# determinant of matrix in c++

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### #1 krish_iitd

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# determinant of matrix in c++

Posted 24 June 2008 - 11:37 AM

hello , i am interested to find the simple function to find the determinant of square matrix in c++ language as possible as simple ,can any one Please help me .
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## Replies To: determinant of matrix in c++

### #2 joske

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## Re: determinant of matrix in c++

Posted 24 June 2008 - 12:40 PM

Here is some code i wrote some time ago as an exercise. It contains a simple matrix class, including function det() to calculate the determinant. For 2x2 matrices the determinant is very easy, for larger matrices it is a little bit more complex, amongst others you have to calculate all minor of the matrix.

It is not a neat C++ program, as I haven't split the code in a header and source file.
```/*
A simple matrix class
c++ code
Author: Jos de Jong, Nov 2007

With this class you can:
- create a matrix
- get/set the values
- use operators +, -, *
- use functions ones(), zeros(), diag(), det(), inv(), size()
- print the content of the matrix

Usage:
you can create a matrix by:
Matrix A;
Matrix A = Matrix(rows, cols);
Matrix A = B;

you can get and set matrix elements by:
A(2,3) = 5.6;        // set an element of Matix A
value = A(3,1);      // get an element of Matrix A
A = B;               // copy content of Matrix B to Matrix A

you can apply operations with matrices and doubles:
A = B + C;
A = B - C;
A = B * C;
A = -B;

the following functions are available:
A = ones(rows, cols);
A = zeros(rows, cols);
A = diag(n);
A = diag(B)/>;
d = det(A);
A = inv(B)/>;
cols = A.get_cols();
rows = A.get_rows();
cols = size(A, 1);
rows = size(A, 2);

you can quick-print the content of a matrix in the console with:
A.print();

Todo:
inverse of a matrix. see [url="http://mathworld.wolfram.com/MatrixInverse.html"]http://mathworld.wolfram.com/MatrixInverse.html[/url]
division with a matrix
multiplying a matrix with a double
*/

#include <cstdlib>
#include <cstdio>
#include <math.h>

using namespace std;

/*
* a simple exception class
* you can create an exeption by entering
*      throw Exception("...Error description...");
* and get the error message from the data msg for displaying:
*      err.msg
*/
class Exception {
public:
const char* msg;
Exception(const char* arg) : msg(arg) { };
};

class Matrix
{
public:
// constructors
Matrix()
{
//printf("Executing constructor Matrix() ...\n");
// create a Matrix object without content
p = NULL;
rows = 0;
cols = 0;
}
Matrix(const int row_count, const int column_count)
{
// create a Matrix object with given number of rows and columns
//printf("Executing constructor Matrix(const int column_count, const int row_count) ...\n");
p = NULL;

if (row_count > 0 && column_count > 0)
{
rows = row_count;
cols = column_count;

p = new double*[rows];
for (int r = 0; r < rows; r++)
{
p[r] = new double[rows];

// initially fill in zeros for all values in the matrix;
for (int c = 0; c < cols; c++)
{
p[r][c] = 0;
}
}
}
}
// assignment operator
Matrix(const Matrix& a)
{
//printf("Executing constructor Matrix(const Matrix& a) ...\n");
rows = a.rows;
cols = a.cols;
p = new double*[a.rows];
for (int r = 0; r < a.rows; r++)
{
p[r] = new double[a.cols];

// copy the values from the matrix a
for (int c = 0; c < a.cols; c++)
{
p[r][c] = a.p[r][c];
}
}
}

// index operator. You can use this class like myMatrix(col, row)
// the indexes are one-based, not zero based.
double& operator()(const int r, const int c)
{
//printf("Executing Matrix operator() ...\n");
if (p != NULL && r > 0 && r <= rows && c > 0 && c <= cols)
{
return p[r-1][c-1];
}
else
{
throw Exception("Subscript out of range");
}
}

// assignment operator
Matrix& operator= (const Matrix& a)
{
//printf("Executing Matrix operator= ...\n");
rows = a.rows;
cols = a.cols;
p = new double*[a.rows];
for (int r = 0; r < a.rows; r++)
{
p[r] = new double[a.cols];

// copy the values from the matrix a
for (int c = 0; c < a.cols; c++)
{
p[r][c] = a.p[r][c];
}
}
return *this;
}

// operator addition
friend Matrix operator+(const Matrix& a, const Matrix& B)/>
{
// check if the dimensions match
if (a.rows == b.rows && a.cols == b.cols)
{
Matrix res(a.rows, a.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = a.p[r][c] + b.p[r][c];
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}

// return an empty matrix (this never happens but just for safety)
return Matrix();
}

// add a double value (elements wise)
Matrix& add(double v)
{
for (int r = 0; r < rows; r++)
{
for (int c = 0; c < cols; c++)
{
p[r][c] += v;
}
}
return *this;
}

// subtract a double value (elements wise)
Matrix& subtract(double v)
{
return add(-v);
}

// multiply a double value (elements wise)
Matrix& multiply(double v)
{
for (int r = 0; r < rows; r++)
{
for (int c = 0; c < cols; c++)
{
p[r][c] *= v;
}
}
return *this;
}

// operator subtraction
friend Matrix operator- (const Matrix& a, const Matrix& B)/>
{
// check if the dimensions match
if (a.rows == b.rows && a.cols == b.cols)
{
Matrix res(a.rows, a.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = a.p[r][c] - b.p[r][c];
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}

// return an empty matrix (this never happens but just for safety)
return Matrix();
}
// operator unary minus
friend Matrix operator- (const Matrix& a)
{
Matrix res(a.rows, a.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = -a.p[r][c];
}
}

return res;
}

// operator multiplication
friend Matrix operator* (const Matrix& a, const Matrix& B)/>
{
// check if the dimensions match
if (a.cols == b.rows)
{
Matrix res(a.rows, b.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c_res = 0; c_res < b.cols; c_res++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c_res] += a.p[r][c] * b.p[c][c_res];
}
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}

// return an empty matrix (this never happens but just for safety)
return Matrix();
}

/**
* returns the minor from the given matrix where
* the selected row and column are removed
*/
Matrix minor(const int row, const int col)
{
//printf("minor(row=%i, col=%i), rows=%i, cols=%i\n", row, col, rows, cols);
Matrix res;
if (row > 0 && row <= rows && col > 0 && col <= cols)
{
res = Matrix(rows - 1, cols - 1);

// copy the content of the matrix to the minor, except the selected
for (int r = 1; r <= (rows - (row >= rows)); r++)
{
for (int c = 1; c <= (cols - (col >= cols)); c++)
{
//printf("r=%i, c=%i, value=%f, rr=%i, cc=%i \n", r, c, p[r-1][c-1], r - (r > row), c - (c > col));
res(r - (r > row), c - (c > col)) = p[r-1][c-1];
}
}
}
else
{
throw Exception("Index for minor out of range");
}

return res;
}

/*
* returns the size of the i-th dimension of the matrix.
* i.e. for i=1 the function returns the number of rows,
* and for i=2 the function returns the number of columns
* else the function returns 0
*/
int size(const int i)
{
if (i == 1)
{
return rows;
}
else if (i == 2)
{
return cols;
}
return 0;
}

// returns the number of rows
int get_rows()
{
return rows;
}

// returns the number of columns
int get_cols()
{
return cols;
}

// print the contents of the matrix
void print()
{
if (p != NULL)
{
printf("[");
for (int r = 0; r < rows; r++)
{
if (r > 0)
{
printf(" ");
}
for (int c = 0; c < cols-1; c++)
{
