# EIGENSYSTEM ANALYSIS

## EIGENVALUE DECOMPOSITION

ROUTINE DESCRIPTION
LIN_EIG_SELF Computes the eigenvalues of a self-adjoint matrix, A.
LIN_EIG_GEN Computes the eigenvalues of an n x n matrix, A.
LIN_GEIG_GEN Computes the generalized eigenvalues of an n x n matrix pencil, Av = λBv.

## EIGENVALUES AND (OPTIONALLY) EIGENVECTORS OF AX = λX

### REAL GENERAL PROBLEM AX = λX

ROUTINE DESCRIPTION
EVLRG Computes all of the eigenvalues of a real matrix.
EVCRG Computes all of the eigenvalues and eigenvectors of a real matrix.
EPIRG Computes the performance index for a real eigensystem.

### COMPLEX GENERAL PROBLEM AX = λX

ROUTINE DESCRIPTION
EVLCG Computes all of the eigenvalues of a complex matrix.
EVCCG Computes all of the eigenvalues and eigenvectors of a complex matrix.
EPICG Computes the performance index for a complex eigensystem.

### REAL SYMMETRIC GENERAL PROBLEM AX = λX

ROUTINE DESCRIPTION
EVLSF Computes all of the eigenvalues of a real symmetric matrix.
EVCSF Computes all of the eigenvalues and eigenvectors of a real symmetric matrix.
EVASF Computes the largest or smallest eigenvalues of a real symmetric matrix.
EVESF Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a real symmetric matrix.
EVBSF Computes selected eigenvalues of a real symmetric matrix.
EVFSF Computes selected eigenvalues and eigenvectors of a real symmetric matrix.
EPISF Computes the performance index for a real symmetric eigensystem.

### REAL BAND SYMMETRIC MATRICIES IN BAND STORAGE MODE

ROUTINE DESCRIPTION
EVLSB Computes all of the eigenvalues of a real symmetric matrix in band symmetric storage mode.
EVCSB Computes all of the eigenvalues and eigenvectors of a real symmetric matrix in band symmetric storage mode.
EVASB Computes the largest or smallest eigenvalues of a real symmetric matrix in band symmetric storage mode.
EVESB Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a real symmetric matrix in band symmetric storage mode.
EVBSB Computes the eigenvalues in a given interval of a real symmetric matrix stored in band symmetric storage mode.
EVFSB Computes the eigenvalues in a given interval and the corresponding eigenvectors of a real symmetric matrix stored in band symmetric storage mode.
EPISB Computes the performance index for a real symmetric eigensystem in band symmetric storage mode.

### COMPLEX HERMITIAN MATRICES

ROUTINE DESCRIPTION
EVLHF Computes all of the eigenvalues of a complex Hermitian matrix.
EVCHF Computes all of the eigenvalues and eigenvectors of a complex Hermitian matrix.
EVAHF Computes the largest or smallest eigenvalues of a complex Hermitian matrix.
EVEHF Computes the largest or smallest eigenvalues and the corresponding eigenvectors of a complex Hermitian matrix.
EVBHF Computes the eigenvalues in a given range of a complex Hermitian matrix.
EVFHF Computes the eigenvalues in a given range and the corresponding eigenvectors of a complex Hermitian matrix.
EPIHF Computes the performance index for a complex Hermitian eigensystem.

### REAL UPPER HESSENBERG MATRICES

ROUTINE DESCRIPTION
EVLRH Computes all of the eigenvalues of a real upper Hessenberg matrix.
EVCRH Computes all of the eigenvalues and eigenvectors of a real upper Hessenberg matrix.

### COMPLEX UPPER HESSENBERG MATRICES

ROUTINE DESCRIPTION
EVLCH Computes all of the eigenvalues of a complex upper Hessenberg matrix.
EVCCH Computes all of the eigenvalues and eigenvectors of a complex upper.

## EIGENVALUES AND (OPTIONALLY) EIGENVECTORS OF Az = λBz

### REAL GENERAL PROBLEM AX = λBz

ROUTINE DESCRIPTION
GVLRG Computes all of the eigenvalues of a generalized real eigensystem Az = λBz.
GVCRG Computes all of the eigenvalues and eigenvectors of a generalized real eigensystem Az = λBz.
GPIRG Computes the performance index for a generalized real eigensystem Az = λBz.

### COMPLEX GENERAL PROBLEM Az = λBz

ROUTINE DESCRIPTION
GVLCG Computes all of the eigenvalues of a generalized complex eigensystem Az = λBz.
GVCCG Computes all of the eigenvalues and eigenvectors of a generalized complex eigensystem Az = λBz.
GPICG Computes the performance index for a generalized complex eigensystem Az = λBz.

### REAL SYMMETRIC PROBLEM Az = λBz

ROUTINE DESCRIPTION
GVLSP Computes all of the eigenvalues of the generalized real symmetric eigenvalue problem Az = λBz, with B symmetric positive definite.
GVCSP Computes all of the eigenvalues and eigenvectors of the generalized real symmetric eigenvalue problem Az = λBz, with B symmetric positive definite.
GPISP Computes the performance index for a generalized real symmetric eigensystem problem.

## EIGENVALUES AND EIGENVECTORS COMPUTED WITH ARPACK

ROUTINE DESCRIPTION
ARPACK_SYMMETRIC Computes some eigenvalues and eigenvectors of the generalized real symmetric eigenvalue problem Ax = λBx.
ARPACK_SVD Computes some singular values and left and right singular vectors of a real rectangular matrix AM x N = USVT.
ARPACK_NONSYMMETRIC Compute some eigenvalues and eigenvectors of the generalized eigenvalue problem Ax = λBx. This can be used for the case B = I.
ARPACK_COMPLEX Compute some eigenvalues and eigenvectors of the generalized eigenvalue problem Ax = λBx.