I have coded up a gauss seidel method that works just fine but i cannot seem to figure out how to convert that to jacobi... I know it should be easy so i must be missing something simple. For the assignment i had to make my own vector and matrix classes so that is why Vector is capital and called differently. Here is my working gauss seidel code:
else if (mode == 3) {
Vector temp;
temp.allocateData(b.numElems());
Vector old = temp;
Vector sum;
double f = 50;
int y = 4;
double tol = 1e-12;
double error = 10;
int max = 999999;
int count = 0;
while ( error > tol && max > count) {
for (int i = 0; i < row_; i++) {
temp.setVal(i, b.getVal(i) / M[i][i]);
for (int j = 0; j < col_; j++) {
if (j == i) {
continue;
}
temp.setVal(i, temp.getVal(i) - ((M[i][j] / M[i][i]) * temp.getVal(j)));
old.setVal(j, temp.getVal(i));
}
cout<<"x"<< i + 1 << "="<< temp.getVal(i) <<" \n";
error = abs(temp.getVal(i)-old.getVal(i))/abs(temp.getVal(i));
old = temp;
}
cout << "\n";
count++;
}
}
and here is my attempt at jacobi:
else if (mode == 2) {
Vector temp;
temp.allocateData(b.numElems());
Vector old = temp;
Vector sum;
double f = 50;
int y = 4;
double tol = 1e-12;
double error = 10;
int max = 999999;
int count = 0;
while ( error > tol && max > count) {
old.allocateData(b.numElems());
for (int i = 0; i < row_; i++) {
old.setVal(i, temp.getVal(i));
temp.setVal(i, b.getVal(i) / M[i][i]);
for (int j = 0; j < col_; j++) {
if (j == i) {
continue;
}
temp.setVal(i, temp.getVal(i) - ((M[i][j] / M[i][i]) * old.getVal(j)));
}
cout<<"x"<< i + 1 << "="<< temp.getVal(i) <<" \n";
error = abs(temp.getVal(i)-old.getVal(i))/abs(temp.getVal(i));
}
cout << "\n";
count++;
}
}
thanks everyone ahead of time for the help!!!
Related
What is wrong with that code?
Sorry, if here bad code.
I'm need to find max value for all column in 2d dimensional of float values, then find them sum.
First of all I write values for Array, then display them at screen and tried to find max values for each column.
Photo: didn't working and correctly work
___________________
[5.7 ; 4.2 ; 5.8;]
[654.87; 5.86; 3.76;] - Work correctly
[8.54; 7.54; 8.4;]
------------------
Max value of 1 column = A[2,1] = 654.87;
Max value of 2 column = A[3,2] = 7.54;
Max value of 3 column = A[3,3] = 8.4;
___________________
[4.6 ; 2.65 ; 76.3;]
[65.64; 7.32; 76.2;] - Work not correctly
[654.8; 1.6; 5.7;]
------------------
Max value of 1 column = A[3,1] = 654.8;
Max value of 2 column = A[3,2] = 7.32;
Max value of 3 column = A[3,3] = 5.7;
#include<iostream>
#include<conio.h>
int main(void)
{
system("cls");
int N;
int suma = 0;
A:
std::cout<<"Write array size N x N : ";
std::cin>>N;
if(N>10 || N<=1)
{
system("cls");
std::cout<<"N must be <= 10 and > 1;"<<std::endl;
goto A;
}
float **A = new float *[N];
for(int i = 0; i < N; i++)
{
A[i] = new float [N];
for(int j = 0; j < N; j++)
{
std::cout<<"A["<<i+1<<"][";
std::cout<<j+1<<"] = ";
std::cin>>(*(*(A+i)+j));
}
}
system("cls");
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
if(j<N-1)
{
std::cout<<"A["<<i+1<<"]["<<j+1<<"] = "<<*(*(A+i)+j);
std::cout<<"; ";
}
else
{
std::cout<<"A["<<i+1<<"]["<<j+1<<"] = "<<*(*(A+i)+j);
std::cout<<";"<<std::endl;
}
}
}
float *max = new float [N];
std::cout<<"------------------------------------";
std::cout<<std::endl;
for(int i = 0; i < N - (N - 1); i++)
{
for(int j = 0; j < N; j++)
{
*(max+j) = *(*(A+i)+j);
}
}
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
if( (*(max+i)) < (*(*(A+j))+i) &&
(*(max+i)) != ((*(*(A+j)))+i) )
{
*(max+i) = *(*(A+j)+i);
}
}
}
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
if( (*(*(A+j)+i)) == (*(max+i)) )
{
std::cout<<"Max value of "<<i+1;
std::cout<<" column = ";
std::cout<<"A["<<j+1<<"]["<<i+1;
std::cout<<"] = "<<(*(max+i));
std::cout<<std::endl;
}
}
suma+=(*(max+i));
}
std::cout<<"Sum of largest value = "<<suma;
_getch();
}
Oh... sorry just a mistake in if() by which i losen more than 3.5 hour...
if( (*(max+i)) < (*(*(A+j))+i)
&&
(*(max+i)) != ((*(*(A+j)))+i) )
{...}
I changed it to:
if( (*(max + i)) < (*(*(A + j) + i))
&&
(*(max + i)) != (*(*(A + j) + i))
)
{...}
After that change all work properly
I'm trying to write a programm to find a maximum value in column in a initialized 5x5 matrix, and change it to -1. I found out the way to do it, but i want to find a better solution.