printf("%.2f, ", p[r][c]);
}
if (r < rows-1)
{
printf("%.2f;\n", p[r][cols-1]);
}
else
{
printf("%.2f]\n", p[r][cols-1]);
}
}
}
else
{
// matrix is empty
printf("[ ]\n");
}
}

public:
// destructor
~Matrix()
{
// clean up allocated memory
for (int r = 0; r < rows; r++)
{
delete p[r];
}
delete p;
p = NULL;
}

private:
int rows;
int cols;
double** p;         // pointer to a matrix with doubles
};

/*
* i.e. for i=1 the function returns the number of rows,
* and for i=2 the function returns the number of columns
* else the function returns 0
*/
int size(Matrix& a, const int i)
{
return a.size(i);
}

// addition of Matrix with double
Matrix operator+ (const Matrix& a, const double B)/>
{
Matrix res = a;
res.add(B)/>;
return res;
}
// addition of double with Matrix
Matrix operator+ (const double b, const Matrix& a)
{
Matrix res = a;
res.add(B)/>;
return res;
}

// subtraction of Matrix with double
Matrix operator- (const Matrix& a, const double B)/>
{
Matrix res = a;
res.subtract(B)/>;
return res;
}
// subtraction of double with Matrix
Matrix operator- (const double b, const Matrix& a)
{
Matrix res = -a;
res.add(B)/>;
return res;
}

// multiplication of Matrix with double
Matrix operator* (const Matrix& a, const double B)/>
{
Matrix res = a;
res.multiply(B)/>;
return res;
}
// multiplication of double with Matrix
Matrix operator* (const double b, const Matrix& a)
{
Matrix res = a;
res.multiply(B)/>;
return res;
}

/**
* returns a matrix with size cols x rows with ones as values
*/
Matrix ones(const int rows, const int cols)
{
Matrix res = Matrix(rows, cols);

for (int r = 1; r <= rows; r++)
{
for (int c = 1; c <= cols; c++)
{
res(r, c) = 1;
}
}
return res;
}

/**
* returns a matrix with size cols x rows with zeros as values
*/
Matrix zeros(const int rows, const int cols)
{
return Matrix(rows, cols);
}

/**
* returns a diagonal matrix with size n x n with ones at the diagonal
* @param   v a vector
* @return  a diagonal matrix with ones on the diagonal
*/
Matrix diag(const int n)
{
Matrix res = Matrix(n, n);
for (int i = 1; i <= n; i++)
{
res(i, i) = 1;
}
return res;
}
/**
* returns a diagonal matrix
* @param   v a vector
* @return  a diagonal matrix with the given vector v on the diagonal
*/
Matrix diag(Matrix& v)
{
Matrix res;
if (v.get_cols() == 1)
{
// the given matrix is a vector n x 1
int rows = v.get_rows();
res = Matrix(rows, rows);

// copy the values of the vector to the matrix
for (int r=1; r <= rows; r++)
{
res(r, r) = v(r, 1);
}
}
else if (v.get_rows() == 1)
{
// the given matrix is a vector 1 x n
int cols = v.get_cols();
res = Matrix(cols, cols);

// copy the values of the vector to the matrix
for (int c=1; c <= cols; c++)
{
res(c, c) = v(1, c);
}
}
else
{
throw Exception("Parameter for diag must be a vector");
}
return res;
}

/*
* returns the determinant of Matrix a
*/
double det(Matrix& a)
{
double d = 0;       // value of the determinant
int rows = a.get_rows();
int cols = a.get_cols();

if (rows == cols)
{
// this is a square matrix
if (rows == 1)
{
// this is a 1 x 1 matrix
d = a(1, 1);
}
else if (rows == 2)
{
// this is a 2 x 2 matrix
// the determinant of [a11,a12;a21,a22] is det = a11*a22-a21*a12
d = a(1, 1) * a(2, 2) - a(2, 1) * a(1, 2);
}
else
{
// this is a matrix of 3 x 3 or larger
for (int c = 1; c <= cols; c++)
{
Matrix M = a.minor(1, c);
//d += pow(-1, 1+c)  * a(1, c) * det(M);
d += (c%2 + c%2 - 1) * a(1, c) * det(M);  // faster than with pow()
}
}
}
else
{
throw Exception("Matrix must be square");
}
return d;
}

// swap two values
void swap(double& a, double& B)/>
{
double temp = a;
a = b;
b = temp;
}

/*
* returns the inverse of Matrix a
*/
Matrix inv(Matrix& a)
{
Matrix res;
double d = 0;       // value of the determinant
int rows = a.get_rows();
int cols = a.get_cols();

d = det(a);
if (rows == cols && d != 0)
{
// this is a square matrix
if (rows == 1)
{
// this is a 1 x 1 matrix
res = Matrix(rows, cols);
res(1, 1) = 1 / a(1, 1);
}
else if (rows == 2)
{
// this is a 2 x 2 matrix
res = Matrix(rows, cols);
res(1, 1) = a(2, 2);
res(1, 2) = -a(1, 2);
res(2, 1) = -a(2, 1);
res(2, 2) = a(1, 1);
res = (1/d) * res;
}
else
{
// this is a matrix of 3 x 3 or larger
// calculate inverse using gauss-jordan elimination
//      [url="http://mathworld.wolfram.com/MatrixInverse.html"]http://mathworld.wolfram.com/MatrixInverse.html[/url]
//      [url="http://math.uww.edu/~mcfarlat/inverse.htm"]http://math.uww.edu/~mcfarlat/inverse.htm[/url]
res = diag(rows);     // a diagonal matrix with ones at the diagonal
Matrix ai = a;        // make a copy of Matrix a

for (int c = 1; c <= cols; c++)
{
// element (c, c) should be non zero. if not, swap content
// of lower rows
int r;
for (r = c; r <= rows && ai(r, c) == 0; r++)
{
}
if (r != c)
{
// swap rows
for (int s = 1; s <= cols; s++)
{
swap(ai(c, s), ai(r, s));
swap(res(c, s), res(r, s));
}
}

// eliminate non-zero values on the other rows at column c
for (int r = 1; r <= rows; r++)
{
if(r != c)
{
// eleminate value at column c and row r
if (ai(r, c) != 0)
{
double f = - ai(r, c) / ai(c, c);

// add (f * row c) to row r to eleminate the value
// at column c
for (int s = 1; s <= cols; s++)
{
ai(r, s) += f * ai(c, s);
res(r, s) += f * res(c, s);
}
}
}
else
{
// make value at (c, c) one,
// divide each value on row r with the value at ai(c,c)
double f = ai(c, c);
for (int s = 1; s <= cols; s++)
{
ai(r, s) /= f;
res(r, s) /= f;
}
}
}
}
}
}
else
{
if (rows == cols)
{
throw Exception("Matrix must be square");
}
else
{
throw Exception("Determinant of matrix is zero");
}
}
return res;
}

int main(int argc, char *argv[])
{
try
{
// create an empty matrix of 3x3 (will initially contain zeros)
int cols = 3;
int rows = 3;
Matrix A = Matrix(cols, rows);

// fill in some values in matrix a
int count = 0;
for (int r = 1; r <= rows; r++)
{
for (int c = 1; c <= cols; c++)
{
count ++;
A(r, c) = count;
}
}

// adjust a value in the matrix  (indexes are one-based)
A(2,1) = 1.23;

// read a value from the matrix  (indexes are one-based)
double centervalue = A(2,2);
printf("centervalue = %f \n", centervalue);
printf("\n");

// print the whole matrix
printf("A = \n");
A.print();
printf("\n");

Matrix B = ones(rows, cols) + diag(rows);
printf("B = \n");
B.print();
printf("\n");

Matrix B2 = Matrix(rows, 1);        // a vector
count = 1;
for (int r = 1; r <= rows; r++)
{
count ++;
B2(r, 1) = count * 2;
}
printf("B2 = \n");
B2.print();
printf("\n");

Matrix C;
C = A + B;
printf("A + B = \n");
C.print();
printf("\n");

C = A - B;
printf("A - B = \n");
C.print();
printf("\n");

C = A * B2;
printf("A * B2 = \n");
C.print();
printf("\n");

// create a diagonal matrix
Matrix E = diag(B2);
printf("E = \n");
E.print();
printf("\n");

// calculate determinant
Matrix D = Matrix(2, 2);
D(1,1) = 2;
D(1,2) = 4;
D(2,1) = 1;
D(2,2) = -2;
printf("D = \n");
D.print();
printf("det(D) = %f\n\n", det(D));

printf("A = \n");
A.print();
printf("\n");
printf("det(A) = %f\n\n", det(A));

Matrix F;
F = 3 - A ;
printf("3 - A = \n");
F.print();
printf("\n");

// test inverse
Matrix G = Matrix(2, 2);
G(1, 1) = 1;
G(1, 2) = 2;
G(2, 1) = 3;
G(2, 2) = 4;
printf("G = \n");
G.print();
printf("\n");
Matrix G_inv = inv(G);
printf("inv(G) = \n");
G_inv.print();
printf("\n");

Matrix A_inv = inv(A);
printf("inv(A) = \n");
A_inv.print();
printf("\n");
}
catch (Exception err)
{
printf("Error: %s\n", err.msg);
}
catch (...)
{
printf("An error occured...\n");
}

printf("\n");
system("PAUSE");
return EXIT_SUCCESS;
}

