Eigenvalues / Eigenvectors of a Symmetric Tridiaognal Matrix

Functions
int	SymmetricTridiagoanlEigenSolver (Vector &eigVal, mkIndex n, const Real *diag, const Real *sdiag)
	Compute all eigenvalues (but not eigenvectors) of a symmetric tridiagonal matrix T. This function invokes the LAPACK routine dstev_() (if Real is double) or stev_() (if Real is float).
int	SymmetricTridiagoanlEigenSolver (Vector &eigVal, Matrix &eigVec, mkIndex n, const Real *diag, const Real *sdiag)
	Compute all eigenvalues and eigenvectors of a symmetric tridiagonal matrix T. This function invokes the LAPACK routine dstev_() (if Real is double) or stev_() (if Real is float).
void	reportTroubleIfAny (std::ostream &outerr, int info, mkIndex n=0)
	Print out an error message to std::ostream outerr if info 0 which signifies an error that occurred in the LAPACK routine xSTEV.

Detailed Description

Function Documentation

reportTroubleIfAny()

void reportTroubleIfAny	(	std::ostream &	outerr,
		int	info,
		mkIndex	n = 0 )

Print out an error message to std::ostream outerr if info 0 which signifies an error that occurred in the LAPACK routine xSTEV.

Parameters

outerr	is an std::ostream for printing out the error message when info 0.
info	is the flag returned from the LAPACK routine dstev_() (if Real is double) or sstev_() (if Real is float). =0: successful exit (nothing will be printed). <0: if info=-i, the ith argument had an illegal value. >0: if info=i, the algorithm failed to converge; i off-diagonal elements did not converge to zero.
n	is the dimension of the symmetric tridiagonal matrix. This information will also be printed out if n is provided (i.e. n 0).

See also

SymmetricTridiagoanlEigenSolver().

SymmetricTridiagoanlEigenSolver() [1/2]

int SymmetricTridiagoanlEigenSolver	(	Vector &	eigVal,
		Matrix &	eigVec,
		mkIndex	n,
		const Real *	diag,
		const Real *	sdiag )

Compute all eigenvalues and eigenvectors of a symmetric tridiagonal matrix T. This function invokes the LAPACK routine dstev_() (if Real is double) or stev_() (if Real is float).

Parameters

n	is the dimension of the symmatrix tridiagonal matrix T.
diag[],sdiag[]	define the symmetric tridiagonal matrix; the diagonal elements are diag[0,...,n-1] and subdiagonal elements are sdiag[0,...,n-2]. In other words, T(i,i) = diag[i-1] for i = 1,...,n. T(i+1,i) = T(i,i+1) = sdiag[i-1] for i = 1,...n-1.
eigVal	is the output vector of length n containing all eigenvalues of T in ascending order.
eigVec	is the output n-by-n matrix with columns as eigenvectors of T, sorted with respect to eigVal.

Returns

The flag returned by dstev_() (if Real is double) or stev_() (if Real is float).

See also

reportTroubleIfAny().

SymmetricTridiagoanlEigenSolver() [2/2]

int SymmetricTridiagoanlEigenSolver	(	Vector &	eigVal,
		mkIndex	n,
		const Real *	diag,
		const Real *	sdiag )

Compute all eigenvalues (but not eigenvectors) of a symmetric tridiagonal matrix T. This function invokes the LAPACK routine dstev_() (if Real is double) or stev_() (if Real is float).

Parameters

n	is the dimension of the symmatrix tridiagonal matrix T.
diag[],sdiag[]	define the symmetric tridiagonal matrix T, whose the diagonal elements are diag[0,...,n-1] and subdiagonal elements are sdiag[0,...,n-2]. In other words, T(i,i) = diag[i-1] for i = 1,...,n. T(i+1,i) = T(i,i+1) = sdiag[i-1] for i = 1,...n-1.
eigVal	is the output vector of length n containing all eigenvalues of T in ascending order.

Returns

The flag returned by the LAPACK routine dstev_() (if Real is double) or stev_() (if Real is float).

See also

reportTroubleIfAny().