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Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 3/31/2023
Public

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ZHEEVX Example Program in Fortran

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*  =============================================================================
*
*  ZHEEVX Example.
*  ==============
*
*  Program computes eigenvalues specified by a selected range of values
*  and corresponding eigenvectors of a complex Hermitian matrix A:
*
*  (  6.51,  0.00) ( -5.92,  9.53) ( -2.46,  2.91) (  8.84,  3.21)
*  ( -5.92, -9.53) ( -1.73,  0.00) (  6.50,  2.09) (  1.32,  8.81)
*  ( -2.46, -2.91) (  6.50, -2.09) (  6.90,  0.00) ( -0.59,  2.47)
*  (  8.84, -3.21) (  1.32, -8.81) ( -0.59, -2.47) ( -2.85,  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.
*  ========================
*
* ZHEEVX Example Program Results
*
* The total number of eigenvalues found: 3
*
* Selected eigenvalues
*   0.09   9.53  18.75
*
* Selected eigenvectors (stored columnwise)
* (  0.18,  0.00) ( -0.54,  0.00) (  0.67,  0.00)
* ( -0.40, -0.31) ( -0.21, -0.17) ( -0.30, -0.43)
* (  0.60,  0.40) ( -0.35, -0.28) ( -0.39, -0.34)
* ( -0.34,  0.26) ( -0.57,  0.35) (  0.05,  0.05)
*  =============================================================================
*
*     .. Parameters ..
INTEGER          N
PARAMETER        ( N = 4 )
INTEGER          LDA, LDZ
PARAMETER        ( LDA = N, LDZ = N )
INTEGER          LWMAX
PARAMETER        ( LWMAX = 1000 )
*
*     .. Local Scalars ..
INTEGER          INFO, LWORK, IL, IU, M
DOUBLE PRECISION ABSTOL, VL, VU
*
*     .. Local Arrays ..
*     IWORK dimension should be at least 5*N
INTEGER          IWORK( 5*N ), IFAIL( N )
*     RWORK dimension should be at least 7*N
DOUBLE PRECISION W( N ), RWORK( 7*N )
COMPLEX*16       A( LDA, N ), Z( LDZ, N ), WORK( LWMAX )
DATA             A/
$( 6.51, 0.00),(-5.92,-9.53),(-2.46,-2.91),( 8.84,-3.21),$ ( 0.00, 0.00),(-1.73, 0.00),( 6.50,-2.09),( 1.32,-8.81),
$( 0.00, 0.00),( 0.00, 0.00),( 6.90, 0.00),(-0.59,-2.47),$ ( 0.00, 0.00),( 0.00, 0.00),( 0.00, 0.00),(-2.85, 0.00)
$/ * * .. External Subroutines .. EXTERNAL ZHEEVX EXTERNAL PRINT_MATRIX, PRINT_RMATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'ZHEEVX Example Program Results' * Negative ABSTOL means using the default value ABSTOL = -1.0 * Set VL, VU to compute eigenvalues in half-open (VL,VU] interval VL = 0.0 VU = 100.0 * * Query the optimal workspace. * LWORK = -1 CALL ZHEEVX( 'Vectors', 'Values', 'Lower', N, A, LDA, VL, VU, IL,$             IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK,
$IFAIL, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Solve eigenproblem. * CALL ZHEEVX( 'Vectors', 'Values', 'Lower', N, A, LDA, VL, VU, IL,$             IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK,
$IFAIL, INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm failed to compute eigenvalues.' STOP END IF * * Print the number of eigenvalues found. * WRITE(*,'(/A,I2)')' The total number of eigenvalues found:', M * * Print eigenvalues. * CALL PRINT_RMATRIX( 'Selected eigenvalues', 1, M, W, 1 ) * * Print eigenvectors. * CALL PRINT_MATRIX( 'Selected eigenvectors (stored columnwise)',$                   N, M, Z, LDZ )
STOP
END
*
*     End of ZHEEVX Example.
*
*  =============================================================================
*
*     Auxiliary routine: printing a matrix.
*
SUBROUTINE PRINT_MATRIX( DESC, M, N, A, LDA )
CHARACTER*(*)    DESC
INTEGER          M, N, LDA
COMPLEX*16       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
DOUBLE PRECISION 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