/**
* <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;
}
/**
* Creates a solver for symmetric positive definite matrices.
*
* @return A new solver for symmetric positive definite matrices.
*/
public static LinearSolverDense <FMatrixRMaj> symmPosDef(int matrixWidth)
{
if (matrixWidth < EjmlParameters.SWITCH_BLOCK64_CHOLESKY)
{
CholeskyDecompositionCommon_FDRM decomp = new CholeskyDecompositionInner_FDRM(true);
return(new LinearSolverChol_FDRM(decomp));
}
else
{
if (EjmlParameters.MEMORY == EjmlParameters.MemoryUsage.FASTER)
{
return(new LinearSolverChol_FDRB());
}
else
{
CholeskyDecompositionCommon_FDRM decomp = new CholeskyDecompositionInner_FDRM(true);
return(new LinearSolverChol_FDRM(decomp));
}
}
}
