eig#

Purpose#

Computes the eigenvalues of a general matrix.

Format#

va = eig(x)#

Parameters:: x (NxN matrix or KxNxN array) – data used to compute the eigenvalues.
Returns:: va (Nx1 vector or KxNx1 array) – the eigenvalues of x.

Examples#

x = {  0.5  1.2  0.3,
       0.6  0.9  0.2,
       0.8  1.5  0.0 };

va = eig(x);

After the above code, va will equal:

1.8626
-0.1871
-0.2754

To calculate eigenvalues and eigenvectors see eigv(). To calculate generalized eigenvalues and eigenvectors, see lapgeig(), or lapgeigv().

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. For example, if x is a 10x4x4 array, va will be a 10x4x1 array containing the eigenvalues 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 \(scalerr(va[1])+1 \to N\) should be correct.

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 unordered except that complex conjugate pairs of eigenvalues will appear consecutively with the eigenvalue having the positive imaginary part first.