```

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### #3 joske

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Reputation: 43
• Posts: 297
• Joined: 04-September 07

## Re: determinant of matrix in c++

Posted 20 March 2010 - 04:17 AM

Here some updated code.

Pete pointed me to an error in the contstructor (there was a line p[r] = new double[rows]; instead of p[r] = new double[cols];. Thanks!

Furthermore, some slight changes to make the code cross platform.

```/*
A simple matrix class
c++ code
Author: Jos de Jong, Nov 2007. Updated March 2010

With this class you can:
- create a matrix
- get/set the values
- use operators +, -, *
- use functions ones(), zeros(), diag(), det(), inv(), size()
- print the content of the matrix

Usage:
you can create a matrix by:
Matrix A;
Matrix A = Matrix(rows, cols);
Matrix A = B;

you can get and set matrix elements by:
A(2,3) = 5.6;        // set an element of Matix A
value = A(3,1);      // get an element of Matrix A
A = B;               // copy content of Matrix B to Matrix A

you can apply operations with matrices and doubles:
A = B + C;
A = B - C;
A = B * C;
A = -B;

the following functions are available:
A = Ones(rows, cols);
A = Zeros(rows, cols);
A = Diag(n);
A = Diag(B)/>;
d = Det(A);
A = Inv(B)/>;
cols = A.GetCols();
rows = A.GetRows();
cols = Size(A, 1);
rows = Size(A, 2);

you can quick-print the content of a matrix in the console with:
A.Print();

Todo:
inverse of a matrix. see http://mathworld.wolfram.com/MatrixInverse.html
division with a matrix
multiplying a matrix with a double
*/

#include <cstdlib>
#include <cstdio>
#include <math.h>

#define PAUSE {printf("Press \"Enter\" to continue\n"); fflush(stdin); getchar(); fflush(stdin);}

/*
* a simple exception class
* you can create an exeption by entering
*      throw Exception("...Error description...");
* and get the error message from the data msg for displaying:
*      err.msg
*/
class Exception {
public:
const char* msg;
Exception(const char* arg) : msg(arg) { };
};

class Matrix
{
public:
// constructors
Matrix()
{
//printf("Executing constructor Matrix() ...\n");
// create a Matrix object without content
p = NULL;
rows = 0;
cols = 0;
}
Matrix(const int row_count, const int column_count)
{
// create a Matrix object with given number of rows and columns
//printf("Executing constructor Matrix(const int column_count, const int row_count) ...\n");
p = NULL;

if (row_count > 0 && column_count > 0)
{
rows = row_count;
cols = column_count;

p = new double*[rows];
for (int r = 0; r < rows; r++)
{
p[r] = new double[cols];

// initially fill in zeros for all values in the matrix;
for (int c = 0; c < cols; c++)
{
p[r][c] = 0;
}
}
}
}
// assignment operator
Matrix(const Matrix& a)
{
//printf("Executing constructor Matrix(const Matrix& a) ...\n");
rows = a.rows;
cols = a.cols;
p = new double*[a.rows];
for (int r = 0; r < a.rows; r++)
{
p[r] = new double[a.cols];

// copy the values from the matrix a
for (int c = 0; c < a.cols; c++)
{
p[r][c] = a.p[r][c];
}
}
}

// index operator. You can use this class like myMatrix(col, row)
// the indexes are one-based, not zero based.
double& operator()(const int r, const int c)
{
//printf("Executing Matrix operator() ...\n");
if (p != NULL && r > 0 && r <= rows && c > 0 && c <= cols)
{
return p[r-1][c-1];
}
else
{
throw Exception("Subscript out of range");
}
}

// assignment operator
Matrix& operator= (const Matrix& a)
{
//printf("Executing Matrix operator= ...\n");
rows = a.rows;
cols = a.cols;
p = new double*[a.rows];
for (int r = 0; r < a.rows; r++)
{
p[r] = new double[a.cols];

// copy the values from the matrix a
for (int c = 0; c < a.cols; c++)
{
p[r][c] = a.p[r][c];
}
}
return *this;
}

// operator addition
friend Matrix operator+(const Matrix& a, const Matrix& B)/>
{
// check if the dimensions match
if (a.rows == b.rows && a.cols == b.cols)
{
Matrix res(a.rows, a.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = a.p[r][c] + b.p[r][c];
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}

// return an empty matrix (this never happens but just for safety)
return Matrix();
}

// add a double value (elements wise)
Matrix& Add(double v)
{
for (int r = 0; r < rows; r++)
{
for (int c = 0; c < cols; c++)
{
p[r][c] += v;
}
}
return *this;
}

// subtract a double value (elements wise)
Matrix& Subtract(double v)
{
return Add(-v);
}

// multiply a double value (elements wise)
Matrix& Multiply(double v)
{
for (int r = 0; r < rows; r++)
{
for (int c = 0; c < cols; c++)
{
p[r][c] *= v;
}
}
return *this;
}

// operator subtraction
friend Matrix operator- (const Matrix& a, const Matrix& B)/>
{
// check if the dimensions match
if (a.rows == b.rows && a.cols == b.cols)
{
Matrix res(a.rows, a.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = a.p[r][c] - b.p[r][c];
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}

// return an empty matrix (this never happens but just for safety)
return Matrix();
}
// operator unary minus
friend Matrix operator- (const Matrix& a)
{
Matrix res(a.rows, a.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = -a.p[r][c];
}
}

return res;
}

// operator multiplication
friend Matrix operator* (const Matrix& a, const Matrix& B)/>
{
// check if the dimensions match
if (a.cols == b.rows)
{
Matrix res(a.rows, b.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c_res = 0; c_res < b.cols; c_res++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c_res] += a.p[r][c] * b.p[c][c_res];
}
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}

// return an empty matrix (this never happens but just for safety)
return Matrix();
}

/**
* returns the minor from the given matrix where
* the selected row and column are removed
*/
Matrix Minor(const int row, const int col)
{
//printf("minor(row=%i, col=%i), rows=%i, cols=%i\n", row, col, rows, cols);
Matrix res;
if (row > 0 && row <= rows && col > 0 && col <= cols)
{
res = Matrix(rows - 1, cols - 1);

// copy the content of the matrix to the minor, except the selected
for (int r = 1; r <= (rows - (row >= rows)); r++)
{
for (int c = 1; c <= (cols - (col >= cols)); c++)
{
//printf("r=%i, c=%i, value=%f, rr=%i, cc=%i \n", r, c, p[r-1][c-1], r - (r > row), c - (c > col));
res(r - (r > row), c - (c > col)) = p[r-1][c-1];
}
}
}
else
{
throw Exception("Index for minor out of range");
}

return res;
}

/*
* returns the size of the i-th dimension of the matrix.
* i.e. for i=1 the function returns the number of rows,
* and for i=2 the function returns the number of columns
* else the function returns 0
*/
int Size(const int i)
{
if (i == 1)
{
return rows;
}
else if (i == 2)
{
return cols;
}
return 0;
}

// returns the number of rows
int GetRows()
{
return rows;
}

// returns the number of columns
int GetCols()
{
return cols;
}

// print the contents of the matrix
void Print()
{
if (p != NULL)
{
printf("[");
for (int r = 0; r < rows; r++)
{
if (r > 0)
{
printf(" ");
}
for (int c = 0; c < cols-1; c++)
{
printf("%.2f, ", p[r][c]);
}
if (r < rows-1)
{
printf("%.2f;\n", p[r][cols-1]);
}
else
{
printf("%.2f]\n", p[r][cols-1]);
}
}
}
else
{
// matrix is empty
printf("[ ]\n");
}
}

public:
// destructor
~Matrix()
{
// clean up allocated memory
for (int r = 0; r < rows; r++)
{
delete p[r];
