NT2_TEST_CASE_TPL ( rref, NT2_REAL_TYPES)
{
typedef typename nt2::meta::as_integer<T, signed>::type itype_t;
typedef nt2::table<itype_t> it_t;
typedef nt2::table<T> table_t;
T A[16] = {
16, 2, 3, 13,
5, 11, 10, 8,
9, 7, 6, 12,
4, 14, 15, 1};
table_t b = nt2::ones(4, 4, nt2::meta::as_<T>())
+ T(10)*nt2::eye(4, 4, nt2::meta::as_<T>());
table_t rref, l, u, p;
table_t a(nt2::of_size(4, 4));
int k = 0;
for(int i=1; i <= 4; ++i)
{
for(int j=1; j <= 4; ++j)
{
a(i, j) = A[k++];
}
}
NT2_DISPLAY(a);
nt2::tie(rref) = nt2::rref(a);
NT2_DISPLAY(rref);
it_t jb;
nt2::tie(rref, jb) = nt2::rref(a);
NT2_DISPLAY(rref);
NT2_DISPLAY(jb);
NT2_TEST(nt2::isulpequal(rref(nt2::_(1, nt2::numel(jb)), jb), nt2::eye(nt2::numel(jb), nt2::meta::as_<T>())));
}
/*
Column-reduced echelon form.
*/
void cref(int *mat, int rows, int cols, int w)
{
int* mT = (int*)malloc(sizeof(int) * rows * cols);
transpose(mat, mT, rows, cols);
rref(mT, cols, rows, w);
transpose(mT, mat, cols, rows);
free(mT);
}
void main(){
double **mx;
int m,n;
printf("Enter m and n ");
scanf("%i %i", &m, &n);
//get space
mx = malloc(m*sizeof(double *));
for(int i=0; i<m; i++)
mx[i] = malloc(n*sizeof(double));
scanMatrix(mx, m, n);
rref(mx, m, n);
printMatrix(mx , m, n);
}
void cGetRREFCommand::Execute()
{
if((1 != m_Expression.terms.size()) || (1 != m_Expression.terms[0].factors.size()))
throw std::runtime_error("Invalid input. Provide a valid matrix to compute the RREF.");
cMatrix *mat = boost::get<cMatrix >(&(m_Expression.terms[0].factors[0].factor));
if(nullptr == mat)
throw std::runtime_error("Invalid input. Provide a valid matrix to compute the RREF.");
double double_cols_no = mat->elements.size()/mat->rows_no;
std::size_t cols_no = mat->elements.size()/mat->rows_no;
if(double_cols_no != std::floor(double_cols_no))
throw std::runtime_error("Invalid input. Provide a valid matrix to compute the RREF.");
//add the matrix stored in row major order
m_Result.resize(mat->rows_no, cols_no);
for(std::size_t rows_idx = 0; rows_idx < mat->rows_no; rows_idx++)
for(std::size_t cols_idx = 0; cols_idx < cols_no; cols_idx++)
m_Result(rows_idx, cols_idx) = mat->elements[cols_idx + rows_idx*cols_no];
rref(m_Result);
}
void crank(double ***matrix, double ***matrix_np1, int nx, int ny, int nz, double alpha, double dx, double C, int border, int NT){
int i, j, k, l, f, g, h;
double d;
int b0;
int bn;
int when = 1;
double ***temp;
double *tempb;
double *mat_b = (double*) malloc(sizeof(double)* nx*ny*nz);
double *mat_newb = (double*) malloc(sizeof(double)* nx*ny*nz);
double **mat_A = (double**) malloc(sizeof(double*) *nx*ny*nz);
double **augmented = (double**) malloc(sizeof(double*) *nx*ny*nz);
