- A
- (
*input/output*)**REAL**or**COMPLEX**square array, shape .

On entry, the matrix .

On exit, the contents of**A**are destroyed. *w*- (
*output*)**REAL**or**COMPLEX**array, shape with (*w*) (**A**,1).

The computed eigenvalues.

::=**WR(:), WI(:)****W(:)**,

where**WR(:), WI(:)**are of**REAL***type*(for the real and imaginary parts) and**W(:)**is of**COMPLEX***type*.

Note: If is real, then a complex-conjugate pair appear consecutively, with the eigenvalue having the positive imaginary part appearing first. - VL
*Optional*(*output*)**REAL**or**COMPLEX**square array, shape with (**VL**,1) (**A**,1).

The left eigenvectors are stored in the columns of**VL**in the order of their eigenvalues. Each eigenvector is scaled so that the Euclidean norm is 1 and the largest component is real.

Note: If is real then complex eigenvectors, like their eigenvalues, occur in complex conjugate pairs. The real and imaginary parts of the first eigenvector of the pair are stored in**VL**and**VL**, respectively. Thus a complex conjugate pair is given by

- VR
*Optional*(*output*)**REAL**or**COMPLEX**square array, shape with (**VR**,1) (**A**,1).

The right eigenvectors are stored in the columns of**VR**in the order of their eigenvalues. Each eigenvector is scaled so that the Euclidean norm is 1 and the largest component is real.

Note: If is real then complex eigenvectors, like their eigenvalues, occur in complex conjugate pairs. The real and imaginary parts of the first eigenvector of the pair are stored in**VR**and**VR**, respectively. Thus a complex conjugate pair is given by

- BALANC
*Optional*(*input*)**CHARACTER(LEN=1)**.

Indicates whether the input matrix should be permuted and/or diagonally scaled.

Default value: 'N'.- ILO,IHI
*Optional*(*output*)**INTEGER**.

**ILO**and**IHI**are determined when is balanced. The balanced if and or .- SCALE
*Optional*(*output*)**REAL**array, shape with (**SCALE**) (**A**,1).

Details of the permutations and scaling factors applied when balancing . If is the index of the row and column interchanged with row and column , and is the scaling factor applied to row and column , then

- ABNRM
*Optional*(*output*)**REAL**.

The norm of the balanced matrix (the maximum of the sum of absolute values of elements of any column).- RCONDE
*Optional*(*output*)**REAL**array, shape with (**RCONDE**) (**A**,1).

**RCONDE**is the reciprocal condition number of the eigenvalue.- RCONDV
*Optional*(*output*)**REAL**array, shape , (**RCONDV**) (**A**,1).

**RCONDV**is the reciprocal condition number of the right eigenvector.- INFO
*Optional*(*output*)**INTEGER**.

If**INFO**is not present and an error occurs, then the program is terminated with an error message.