Input:
double array2d[5][5];
double *ptr;
ptr = array2d[0];
// initializing matrix
for (int i = 0; i < 5; ++i) {
for (int j = 0; j < 5; ++j) {
if (j % 2 != 0) {
array2d[i][j] = (i + 1) - 2.5;
} else {
array2d[i][j] = 2 * (i + 1) + 0.5;
}
}
}
This is my solution for the first column :
// Changing the matrix using pointer arithmetic
for (int i = 0; i < (sizeof(array2d) / sizeof(array2d[0][0])); ++i) {
if (i % 5 == 0) {
if (maxTemp <= *(ptr + i)) {
maxTemp = *(ptr + i);
}
}
}
for (int i = 0; i < (sizeof(array2d) / sizeof(array2d[0][0])); ++i) {
if (i % 5 == 0) {
if (*(ptr + i) == maxTemp) {
*(ptr + i) = -1;
}
}
}
I can repeat this code 5 times, and get the result, but i want a better solution. THX.
Below is the complete program that uses pointer arithmetic. This program replaces all the maximum values in each column of the 2D array -1 as you desire.
#include <iostream>
int main()
{
double array2d[5][5];
double *ptr;
ptr = array2d[0];
// initializing matrix
for (int i = 0; i < 5; ++i) {
for (int j = 0; j < 5; ++j) {
if (j % 2 != 0) {
array2d[i][j] = (i + 1) - 2.5;
} else {
array2d[i][j] = 2 * (i + 1) + 0.5;
}
}
}
//these(from this point on) are the things that i have added.
//Everything above this comment is the same as your code.
double (*rowBegin)[5] = std::begin(array2d);
double (*rowEnd)[5] = std::end(array2d);
while(rowBegin != rowEnd)
{
double *colBegin = std::begin(rowBegin[0]);
double *colEnd = std::end(rowBegin[0]);
double lowestvalue = *colBegin;//for comparing elements
//double *pointerToMaxValue = colBegin;
while(colBegin!= colEnd)
{
if(*colBegin > lowestvalue)
{
lowestvalue = *colBegin;
//pointerToMaxValue = colBegin ;
}
colBegin = colBegin + 1;
}
double *newcolBegin = std::begin(rowBegin[0]);
double *newcolEnd = std::end(rowBegin[0]);
while(newcolBegin!=newcolEnd)
{
if(*newcolBegin == lowestvalue)
{
*newcolBegin = -1;
}
++newcolBegin;
}
++rowBegin;
}
return 0;
}
The program can be checked here.
You can add print out all the element of the array to check whether the above program replaced all the maximum value in each column with -1.
I have written it in java but I think u can understand. This one is for all 5 columns at the same time. You can try this:
int count = 0;
double max = 0;
for (int i = 0; i < 5; ++i) {
for (int j = 0; j < 5; ++j) {
if (j == 0) {
max = array2d[j][I];
count = 0;
}
if (array2d[j][i] > max) {
count = j;
}
}
array2d[count][i] = -1;
}
I'm stuck trying to get the value of what A[i][j] is pointing to. double a = A[i][j];. How do I correctly do it? Could someone please explain?
