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Merge pull request #5 from pablooliveira/flatten

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C++ redesign of data-structures
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François Coppens 2021-02-09 17:03:56 +01:00 committed by GitHub
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9 changed files with 153 additions and 353 deletions
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52
Helpers.hpp
View File

@ -34,12 +34,12 @@ void showVector(T *vector, unsigned int size, string name) {
} }
template<typename T> template<typename T>
void showMatrix(T **matrix, unsigned int size, string name) { void showMatrix(T *matrix, unsigned int M, string name) {
cout << name << " = " << endl; cout << name << " = " << endl;
for (unsigned int i = 0; i < size; i++) { for (unsigned int i = 0; i < M; i++) {
cout << "[ "; cout << "[ ";
for (unsigned int j = 0; j < size; j++) { for (unsigned int j = 0; j < M; j++) {
cout << matrix[i][j] << " "; cout << matrix[i*M+j] << " ";
} }
cout << " ]" << endl; cout << " ]" << endl;
} }
@ -60,31 +60,12 @@ void showMatrixT(T **matrix, unsigned int size, string name) {
} }
template<typename T> template<typename T>
T **matMul(T **A, T **B, unsigned int size) { T *matMul(T *A, T *B, unsigned int M) {
T **C = new T*[size]; T *C = new T[M*M];
for (unsigned int i = 0; i < size; i++) { for (unsigned int i = 0; i < M; i++) {
C[i] = new T[size]; for (unsigned int j = 0; j < M; j++) {
} for (unsigned int k = 0; k < M; k++) {
for (unsigned int i = 0; i < size; i++) { C[i*M+j] += A[i*M+k] * B[k*M+j];
for (unsigned int j = 0; j < size; j++) {
for (unsigned int k = 0; k < size; k++) {
C[i][j] += A[i][k] * B[k][j];
}
}
}
return C;
}
template<typename T>
T **matMul2(T **A, T (*B)[], unsigned int size) {
T **C = new T*[size];
for (unsigned int i = 0; i < size; i++) {
C[i] = new T[size];
}
for (unsigned int i = 0; i < size; i++) {
for (unsigned int j = 0; j < size; j++) {
for (unsigned int k = 0; k < size; k++) {
C[i][j] += A[i][k] * B[k][j];
} }
} }
} }
@ -93,14 +74,11 @@ T **matMul2(T **A, T (*B)[], unsigned int size) {
template<typename T1, typename T2> template<typename T1, typename T2>
T1 **outProd(T1 *vec1, T2 *vec2, unsigned int size) { T1 *outProd(T1 *vec1, T2 *vec2, unsigned int M) {
T1 **C = new T1*[size]; T1 *C = new T1[M*M];
for (unsigned int i = 0; i < size; i++) { for (unsigned int i = 0; i < M; i++) {
C[i] = new T1[size]; for (unsigned int j = 0; j < M; j++) {
} C[i*M+j] = vec1[i+1] * vec2[j];
for (unsigned int i = 0; i < size; i++) {
for (unsigned int j = 0; j < size; j++) {
C[i][j] = vec1[i+1] * vec2[j];
} }
} }
return C; return C;

6
Makefile
View File

@ -3,8 +3,8 @@ CXX = icpc
FC = ifort FC = ifort
## Compiler flags ## Compiler flags
CXXFLAGS = -O0 -debug full -traceback CXXFLAGS = -O0 #-debug full -traceback
FFLAGS = -O0 -debug full -traceback FFLAGS = -O0 #-debug full -traceback
# ARCH = -xCORE-AVX2 # ARCH = -xCORE-AVX2
## Deps & objs for the C++ stuff ## Deps & objs for the C++ stuff
@ -13,7 +13,7 @@ cppOBJ = cppmain.o SM_MaponiA3.o
## Deps & objs for the Fortran stuff ## Deps & objs for the Fortran stuff
fDEPS = fmain.f90 SM_MaponiA3_mod.f90 fDEPS = fmain.f90 SM_MaponiA3_mod.f90
fOBJ = SM_MaponiA3_f.o SM_MaponiA3_mod.o fmain.o fOBJ = SM_MaponiA3.o SM_MaponiA3_mod.o fmain.o
fLIBS = -lstdc++ fLIBS = -lstdc++
## Compile recipes for C++ stuff ## Compile recipes for C++ stuff

