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Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
Public

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SSYEVR Example Program in Fortran

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*  =============================================================================
*
*  SSYEVR Example.
*  ==============
*
*  Program computes the smallest eigenvalues and the corresponding
*  eigenvectors of a real symmetric matrix A using the Relatively Robust
*  Representations, where A is:
*
*    0.67  -0.20   0.19  -1.06   0.46
*   -0.20   3.82  -0.13   1.06  -0.48
*    0.19  -0.13   3.27   0.11   1.10
*   -1.06   1.06   0.11   5.86  -0.98
*    0.46  -0.48   1.10  -0.98   3.54
*
*  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.
*  ========================
*
* SSYEVR Example Program Results
*
* The total number of eigenvalues found: 3
*
* Selected eigenvalues
*   0.43   2.14   3.37
*
* Selected eigenvectors (stored columnwise)
*  -0.98  -0.01  -0.08
*   0.01   0.02  -0.93
*   0.04  -0.69  -0.07
*  -0.18   0.19   0.31
*   0.07   0.69  -0.13
*  =============================================================================
*
*     .. 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, LIWORK, IL, IU, M
REAL             ABSTOL, VL, VU
*
*     .. Local Arrays ..
INTEGER          ISUPPZ( N ), IWORK( LWMAX )
REAL             A( LDA, N ), W( N ), Z( LDZ, NSELECT ),
$WORK( LWMAX ) DATA A/$  0.67, 0.00, 0.00, 0.00, 0.00,
$-0.20, 3.82, 0.00, 0.00, 0.00,$  0.19,-0.13, 3.27, 0.00, 0.00,
$-1.06, 1.06, 0.11, 5.86, 0.00,$  0.46,-0.48, 1.10,-0.98, 3.54
$/ * * .. External Subroutines .. EXTERNAL SSYEVR EXTERNAL PRINT_MATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'SSYEVR Example Program Results' * Negative ABSTOL means using the default value ABSTOL = -1.0 * Set IL, IU to compute NSELECT smallest eigenvalues IL = 1 IU = NSELECT * * Query the optimal workspace. * LWORK = -1 LIWORK = -1 CALL SSYEVR( 'Vectors', 'Indices', 'Upper', N, A, LDA, VL, VU, IL,$             IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
$LIWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) LIWORK = MIN( LWMAX, IWORK( 1 ) ) * * Solve eigenproblem. * CALL SSYEVR( 'Vectors', 'Indices', 'Upper', N, A, LDA, VL, VU, IL,$             IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
$LIWORK, INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm failed to compute eigenvalues.' STOP END IF * * Print the number of eigenvalues found. * WRITE(*,'(/A,I2)')' The total number of eigenvalues found:', M * * Print eigenvalues. * CALL PRINT_MATRIX( 'Selected eigenvalues', 1, M, W, 1 ) * * Print eigenvectors. * CALL PRINT_MATRIX( 'Selected eigenvectors (stored columnwise)',$                   N, M, Z, LDZ )
STOP
END
*
*     End of SSYEVR 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