// g++ jacobi.cpp -O0 -o jacobi && ./jacobi
#include <iostream>
#include <iomanip>
#include <vector>
#include <climits>
using namespace std;
void print_matrix(vector<vector<double>>& m) {
for (int i = 0; i < m.size(); i++) {
for (int j = 0; j < m[0].size(); j++) {
cout << setw(5) << fixed << setprecision(2) << m[i][j] << " ";
}
cout << endl;
}
cout << "==================================" << endl;
}
// calculate average temperature based on average of adjacent cells
double avg_temp_at(vector<vector<double>>& matrix, int i, int j) {
return (
matrix[i][j] +
(j-1 >= 0 ? matrix[i][j-1] : 0) +
(i-1 >= 0 ? matrix[i-1][j] : 0) +
(j+1 < matrix[0].size() ? matrix[i][j+1] : 0) +
(i+1 < matrix.size() ? matrix[i+1][j] : 0)
) / 5;
}
// sequential Jacobi algorithm
vector<vector<double>> jacobi_relaxation(vector<vector<double>>& matrix, int& threshold) {
vector<vector<double>> B (matrix.size(), vector<double>(matrix[0].size(), 0));
vector<vector<double>>* A = &matrix;
double max_delta = INT_MAX;
while (max_delta > threshold) {
max_delta = 0;
for (int i = 0; i < matrix.size(); i++) {
for (int j = 0; j < matrix[0].size(); j++) {
B[i][j] = avg_temp_at(*A, i, j);
double a = A[i][j];
double delta = abs(B[i][j] - a);
max_delta = max(max_delta, delta);
}
}
print_matrix(B);
A = &B;
}
return *A;
}
int main() {
int threshold = 1;
int n = 6;
vector<vector<double>> matrix (n, vector<double>(n, 0));
matrix[1][2] = 100;
matrix[2][2] = 100;
matrix[3][2] = 100;
print_matrix(matrix);
vector<vector<double>> x = jacobi_relaxation(matrix, threshold);
}
I tried your code and it gave me error on this line:
double a = A[i][j];
Change that line into this:
double a = (*A)[i][j];
and it will work.
Explanation:
It's basically the same trick as in line B[i][j] = avg_temp_at(*A, i, j);. A is a pointer, which is pointing to a vector. To accessing to pointers "real data" you must use the *.
Here you can find more info about pointers.
Hope it helps.
I have a computation with a matrix(88147*2000) and it runs very slow.
So I want to use openMP to speed it up. This is my first time to use
openMP so I just use it in "loop-for".
This is my code:
#include<iostream>
#include<fstream>
#include<math.h>
#include<omp.h>
using namespace std;
#define LONGTH 88147
int label[LONGTH] ;
float data[LONGTH][2000] ;
float w[2000];
float e[2000];
void Input()
{
ifstream fin;
float a;
fin.open("/home/data.train");
if (!fin)
{
cout << "file error";
return;
}
for (int i = 0; i < LONGTH; i++)
{
fin >> a;
label[i] = int(a);
for (int j = 0; j < 2000; j++)
{
fin>>data[i][j];
}
}
fin.close();
cout<<"input over"<<endl;
return;
}
void Initial()
{
for (int i = 0; i < 2000; i++)
{
w[i] = 1;
e[i] = 1;
}
return;
}
bool End()
{
for (int i = 0; i < 2000; i++)
{
if (fabs(e[i])>pow(0.1, 6))
return 0;
}
return 1;
}
float Tkj(int i, int j, int k,float w[2000])
{
return w[i] * data[k][i] - w[j] * data[k][j];
}
float En(int n)//*computation*
{
float result = 0;
#pragma omp parallel for num_threads(64) reduction(+:result)
for (int k = 0; k < LONGTH; k++)
{
int tnum = omp_get_thread_num();
float tmp = 0;
int i = label[k] - 1;
for (int j = 0; j < 2000; j++)
{
if (j != i)
{
float l = 0;
if (n == i)
{
l = data[k][i];
float e = exp(Tkj(i, j, k,w));
tmp = tmp + (-e*l) / pow(1 + e, 2);
}
else if (n == j)
{
l = -data[k][j];
float e = exp(Tkj(i, j, k,w));
tmp = tmp + (-e*l) / pow(1 + e, 2);
}
else
{
continue;
}
}
}
result = result + tmp;
}
return result;
}
float Ex(float w[2000])
{
float result = 0;
#pragma omp parallel for num_threads(64) reduction(+:result)
for (int k = 0; k < LONGTH; k++)
{
int i = label[k] - 1;
float tmp = 0;
int tnum = omp_get_thread_num();
for (int j = 0; j < 2000; j++)
{
if (j != i)
{
tmp = tmp + 1 / (1 + exp(Tkj(i,j,k,w)));
}
}
result = result+tmp;
}
return result;
}
int main()
{
Input();
Initial();
float w2[2000] = { 0 };
float b = pow(0.1,5);
int times = 0;
while (!End()&×<=30000)
{
times++;
cout<<times<<endl;
for (int i = 0; i < 2000; i++)
{
e[i] = En(i);
w2[i] = w[i] - b*e[i];
}
if (Ex(w2)<=Ex(w))//better
{
b = b * 2;
for (int i = 0; i < 2000; i++)
w[i] = w2[i];
}
else//worser
{
b = b / 2;
}
}
ofstream fout("/home/w.txt");
for(int i=0;i<2000;i++)
{
fout<<w[i]<<' ';
}
fout.close();
return 0;
}
The function 'En' costs most of time,so I use "#pragma omp parallel for num_threads(64) reduction(+:result)"to speed it up.