106
SM_MaponiA3.cpp
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@ -1,94 +1,74 @@
// SM-MaponiA3.cpp // SM-MaponiA3_f.cpp
// Algorithm 3 from P. Maponi, // Algorithm 3 from P. Maponi,
// p. 283, doi:10.1016/j.laa.2006.07.007 // p. 283, doi:10.1016/j.laa.2006.07.007
#include "SM_MaponiA3.hpp" #include "SM_MaponiA3.hpp"
#include "Helpers.hpp" #include "Helpers.hpp"
void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index) { void MaponiA3(double *Slater0, double *Slater_inv, unsigned int M,
unsigned int k, l, lbar, i, j, tmp, M = *Dim; unsigned int N_updates, double *Updates,
unsigned int *p = new unsigned int[M+1]; unsigned int *Updates_index) {
unsigned int **Id = new unsigned int*[M];
unsigned int k, l, lbar, i, j, tmp = M;
unsigned int *p = new unsigned int[M + 1];
double alpha, beta; double alpha, beta;
double **U, *breakdown = new double[M+1]; double *breakdown = new double[M + 1];
double **Al = new double*[M]; double *Al = new double[M * M];
p[0] = 0; p[0] = 0;
for (i = 0; i < M; i++) { for (i = 0; i < M; i++) {
p[i+1] = i + 1; p[i + 1] = i + 1;
Id[i] = new unsigned int[M];
Al[i] = new double[M];
} }
// Declare auxiliary solution matrix ylk // Declare auxiliary solution matrix ylk
double ***ylk = new double**[M]; double ***ylk = new double **[M];
for (l = 0; l < M; l++) { for (l = 0; l < M; l++) {
ylk[l] = new double*[M+1]; ylk[l] = new double *[M + 1];
for (k = 0; k < M+1; k++) { for (k = 0; k < M + 1; k++) {
ylk[l][k] = new double[M+1]; ylk[l][k] = new double[M + 1] {0};
}
}
// Initialize identity matrix
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
if (i != j) Id[i][j] = 0;
else Id[i][j] = 1;
}
}
// Initialize ylk with zeros
for (l = 0; l < M; l++) {
for (k = 0; k < M+1; k++) {
for (i = 0; i < M+1; i++) {
ylk[l][k][i] = 0;
}
} }
} }
// Calculate all the y0k in M^2 multiplications instead of M^3 // Calculate all the y0k in M^2 multiplications instead of M^3
for (k = 1; k < M+1; k++) { for (k = 1; k < M + 1; k++) {
for (i = 1; i < M+1; i++) { for (i = 1; i < M + 1; i++) {
ylk[0][k][i] = Slater_inv[i-1][i-1] * Updates[i-1][k-1]; ylk[0][k][i] =
Slater_inv[(i - 1) * M + (i - 1)] * Updates[(i - 1) * M + (k - 1)];
} }
} }
// Calculate all the ylk from the y0k // Calculate all the ylk from the y0k
for (l = 1; l < M; l++) { for (l = 1; l < M; l++) {
for (j = l; j < M+1; j++) { for (j = l; j < M + 1; j++) {
breakdown[j] = abs( 1 + ylk[l-1][p[j]][p[j]] ); breakdown[j] = abs(1 + ylk[l - 1][p[j]][p[j]]);
}
lbar = getMaxIndex(breakdown, M+1);
for (i = 0; i < M; i++) {
breakdown[i] = 0;
} }
lbar = getMaxIndex(breakdown, M + 1);
tmp = p[l]; tmp = p[l];
p[l] = p[lbar]; p[l] = p[lbar];
p[lbar] = tmp; p[lbar] = tmp;
