Developer Reference

ID 766877
Date 3/31/2023
Public

## CHEEVR Example Program in Fortran

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*  in writing.
*  =============================================================================
*
*  CHEEVR Example.
*  ==============
*
*  Program computes eigenvalues specified by a selected range of values
*  and corresponding eigenvectors of a complex Hermitian matrix A using the
*  Relatively Robust Representations, where A is:
*
*  ( -2.16,  0.00) ( -0.16, -4.86) ( -7.23, -9.38) ( -0.04,  6.86)
*  ( -0.16,  4.86) (  7.45,  0.00) (  4.39,  6.29) ( -8.11, -4.41)
*  ( -7.23,  9.38) (  4.39, -6.29) ( -9.03,  0.00) ( -6.89, -7.66)
*  ( -0.04, -6.86) ( -8.11,  4.41) ( -6.89,  7.66) (  7.76,  0.00)
*
*  Description.
*  ============
*
*  The routine computes selected eigenvalues and, optionally, eigenvectors of
*  an n-by-n complex Hermitian 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.
*  ========================
*
* CHEEVR Example Program Results
*
* The total number of eigenvalues found: 2
*
* Selected eigenvalues
*  -4.18   3.57
*
* Selected eigenvectors (stored columnwise)
* (  0.68,  0.00) (  0.38,  0.00)
* (  0.03,  0.18) (  0.54, -0.57)
* ( -0.03,  0.21) ( -0.40,  0.04)
* (  0.20,  0.64) ( -0.14, -0.26)
*  =============================================================================
*
*     .. Parameters ..
INTEGER          N
PARAMETER        ( N = 4 )
INTEGER          LDA, LDZ
PARAMETER        ( LDA = N, LDZ = N )
INTEGER          LWMAX
PARAMETER        ( LWMAX = 1000 )
*
*     .. Local Scalars ..
INTEGER          INFO, LWORK, LRWORK, LIWORK, IL, IU, M
REAL             ABSTOL, VL, VU
*
*     .. Local Arrays ..
INTEGER          ISUPPZ( N ), IWORK( LWMAX )
REAL             W( N ), RWORK( LWMAX )
COMPLEX          A( LDA, N ), Z( LDZ, N ), WORK( LWMAX )
DATA             A/
$(-2.16, 0.00),(-0.16, 4.86),(-7.23, 9.38),(-0.04,-6.86),$ ( 0.00, 0.00),( 7.45, 0.00),( 4.39,-6.29),(-8.11, 4.41),
$( 0.00, 0.00),( 0.00, 0.00),(-9.03, 0.00),(-6.89, 7.66),$ ( 0.00, 0.00),( 0.00, 0.00),( 0.00, 0.00),( 7.76, 0.00)
$/ * * .. External Subroutines .. EXTERNAL CHEEVR EXTERNAL PRINT_MATRIX, PRINT_RMATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'CHEEVR Example Program Results' * Negative ABSTOL means using the default value ABSTOL = -1.0 * Set VL, VU to compute eigenvalues in half-open (VL,VU] interval VL = -5.0 VU = 5.0 * * Query the optimal workspace. * LWORK = -1 LRWORK = -1 LIWORK = -1 CALL CHEEVR( 'Vectors', 'Values', 'Lower', N, A, LDA, VL, VU, IL,$             IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, RWORK,
$LRWORK, IWORK, LIWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) LRWORK = MIN( LWMAX, INT( RWORK( 1 ) ) ) LIWORK = MIN( LWMAX, IWORK( 1 ) ) * * Solve eigenproblem. * CALL CHEEVR( 'Vectors', 'Values', 'Lower', N, A, LDA, VL, VU, IL,$             IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, RWORK,
$LRWORK, IWORK, LIWORK, INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm failed to compute eigenvalues.' STOP END IF * * Print the number of eigenvalues found. * WRITE(*,'(/A,I2)')' The total number of eigenvalues found:', M * * Print eigenvalues. * CALL PRINT_RMATRIX( 'Selected eigenvalues', 1, M, W, 1 ) * * Print eigenvectors. * CALL PRINT_MATRIX( 'Selected eigenvectors (stored columnwise)',$                   N, M, Z, LDZ )
STOP
END
*
*     End of CHEEVR Example.
*
*  =============================================================================
*
*     Auxiliary routine: printing a matrix.
*
SUBROUTINE PRINT_MATRIX( DESC, M, N, A, LDA )
CHARACTER*(*)    DESC
INTEGER          M, N, LDA
COMPLEX          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,',',F6.2,')') )
RETURN
END
*
*     Auxiliary routine: printing a real matrix.
*
SUBROUTINE PRINT_RMATRIX( 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