Computes all of the eigenvalues of a real symmetric matrix.

Required Arguments

A — Real symmetric matrix of order N.   (Input)

EVAL — Real vector of length N containing the eigenvalues of A in decreasing order of magnitude.   (Output)

Optional Arguments

N — Order of the matrix A.   (Input)
Default: N = size (A,2).

LDA — Leading dimension of A exactly as specified in the dimension statement in the calling program.   (Input)
Default: LDA = size (A,1).

FORTRAN 90 Interface

Generic:          CALL EVLSF (A, EVAL [,…])

Specific:         The specific interface names are S_EVLSF and D_EVLSF.

FORTRAN 77 Interface

Single:            CALL EVLSF (N, A, LDA, EVAL)

Double:          The double precision name is DEVLSF.

Description

Routine EVLSF computes the eigenvalues of a real symmetric matrix. Orthogonal similarity transformations are used to reduce the matrix to an equivalent symmetric tridiagonal matrix. Then, an implicit rational QR algorithm is used to compute the eigenvalues of this tridiagonal matrix.

The underlying code is based on either EISPACK or LAPACK code depending upon which supporting libraries are used during linking. For a detailed explanation, see “Using ScaLAPACK, LAPACK, LINPACK, and EISPACK” in the Introduction section of this manual.

Comments

1.         Workspace may be explicitly provided, if desired, by use of E4LSF/DE4LSF. The reference is:

CALL E4LSF (N, A, LDA, EVAL, WORK, IWORK)

The additional arguments are as follows:

WORK — Work array of length 2N.

IWORK — Integer array of length N.

2.         Informational error

Type   Code

3           1                  The iteration for the eigenvalue failed to converge in 100 iterations before deflating.

Example

In this example, the eigenvalues of a real symmetric matrix are computed and printed. This matrix is given by Gregory and Karney (1969, page 56).

 

      USE EVLSF_INT

      USE WRRRN_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    LDA, N

      PARAMETER  (N=4, LDA=N)

!

      REAL       A(LDA,N), EVAL(N)

!                                 Set values of A

!

!                                 A = (  6.0    4.0    4.0    1.0)

!                                     (  4.0    6.0    1.0    4.0)

!                                     (  4.0    1.0    6.0    4.0)

!                                     (  1.0    4.0    4.0    6.0)

!

      DATA A /6.0, 4.0, 4.0, 1.0, 4.0, 6.0, 1.0, 4.0, 4.0, 1.0, 6.0, &

             4.0, 1.0, 4.0, 4.0, 6.0 /

!

!                                 Find eigenvalues of A

      CALL EVLSF (A, EVAL)

!                                 Print results

      CALL WRRRN ('EVAL', EVAL, 1, N, 1)

      END

Output

 

              EVAL

      1       2       3       4

  15.00    5.00    5.00   -1.00

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