for (k = l+1; k < M+1; k++) { for (k = l + 1; k < M + 1; k++) {
beta = 1 + ylk[l-1][p[l]][p[l]]; beta = 1 + ylk[l - 1][p[l]][p[l]];
if (beta == 0) { if (beta == 0) {
cout << "Break-down condition occured. Exiting..." << endl; cout << "Break-down condition occured. Exiting..." << endl;
exit; exit;
} }
for (i = 1; i < M+1; i++) { for (i = 1; i < M + 1; i++) {
alpha = ylk[l-1][p[k]][p[l]] / beta; alpha = ylk[l - 1][p[k]][p[l]] / beta;
ylk[l][p[k]][i] = ylk[l-1][p[k]][i] - alpha * ylk[l-1][p[l]][i]; ylk[l][p[k]][i] = ylk[l - 1][p[k]][i] - alpha * ylk[l - 1][p[l]][i];
} }
} }
} }
// Keep the memory location of the passed array 'Slater_inv' before
// 'Slater_inv' gets reassigned by 'matMul(...)' in the next line, by creating
// a new pointer 'copy' that points to whereever 'Slater_inv' points to now.
double *copy = Slater_inv;
// Construct A-inverse from A0-inverse and the ylk // Construct A-inverse from A0-inverse and the ylk
// Keep the memory location of the passed array 'Slater_inv' before 'Slater_inv'
// gets reassigned by 'matMul(...)' in the next line, by creating a new
// pointer 'copy' that points to whereever 'Slater_inv' points to now.
double **copy = Slater_inv;
for (l = 0; l < M; l++) { for (l = 0; l < M; l++) {
k = l+1; k = l + 1;
U = outProd(ylk[l][p[k]], Id[p[k]-1], M);
beta = 1 + ylk[l][p[k]][p[k]]; beta = 1 + ylk[l][p[k]][p[k]];
for (i = 0; i < M; i++) { for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) { for (j = 0; j < M; j++) {
Al[i][j] = Id[i][j] - U[i][j] / beta; Al[i * M + j] = (i == j) - (j == p[k]-1) * ylk[l][p[k]][i + 1] / beta;
} }
} }
Slater_inv = matMul(Al, Slater_inv, M); Slater_inv = matMul(Al, Slater_inv, M);
@ -97,15 +77,25 @@ void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, uns
// Assign the new values of 'Slater_inv' to the old values in 'copy[][]' // Assign the new values of 'Slater_inv' to the old values in 'copy[][]'
for (i = 0; i < M; i++) { for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) { for (j = 0; j < M; j++) {
copy[i][j] = Slater_inv[i][j]; copy[i * M + j] = Slater_inv[i * M + j];
} }
} }
for (l = 0; l < M; l++) { for (l = 0; l < M; l++) {
for (k = 0; k < M+1; k++) { for (k = 0; k < M + 1; k++) {
delete [] ylk[l][k]; delete[] ylk[l][k];
} }
delete [] ylk[l], Id[l], U[l], Al[l], Slater_inv[l]; delete[] ylk[l];
} }
delete [] p, breakdown; delete[] Al;
delete[] p, breakdown;
}
extern "C" {
void MaponiA3_f(double **linSlater0, double **linSlater_inv, unsigned int *Dim,
unsigned int *N_updates, double **linUpdates,
unsigned int **Updates_index) {
MaponiA3(*linSlater0, *linSlater_inv, *Dim, *N_updates, *linUpdates,
*Updates_index);
}
} }