}
delete p;
p = NULL;
}

private:
int rows;
int cols;
double** p;         // pointer to a matrix with doubles
};

/*
* i.e. for i=1 the function returns the number of rows,
* and for i=2 the function returns the number of columns
* else the function returns 0
*/
int Size(Matrix& a, const int i)
{
return a.Size(i);
}

// addition of Matrix with double
Matrix operator+ (const Matrix& a, const double B)/>
{
Matrix res = a;
res.Add(B)/>;
return res;
}
// addition of double with Matrix
Matrix operator+ (const double b, const Matrix& a)
{
Matrix res = a;
res.Add(B)/>;
return res;
}

// subtraction of Matrix with double
Matrix operator- (const Matrix& a, const double B)/>
{
Matrix res = a;
res.Subtract(B)/>;
return res;
}
// subtraction of double with Matrix
Matrix operator- (const double b, const Matrix& a)
{
Matrix res = -a;
res.Add(B)/>;
return res;
}

// multiplication of Matrix with double
Matrix operator* (const Matrix& a, const double B)/>
{
Matrix res = a;
res.Multiply(B)/>;
return res;
}
// multiplication of double with Matrix
Matrix operator* (const double b, const Matrix& a)
{
Matrix res = a;
res.Multiply(B)/>;
return res;
}

/**
* returns a matrix with size cols x rows with ones as values
*/
Matrix Ones(const int rows, const int cols)
{
Matrix res = Matrix(rows, cols);

for (int r = 1; r <= rows; r++)
{
for (int c = 1; c <= cols; c++)
{
res(r, c) = 1;
}
}
return res;
}

/**
* returns a matrix with size cols x rows with zeros as values
*/
Matrix Zeros(const int rows, const int cols)
{
return Matrix(rows, cols);
}

/**
* returns a diagonal matrix with size n x n with ones at the diagonal
* @param   v a vector
* @return  a diagonal matrix with ones on the diagonal
*/
Matrix Diag(const int n)
{
Matrix res = Matrix(n, n);
for (int i = 1; i <= n; i++)
{
res(i, i) = 1;
}
return res;
}
/**
* returns a diagonal matrix
* @param   v a vector
* @return  a diagonal matrix with the given vector v on the diagonal
*/
Matrix Diag(Matrix& v)
{
Matrix res;
if (v.GetCols() == 1)
{
// the given matrix is a vector n x 1
int rows = v.GetRows();
res = Matrix(rows, rows);

// copy the values of the vector to the matrix
for (int r=1; r <= rows; r++)
{
res(r, r) = v(r, 1);
}
}
else if (v.GetRows() == 1)
{
// the given matrix is a vector 1 x n
int cols = v.GetCols();
res = Matrix(cols, cols);

// copy the values of the vector to the matrix
for (int c=1; c <= cols; c++)
{
res(c, c) = v(1, c);
}
}
else
{
throw Exception("Parameter for diag must be a vector");
}
return res;
}

/*
* returns the determinant of Matrix a
*/
double Det(Matrix& a)
{
double d = 0;       // value of the determinant
int rows = a.GetRows();
int cols = a.GetRows();

if (rows == cols)
{
// this is a square matrix
if (rows == 1)
{
// this is a 1 x 1 matrix
d = a(1, 1);
}
else if (rows == 2)
{
// this is a 2 x 2 matrix
// the determinant of [a11,a12;a21,a22] is det = a11*a22-a21*a12
d = a(1, 1) * a(2, 2) - a(2, 1) * a(1, 2);
}
else
{
// this is a matrix of 3 x 3 or larger
for (int c = 1; c <= cols; c++)
{
Matrix M = a.Minor(1, c);
//d += pow(-1, 1+c)  * a(1, c) * Det(M);
d += (c%2 + c%2 - 1) * a(1, c) * Det(M);  // faster than with pow()
}
}
}
else
{
throw Exception("Matrix must be square");
}
return d;
}

// swap two values
void Swap(double& a, double& B)/>
{
double temp = a;
a = b;
b = temp;
}

/*
* returns the inverse of Matrix a
*/
Matrix Inv(Matrix& a)
{
Matrix res;
double d = 0;       // value of the determinant
int rows = a.GetRows();
int cols = a.GetRows();

d = Det(a);
if (rows == cols && d != 0)
{
// this is a square matrix
if (rows == 1)
{
// this is a 1 x 1 matrix
res = Matrix(rows, cols);
res(1, 1) = 1 / a(1, 1);
}
else if (rows == 2)
{
// this is a 2 x 2 matrix
res = Matrix(rows, cols);
res(1, 1) = a(2, 2);
res(1, 2) = -a(1, 2);
res(2, 1) = -a(2, 1);
res(2, 2) = a(1, 1);
res = (1/d) * res;
}
else
{
// this is a matrix of 3 x 3 or larger
// calculate inverse using gauss-jordan elimination
//      http://mathworld.wolfram.com/MatrixInverse.html
//      http://math.uww.edu/~mcfarlat/inverse.htm
res = Diag(rows);     // a diagonal matrix with ones at the diagonal
Matrix ai = a;        // make a copy of Matrix a

for (int c = 1; c <= cols; c++)
{
// element (c, c) should be non zero. if not, swap content
// of lower rows
int r;
for (r = c; r <= rows && ai(r, c) == 0; r++)
{
}
if (r != c)
{
// swap rows
for (int s = 1; s <= cols; s++)
{
Swap(ai(c, s), ai(r, s));
Swap(res(c, s), res(r, s));
}
}

// eliminate non-zero values on the other rows at column c
for (int r = 1; r <= rows; r++)
{
if(r != c)
{
// eleminate value at column c and row r
if (ai(r, c) != 0)
{
double f = - ai(r, c) / ai(c, c);

// add (f * row c) to row r to eleminate the value
// at column c
for (int s = 1; s <= cols; s++)
{
ai(r, s) += f * ai(c, s);
res(r, s) += f * res(c, s);
}
}
}
else
{
// make value at (c, c) one,
// divide each value on row r with the value at ai(c,c)
double f = ai(c, c);
for (int s = 1; s <= cols; s++)
{
ai(r, s) /= f;
res(r, s) /= f;
}
}
}
}
}
}
else
{
if (rows == cols)
{
throw Exception("Matrix must be square");
}
else
{
throw Exception("Determinant of matrix is zero");
}
}
return res;
}

int main(int argc, char *argv[])
{
try
{
// create an empty matrix of 3x3 (will initially contain zeros)
int cols = 3;
int rows = 3;
Matrix A = Matrix(cols, rows);

// fill in some values in matrix a
int count = 0;
for (int r = 1; r <= rows; r++)
{
for (int c = 1; c <= cols; c++)
{
count ++;
A(r, c) = count;
}
}

// adjust a value in the matrix  (indexes are one-based)
A(2,1) = 1.23;

// read a value from the matrix  (indexes are one-based)
double centervalue = A(2,2);
printf("centervalue = %f \n", centervalue);
printf("\n");

// print the whole matrix
printf("A = \n");
A.Print();
printf("\n");

Matrix B = Ones(rows, cols) + Diag(rows);
printf("B = \n");
B.Print();
printf("\n");

Matrix B2 = Matrix(rows, 1);        // a vector
count = 1;
for (int r = 1; r <= rows; r++)
{
count ++;
B2(r, 1) = count * 2;
}
printf("B2 = \n");
B2.Print();
printf("\n");

Matrix C;
C = A + B;
printf("A + B = \n");
C.Print();
printf("\n");

C = A - B;
printf("A - B = \n");
C.Print();
printf("\n");

C = A * B2;
printf("A * B2 = \n");
C.Print();
printf("\n");

// create a diagonal matrix
Matrix E = Diag(B2);
printf("E = \n");
E.Print();
printf("\n");

// calculate determinant
Matrix D = Matrix(2, 2);
D(1,1) = 2;
D(1,2) = 4;
D(2,1) = 1;
D(2,2) = -2;
printf("D = \n");
D.Print();
printf("Det(D) = %f\n\n", Det(D));

printf("A = \n");
A.Print();
printf("\n");
printf("Det(A) = %f\n\n", Det(A));

Matrix F;
F = 3 - A ;
printf("3 - A = \n");
F.Print();
printf("\n");

// test inverse
Matrix G = Matrix(2, 2);
G(1, 1) = 1;
G(1, 2) = 2;
G(2, 1) = 3;
G(2, 2) = 4;
printf("G = \n");
G.Print();
printf("\n");
Matrix G_inv = Inv(G);
printf("Inv(G) = \n");
G_inv.Print();
printf("\n");

Matrix A_inv = Inv(A);
printf("Inv(A) = \n");
A_inv.Print();
printf("\n");

rows = 2;
cols = 5;
Matrix H = Matrix(rows, cols);
for (int r = 1; r <= rows; r++)
{
for (int c = 1; c <= cols; c++)
{
count ++;
H(r, c) = count;
}
}
printf("H = \n");
H.Print();
printf("\n");
}
catch (Exception err)
{
printf("Error: %s\n", err.msg);
}
catch (...)
{
printf("An error occured...\n");
}

printf("\n");
PAUSE;

return EXIT_SUCCESS;
}

