/**
* <p>
* Checks to see if the matrix is positive semidefinite:
* </p>
* <p>
* x<sup>T</sup> A x ≥ 0<br>
* for all x where x is a non-zero vector and A is a symmetric matrix.
* </p>
*
* @param A square symmetric matrix. Not modified.
*
* @return True if it is positive semidefinite and false if it is not.
*/
public static bool isPositiveSemidefinite(FMatrixRMaj A)
{
if (!isSquare(A))
{
return(false);
}
EigenDecomposition_F32 <FMatrixRMaj> eig = DecompositionFactory_FDRM.eig(A.numCols, false);
if (eig.inputModified())
{
A = (FMatrixRMaj)A.copy();
}
eig.decompose(A);
for (int i = 0; i < A.numRows; i++)
{
Complex_F32 v = eig.getEigenvalue(i);
if (v.getReal() < 0)
{
return(false);
}
}
return(true);
}
/**
* <p>
* Checks to see if the matrix is positive definite.
* </p>
* <p>
* x<sup>T</sup> A x > 0<br>
* for all x where x is a non-zero vector and A is a symmetric matrix.
* </p>
*
* @param A square symmetric matrix. Not modified.
*
* @return True if it is positive definite and false if it is not.
*/
public static bool isPositiveDefinite(FMatrixRMaj A)
{
if (!isSquare(A))
{
return(false);
}
CholeskyDecompositionInner_FDRM chol = new CholeskyDecompositionInner_FDRM(true);
if (chol.inputModified())
{
A = (FMatrixRMaj)A.copy();
}
return(chol.decompose(A));
}
/**
* Creates a random distribution with the specified mean and covariance. The references
* to the variables are not saved, their value are copied.
*
* @param rand Used to create the random numbers for the draw. Reference is saved.
* @param cov The covariance of the distribution. Not modified.
*/
public CovarianceRandomDraw_FDRM(IMersenneTwister rand, FMatrixRMaj cov)
{
r = new FMatrixRMaj(cov.numRows, 1);
CholeskyDecompositionInner_FDRM cholesky = new CholeskyDecompositionInner_FDRM(true);
if (cholesky.inputModified())
{
cov = (FMatrixRMaj)cov.copy();
}
if (!cholesky.decompose(cov))
{
throw new InvalidOperationException("Decomposition failed!");
}
A = cholesky.getT();
this.rand = rand;
}
/**
* Computes the nullity of a matrix using the specified tolerance.
*
* @param A Matrix whose rank is to be calculated. Not modified.
* @param threshold The numerical threshold used to determine a singular value.
* @return The matrix's nullity.
*/
public static int nullity(FMatrixRMaj A, float threshold)
{
SingularValueDecomposition_F32 <FMatrixRMaj> svd =
DecompositionFactory_FDRM.svd(A.numRows, A.numCols, false, false, true);
if (svd.inputModified())
{
A = (FMatrixRMaj)A.copy();
}
if (!svd.decompose(A))
{
throw new InvalidOperationException("Decomposition failed");
}
return(SingularOps_FDRM.nullity(svd, threshold));
}
/**
* Checks to see if the rows of the provided matrix are linearly independent.
*
* @param A Matrix whose rows are being tested for linear independence.
* @return true if linearly independent and false otherwise.
*/
public static bool isRowsLinearIndependent(FMatrixRMaj A)
{
// LU decomposition
LUDecomposition <FMatrixRMaj> lu = DecompositionFactory_FDRM.lu(A.numRows, A.numCols);
if (lu.inputModified())
{
A = (FMatrixRMaj)A.copy();
}
if (!lu.decompose(A))
{
throw new InvalidOperationException("Decompositon failed?");
}
// if they are linearly independent it should not be singular
return(!lu.isSingular());
}
public void setup(FMatrixRMaj A)
{
if (A.numRows != A.numCols)
{
throw new InvalidOperationException("Must be square");
}
if (N != A.numRows)
{
N = A.numRows;
this.A = (FMatrixRMaj)A.copy();
u = new FMatrixRMaj(A.numRows, 1);
_temp = new FMatrixRMaj(A.numRows, 1);
numStepsFind = new int[A.numRows];
}
else
{
this.A.set(A);
UtilEjml.memset(numStepsFind, 0, numStepsFind.Length);
}
// zero all the off numbers that should be zero for a hessenberg matrix
for (int i = 2; i < N; i++)
{
for (int j = 0; j < i - 1; j++)
{
this.A.set(i, j, 0);
}
}
eigenvalues = new Complex_F32[A.numRows];
for (int i = 0; i < eigenvalues.Length; i++)
{
eigenvalues[i] = new Complex_F32();
}
numEigen = 0;
lastExceptional = 0;
numExceptional = 0;
steps = 0;
}