5
SM_MaponiA3.hpp
View File

@ -1,2 +1,3 @@
// SM-MaponiA3.hpp void MaponiA3(double *Slater0, double *Slater_inv, unsigned int M,
void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index); unsigned int N_updates, double *Updates,
unsigned int *Updates_index);

144
SM_MaponiA3_f.cpp
View File

@ -1,144 +0,0 @@
// SM-MaponiA3_f.cpp
// Algorithm 3 from P. Maponi,
// p. 283, doi:10.1016/j.laa.2006.07.007
#include "SM_MaponiA3_f.hpp"
#include "Helpers.hpp"
void MaponiA3(int **linSlater0, double **linSlater_inv, unsigned int *Dim, unsigned int *N_updates, int **linUpdates, unsigned int *Updates_index) {
// Define new 2D arrays and copy the elements of the
// linear passed Fortran arrays. This block needs to
// be replaced with a suitable casting mechanism to
// avoid copying of memory.
int **Slater0 = new int*[*Dim];
int **Updates = new int*[*Dim];
double **Slater_inv = new double*[*Dim];
for (int i = 0; i < *Dim; i++) {
Slater0[i] = new int[*Dim];
Updates[i] = new int[*Dim];
Slater_inv[i] = new double[*Dim];
}
for (unsigned int i = 0; i < *Dim; i++) {
for (unsigned int j = 0; j < *Dim; j++) {
Slater0[i][j] = linSlater0[0][i+*Dim*j];
Slater_inv[i][j] = linSlater_inv[0][i+*Dim*j];
Updates[i][j] = linUpdates[0][i+*Dim*j];
}
}
// Possible casting candidates
// int (*Slater0)[*Dim] = (int(*)[*Dim])linSlater0[0];
// double (*Slater_inv)[*Dim] = (double(*)[*Dim])linSlater_inv[0];
// int (*Updates)[*Dim] = (int(*)[*Dim])linUpdates[0];
////////////////////////////////////////////////////////////////////////
unsigned int k, l, lbar, i, j, tmp, M = *Dim;
unsigned int *p = new unsigned int[M+1];
unsigned int **Id = new unsigned int*[M];
double alpha, beta;
double **U, *breakdown = new double[M+1];
double **Al = new double*[M];
p[0] = 0;
for (i = 0; i < M; i++) {
p[i+1] = i + 1;
Id[i] = new unsigned int[M];
Al[i] = new double[M];
}
// Declare auxiliary solution matrix ylk
double ***ylk = new double**[M];
for (l = 0; l < M; l++) {
ylk[l] = new double*[M+1];
for (k = 0; k < M+1; k++) {
ylk[l][k] = new double[M+1];
}
}
// Initialize identity matrix
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
if (i != j) Id[i][j] = 0;
else Id[i][j] = 1;
}
}
// Initialize ylk with zeros
for (l = 0; l < M; l++) {
for (k = 0; k < M+1; k++) {
for (i = 0; i < M+1; i++) {
ylk[l][k][i] = 0;
}
}
}
// Calculate all the y0k in M^2 multiplications instead of M^3
for (k = 1; k < M+1; k++) {
for (i = 1; i < M+1; i++) {
ylk[0][k][i] = Slater_inv[i-1][i-1] * Updates[i-1][k-1];
}
}
// Calculate all the ylk from the y0k
for (l = 1; l < M; l++) {
for (j = l; j < M+1; j++) {
breakdown[j] = abs( 1 + ylk[l-1][p[j]][p[j]] );
}
lbar = getMaxIndex(breakdown, M+1);
for (i = 0; i < M; i++) {
breakdown[i] = 0;
}
tmp = p[l];
p[l] = p[lbar];
p[lbar] = tmp;
for (k = l+1; k < M+1; k++) {
beta = 1 + ylk[l-1][p[l]][p[l]];
if (beta == 0) {
cout << "Break-down condition occured. Exiting..." << endl;
exit;
}
for (i = 1; i < M+1; i++) {
alpha = ylk[l-1][p[k]][p[l]] / beta;
ylk[l][p[k]][i] = ylk[l-1][p[k]][i] - alpha * ylk[l-1][p[l]][i];
}
}
}
// Keep the memory location of the passed array 'Slater_inv' before 'Slater_inv'
// gets reassigned by 'matMul(...)' in the next line, by creating a new
// pointer 'copy' that points to whereever 'Slater_inv' points to now.
// double **copy = Slater_inv;
// Construct A-inverse from A0-inverse and the ylk
for (l = 0; l < M; l++) {
k = l+1;
U = outProd(ylk[l][p[k]], Id[p[k]-1], M);
beta = 1 + ylk[l][p[k]][p[k]];
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
Al[i][j] = Id[i][j] - U[i][j] / beta;
}
}
Slater_inv = matMul(Al, Slater_inv, M);
}
// Overwrite the old values in 'copy' with the new ones in Slater_inv
// for (i = 0; i < M; i++) {
// for (j = 0; j < M; j++) {
// copy[i][j] = Slater_inv[i][j];
// }
// }
// Overwrite the old values in 'linSlater_inv' with the new values in Slater_inv
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
linSlater_inv[0][i+*Dim*j] = Slater_inv[i][j];
}
}
for (l = 0; l < M; l++) {
for (k = 0; k < M+1; k++) {
delete [] ylk[l][k];
}
delete [] ylk[l], Id[l], U[l], Al[l], Slater_inv[l];
}
delete [] p, breakdown;
}

