float Matrix::matrixDeterminant(Matrix *matrix)
{
float matrix3x3[9];
float determinant3x3 = 0.0f;
float result = 0.0f;
/* Remove (i, j) (1, 1) to form new 3x3 matrix. */
matrix3x3[0] = matrix->elements[ 5];
matrix3x3[1] = matrix->elements[ 6];
matrix3x3[2] = matrix->elements[ 7];
matrix3x3[3] = matrix->elements[ 9];
matrix3x3[4] = matrix->elements[10];
matrix3x3[5] = matrix->elements[11];
matrix3x3[6] = matrix->elements[13];
matrix3x3[7] = matrix->elements[14];
matrix3x3[8] = matrix->elements[15];
determinant3x3 = matrixDeterminant(matrix3x3);
result += matrix->elements[0] * determinant3x3;
/* Remove (i, j) (1, 2) to form new 3x3 matrix. */
matrix3x3[0] = matrix->elements[ 1];
matrix3x3[1] = matrix->elements[ 2];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 9];
matrix3x3[4] = matrix->elements[10];
matrix3x3[5] = matrix->elements[11];
matrix3x3[6] = matrix->elements[13];
matrix3x3[7] = matrix->elements[14];
matrix3x3[8] = matrix->elements[15];
determinant3x3 = matrixDeterminant(matrix3x3);
result -= matrix->elements[4] * determinant3x3;
/* Remove (i, j) (1, 3) to form new 3x3 matrix. */
matrix3x3[0] = matrix->elements[ 1];
matrix3x3[1] = matrix->elements[ 2];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 5];
matrix3x3[4] = matrix->elements[ 6];
matrix3x3[5] = matrix->elements[ 7];
matrix3x3[6] = matrix->elements[13];
matrix3x3[7] = matrix->elements[14];
matrix3x3[8] = matrix->elements[15];
determinant3x3 = matrixDeterminant(matrix3x3);
result += matrix->elements[8] * determinant3x3;
/* Remove (i, j) (1, 4) to form new 3x3 matrix. */
matrix3x3[0] = matrix->elements[ 1];
matrix3x3[1] = matrix->elements[ 2];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 5];
matrix3x3[4] = matrix->elements[ 6];
matrix3x3[5] = matrix->elements[ 7];
matrix3x3[6] = matrix->elements[ 9];
matrix3x3[7] = matrix->elements[10];
matrix3x3[8] = matrix->elements[11];
determinant3x3 = matrixDeterminant(matrix3x3);
result -= matrix->elements[12] * determinant3x3;
return result;
}
/* Main method to test math */
int main() {
// Test matrix math
struct Matrix a;
//double valuesa[9] = { 5.0, -2.0, 1.0, 0.0, 3.0, -1.0, 2.0, 0.0, 7.0 };
double valuesa[16] = { 1.0, 3.0, -2.0, 1.0, 5.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, -2.0, 2.0, -1.0, 0.0, 3.0 };
newMatrix(&a, valuesa, 4, 4);
struct Matrix b;
double valuesb[9] = { 1.0, 2.0, 3.0, 0.0, -4.0, 1.0, 0.0, 3.0, -1.0 };
newMatrix(&b, valuesb, 3, 3);
struct Matrix cofa;
matrixCofactor(&cofa, a);
printf("A Cofactor=\n");
matrixToString(cofa);
struct Matrix inva;
matrixInverse(&inva, a);
printf("A Inverse=\n");
matrixToString(inva);
printf("A=\n");
matrixToString(a);
printf("B=\n");
matrixToString(b);
printf("A is %sa square matrix.\n", matrixIsSquare(a) ? "" : "not ");
printf("B is %sa square matrix.\n", matrixIsSquare(b) ? "" : "not ");
printf("The determinant of A is %f.\n", matrixDeterminant(a));
printf("A is %sunique.\n", matrixIsUnique(a) ? "" : "not ");
printf("The determinant of B is %f.\n", matrixDeterminant(b));