```

Was This Post Helpful? 0

### #4 joske

• D.I.C Regular

Reputation: 43
• Posts: 297
• Joined: 04-September 07

## Re: determinant of matrix in c++

Posted 21 March 2010 - 09:28 AM

I cleaned up the code a little bit, and added matrix division.

```/*
A simple matrix class
c++ code
Author: Jos de Jong, Nov 2007. Updated March 2010

With this class you can:
- create a matrix
- get/set the cell values
- use operators +, -, *, /
- use functions Ones(), Zeros(), Diag(), Det(), Inv(), Size()
- print the content of the matrix

Usage:
you can create a matrix by:
Matrix A;
Matrix A = Matrix(rows, cols);
Matrix A = B;

you can get and set matrix elements by:
A(2,3) = 5.6;        // set an element of Matix A
value = A(3,1);      // get an element of Matrix A
value = A.get(3,1);  // get an element of a constant Matrix A
A = B;               // copy content of Matrix B to Matrix A

you can apply operations with matrices and doubles:
A = B + C;
A = B - C;
A = -B;
A = B * C;
A = B / C;

the following functions are available:
A = Ones(rows, cols);
A = Zeros(rows, cols);
A = Diag(n);
A = Diag(B)/>;
d = Det(A);
A = Inv(B)/>;
cols = A.GetCols();
rows = A.GetRows();
cols = Size(A, 1);
rows = Size(A, 2);

you can quick-print the content of a matrix in the console with:
A.Print();
*/

#include <cstdlib>
#include <cstdio>
#include <math.h>

#define PAUSE {printf("Press \"Enter\" to continue\n"); fflush(stdin); getchar(); fflush(stdin);}

// Declarations
class Matrix;
double Det(const Matrix& a);
Matrix Diag(const int n);
Matrix Diag(const Matrix& v);
Matrix Inv(const Matrix& a);
Matrix Ones(const int rows, const int cols);
int Size(const Matrix& a, const int i);
Matrix Zeros(const int rows, const int cols);

/*
* a simple exception class
* you can create an exeption by entering
*      throw Exception("...Error description...");
* and get the error message from the data msg for displaying:
*      err.msg
*/
class Exception
{
public:
const char* msg;
Exception(const char* arg)
: msg(arg)
{
}
};

class Matrix
{
public:
// constructor
Matrix()
{
//printf("Executing constructor Matrix() ...\n");
// create a Matrix object without content
p = NULL;
rows = 0;
cols = 0;
}

// constructor
Matrix(const int row_count, const int column_count)
{
// create a Matrix object with given number of rows and columns
p = NULL;

if (row_count > 0 && column_count > 0)
{
rows = row_count;
cols = column_count;

p = new double*[rows];
for (int r = 0; r < rows; r++)
{
p[r] = new double[cols];

// initially fill in zeros for all values in the matrix;
for (int c = 0; c < cols; c++)
{
p[r][c] = 0;
}
}
}
}

// assignment operator
Matrix(const Matrix& a)
{
rows = a.rows;
cols = a.cols;
p = new double*[a.rows];
for (int r = 0; r < a.rows; r++)
{
p[r] = new double[a.cols];

// copy the values from the matrix a
for (int c = 0; c < a.cols; c++)
{
p[r][c] = a.p[r][c];
}
}
}

// index operator. You can use this class like myMatrix(col, row)
// the indexes are one-based, not zero based.
double& operator()(const int r, const int c)
{
if (p != NULL && r > 0 && r <= rows && c > 0 && c <= cols)
{
return p[r-1][c-1];
}
else
{
throw Exception("Subscript out of range");
}
}

// index operator. You can use this class like myMatrix.get(col, row)
// the indexes are one-based, not zero based.
// use this function get if you want to read from a const Matrix
double get(const int r, const int c) const
{
if (p != NULL && r > 0 && r <= rows && c > 0 && c <= cols)
{
return p[r-1][c-1];
}
else
{
throw Exception("Subscript out of range");
}
}

// assignment operator
Matrix& operator= (const Matrix& a)
{
rows = a.rows;
cols = a.cols;
p = new double*[a.rows];
for (int r = 0; r < a.rows; r++)
{
p[r] = new double[a.cols];

// copy the values from the matrix a
for (int c = 0; c < a.cols; c++)
{
p[r][c] = a.p[r][c];
}
}
return *this;
}

// add a double value (elements wise)
Matrix& Add(const double v)
{
for (int r = 0; r < rows; r++)
{
for (int c = 0; c < cols; c++)
{
p[r][c] += v;
}
}
return *this;
}

// subtract a double value (elements wise)
Matrix& Subtract(const double v)
{
return Add(-v);
}

// multiply a double value (elements wise)
Matrix& Multiply(const double v)
{
for (int r = 0; r < rows; r++)
{
for (int c = 0; c < cols; c++)
{
p[r][c] *= v;
}
}
return *this;
}

// divide a double value (elements wise)
Matrix& Divide(const double v)
{
return Multiply(1/v);
}

// addition of Matrix with Matrix
friend Matrix operator+(const Matrix& a, const Matrix& B)/>
{
// check if the dimensions match
if (a.rows == b.rows && a.cols == b.cols)
{
Matrix res(a.rows, a.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = a.p[r][c] + b.p[r][c];
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}

// return an empty matrix (this never happens but just for safety)
return Matrix();
}

// addition of Matrix with double
friend Matrix operator+ (const Matrix& a, const double B)/>
{
Matrix res = a;
res.Add(B)/>;
return res;
}
// addition of double with Matrix
friend Matrix operator+ (const double b, const Matrix& a)
{
Matrix res = a;
res.Add(B)/>;
return res;
}

// subtraction of Matrix with Matrix
friend Matrix operator- (const Matrix& a, const Matrix& B)/>
{
// check if the dimensions match
if (a.rows == b.rows && a.cols == b.cols)
