source-sdk-2013-mapbase/sp/src/utils/vbsp/matrixinvert.h

// By Jason Yu-Tseh Chi
// From http://chi3x10.wordpress.com/2008/05/28/calculate-matrix-inversion-in-c/
// Modified to work with valve's matrix_3x4_t

#include "mathlib\mathlib.h"

// Calculate the cofactor of element (row,col)
int GetMatrixMinor(float **src, float **dest, int row, int col, int order)
{
	// Indicate which col and row is being copied to dest
	int colCount = 0, rowCount = 0;

	for (int i = 0; i < order; i++)
	{
		if (i != row)
		{
			colCount = 0;
			for (int j = 0; j < order; j++)
			{
				// When j is not the element
				if (j != col)
				{
					dest[rowCount][colCount] = src[i][j];
					colCount++;
				}
			}
			rowCount++;
		}
	}

	return 1;
}

// Calculate the determinant recursively.
double CalcMatrixDeterminant(float **mat, int order)
{
	// Order must be >= 0
	// Stop the recursion when matrix is a single element
	if (order == 1)
		return mat[0][0];

	// The determinant value
	float det = 0;

	// Allocate the cofactor matrix
	float **minor;
	minor = new float*[order - 1];
	for (int i = 0; i<order - 1; i++)
		minor[i] = new float[order - 1];

	for (int i = 0; i < order; i++)
	{
		// Get minor of element (0,i)
		GetMatrixMinor(mat, minor, 0, i, order);
		// The recusion is here!

		det += (i % 2 == 1 ? -1.0 : 1.0) * mat[0][i] * CalcMatrixDeterminant(minor, order - 1);
		//det += pow( -1.0, i ) * mat[0][i] * CalcMatrixDeterminant( minor,order-1 );
	}

	// Release memory
	for (int i = 0; i<order - 1; i++)
		delete[] minor[i];
	delete[] minor;

	return det;
}

// Matrix inversion
void MatrixInversion(matrix3x4_t &in, matrix3x4_t &out)
{
	float **A;
	A = new float*[4];
	for (int i = 0; i < 4; i++)
		A[i] = new float[4];
	int order = 4;

	// Load in into A
	for (int i = 0; i < 3; i++)
	{
		for (int j = 0; j < 4; j++)
		{
			A[i][j] = in[i][j];
		}
	}
	A[3][0] = A[3][1] = A[3][2] = 0;
	A[3][3] = 1;

	// Get the determinant of a
	double det = 1.0 / CalcMatrixDeterminant((float**)A, order);

	// Memory allocation
	float *temp = new float[(order - 1)*(order - 1)];
	float **minor = new float*[order - 1];
	for (int i = 0; i<order - 1; i++)
		minor[i] = temp + (i*(order - 1));

	for (int j = 0; j<order; j++)
	{
		for (int i = 0; i<order; i++)
		{
			// Get the co-factor (matrix) of A(j,i)
			GetMatrixMinor((float**)A, minor, j, i, order);
			out[i][j] = det*CalcMatrixDeterminant(minor, order - 1);
			if ((i + j) % 2 == 1)
				out[i][j] = -out[i][j];
		}
	}

	// Release memory
	for (int i = 0; i < 4; i++)
		delete A[i];
	delete A;
	//delete [] minor[0];
	delete[] temp;
	delete[] minor;
}