Extracts the eigenvalues and eigenvectors of a symmetric banded matrix.

Syntax

e, v = EigSB(M,k)

Arguments

Name

Description

M

Compressed diagonal storage matrix form of the banded square matrix A.  Use SymBandMatrix to create it and SymBandMatrixIndices to populate it. The upper triangle of A is ignored due to symmetry.

k

The number of super or sub-diagonals in the lower or upper band of the original matrix.  It should include off-diagonals with zero entries that are in between diagonals with non-zero entries.

Output

Name

Description

e

A vector of the eigenvalues of the matrix.

v

A matrix whose columns are the eigenvectors of A.

Example

Extract the eigenvalues of the symmetric banded matrix [40,2,0;2,40,4;0,4,40].

Syntax

M = [40, 40, 40; 2, 4, 0];

k = 1;

e = EigSB(M, k);

print(e)

Result

A row vector of the eigenvalues.

[Matrix] 1 x 3

35.528  40  44.472

Comments

For efficiency, the matrix M should be generated directly without creating the matrix A. The number of columns of M is k+1 and the number of columns is same as of A..  Hence, the narrower the band compared to the size of A, the smaller the size of M in comparison to A.

EigSB calls dsbev from LAPACK

See Also:

SymBandMatrix

SymBandMatrixIndices

LSolve

LSolveB

LSolveSPDB