{
Matrix res(a.rows, a.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = a.p[r][c] - b.p[r][c];
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}

// return an empty matrix (this never happens but just for safety)
return Matrix();
}

// subtraction of Matrix with double
friend Matrix operator- (const Matrix& a, const double B)/>
{
Matrix res = a;
res.Subtract(B)/>;
return res;
}
// subtraction of double with Matrix
friend Matrix operator- (const double b, const Matrix& a)
{
Matrix res = -a;
res.Add(B)/>;
return res;
}

// operator unary minus
friend Matrix operator- (const Matrix& a)
{
Matrix res(a.rows, a.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c] = -a.p[r][c];
}
}

return res;
}

// operator multiplication
friend Matrix operator* (const Matrix& a, const Matrix& B)/>
{
// check if the dimensions match
if (a.cols == b.rows)
{
Matrix res(a.rows, b.cols);

for (int r = 0; r < a.rows; r++)
{
for (int c_res = 0; c_res < b.cols; c_res++)
{
for (int c = 0; c < a.cols; c++)
{
res.p[r][c_res] += a.p[r][c] * b.p[c][c_res];
}
}
}
return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}

// return an empty matrix (this never happens but just for safety)
return Matrix();
}

// multiplication of Matrix with double
friend Matrix operator* (const Matrix& a, const double B)/>
{
Matrix res = a;
res.Multiply(B)/>;
return res;
}
// multiplication of double with Matrix
friend Matrix operator* (const double b, const Matrix& a)
{
Matrix res = a;
res.Multiply(B)/>;
return res;
}

// division of Matrix with Matrix
friend Matrix operator/ (const Matrix& a, const Matrix& B)/>
{
// check if the dimensions match: must be square and equal sizes
if (a.rows == a.cols && a.rows == a.cols && b.rows == b.cols)
{
Matrix res(a.rows, a.cols);

res = a * Inv(B)/>;

return res;
}
else
{
// give an error
throw Exception("Dimensions does not match");
}

// return an empty matrix (this never happens but just for safety)
return Matrix();
}

// division of Matrix with double
friend Matrix operator/ (const Matrix& a, const double B)/>
{
Matrix res = a;
res.Divide(B)/>;
return res;
}

// division of double with Matrix
friend Matrix operator/ (const double b, const Matrix& a)
{
Matrix b_matrix(1, 1);
b_matrix(1,1) = b;

Matrix res = b_matrix / a;
return res;
}

/**
* returns the minor from the given matrix where
* the selected row and column are removed
*/
Matrix Minor(const int row, const int col) const
{
Matrix res;
if (row > 0 && row <= rows && col > 0 && col <= cols)
{
res = Matrix(rows - 1, cols - 1);

// copy the content of the matrix to the minor, except the selected
for (int r = 1; r <= (rows - (row >= rows)); r++)
{
for (int c = 1; c <= (cols - (col >= cols)); c++)
{
res(r - (r > row), c - (c > col)) = p[r-1][c-1];
}
}
}
else
{
throw Exception("Index for minor out of range");
}

return res;
}

/*
* returns the size of the i-th dimension of the matrix.
* i.e. for i=1 the function returns the number of rows,
* and for i=2 the function returns the number of columns
* else the function returns 0
*/
int Size(const int i) const
{
if (i == 1)
{
return rows;
}
else if (i == 2)
{
return cols;
}
return 0;
}

// returns the number of rows
int GetRows() const
{
return rows;
}

// returns the number of columns
int GetCols() const
{
return cols;
}

// print the contents of the matrix
void Print() const
{
if (p != NULL)
{
printf("[");
for (int r = 0; r < rows; r++)
{
if (r > 0)
{
printf(" ");
}
for (int c = 0; c < cols-1; c++)
{
printf("%.2f, ", p[r][c]);
}
if (r < rows-1)
{
printf("%.2f;\n", p[r][cols-1]);
}
else
{
printf("%.2f]\n", p[r][cols-1]);
}
}
}
else
{
// matrix is empty
printf("[ ]\n");
}
}

public:
// destructor
~Matrix()
{
// clean up allocated memory
for (int r = 0; r < rows; r++)
{
delete p[r];
}
delete p;
p = NULL;
}

private:
int rows;
int cols;
double** p;         // pointer to a matrix with doubles
};

/*
* i.e. for i=1 the function returns the number of rows,
* and for i=2 the function returns the number of columns
* else the function returns 0
*/
int Size(const Matrix& a, const int i)
{
return a.Size(i);
}

/**
* returns a matrix with size cols x rows with ones as values
*/
Matrix Ones(const int rows, const int cols)
{
Matrix res = Matrix(rows, cols);

for (int r = 1; r <= rows; r++)
{
for (int c = 1; c <= cols; c++)
{
res(r, c) = 1;
}
}
return res;
}

/**
* returns a matrix with size cols x rows with zeros as values
*/
Matrix Zeros(const int rows, const int cols)
{
return Matrix(rows, cols);
}

/**
* returns a diagonal matrix with size n x n with ones at the diagonal
* @param   v a vector
* @return  a diagonal matrix with ones on the diagonal
*/
Matrix Diag(const int n)
{
Matrix res = Matrix(n, n);
for (int i = 1; i <= n; i++)
{
res(i, i) = 1;
}
return res;
}
/**
* returns a diagonal matrix
* @param   v a vector
* @return  a diagonal matrix with the given vector v on the diagonal
*/
Matrix Diag(const Matrix& v)
{
Matrix res;
if (v.GetCols() == 1)
{
// the given matrix is a vector n x 1
int rows = v.GetRows();
res = Matrix(rows, rows);

// copy the values of the vector to the matrix
for (int r=1; r <= rows; r++)
{
res(r, r) = v.get(r, 1);
}
}
else if (v.GetRows() == 1)
{
// the given matrix is a vector 1 x n
int cols = v.GetCols();
