public static boolean checkPosDef(DenseMatrix covar) {
final EigenDecompositionRightMTJ decomp = EigenDecompositionRightMTJ.create(covar);
for (final ComplexNumber eigenVal : decomp.getEigenValues()) {
if (eigenVal.getRealPart() < 0) return false;
}
return true;
}
public ComplexNumber logDeterminant() {
if (this.isSquare() == false) {
throw new IllegalArgumentException("Matrix must be square");
}
DenseMatrix decompositionMatrix;
if (this instanceof DenseMatrix) {
decompositionMatrix = (DenseMatrix) this;
} else {
decompositionMatrix = new DenseMatrix(this);
}
boolean useEVD = false;
if (useEVD) {
EigenDecompositionRightMTJ evd = EigenDecompositionRightMTJ.create(decompositionMatrix);
return evd.getLogDeterminant();
} else {
// Note: It's generally faster to use LU decomposition for
// determinants, but QR can be more stable in some circumstances
no.uib.cipr.matrix.UpperTriangDenseMatrix triangularMatrix;
boolean useQR = false;
int sign;
if (useQR) {
no.uib.cipr.matrix.QR decomposition = no.uib.cipr.matrix.QR.factorize(this.internalMatrix);
triangularMatrix = decomposition.getR();
sign = 1;
} else {
no.uib.cipr.matrix.DenseLU decomposition =
no.uib.cipr.matrix.DenseLU.factorize(this.internalMatrix);
triangularMatrix = decomposition.getU();
sign = 1;
for (int i = 0; i < decomposition.getPivots().length; i++) {
if (decomposition.getPivots()[i] != (i + 1)) {
sign = -sign;
}
}
}
int M = triangularMatrix.numRows();
int N = triangularMatrix.numColumns();
int maxIndex = (M < N) ? M : N;
// Both LU and QR return upper triangular matrices and the "L" and
// "Q" matrices have a determinant of one, so the real action is
// in the "U" and "R" matrices, which are both upper (right)
// triangular. As we remember from our algebra courses, the
// eigenvalues of a triangular matrix are the diagonal elements
// themselves. We also remember that the product of the eigenvalues
// is the determinant.
//
// The diagonal elements (for either LU or QR) will be REAL, but
// they may be negative. The logarithm of a negative number is
// the logarithm of the absolute value of the number, with an
// imaginary part of PI. The exponential is all that matters, so
// the log-determinant is equivalent, MODULO PI (3.14...), so
// we just toggle this sign bit.
double logsum = 0.0;
for (int i = 0; i < maxIndex; i++) {
double eigenvalue = triangularMatrix.get(i, i);
if (eigenvalue < 0.0) {
sign = -sign;
logsum += Math.log(-eigenvalue);
} else {
logsum += Math.log(eigenvalue);
}
}
return new ComplexNumber(logsum, (sign < 0) ? Math.PI : 0.0);
}
}