printf("B is %sunique.\n", matrixIsUnique(b) ? "" : "not ");
struct Matrix aplusb;
matrixAdd(&aplusb, a, b);
printf("A+B=\n");
matrixToString(aplusb);
struct Matrix asubb;
matrixSubtract(&asubb, a, b);
printf("A-B=\n");
matrixToString(asubb);
struct Matrix ascale;
matrixScale(&ascale, a, 5);
printf("5A=\n");
matrixToString(ascale);
struct Matrix bscale;
matrixScale(&bscale, b, 5);
printf("5B=\n");
matrixToString(bscale);
printf("A and B are %sthe same size.\n", matrixIsSameSize(a, b) ? "" : "not ");
printf("A=\n");
matrixToString(a);
printf("B=\n");
matrixToString(b);
// Test 3D vector math
}
/* Calculate the cofactor of a matrix */
void matrixCofactor(struct Matrix *out, const struct Matrix a) {
if(!matrixIsSquare(a)) {
printf("Error: The matrix is not square.");
return;
}
double *newValues = malloc(a.numValues * sizeof(double));
for(int i = 0; i < a.numRows; i++) {
for(int j = 0; j < a.numColumns; j++) {
struct Matrix temp;
int tempsize = (a.numRows-1) * (a.numColumns-1);
double valuestemp[tempsize];
int o = 0;
for (int k = 0; k < a.numRows; k++) {
for (int l = 0; l < a.numColumns; l++) {
if(l == j) l++;
if(k == i) k++;
if(k == a.numRows || l == a.numColumns) break;
valuestemp[o] = a.values[k*a.numColumns+l];
o++;
}
}
newMatrix(&temp, valuestemp, a.numRows-1, a.numRows-1);
newValues[j*a.numRows+i] = matrixDeterminant(temp);
}
}
newMatrix(out, newValues, a.numRows, a.numColumns);
}
void testMatrixDeterminant(){
int n;
double **C;
n=3;
C=allocateDoubleMatrix(3, 3);
C[0][0]=6.0; C[0][1]=1.0; C[0][2]=1.0;
C[1][0]=4.0; C[1][1]=-2.0; C[1][2]=5.0;
C[2][0]=2.0; C[2][1]=8.0; C[2][2]=7.0;
fprintf(stdout,"Matrix Determinant\n");
fprintf(stdout,"%f \n", matrixDeterminant(C,n));
}
double matrixDeterminant(double **A, int n){
int i;
double det=0;
double **B;
B=allocateDoubleMatrix(n-1, n-1);
if(n==2){
det=(A[0][0]*A[1][1])-(A[0][1]*A[1][0]);
}
else{
for(i=0;i<n;i++){
B=minorMatrix(A, n, i, 0);
det += pow(-1,i)*A[0][i]*matrixDeterminant(B,n-1);
}
}
return(det);
}
/* Check if a matrix has a unique solution */
char matrixIsUnique(const struct Matrix a) {
if(matrixDeterminant(a) != 0)
return 1;
return 0;
}
/* Calculate the inverse of a matrix */
void matrixInverse(struct Matrix *out, const struct Matrix a) {
struct Matrix temp;
matrixCofactor(&temp, a);
matrixScale(out, temp, 1/matrixDeterminant(a));
}
Matrix Matrix::matrixInvert(Matrix *matrix)
{
Matrix result;
float matrix3x3[9];
/* Find the cofactor of each element. */
/* Element (i, j) (1, 1) */
matrix3x3[0] = matrix->elements[ 5];
matrix3x3[1] = matrix->elements[ 6];
matrix3x3[2] = matrix->elements[ 7];
matrix3x3[3] = matrix->elements[ 9];
matrix3x3[4] = matrix->elements[10];
matrix3x3[5] = matrix->elements[11];
matrix3x3[6] = matrix->elements[13];
matrix3x3[7] = matrix->elements[14];
matrix3x3[8] = matrix->elements[15];
result.elements[0] = matrixDeterminant(matrix3x3);
/* Element (i, j) (1, 2) */
matrix3x3[0] = matrix->elements[ 1];
matrix3x3[1] = matrix->elements[ 2];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 9];
matrix3x3[4] = matrix->elements[10];