4
SM_MaponiA3_f.hpp
View File

@ -1,4 +0,0 @@
// SM-MaponiA3_f.hpp
extern "C" {
void MaponiA3(int **linSlater0, double **linSlater_inv, unsigned int *Dim, unsigned int *N_updates, int **linUpdates, unsigned int *Updates_index);
}

4
SM_MaponiA3_mod.f90
View File

@ -1,10 +1,10 @@
module Sherman_Morrison module Sherman_Morrison
interface interface
subroutine MaponiA3(Slater0, Slater_inv, dim, n_updates, Updates, Updates_index) bind(C, name="MaponiA3") subroutine MaponiA3(Slater0, Slater_inv, dim, n_updates, Updates, Updates_index) bind(C, name="MaponiA3_f")
use, intrinsic :: iso_c_binding, only : c_int, c_double use, intrinsic :: iso_c_binding, only : c_int, c_double
integer(c_int), intent(in) :: dim, n_updates integer(c_int), intent(in) :: dim, n_updates
integer(c_int), dimension(:), allocatable, intent(in) :: Updates_index integer(c_int), dimension(:), allocatable, intent(in) :: Updates_index
integer(c_int), dimension(:,:), allocatable, intent(in) :: Slater0, Updates real(c_double), dimension(:,:), allocatable, intent(in) :: Slater0, Updates
real(c_double), dimension(:,:), allocatable, intent(in out) :: Slater_inv real(c_double), dimension(:,:), allocatable, intent(in out) :: Slater_inv
end subroutine MaponiA3 end subroutine MaponiA3
end interface end interface

57
cppmain.cpp
View File

@ -7,73 +7,52 @@
int main() { int main() {
srand((unsigned) time(0)); srand((unsigned) time(0));
unsigned int randRange = 1; // to get random integers in range [-randRange, randRange]
unsigned int M = 3; // Dimension of the Slater-matrix unsigned int M = 3; // Dimension of the Slater-matrix
unsigned int i, j; // Indices for iterators unsigned int i, j; // Indices for iterators
// Declare, allocate all vectors and matrices and fill them with zeros // Declare, allocate all vectors and matrices and fill them with zeros
unsigned int *Ar_index = new unsigned int[M]; unsigned int *Ar_index = new unsigned int[M];
int **A = new int*[M]; // The matrix to be inverted double *A = new double[M*M]; // The matrix to be inverted
int **A0 = new int*[M]; // A diagonal matrix with the digonal elements of A double *A0 = new double[M*M]; // A diagonal matrix with the digonal elements of A
int **Ar = new int*[M]; // The update matrix double *Ar = new double[M*M]; // The update matrix
double **A0_inv = new double*[M]; // Inverse of A0 double *A0_inv = new double[M*M]; // The inverse
for (i = 0; i < M; i++) {
A[i] = new int[M];
A0[i] = new int[M];
Ar[i] = new int[M];
A0_inv[i] = new double[M];
}
// Fill with zeros // Fill with zeros
for (i = 0; i < M; i++) { for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) { for (j = 0; j < M; j++) {
A0[i][j] = 0; A0[i*M+j] = 0;
Ar[i][j] = 0; Ar[i*M+j] = 0;
A0_inv[i][j] = 0; A0_inv[i*M+j] = 0;
} }
} }
// Initialize A with M=3 and fill acc. to Eq. (17) from paper // Initialize A with M=3 and fill acc. to Eq. (17) from paper
A[0][0] = 1; A[0][1] = 1; A[0][2] = -1; A[0] = 1; A[3] = 1; A[6] = -1;
A[1][0] = 1; A[1][1] = 1; A[1][2] = 0; A[1] = 1; A[4] = 1; A[7] = 0;
A[2][0] = -1; A[2][1] = 0; A[2][2] = -1; A[2] = -1; A[5] = 0; A[8] = -1;
// // Fill A with random numbers from [-randRange,randRange]
// // and check if A and A0 are invertable
// do {
// for (i = 0; i < M; i++) {
// for (j = 0; j < M; j++) {
// A[i][j] = rand()%(2*randRange+1)-randRange;
// }
// }
// for (i = 0; i < M; i++) {
// A0[i][i] = A[i][i];
// }
// } while (matDet(A, M) == 0 || matDet(A0, M) == 0);
showMatrix(A, M, "A"); showMatrix(A, M, "A");
// Initialize the diagonal matrix A0, // Initialize the diagonal matrix A0,
// the inverse of A0_inv of diagonal matrix A0_inv // the inverse of A0_inv of diagonal matrix A0_inv
// and the update matrix Ar // and the update matrix Ar
for (i = 0; i < M; i++) { for (i = 0; i < M; i++) {
A0[i][i] = A[i][i]; A0[i*M+i] = A[i*M+i];
A0_inv[i][i] = 1.0/A[i][i]; A0_inv[i*M+i] = 1.0/A[i*M+i];
Ar_index[i] = i; Ar_index[i] = i;
for (j = 0; j < M; j++) { for (j = 0; j < M; j++) {
Ar[i][j] = A[i][j] - A0[i][j]; Ar[i*M+j] = A[i*M+j] - A0[i*M+j];
} }
} }
// Define pointers dim and n_updates to use in Sherman-Morrison(...) function call // Define pointers dim and n_updates to use in Sherman-Morrison(...) function call
unsigned int *dim = new unsigned int(M); unsigned int dim = M;
unsigned int *n_updates = new unsigned int(M); unsigned int n_updates = M;
Sherman_Morrison(A0, A0_inv, dim, n_updates, Ar, Ar_index); MaponiA3(A0, A0_inv, dim, n_updates, Ar, Ar_index);
showMatrix(A0_inv, M, "A0_inv"); showMatrix(A0_inv, M, "A0_inv");
// Deallocate all vectors and matrices // Deallocate all vectors and matrices
for (i = 0; i < M; i++) {
delete [] A[i], A0[i], A0_inv[i], Ar[i];
}
delete [] A, A0, A0_inv, Ar, Ar_index; delete [] A, A0, A0_inv, Ar, Ar_index;
delete dim, n_updates;
return 0; return 0;
} }

