How to calculate matrix determinant? n*n or just 5*5
everyone. I need to find matrix n*n (or 5*5) determinant. I have a function translated from Pascal, but there's INDEX OUT OF RANGE EXCEPTION. Could somebody help me?
Here's my code:
public static double DET(double[,] a, int n)
{
int i, j, k;
double det = 0;
for (i = 0; i < n - 1; i++)
{
for (j = i + 1; j < n + 1; j++)
{
det = a[j, i] / a[i, i];
for (k = i; k < n; k++)
a[j, k] = a[j, k] - det * a[i, k]; // Here's exception
}
}
det = 1;
for (i = 0; i < n; i++)
det = det * a[i, i];
return det;
}
Thanx for any help.
Answer
Working solution for calculating n * n determinant looks like:
using System;
internal class MatrixDecompositionProgram
{
private static void Main(string[] args)
{
float[,] m = MatrixCreate(4, 4);
m[0, 0] = 3.0f; m[0, 1] = 7.0f; m[0, 2] = 2.0f; m[0, 3] = 5.0f;
m[1, 0] = 1.0f; m[1, 1] = 8.0f; m[1, 2] = 4.0f; m[1, 3] = 2.0f;
m[2, 0] = 2.0f; m[2, 1] = 1.0f; m[2, 2] = 9.0f; m[2, 3] = 3.0f;
m[3, 0] = 5.0f; m[3, 1] = 4.0f; m[3, 2] = 7.0f; m[3, 3] = 1.0f;
int[] perm;
int toggle;
float[,] luMatrix = MatrixDecompose(m, out perm, out toggle);
float[,] lower = ExtractLower(luMatrix);
float[,] upper = ExtractUpper(luMatrix);
float det = MatrixDeterminant(m);
Console.WriteLine("Determinant of m computed via decomposition = " + det.ToString("F1"));
}
// --------------------------------------------------------------------------------------------------------------
private static float[,] MatrixCreate(int rows, int cols)
{
// allocates/creates a matrix initialized to all 0.0. assume rows and cols > 0
// do error checking here
float[,] result = new float[rows, cols];
return result;
}
// --------------------------------------------------------------------------------------------------------------
private static float[,] MatrixDecompose(float[,] matrix, out int[] perm, out int toggle)
{
// Doolittle LUP decomposition with partial pivoting.
// rerturns: result is L (with 1s on diagonal) and U; perm holds row permutations; toggle is +1 or -1 (even or odd)
int rows = matrix.GetLength(0);
int cols = matrix.GetLength(1);
//Check if matrix is square
if (rows != cols)
throw new Exception("Attempt to MatrixDecompose a non-square mattrix");
float[,] result = MatrixDuplicate(matrix); // make a copy of the input matrix
perm = new int[rows]; // set up row permutation result
for (int i = 0; i < rows; ++i) { perm[i] = i; } // i are rows counter
toggle = 1; // toggle tracks row swaps. +1 -> even, -1 -> odd. used by MatrixDeterminant
for (int j = 0; j < rows - 1; ++j) // each column, j is counter for coulmns
{
float colMax = Math.Abs(result[j, j]); // find largest value in col j
int pRow = j;
for (int i = j + 1; i < rows; ++i)
{
if (result[i, j] > colMax)
{
colMax = result[i, j];
pRow = i;
}
}
if (pRow != j) // if largest value not on pivot, swap rows
{
float[] rowPtr = new float[result.GetLength(1)];
//in order to preserve value of j new variable k for counter is declared
//rowPtr[] is a 1D array that contains all the elements on a single row of the matrix
//there has to be a loop over the columns to transfer the values
//from the 2D array to the 1D rowPtr array.
//----tranfer 2D array to 1D array BEGIN
for (int k = 0; k < result.GetLength(1); k++)
{
rowPtr[k] = result[pRow, k];
}
for (int k = 0; k < result.GetLength(1); k++)
{
result[pRow, k] = result[j, k];
}
for (int k = 0; k < result.GetLength(1); k++)
{
result[j, k] = rowPtr[k];
}
//----tranfer 2D array to 1D array END
int tmp = perm[pRow]; // and swap perm info
perm[pRow] = perm[j];
perm[j] = tmp;
toggle = -toggle; // adjust the row-swap toggle
}
if (Math.Abs(result[j, j]) < 1.0E-20) // if diagonal after swap is zero . . .
return null; // consider a throw
for (int i = j + 1; i < rows; ++i)
{
result[i, j] /= result[j, j];
for (int k = j + 1; k < rows; ++k)
{
result[i, k] -= result[i, j] * result[j, k];
}
}
} // main j column loop
return result;
} // MatrixDecompose
// --------------------------------------------------------------------------------------------------------------
private static float MatrixDeterminant(float[,] matrix)
{
int[] perm;
int toggle;
float[,] lum = MatrixDecompose(matrix, out perm, out toggle);
if (lum == null)
throw new Exception("Unable to compute MatrixDeterminant");
float result = toggle;
for (int i = 0; i < lum.GetLength(0); ++i)
result *= lum[i, i];
return result;
}
// --------------------------------------------------------------------------------------------------------------
private static float[,] MatrixDuplicate(float[,] matrix)
{
// allocates/creates a duplicate of a matrix. assumes matrix is not null.
float[,] result = MatrixCreate(matrix.GetLength(0), matrix.GetLength(1));
for (int i = 0; i < matrix.GetLength(0); ++i) // copy the values
for (int j = 0; j < matrix.GetLength(1); ++j)
result[i, j] = matrix[i, j];
return result;
}
// --------------------------------------------------------------------------------------------------------------
private static float[,] ExtractLower(float[,] matrix)
{
// lower part of a Doolittle decomposition (1.0s on diagonal, 0.0s in upper)
int rows = matrix.GetLength(0); int cols = matrix.GetLength(1);
float[,] result = MatrixCreate(rows, cols);
for (int i = 0; i < rows; ++i)
{
for (int j = 0; j < cols; ++j)
{
if (i == j)
result[i, j] = 1.0f;
else if (i > j)
result[i, j] = matrix[i, j];
}
}
return result;
}
// --------------------------------------------------------------------------------------------------------------
private static float[,] ExtractUpper(float[,] matrix)
{
// upper part of a Doolittle decomposition (0.0s in the strictly lower part)
int rows = matrix.GetLength(0); int cols = matrix.GetLength(1);
float[,] result = MatrixCreate(rows, cols);
for (int i = 0; i < rows; ++i)
{
for (int j = 0; j < cols; ++j)
{
if (i <= j)
result[i, j] = matrix[i, j];
}
}
return result;
}
}