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C++ implementation of algo 3 is working. Not optimised yet.

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This commit is contained in:
François Coppens 2021-01-27 17:19:41 +01:00
parent e509f28ba6
commit d45df44e5e
3 changed files with 267 additions and 36 deletions
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3
.vscode/settings.json vendored
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@ -1,6 +1,7 @@
{
"files.associations": {
"ostream": "cpp",
"new": "cpp"
"new": "cpp",
"iostream": "cpp"
}
}

9
Makefile
View File

@ -1,16 +1,17 @@
CC=icc
CXX=icpc
CFLAGS=-xCORE-AVX2 -O0 -debug full
CXXFLAGS=-xCORE-AVX2 -O0 -debug full
CFLAGS=-O0 -debug full
CXXFLAGS=-O0 -debug full -traceback
# ARCH=-xCORE-AVX2
DEPS = SM-MaponiA3.cpp
OBJ = SM-MaponiA3.o
%.o: %.c $(DEPS)
$(CXX) -c -o $@ $< $(CFLAGS)
$(CXX) $(ARCH) -c -o $@ $< $(CFLAGS)
SM-MaponiA3: $(OBJ)
$(CXX) -o $@ $^ $(CFLAGS)
$(CXX) $(ARCH) -o $@ $^ $(CFLAGS)
clean:
@rm -vf *.o

291
SM-MaponiA3.cpp
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@ -2,26 +2,46 @@
// p. 283, doi:10.1016/j.laa.2006.07.007
#include <iostream>
#include <string>
using namespace std;
int M = 3;
uint getMaxIndex(double* arr, uint size);
void showScalar(uint scalar, string name);
void showScalar(int scalar, string name);
void showScalar(double scalar, string name);
void showVector(uint* vector, uint size, string name);
void showVector(int* vector, uint size, string name);
void showVector(double* vector, uint size, string name);
void showMatrix(uint** matrix, uint sizeR, uint sizeC, string name);
void showMatrix(int** matrix, uint sizeR, uint sizeC, string name);
void showMatrix(double** matrix, uint sizeR, uint sizeC, string name);
void showMatrixT(uint** matrix, uint sizeR, uint sizeC, string name);
void showMatrixT(int** matrix, uint sizeR, uint sizeC, string name);
void showMatrixT(double** matrix, uint sizeR, uint sizeC, string name);
int** matMul(int** A, int** B, uint size);
double** matMul(double** A, double** B, uint size);
int** outProd(int* vec1, int* vec2, uint size);
double** outProd(double* vec1, int* vec2, uint size);
int main() {
uint M = 3;
uint i, j, k, l, lbar, tmp;
double alpha, beta;
// Declare and allocate all vectors and matrices
int* p = new int[M+1];
int* breakdown = new int[M];
uint* p = new uint[M+1];
double* breakdown = new double[M+1];
int** A = new int*[M];
int** A0 = new int*[M];
int** Ar = new int*[M];
int** Id = new int*[M];
double** A0inv = new double*[M];
double** Ainv = new double*[M];
double** Ainv; //= new double*[M];
for (i = 0; i < M; i++) {
A[i] = new int[M];
Ainv[i] = new double[M];
//Ainv[i] = new double[M];
A0[i] = new int[M];
A0inv[i] = new double[M];
Ar[i] = new int[M];
@ -32,7 +52,7 @@ int main() {
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];
ylk[l][k] = new double[M+1];
}
}
@ -40,7 +60,7 @@ int main() {
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
A[i][j] = 0;
Ainv[i][j] = 0;
//Ainv[i][j] = 0;
A0[i][j] = 0;
A0inv[i][j] = 0;