matrix3x3[5] = matrix->elements[11];
matrix3x3[6] = matrix->elements[13];
matrix3x3[7] = matrix->elements[14];
matrix3x3[8] = matrix->elements[15];
result.elements[4] = -matrixDeterminant(matrix3x3);
/* Element (i, j) (1, 3) */
matrix3x3[0] = matrix->elements[ 1];
matrix3x3[1] = matrix->elements[ 2];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 5];
matrix3x3[4] = matrix->elements[ 6];
matrix3x3[5] = matrix->elements[ 7];
matrix3x3[6] = matrix->elements[13];
matrix3x3[7] = matrix->elements[14];
matrix3x3[8] = matrix->elements[15];
result.elements[8] = matrixDeterminant(matrix3x3);
/* Element (i, j) (1, 4) */
matrix3x3[0] = matrix->elements[ 1];
matrix3x3[1] = matrix->elements[ 2];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 5];
matrix3x3[4] = matrix->elements[ 6];
matrix3x3[5] = matrix->elements[ 7];
matrix3x3[6] = matrix->elements[ 9];
matrix3x3[7] = matrix->elements[10];
matrix3x3[8] = matrix->elements[11];
result.elements[12] = -matrixDeterminant(matrix3x3);
/* Element (i, j) (2, 1) */
matrix3x3[0] = matrix->elements[ 4];
matrix3x3[1] = matrix->elements[ 6];
matrix3x3[2] = matrix->elements[ 7];
matrix3x3[3] = matrix->elements[ 8];
matrix3x3[4] = matrix->elements[10];
matrix3x3[5] = matrix->elements[11];
matrix3x3[6] = matrix->elements[12];
matrix3x3[7] = matrix->elements[14];
matrix3x3[8] = matrix->elements[15];
result.elements[1] = -matrixDeterminant(matrix3x3);
/* Element (i, j) (2, 2) */
matrix3x3[0] = matrix->elements[ 0];
matrix3x3[1] = matrix->elements[ 2];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 8];
matrix3x3[4] = matrix->elements[10];
matrix3x3[5] = matrix->elements[11];
matrix3x3[6] = matrix->elements[12];
matrix3x3[7] = matrix->elements[14];
matrix3x3[8] = matrix->elements[15];
result.elements[5] = matrixDeterminant(matrix3x3);
/* Element (i, j) (2, 3) */
matrix3x3[0] = matrix->elements[ 0];
matrix3x3[1] = matrix->elements[ 2];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 4];
matrix3x3[4] = matrix->elements[ 6];
matrix3x3[5] = matrix->elements[ 7];
matrix3x3[6] = matrix->elements[12];
matrix3x3[7] = matrix->elements[14];
matrix3x3[8] = matrix->elements[15];
result.elements[9] = -matrixDeterminant(matrix3x3);
/* Element (i, j) (2, 4) */
matrix3x3[0] = matrix->elements[ 0];
matrix3x3[1] = matrix->elements[ 2];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 4];
matrix3x3[4] = matrix->elements[ 6];
matrix3x3[5] = matrix->elements[ 7];
matrix3x3[6] = matrix->elements[ 8];
matrix3x3[7] = matrix->elements[10];
matrix3x3[8] = matrix->elements[11];
result.elements[13] = matrixDeterminant(matrix3x3);
/* Element (i, j) (3, 1) */
matrix3x3[0] = matrix->elements[ 4];
matrix3x3[1] = matrix->elements[ 5];
matrix3x3[2] = matrix->elements[ 7];
matrix3x3[3] = matrix->elements[ 8];
matrix3x3[4] = matrix->elements[ 9];
matrix3x3[5] = matrix->elements[11];
matrix3x3[6] = matrix->elements[12];
matrix3x3[7] = matrix->elements[13];
matrix3x3[8] = matrix->elements[15];
result.elements[2] = matrixDeterminant(matrix3x3);
/* Element (i, j) (3, 2) */
