eighv#

Purpose#

Computes eigenvalues and eigenvectors of a complex hermitian or real symmetric matrix.

Format#

{ va, ve } = eighv(x)#

Parameters:

x (NxN matrix or KxNxN array) – data used to compute the eigenvalues and eigenvectors.

Returns:

va (Nx1 vector or KxNx1 array) – the eigenvalues of x.
ve (NxN matrix or KxNxN array) – the eigenvectors of x.

Remarks#

If x is an array, va will be an array containing the eigenvalues of each 2-dimensional array described by the two trailing dimensions of x, and ve will be an array containing the corresponding eigenvectors. For example, if x is a 10x4x4 array, va will be a 10x4x1 array containing the eigenvalues and ve a 10x4x4 array containing the eigenvectors of each of the 10 4x4 arrays contained in x.

Errors

If the eigenvalues cannot all be determined, va[1] is set to an error code. Passing va[1] to the scalerr() function will return the index of the eigenvalue that failed. The eigenvalues for indices \(1 \to scalerr(va[1])-1\) should be correct. The eigenvectors are not computed.

Error handling is controlled with the low bit of the trap flag.

`trap 0`	set va[1] and terminate with message
`trap 1`	set va[1] and continue execution

Invalid inputs, such as an \(\infty\), missing value or Nan will cause an error. If the trap is set to 1, va will be set to a scalar error code and program execution will continue. Passing this scalar error code to the scalerr() function will return -1.

Eigenvalue ordering

The eigenvalues are in ascending order. The columns of ve contain the eigenvectors of x in the same order as the eigenvalues. The eigenvectors are orthonormal.

The eigenvalues of a complex hermitian or real symmetric matrix are always real.