res = Matrix(cols, cols);

// copy the values of the vector to the matrix
for (int c=1; c <= cols; c++)
{
res(c, c) = v.get(1, c);
}
}
else
{
throw Exception("Parameter for diag must be a vector");
}
return res;
}

/*
* returns the determinant of Matrix a
*/
double Det(const Matrix& a)
{
double d = 0;       // value of the determinant
int rows = a.GetRows();
int cols = a.GetRows();

if (rows == cols)
{
// this is a square matrix
if (rows == 1)
{
// this is a 1 x 1 matrix
d = a.get(1, 1);
}
else if (rows == 2)
{
// this is a 2 x 2 matrix
// the determinant of [a11,a12;a21,a22] is det = a11*a22-a21*a12
d = a.get(1, 1) * a.get(2, 2) - a.get(2, 1) * a.get(1, 2);
}
else
{
// this is a matrix of 3 x 3 or larger
for (int c = 1; c <= cols; c++)
{
Matrix M = a.Minor(1, c);
//d += pow(-1, 1+c)  * a(1, c) * Det(M);
d += (c%2 + c%2 - 1) * a.get(1, c) * Det(M);  // faster than with pow()
}
}
}
else
{
throw Exception("Matrix must be square");
}
return d;
}

// swap two values
void Swap(double& a, double& B)/>
{
double temp = a;
a = b;
b = temp;
}

/*
* returns the inverse of Matrix a
*/
Matrix Inv(const Matrix& a)
{
Matrix res;
double d = 0;       // value of the determinant
int rows = a.GetRows();
int cols = a.GetRows();

d = Det(a);
if (rows == cols && d != 0)
{
// this is a square matrix
if (rows == 1)
{
// this is a 1 x 1 matrix
res = Matrix(rows, cols);
res(1, 1) = 1 / a.get(1, 1);
}
else if (rows == 2)
{
// this is a 2 x 2 matrix
res = Matrix(rows, cols);
res(1, 1) = a.get(2, 2);
res(1, 2) = -a.get(1, 2);
res(2, 1) = -a.get(2, 1);
res(2, 2) = a.get(1, 1);
res = (1/d) * res;
}
else
{
// this is a matrix of 3 x 3 or larger
// calculate inverse using gauss-jordan elimination
//      http://mathworld.wolfram.com/MatrixInverse.html
//      http://math.uww.edu/~mcfarlat/inverse.htm
res = Diag(rows);     // a diagonal matrix with ones at the diagonal
Matrix ai = a;        // make a copy of Matrix a

for (int c = 1; c <= cols; c++)
{
// element (c, c) should be non zero. if not, swap content
// of lower rows
int r;
for (r = c; r <= rows && ai(r, c) == 0; r++)
{
}
if (r != c)
{
// swap rows
for (int s = 1; s <= cols; s++)
{
Swap(ai(c, s), ai(r, s));
Swap(res(c, s), res(r, s));
}
}

// eliminate non-zero values on the other rows at column c
for (int r = 1; r <= rows; r++)
{
if(r != c)
{
// eleminate value at column c and row r
if (ai(r, c) != 0)
{
double f = - ai(r, c) / ai(c, c);

// add (f * row c) to row r to eleminate the value
// at column c
for (int s = 1; s <= cols; s++)
{
ai(r, s) += f * ai(c, s);
res(r, s) += f * res(c, s);
}
}
}
else
{
// make value at (c, c) one,
// divide each value on row r with the value at ai(c,c)
double f = ai(c, c);
for (int s = 1; s <= cols; s++)
{
ai(r, s) /= f;
res(r, s) /= f;
}
}
}
}
}
}
else
{
if (rows == cols)
{
throw Exception("Matrix must be square");
}
else
{
throw Exception("Determinant of matrix is zero");
}
}
return res;
}

int main(int argc, char *argv[])
{
try
{
// create an empty matrix of 3x3 (will initially contain zeros)
int cols = 3;
int rows = 3;
Matrix A = Matrix(cols, rows);

// fill in some values in matrix a
int count = 0;
for (int r = 1; r <= rows; r++)
{
for (int c = 1; c <= cols; c++)
{
count ++;
A(r, c) = count;
}
}

// adjust a value in the matrix  (indexes are one-based)
A(2,1) = 1.23;

// read a value from the matrix  (indexes are one-based)
double centervalue = A(2,2);
printf("centervalue = %f \n", centervalue);
printf("\n");

// print the whole matrix
printf("A = \n");
A.Print();
printf("\n");

Matrix B = Ones(rows, cols) + Diag(rows);
printf("B = \n");
B.Print();
printf("\n");

Matrix B2 = Matrix(rows, 1);        // a vector
count = 1;
for (int r = 1; r <= rows; r++)
{
count ++;
B2(r, 1) = count * 2;
}
printf("B2 = \n");
B2.Print();
printf("\n");

Matrix C;
C = A + B;
printf("A + B = \n");
C.Print();
printf("\n");

C = A - B;
printf("A - B = \n");
C.Print();
printf("\n");

C = A * B2;
printf("A * B2 = \n");
C.Print();
printf("\n");

// create a diagonal matrix
Matrix E = Diag(B2);
printf("E = \n");
E.Print();
printf("\n");

// calculate determinant
Matrix D = Matrix(2, 2);
D(1,1) = 2;
D(1,2) = 4;
D(2,1) = 1;
D(2,2) = -2;
printf("D = \n");
D.Print();
printf("Det(D) = %f\n\n", Det(D));

printf("A = \n");
A.Print();
printf("\n");
printf("Det(A) = %f\n\n", Det(A));

Matrix F;
F = 3 - A ;
printf("3 - A = \n");
F.Print();
printf("\n");

// test inverse
Matrix G = Matrix(2, 2);
G(1, 1) = 1;
G(1, 2) = 2;
G(2, 1) = 3;
G(2, 2) = 4;
printf("G = \n");
G.Print();
printf("\n");
Matrix G_inv = Inv(G);
printf("Inv(G) = \n");
G_inv.Print();
printf("\n");

Matrix A_inv = Inv(A);
printf("Inv(A) = \n");
A_inv.Print();
printf("\n");

Matrix A_A_inv = A * Inv(A);
printf("A * Inv(A) = \n");
A_A_inv.Print();
printf("\n");

Matrix B_A = B / A;
printf("B / A = \n");
B_A.Print();
printf("\n");

Matrix A_3 = A / 3;
printf("A / 3 = \n");
A_3.Print();
printf("\n");

rows = 2;
cols = 5;
Matrix H = Matrix(rows, cols);
for (int r = 1; r <= rows; r++)
{
for (int c = 1; c <= cols; c++)
{
count ++;
H(r, c) = count;
}
}
printf("H = \n");
H.Print();
printf("\n");
}
catch (Exception err)
{
printf("Error: %s\n", err.msg);
}
catch (...)
{
printf("An error occured...\n");
}

printf("\n");
PAUSE;

return EXIT_SUCCESS;
}