Ar[i][j] = 0;
@ -48,17 +68,27 @@ int main() {
}
}
// Initialize all vectors and matrices
// 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;
}
}
}
// Initialize A
A[0][0] = 1; A[0][1] = 1; A[0][2] = -1;
A[1][0] = 1; A[1][1] = 1; A[1][2] = 0;
A[2][0] = -1; A[2][1] = 0; A[2][2] = -1;
// Define identity matrix, A0, A0inv and p
p[0] = 0;
for (i = 0; i < M; i++) {
Id[i][i] = 1;
A0[i][i] = A[i][i];
A0inv[i][i] = 1.0/A[i][i];
p[i] = i;
p[i+1] = i+1;
}
// Init Ar
@ -68,48 +98,80 @@ int main() {
}
}
showMatrix(A, M, M, "A");
// showMatrix(A0, M, M, "A0");
// showMatrix(Ar, M, M, "Ar");
// showMatrix(A0inv, M, M, "A0inv");
// Calculate all the y0k in M^2 multiplications instead of M^3
for (k = 1; i < M+1; k++) {
for (i = 0; i < M; i++) {
ylk[0][k][i] = A0inv[i][i] * Ar[i][k];
for (k = 1; k < M+1; k++) {
for (i = 1; i < M+1; i++) {
ylk[0][k][i] = A0inv[i-1][i-1] * Ar[i-1][k-1];
}
// showVector(ylk[0][k], M+1, "y0k");
}
showMatrixT(ylk[0], M+1, M+1, "y0k");
// Calculate all the ylk from the y0k
// showVector(p, M+1, "p");
for (l = 1; l < M; l++) {
for (j = l; j < M; j++) {
breakdown[j] = abs( 1 + ylk[l][p[j]][p[j]-1] );
for (j = l; j < M+1; j++) {
breakdown[j] = abs( 1 + ylk[l-1][p[j]][p[j]] );
}
lbar = findMaxElmnt(breakdown); // NOT IMPLEMENTED YET
// showVector(breakdown, M+1, "break-down vector");
lbar = getMaxIndex(breakdown, M+1);
// showScalar(lbar, "lbar");
for (i = 0; i < M; i++) {
breakdown[i] = 0;
}
tmp = p
}
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
cout << "A["<<i<<"]["<<j<<"] = " << A0inv[i][j] << " ";
tmp = p[l];
p[l] = p[lbar];
p[lbar] = tmp;
// showVector(p, M+1, "p");
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];
}
// showVector(ylk[l][p[k]], M+1, "ylk");
}
cout << endl;
}
showMatrixT(ylk[1], M+1, M+1, "y1k");
showMatrixT(ylk[2], M+1, M+1, "y2k");
// EVERYTHING WORKS UPTO HERE
// Construct A-inverse from A0-inverse and the ylk
double** U;
double** Ap = new double*[M];
for (i = 0; i < M; i++) Ap[i] = new double[M];
Ainv = A0inv;
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++) {
Ap[i][j] = Id[i][j] - U[i][j] / beta;
}
}
Ainv = matMul(Ap, Ainv, M);
}
showMatrixT(Ainv, M, M, "Ainv");
// Deallocate all vectors and matrices
for (i = 0; i < M; i++) {
delete [] A[i];
delete [] Ainv[i];
delete [] A0[i];
delete [] A0inv[i];
delete [] Ar[i];
delete [] Id[i];
delete [] U[i];
delete [] Ap[i];
}
for (l = 0; l < M; l++) {
@ -123,3 +185,170 @@ int main() {
return 0;
}
uint getMaxIndex(double* arr, uint size) {
uint i;
uint max = arr[0];
uint maxi = 0;
for (i = 1; i < size; i++) {
if (arr[i] > max) {
max = arr[i];
maxi = i;
}
}
return maxi;
}
void showScalar(uint scalar, string name) {
cout << name << " = " << scalar << endl << endl;
}
void showScalar(int scalar, string name) {
cout << name << " = " << scalar << endl << endl;
}
void showScalar(double scalar, string name) {
cout << name << " = " << scalar << endl << endl;
}
void showVector(uint* vector, uint size, string name) {
cout << name << " = " << endl;
for (uint i = 0; i < size; i++) {