matrix3x3[0] = matrix->elements[ 0];
matrix3x3[1] = matrix->elements[ 1];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 8];
matrix3x3[4] = matrix->elements[ 9];
matrix3x3[5] = matrix->elements[11];
matrix3x3[6] = matrix->elements[12];
matrix3x3[7] = matrix->elements[13];
matrix3x3[8] = matrix->elements[15];
result.elements[6] = -matrixDeterminant(matrix3x3);
/* Element (i, j) (3, 3) */
matrix3x3[0] = matrix->elements[ 0];
matrix3x3[1] = matrix->elements[ 1];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 4];
matrix3x3[4] = matrix->elements[ 5];
matrix3x3[5] = matrix->elements[ 7];
matrix3x3[6] = matrix->elements[12];
matrix3x3[7] = matrix->elements[13];
matrix3x3[8] = matrix->elements[15];
result.elements[10] = matrixDeterminant(matrix3x3);
/* Element (i, j) (3, 4) */
matrix3x3[0] = matrix->elements[ 0];
matrix3x3[1] = matrix->elements[ 1];
matrix3x3[2] = matrix->elements[ 3];
matrix3x3[3] = matrix->elements[ 4];
matrix3x3[4] = matrix->elements[ 5];
matrix3x3[5] = matrix->elements[ 7];
matrix3x3[6] = matrix->elements[ 8];
matrix3x3[7] = matrix->elements[ 9];
matrix3x3[8] = matrix->elements[11];
result.elements[14] = -matrixDeterminant(matrix3x3);
/* Element (i, j) (4, 1) */
matrix3x3[0] = matrix->elements[ 4];
matrix3x3[1] = matrix->elements[ 5];
matrix3x3[2] = matrix->elements[ 6];
matrix3x3[3] = matrix->elements[ 8];
matrix3x3[4] = matrix->elements[ 9];
matrix3x3[5] = matrix->elements[10];
matrix3x3[6] = matrix->elements[12];
matrix3x3[7] = matrix->elements[13];
matrix3x3[8] = matrix->elements[14];
result.elements[3] = -matrixDeterminant(matrix3x3);
/* Element (i, j) (4, 2) */
matrix3x3[0] = matrix->elements[ 0];
matrix3x3[1] = matrix->elements[ 1];
matrix3x3[2] = matrix->elements[ 2];
matrix3x3[3] = matrix->elements[ 8];
matrix3x3[4] = matrix->elements[ 9];
matrix3x3[5] = matrix->elements[10];
matrix3x3[6] = matrix->elements[12];
matrix3x3[7] = matrix->elements[13];
matrix3x3[8] = matrix->elements[14];
result.elements[7] = matrixDeterminant(matrix3x3);
/* Element (i, j) (4, 3) */
matrix3x3[0] = matrix->elements[ 0];
matrix3x3[1] = matrix->elements[ 1];
matrix3x3[2] = matrix->elements[ 2];
matrix3x3[3] = matrix->elements[ 4];
matrix3x3[4] = matrix->elements[ 5];
matrix3x3[5] = matrix->elements[ 6];
matrix3x3[6] = matrix->elements[12];
matrix3x3[7] = matrix->elements[13];
matrix3x3[8] = matrix->elements[14];
result.elements[11] = -matrixDeterminant(matrix3x3);
/* Element (i, j) (4, 4) */
matrix3x3[0] = matrix->elements[ 0];
matrix3x3[1] = matrix->elements[ 1];
matrix3x3[2] = matrix->elements[ 2];
matrix3x3[3] = matrix->elements[ 4];
matrix3x3[4] = matrix->elements[ 5];
matrix3x3[5] = matrix->elements[ 6];
matrix3x3[6] = matrix->elements[ 8];
matrix3x3[7] = matrix->elements[ 9];
matrix3x3[8] = matrix->elements[10];
result.elements[15] = matrixDeterminant(matrix3x3);
/* The adjoint is the transpose of the cofactor matrix. */
matrixTranspose(&result);
/* The inverse is the adjoint divided by the determinant. */
result = matrixScale(&result, 1.0f / matrixDeterminant(matrix));
return result;
}