double *data = (double*) malloc(sizeof(double) * nx*nx*ny*ny*nz*nz);
double *augdata = (double*) malloc(sizeof(double) * nx*nx*ny*ny*nz*nz+nx*ny*nz);/*care for last column - b*/
/*now need to make augmented matrix to pass into rref*/
for(h=0;h<nx*ny*nz;h++){
*(augmented+h) = augdata + h*nx*ny*nz+1;/*care for augmented with b*/
}
switch(border){
case 0:
b0 = 0;
bn = 0;
break;
case 1:
b0 = 3;
bn = 3;
break;
case 2:
b0 = nx;
bn = 0;
break;
default :
b0 = 0;
bn = 0;
}
print3DMatrix(matrix, nx, ny, nz, dx, dx, dx, when);
when++;
/*malloc space for A*/
for(i=0;i<nx*ny*nz;i++){
*(mat_A+i) = data + i*nx*ny*nz;
}
/*make matrix b which is 1-D from init 3-D matrix --flattened*/
for(i = 0 ; i< nx ; i++){
for(j = 0 ; j < ny ; j++){
for(k = 0 ; k < nz ; k++){
*(mat_b + i*ny*nz + j*nz + k) = *(*(*(matrix + i) + j) +k);
}
}
}
for(k=0;k<NT;k++){
for(i = 0; i< nx*ny*nz ; i++){
for(j = 0;j< nx*ny*nz ; j++){
if( i == j){
*(*(mat_A+i)+j) = /*mat_b[i]**/1+6.0*C;
}
else if (i == j-1 ){
if( i != 0%nz){
*(*(mat_A+i)+j) = /**(mat_b + i-1)**/(-1.0*C);
}
else if(i ==0%nz && border== 2){
*(*(mat_A+i)+j) = /**(mat_b + (i-1)%nz)**/(-1.0*C);
}
}
else if (i == j+1){
if( i != (nz-1)%(nz-1)){
*(*(mat_A+i)+j) =/* *(mat_b + i+1)**/(-1.0*C);
}
else if(i == (nz-1)%(nz-1) && border == 2){
*(*(mat_A+i)+j) =/* *(mat_b + (i+1)%nz)**/(-1.0*C);
}
}
else if(i == j-ny*nz){
if( i > ny*nz){
*(*(mat_A+i)+j) =/* *(mat_b + i-ny*nz)**/(-1.0*C);
}
else if(i <= ny*nz && border == 2){
*(*(mat_A+i)+j) =/* *(mat_b + (i-ny*nz)%(nx*ny*nz))**/(-1.0*C);
}
}
else if(i == j+ny*nz){
if( i < ny*nz){
*(*(mat_A+i)+j) = /**(mat_b + i+ny*nz)**/(-1.0*C);
}
else if(i >= ny*nz && border == 2){
*(*(mat_A+i)+j) = /**(mat_b + (i+ny*nz)%(nx*ny*nz))**/(-1.0*C);
}
}
else if(i == j+ny){
if( i != (ny-1)%(ny-1)){
*(*(mat_A+i)+j) =/* *(mat_b + i+ny)**/(-1.0*C);
}
else if(i ==(ny-1)%(ny-1) && border == 2){
*(*(mat_A+i)+j) =/* *(mat_b + (i+ny)%ny)**/(-1.0*C);
}
}
else if(i == j-ny){
if( i != 0%ny){
*(*(mat_A+i)+j) =/* *(mat_b + i-ny)**/(-1.0*C);
}
else if(i == 0%ny && border == 2){
*(*(mat_A+i)+j) =/* *(mat_b + (i-ny)%ny)**/(-1.0*C);
}
}
else{
*(*(mat_A+i)+j) = 0.0;
}
}
/*at this point A is created*/
for(g = 0; g< nx*ny*nz ; g++){
for(h = 0;h< nx*ny*nz ; h++){
if(h == nx*ny*nz-1){
*(*(augmented+g)+h) = *(mat_b+g);
}
else{
*(*(augmented+g)+h) = *(*(mat_A+g)+h);
}
}
}
/*at this point i have Ax=b in augmented matrix form to use rref on {augmented | b} */
rref(augmented, nx*ny*nz, nx*ny*nz+1);
/*now i need to extract the nx*ny*nz+1 column to cpy back to my old mat_b, mat_A*/
for(g = 0; g< nx*ny*nz ; g++){
for(h = 0;h< nx*ny*nz ; h++){
if(h == nx*ny*nz-1){
*(mat_newb+g) = *(*(augmented+g)+h);
}
/* else{