cout << "[ " << vector[i] << " ]" << endl;
}
cout << endl;
}
void showVector(int* vector, uint size, string name) {
cout << name << " = " << endl;
for (uint i = 0; i < size; i++) {
cout << "[ " << vector[i] << " ]" << endl;
}
cout << endl;
}
void showVector(double* vector, uint size, string name) {
cout << name << " = " << endl;
for (uint i = 0; i < size; i++) {
cout << "[ " << vector[i] << " ]" << endl;
}
cout << endl;
}
void showMatrix(uint** matrix, uint sizeR, uint sizeC, string name) {
cout << name << " = " << endl;
for (uint i = 0; i < sizeR; i++) {
cout << "[ ";
for (uint j = 0; j < sizeC; j++) {
cout << matrix[i][j] << " ";
}
cout << " ]" << endl;
}
cout << endl;
}
void showMatrix(int** matrix, uint sizeR, uint sizeC, string name) {
cout << name << " = " << endl;
for (uint i = 0; i < sizeR; i++) {
cout << "[ ";
for (uint j = 0; j < sizeC; j++) {
cout << matrix[i][j] << " ";
}
cout << " ]" << endl;
}
cout << endl;
}
void showMatrix(double** matrix, uint sizeR, uint sizeC, string name) {
cout << name << " = " << endl;
for (uint i = 0; i < sizeR; i++) {
cout << "[ ";
for (uint j = 0; j < sizeC; j++) {
cout << matrix[i][j] << " ";
}
cout << " ]" << endl;
}
cout << endl;
}
void showMatrixT(uint** matrix, uint sizeR, uint sizeC, string name) {
cout << name << " = " << endl;
for (uint i = 0; i < sizeR; i++) {
cout << "[ ";
for (uint j = 0; j < sizeC; j++) {
cout << matrix[j][i] << " ";
}
cout << " ]" << endl;
}
cout << endl;
}
void showMatrixT(int** matrix, uint sizeR, uint sizeC, string name) {
cout << name << " = " << endl;
for (uint i = 0; i < sizeR; i++) {
cout << "[ ";
for (uint j = 0; j < sizeC; j++) {
cout << matrix[j][i] << " ";
}
cout << " ]" << endl;
}
cout << endl;
}
void showMatrixT(double** matrix, uint sizeR, uint sizeC, string name) {
cout << name << " = " << endl;
for (uint i = 0; i < sizeR; i++) {
cout << "[ ";
for (uint j = 0; j < sizeC; j++) {
cout << matrix[j][i] << " ";
}
cout << " ]" << endl;
}
cout << endl;
}
int** matMul(int** A, int** B, uint size) {
int** C = new int*[size];
for (uint i = 0; i < size; i++) {
C[i] = new int[size];
}
for (uint i = 0; i < size; i++) {
for (uint j = 0; j < size; j++) {
for (uint k = 0; k < size; k++) {
C[i][j] += A[i][k] * B[k][j];
}
}
}
return C;
}
double** matMul(double** A, double** B, uint size) {
double** C = new double*[size];
for (uint i = 0; i < size; i++) {
C[i] = new double[size];
}
for (uint i = 0; i < size; i++) {
for (uint j = 0; j < size; j++) {
for (uint k = 0; k < size; k++) {
C[i][j] += A[i][k] * B[k][j];
}
}
}
return C;
}
int** outProd(int* vec1, int* vec2, uint size) {
int** C = new int*[size];
for (uint i = 0; i < size; i++) {
C[i] = new int[size];
}
for (uint i = 0; i < size; i++) {
for (uint j = 0; j < size; j++) {
C[i][j] = vec1[i+1] * vec2[j];
}
}
return C;
}
double** outProd(double* vec1, int* vec2, uint size) {
double** C = new double*[size];
for (uint i = 0; i < size; i++) {
C[i] = new double[size];
}
for (uint i = 0; i < size; i++) {
for (uint j = 0; j < size; j++) {
C[i][j] = vec1[i+1] * vec2[j];
}
}
return C;
}