22
fmain.f90
View File

@ -6,7 +6,7 @@ program Interface_test
integer i, j !! Iterators integer i, j !! Iterators
integer(c_int) :: dim, N_updates integer(c_int) :: dim, N_updates
integer(c_int), dimension(:), allocatable :: Ar_index integer(c_int), dimension(:), allocatable :: Ar_index
integer(c_int), dimension(:,:), allocatable :: A, A0, Ar real(c_double), dimension(:,:), allocatable :: A, A0, Ar
real(c_double), dimension(:,:), allocatable :: A0_inv real(c_double), dimension(:,:), allocatable :: A0_inv
dim = 3 dim = 3
@ -14,15 +14,15 @@ program Interface_test
allocate(Ar_index(dim), A(dim,dim), A0(dim,dim), Ar(dim,dim), A0_inv(dim,dim)) allocate(Ar_index(dim), A(dim,dim), A0(dim,dim), Ar(dim,dim), A0_inv(dim,dim))
!! Initialize A with M=3 and fill acc. to Eq. (17) from paper !! Initialize A with M=3 and fill acc. to Eq. (17) from paper
A(1,1) = 1 A(1,1) = 1.0d0
A(1,2) = 1 A(1,2) = 1.0d0
A(1,3) = -1 A(1,3) = -1.0d0
A(2,1) = 1 A(2,1) = 1.0d0
A(2,2) = 1 A(2,2) = 1.0d0
A(2,3) = 0 A(2,3) = 0.0d0
A(3,1) = -1 A(3,1) = -1.0d0
A(3,2) = 0 A(3,2) = 0.0d0
A(3,3) = -1 A(3,3) = -1.0d0
!! Prepare the diagonal matrix A0 and the update matrix Ar !! Prepare the diagonal matrix A0 and the update matrix Ar
do i=1,dim do i=1,dim
@ -32,7 +32,7 @@ program Interface_test
A0(i,j) = A(i,j) A0(i,j) = A(i,j)
A0_inv(i,j) = 1.0d0 / A0(i,j) A0_inv(i,j) = 1.0d0 / A0(i,j)
else else
A0(i,j) = 0 A0(i,j) = 0.0d0
A0_inv(i,j) = 0.0d0 A0_inv(i,j) = 0.0d0
end if end if
Ar(i,j) = A(i,j) - A0(i,j) Ar(i,j) = A(i,j) - A0(i,j)