*(*(mat_A+g)+h) = *(*(augmented+g)+h);
}*/
}
}
d = distanceFormula(mat_newb, mat_b, nx*ny*nz);
//printf("%f \n",d);
tempb = mat_b;
mat_b = mat_newb;
mat_newb = tempb;
for(f = 0 ; f< nx ; f++){
for(g = 0 ; g < ny ; g++){
for( h = 0 ; h < nz ; h++){
*(*(*(matrix + f) + g) +h) = *(mat_b + f*ny*nz + g*nz + h);
}
}
}
}
if( k==0){
print3DMatrix(matrix, nx, ny, nz, dx, dx, dx, when);
when++;
}
}
}
void adi(double ***matrix, double ***matrix_np1, int nx, int ny, int nz, double alpha, double dx, double C, int border, int NT){
int i, j, k, l, f, g, h;
int dir;
int when =1;
double d;
double ***temp;
double *tempb;
double *mat_b = (double*) malloc(sizeof(double)* nx*ny*nz);
double *mat_newb = (double*) malloc(sizeof(double)* nx*ny*nz);
double **mat_A = (double**) malloc(sizeof(double*) *nx*ny*nz);
double **augmented = (double**) malloc(sizeof(double*) *nx*ny*nz);
double *data = (double*) malloc(sizeof(double) * nx*nx*ny*ny*nz*nz);
double *augdata = (double*) malloc(sizeof(double) * nx*nx*ny*ny*nz*nz+nx*ny*nz);/*care for last column - b*/
print3DMatrix(matrix, nx, ny, nz, dx, dx, dx, when);
when++;
/*now need to make augmented matrix to pass into rref*/
for(h=0;h<nx*ny*nz;h++){
*(augmented+h) = augdata + h*nx*ny*nz+1;/*care for augmented with b*/
}
/*malloc space for A*/
for(i=0;i<nx*ny*nz;i++){
*(mat_A+i) = data + i*nx*ny*nz;
}
/*make matrix b which is 1-D from init 3-D matrix --flattened*/
for(i = 0 ; i< nx ; i++){
for(j = 0 ; j < ny ; j++){
for(k = 0 ; k < nz ; k++){
*(mat_b + i*ny*nz + j*nz + k) = *(*(*(matrix + i) + j) +k);
}
}
}
/*run in each direction, without X, then without Y, then without Z, so A is made up of 3 different 2 D variations*/
for(k=0;k<NT;k++){
for(dir=0;dir<3;dir++){
switch(dir){
case 0:
for(i = 0; i< nx*ny*nz ; i++){
for(j = 0;j< nx*ny*nz ; j++){
if( i == j){
*(*(mat_A+i)+j) = /*mat_b[i]**/1+4.0*C;
}
else if (i == j-1){
if( i != 0%nz){
*(*(mat_A+i)+j) = /**(mat_b + i-1)**/(-1.0*C);
}
else if(i ==0%nz && border== 2){
*(*(mat_A+i)+j) = /**(mat_b + (i-1)%nz)**/(-1.0*C);
}
}
else if (i == j+1){
if( i != (nz-1)%(nz-1)){
*(*(mat_A+i)+j) = /**(mat_b + i+1)**/(-1.0*C);
}
else if(i == (nz-1)%(nz-1) && border == 2){
*(*(mat_A+i)+j) =/* *(mat_b + (i+1)%nz)**/(-1.0*C);
}
}
else if(i == j+ny){
if( i != (ny-1)%(ny-1)){
*(*(mat_A+i)+j) = /**(mat_b + i+ny)**/(-1.0*C);
}
else if(i ==(ny-1)%(ny-1) && border == 2){
*(*(mat_A+i)+j) =/* *(mat_b + (i+ny)%ny)**/(-1.0*C);
}
}
else if(i == j-ny){
if( i != 0%ny){
*(*(mat_A+i)+j) = /**(mat_b + i-ny)**/(-1.0*C);
}
else if(i == 0%ny && border == 2){
*(*(mat_A+i)+j) = /**(mat_b + (i-ny)%ny)**/(-1.0*C);
}
}
else{
*(*(mat_A+i)+j) = 0.0;
}
}
}
break;
case 1:
for(i = 0; i< nx*ny*nz ; i++){
for(j = 0;j< nx*ny*nz ; j++){