I run it in a CentOS server which has 32 cores and use "-fopenmp" to compile it.But it doesn't be a little quicker.
How can I speed this program up more?
I have an array of 20 x 20 that outputs how hot a plate is. I need to reiterate through a loop until no cell in the array changes more than 0.1 degree(I refresh the values through every iteration. How would you monitor the largest change for any cell in an array in order to determine when to stop iterating? Right now I have tried, but the below doesn't output correctly.
#include <iostream>
#include <string>
#include <fstream>
using namespace std;
const int ARRAY_SIZE = 20;
const int NEIGHBORS = 4;
void initialize(double hot_plate[][ARRAY_SIZE]);
bool writeFile(const double HOT_PLATE[][ARRAY_SIZE],
const string FILE_NAME);
double sum_cell(const double HOT_PLATE[][ARRAY_SIZE],
const int CELL_X, const int CELL_Y);
int main()
{
double hot_plate[ARRAY_SIZE][ARRAY_SIZE];
double hot_plate_prev[ARRAY_SIZE][ARRAY_SIZE];
initialize(hot_plate);
string file_name = "hot_plate.csv";
//accuracy up to 4 decmials
int runs = 724;
double hot_plate[ARRAY_SIZE][ARRAY_SIZE];
double hot_plate_prev[ARRAY_SIZE][ARRAY_SIZE];
while (true)
{
// This is your code
for (int i = 0; i < ARRAY_SIZE; i++)
{
for (int j = 0; j < ARRAY_SIZE; j++)
{
if (i > 0 && i < ARRAY_SIZE - 1 && j > 0 && j < ARRAY_SIZE - 1)
{
hot_plate[i][j] = sum_cell(hot_plate, j, i);
}
}
}
bool theSame = true;
for (int i = 0; i < ARRAY_SIZE; i++)
{
for (int j = 0; j < ARRAY_SIZE; j++)
{
if (abs(hot_plate[i][j] - hot_plate_prev[i][j]) < 0.1)
{
theSame = false;
}
hot_plate_prev[i][j] = hot_plate[i][j];
}
}
if (!theSame) break;
}
}
if (writeFile(hot_plate, file_name))
{
cout << "File wrote correctly\n";
}
else
{
cout << "The file did not write!\n";
}
//system("pause");
return 0;
}
double sum_cell(const double HOT_PLATE[][ARRAY_SIZE],
const int CELL_X, const int CELL_Y)
{
/* This code should never go out of bounds as it's in an if statement
if (i > 0 && i < ARRAY_SIZE - 1 && j > 0 && j < ARRAY_SIZE - 1)
*/
double cell_num = HOT_PLATE[CELL_X - 1][CELL_Y]; // Top
cell_num += HOT_PLATE[CELL_X][CELL_Y - 1]; // Left
cell_num += HOT_PLATE[CELL_X][CELL_Y + 1]; // Right
cell_num += HOT_PLATE[CELL_X + 1][CELL_Y]; // Bottom
cell_num /= NEIGHBORS;
return cell_num;
}
// setup the Array so all values are defined when starting
void initialize(double hot_plate[][ARRAY_SIZE])
{
for (int i = 0; i < ARRAY_SIZE; i++)
{
for (int j = 0; j < ARRAY_SIZE; j++)
{
if (i == 0 || i == ARRAY_SIZE - 1)
{
if (j == 0 || j == ARRAY_SIZE - 1)
{
hot_plate[i][j] = 0.0;
}
else
{
hot_plate[i][j] = 100.0;
}
}
else
{
hot_plate[i][j] = 0.0;
}
}
}
}
// Write the data to the CSV file
bool writeFile(const double HOT_PLATE[][ARRAY_SIZE],
const string FILE_NAME)
{
// open the file
ofstream fout(FILE_NAME);
if (fout.fail())
return false;
for (int i = 0; i < ARRAY_SIZE; i++)
{
for (int j = 0; j < ARRAY_SIZE; j++)
{
fout << HOT_PLATE[i][j];
if ( j < ARRAY_SIZE - 1)
{
fout << ", ";
}
else if (i != ARRAY_SIZE - 1)
{
fout << endl;
}
}
}
// close the input stream from the file.
fout.close();
return true;
}
At the beginning of your while loop, you can set a boolean variable called something like allSmallChanges to true. In your inner if statement, you can check to see if the change to hot_plate[i][j] is "too big". If it is too big, then set allSmallChanges to false. Then, just before the end of the while loop, you can break if allSmallChanges is still true.
If you don't want to have that cap of 724 iterations, you can get rid of your runs variable, and change the loop to while(true).
Note: The code in the question got changed after I wrote this answer. I'm not sure this answer still applies. However, I'm also sure that will be the last change to the code in the question. So, I'll leave this answer as-is for now.