/**
* Returns the determinant of the matrix. If the inverse of the matrix is also
* needed, then using {@link org.ejml.interfaces.decomposition.LUDecomposition_F64} directly (or any
* similar algorithm) can be more efficient.
*
* @param A The matrix whose determinant is to be computed. Not modified.
* @return The determinant.
*/
public static double det(DMatrixSparseCSC A)
{
LUSparseDecomposition_F64 <DMatrixSparseCSC> alg = DecompositionFactory_DSCC.lu(FillReducing.NONE);
if (alg.inputModified())
{
A = (DMatrixSparseCSC)A.copy();
}
if (!alg.decompose(A))
{
return(0.0);
}
return(alg.computeDeterminant().real);
}
public static void main(string[] args)
{
// create a random matrix that can be solved
int N = 5;
IMersenneTwister rand = new MersenneTwisterFast(234);
DMatrixSparseCSC A = RandomMatrices_DSCC.rectangle(N, N, N * N / 4, rand);
RandomMatrices_DSCC.ensureNotSingular(A, rand);
// Create the LU decomposition
LUSparseDecomposition_F64 <DMatrixSparseCSC> decompose =
DecompositionFactory_DSCC.lu(FillReducing.NONE);
// Decompose the matrix.
// If you care about the A matrix being modified call decompose.inputModified()
if (!decompose.decompose(A))
{
throw new InvalidOperationException("The matrix is singular");
}
// Extract new copies of the L and U matrices
DMatrixSparseCSC L = decompose.getLower(null);
DMatrixSparseCSC U = decompose.getUpper(null);
DMatrixSparseCSC P = decompose.getRowPivot(null);
// Storage for an intermediate step
DMatrixSparseCSC tmp = (DMatrixSparseCSC)A.createLike();
// Storage for the inverse matrix
DMatrixSparseCSC Ainv = (DMatrixSparseCSC)A.createLike();
// Solve for the inverse: P*I = L*U*inv(A)
TriangularSolver_DSCC.solve(L, true, P, tmp, null, null, null);
TriangularSolver_DSCC.solve(U, false, tmp, Ainv, null, null, null);
// Make sure the inverse has been found. A*inv(A) = identity should be an identity matrix
DMatrixSparseCSC found = (DMatrixSparseCSC)A.createLike();
CommonOps_DSCC.mult(A, Ainv, found);
found.print();
}