if( i == j){
*(*(mat_A+i)+j) =/* mat_b[i]**/1+4.0*C;
}
else if (i == j-1){
if( i != 0%nz){
*(*(mat_A+i)+j) = /**(mat_b + i-1)**/(-1.0*C);
}
else if(i ==0%nz && border== 2){
*(*(mat_A+i)+j) = /**(mat_b + (i-1)%nz)**/(-1.0*C);
}
}
else if (i == j+1){
if( i != (nz-1)%(nz-1)){
*(*(mat_A+i)+j) = /**(mat_b + i+1)**/(-1.0*C);
}
else if(i == (nz-1)%(nz-1) && border == 2){
*(*(mat_A+i)+j) = /**(mat_b + (i+1)%nz)**/(-1.0*C);
}
}
else if(i == j-ny*nz){
if( i > ny*nz){
*(*(mat_A+i)+j) = /**(mat_b + i-ny*nz)**/(-1.0*C);
}
else if(i <= ny*nz && border == 2){
*(*(mat_A+i)+j) =/* *(mat_b + (i-ny*nz)%(nx*ny*nz))**/(-1.0*C);
}
}
else if(i == j+ny*nz){
if( i < ny*nz){
*(*(mat_A+i)+j) = /**(mat_b + i+ny*nz)**/(-1.0*C);
}
else if(i >= ny*nz && border == 2){
*(*(mat_A+i)+j) = /**(mat_b + (i+ny*nz)%(nx*ny*nz))**/(-1.0*C);
}
}
else{
*(*(mat_A+i)+j) = 0.0;
}
}
}
break;
case 2:
for(i = 0; i< nx*ny*nz ; i++){
for(j = 0;j< nx*ny*nz ; j++){
if( i == j){
*(*(mat_A+i)+j) = /*mat_b[i]**/1+4.0*C;
}
else if(i == j-ny*nz){
if( i > ny*nz){
*(*(mat_A+i)+j) = /**(mat_b + i-ny*nz)**/(-1.0*C);
}
else if(i <= ny*nz && border == 2){
*(*(mat_A+i)+j) = /**(mat_b + (i-ny*nz)%(nx*ny*nz))**/(-1.0*C);
}
}
else if(i == j+ny*nz){
if( i < ny*nz){
*(*(mat_A+i)+j) = /**(mat_b + i+ny*nz)**/(-1.0*C);
}
else if(i >= ny*nz && border == 2){
*(*(mat_A+i)+j) = /**(mat_b + (i+ny*nz)%(nx*ny*nz))**/(-1.0*C);
}
}
else if(i == j+ny){
if( i != (ny-1)%(ny-1)){
*(*(mat_A+i)+j) = /**(mat_b + i+ny)**/(-1.0*C);
}
else if(i ==(ny-1)%(ny-1) && border == 2){
*(*(mat_A+i)+j) = /**(mat_b + (i+ny)%ny)**/(-1.0*C);
}
}
else if(i == j-ny){
if( i != 0%ny){
*(*(mat_A+i)+j) = /**(mat_b + i-ny)**/(-1.0*C);
}
else if(i == 0%ny && border == 2){
*(*(mat_A+i)+j) = /**(mat_b + (i-ny)%ny)**/(-1.0*C);
}
}
else{
*(*(mat_A+i)+j) = 0.0;
}
}
}
break;
}
/*at this point A is created*/
for(g = 0; g< nx*ny*nz ; g++){
for(h = 0;h< nx*ny*nz ; h++){
if(h == nx*ny*nz-1){
*(*(augmented+g)+h) = *(mat_b+g);
}
else{
*(*(augmented+g)+h) = *(*(mat_A+g)+h);
}
}
}
/*at this point i have Ax=b in augmented matrix form to use rref on {augmented | b} */
rref(augmented, nx*ny*nz, nx*ny*nz+1);
/*now i need to extract the nx*ny*nz+1 column to cpy back to my old mat_b, mat_A*/
for(g = 0; g< nx*ny*nz ; g++){
for(h = 0;h< nx*ny*nz ; h++){
if(h == nx*ny*nz-1){
*(mat_newb+g) = *(*(augmented+g)+h);
}
/* else{
*(*(mat_A+g)+h) = *(*(augmented+g)+h);
}*/
}
}
tempb = mat_b;
mat_b = mat_newb;
mat_newb = tempb;
}
for(f = 0 ; f< nx ; f++){
for(g = 0 ; g < ny ; g++){
for( h = 0 ; h < nz ; h++){
*(*(*(matrix + f) + g) +h) = *(mat_b + f*ny*nz + g*nz + h);
}
}
}
if(k == 1){
print3DMatrix(matrix, nx, ny, nz, dx, dx, dx, when);
when++;
}
}
}