```

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Reputation:

## Re: determinant of matrix in c++

Posted 19 November 2010 - 07:23 AM

Yikes!
After finding this thread, I got scared so wrote my own:

```/* const int dim  is the dimensionality of the matrix */
double det = 0.0;
for (int i = 0; i < dim; i++)
{
double a = 1.0, b = 1.0;
for (int row = 0; row < dim; row++)
{
a *= m[row][(i+row)%dim];
b *= m[row][(dim-1) - (i+row)%dim];
}
det += a - b;
}
return det;
```

MOD EDIT: When posting code...USE CODE TAGS!!!

This post has been edited by JackOfAllTrades: 19 November 2010 - 08:22 AM

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### #6 Yiannis_Spyridakis

• New D.I.C Head

Reputation: 0
• Posts: 2
• Joined: 19-June 11

## Re: determinant of matrix in c++

Posted 19 June 2011 - 05:11 AM

joske, on 21 March 2010 - 09:28 AM, said:

```//...
public:
// destructor
~Matrix()
{
// clean up allocated memory
for (int r = 0; r < rows; r++)
{
delete p[r];
}
delete p;
p = NULL;
}

```

Thanks Joske, this is very useful.

The destructor needs one correction, I think: You need to call delete[] instead of delete when deallocating both the whole array and individual rows (otherwise you leak memory)

So the destructor becomes:
```//...
public:
// destructor
~Matrix()
{
// clean up allocated memory
for (int r = 0; r < rows; r++)
{
delete[] p[r];
}
delete[] p;
p = NULL;
}

```

Cheers,
Yiannis
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### #7 Yiannis_Spyridakis

• New D.I.C Head

Reputation: 0
• Posts: 2
• Joined: 19-June 11

## Re: determinant of matrix in c++

Posted 19 June 2011 - 05:57 AM

Yiannis_Spyridakis, on 19 June 2011 - 05:11 AM, said:

...
The destructor needs one correction, I think: You need to call delete[] instead of delete when deallocating both the whole array and individual rows (otherwise you leak memory)

So the destructor becomes:
...
Cheers,
Yiannis

Similarily, the assignment operator needs to check for previously allocated memory and deallocate it if necessary. That is, if you 1) allocate a Matrix and then 2) assign it to another matrix the code as it now is will cause a memory leak.

It's often convenient to introduce a 'destroy' private function that does all the deallocation and implement the copy constructor by delegating to the assignment operator.
Here is how I would implement it (I had to rename the class to MyMatrix to avoid name clashes. Also I am currently refreshing my C++, so I wouldn't blindly trust this code )

```// Copy constructor
MyMatrix::MyMatrix(const MyMatrix& RHS)
: p(nullptr), cols(0), rows(0)
{
this->operator=(RHS);
}

// Assignment operator
MyMatrix& MyMatrix::operator=(const MyMatrix& RHS){

if (p){
this->destroy();
}

rows = RHS.rows;
cols = RHS.cols;
p = new double*[rows];

int r, c;
for (r = 0; r < rows; ++r){
// Allocate a new row of elements
p[r] = new double[cols];
// Copy the values from matrix RHS
for (c = 0; c < cols; ++c){
p[r][c] = RHS.p[r][c];
}
}
return *this;
}

// Private helper (used for deallocation)
void MyMatrix::destroy(){
// Clean up allocated memory
for (int r = 0; r < rows; ++r){
delete[] p[r];
}
delete[] p; p = nullptr;
cols = rows = 0;
}

// Destructor
MyMatrix::~MyMatrix()
{
this->destroy();
}

```

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### #8 rnarozniak

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Reputation: 0
• Posts: 1
• Joined: 06-February 12

## Re: determinant of matrix in c++

Posted 06 February 2012 - 05:36 PM

this thread is kind of old, but I would like to make a couple of suggestions re your matrix class:

1. the recursive, laplacian expansion algorithm you are using scales at O(n!). The preferred approach is to use the fact that the determinant of an n^2 matrix is simply the product of the elements in the diag of the upper triangular matrix. This reduces the order to ~O(2n^2/3). Your recursive algorithm will be out of control for, say, n>12.

2. I would also suggest using LU decomposition for your inversion algorithm. This reduces the number of flops from about O(n^3) to O(n^2).

I hope this helps.

Regards,

This post has been edited by modi123_1: 06 February 2012 - 06:09 PM
Reason for edit:: removed excessively long quote

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