent(in) , value :: Dim
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real (c_double ) , intent(in) :: Updates(2*Dim)
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integer (c_int64_t) , intent(in) :: Updates_index(2)
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real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
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end function qmckl_woodbury_2
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end interface
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#+end_src
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*** Test :noexport:
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[TODO: FMJC] Write tests for the Sherman-Morrison part.
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#+begin_src c :tangle (eval c_test)
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const uint64_t Dim2 = 2;
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const uint64_t Updates_index2[2] = {0, 0};
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const double Updates2[4] = {0.0, 0.0, 0.0, 0.0};
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double Slater_inv2[4] = {0.0, 0.0, 0.0, 0.0};
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rc = qmckl_woodbury_2_c(context, Dim, Updates, Updates_index, Slater_inv);
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assert(rc == QMCKL_SUCCESS);
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#+end_src
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* End of files
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#+begin_src c :comments link :tangle (eval c_test)
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