Developer Reference

ID 766877
Date 3/22/2024
Public

## SSYEVX Example Program in Fortran

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*  in writing.
*  =============================================================================
*
*  SSYEVX Example.
*  ==============
*
*  Program computes the smallest eigenvalues and the corresponding
*  eigenvectors of a real symmetric matrix A:
*
*    6.29  -0.39   0.61   1.18  -0.08
*   -0.39   7.19   0.81   1.19  -0.08
*    0.61   0.81   5.48  -3.13   0.22
*    1.18   1.19  -3.13   3.79  -0.26
*   -0.08  -0.08   0.22  -0.26   0.83
*
*  Description.
*  ============
*
*  The routine computes selected eigenvalues and, optionally, eigenvectors of
*  an n-by-n real symmetric matrix A. The eigenvector v(j) of A satisfies
*
*  A*v(j) = lambda(j)*v(j)
*
*  where lambda(j) is its eigenvalue. The computed eigenvectors are
*  orthonormal.
*  Eigenvalues and eigenvectors can be selected by specifying either a range
*  of values or a range of indices for the desired eigenvalues.
*
*  Example Program Results.
*  ========================
*
* SSYEVX Example Program Results
*
* The total number of eigenvalues found: 3
*
* Selected eigenvalues
*   0.71   0.82   6.58
*
* Selected eigenvectors (stored columnwise)
*   0.22   0.09  -0.95
*   0.21   0.08  -0.04
*  -0.52  -0.22  -0.29
*  -0.73  -0.21  -0.09
*  -0.32   0.94   0.01
*  =============================================================================
*
*     .. Parameters ..
INTEGER          N, NSELECT
PARAMETER        ( N = 5, NSELECT = 3 )
INTEGER          LDA, LDZ
PARAMETER        ( LDA = N, LDZ = N )
INTEGER          LWMAX
PARAMETER        ( LWMAX = 1000 )
*
*     .. Local Scalars ..
INTEGER          INFO, LWORK, IL, IU, M
REAL             ABSTOL, VL, VU
*
*     .. Local Arrays ..
*     IWORK dimension should be at least 5*N
INTEGER          IFAIL( N ), IWORK( 5*N )
REAL             A( LDA, N ), W( N ), Z( LDZ, NSELECT ),
$WORK( LWMAX ) DATA A/$  6.29, 0.00, 0.00, 0.00, 0.00,
$-0.39, 7.19, 0.00, 0.00, 0.00,$  0.61, 0.81, 5.48, 0.00, 0.00,
$1.18, 1.19,-3.13, 3.79, 0.00,$ -0.08,-0.08, 0.22,-0.26, 0.83
$/ * * .. External Subroutines .. EXTERNAL SSYEVX EXTERNAL PRINT_MATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'SSYEVX Example Program Results' * Negative ABSTOL means using the default value ABSTOL = -1.0 * Set IL, IU to compute NSELECT smallest eigenvalues IL = 1 IU = NSELECT * * Query the optimal workspace. * LWORK = -1 CALL SSYEVX( 'Vectors', 'Indices', 'Upper', N, A, LDA, VL, VU, IL,$             IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL,
$INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Solve eigenproblem. * CALL SSYEVX( 'Vectors', 'Indices', 'Upper', N, A, LDA, VL, VU, IL,$             IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL,
$INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm failed to compute eigenvalues.' STOP END IF * * Print the number of eigenvalues found. * WRITE(*,'(/A,I2)')' The total number of eigenvalues found:', M * * Print eigenvalues. * CALL PRINT_MATRIX( 'Selected eigenvalues', 1, M, W, 1 ) * * Print eigenvectors. * CALL PRINT_MATRIX( 'Selected eigenvectors (stored columnwise)',$                   N, M, Z, LDZ )
STOP
END
*
*     End of SSYEVX Example.
*
*  =============================================================================
*
*     Auxiliary routine: printing a matrix.
*
SUBROUTINE PRINT_MATRIX( DESC, M, N, A, LDA )
CHARACTER*(*)    DESC
INTEGER          M, N, LDA
REAL             A( LDA, * )
*
INTEGER          I, J
*
WRITE(*,*)
WRITE(*,*) DESC
DO I = 1, M
WRITE(*,9998) ( A( I, J ), J = 1, N )
END DO
*
9998 FORMAT( 11(:,1X,F6.2) )
RETURN
END