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  • 2022.1
  • 12/20/2021
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ZHEEVD Example Program in Fortran

* Copyright (C) 2009-2015 Intel Corporation. All Rights Reserved. * The information and material ("Material") provided below is owned by Intel * Corporation or its suppliers or licensors, and title to such Material remains * with Intel Corporation or its suppliers or licensors. The Material contains * proprietary information of Intel or its suppliers and licensors. The Material * is protected by worldwide copyright laws and treaty provisions. No part of * the Material may be copied, reproduced, published, uploaded, posted, * transmitted, or distributed in any way without Intel's prior express written * permission. No license under any patent, copyright or other intellectual * property rights in the Material is granted to or conferred upon you, either * expressly, by implication, inducement, estoppel or otherwise. Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ============================================================================= * * ZHEEVD Example. * ============== * * Program computes all eigenvalues and eigenvectors of a complex Hermitian * matrix A using divide and conquer algorithm, where A is: * * ( 3.40, 0.00) ( -2.36, -1.93) ( -4.68, 9.55) ( 5.37, -1.23) * ( -2.36, 1.93) ( 6.94, 0.00) ( 8.13, -1.47) ( 2.07, -5.78) * ( -4.68, -9.55) ( 8.13, 1.47) ( -2.14, 0.00) ( 4.68, 7.44) * ( 5.37, 1.23) ( 2.07, 5.78) ( 4.68, -7.44) ( -7.42, 0.00) * * Description. * ============ * * The routine computes all 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. * If the eigenvectors are requested, then this routine uses a divide and * conquer algorithm to compute eigenvalues and eigenvectors. * * Example Program Results. * ======================== * * ZHEEVD Example Program Results * * Eigenvalues * -21.97 -0.05 6.46 16.34 * * Eigenvectors (stored columnwise) * ( 0.41, 0.00) ( -0.34, 0.00) ( -0.69, 0.00) ( 0.49, 0.00) * ( 0.02, -0.30) ( 0.32, -0.21) ( -0.57, -0.22) ( -0.59, -0.21) * ( 0.18, 0.57) ( -0.42, -0.32) ( 0.06, 0.16) ( -0.35, -0.47) * ( -0.62, -0.09) ( -0.58, 0.35) ( -0.15, -0.31) ( -0.10, -0.12) * ============================================================================= * * .. Parameters .. INTEGER N PARAMETER ( N = 4 ) INTEGER LDA PARAMETER ( LDA = N ) INTEGER LWMAX PARAMETER ( LWMAX = 1000 ) * * .. Local Scalars .. INTEGER INFO, LWORK, LIWORK, LRWORK * * .. Local Arrays .. INTEGER IWORK( LWMAX ) DOUBLE PRECISION W( N ), RWORK( LWMAX ) COMPLEX*16 A( LDA, N ), WORK( LWMAX ) DATA A/ $ ( 3.40, 0.00),(-2.36, 1.93),(-4.68,-9.55),( 5.37, 1.23), $ ( 0.00, 0.00),( 6.94, 0.00),( 8.13, 1.47),( 2.07, 5.78), $ ( 0.00, 0.00),( 0.00, 0.00),(-2.14, 0.00),( 4.68,-7.44), $ ( 0.00, 0.00),( 0.00, 0.00),( 0.00, 0.00),(-7.42, 0.00) $ / * * .. External Subroutines .. EXTERNAL ZHEEVD EXTERNAL PRINT_MATRIX, PRINT_RMATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'ZHEEVD Example Program Results' * * Query the optimal workspace. * LWORK = -1 LIWORK = -1 LRWORK = -1 CALL ZHEEVD( 'Vectors', 'Lower', N, A, LDA, W, 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 ZHEEVD( 'Vectors', 'Lower', N, A, LDA, W, 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 eigenvalues. * CALL PRINT_RMATRIX( 'Eigenvalues', 1, N, W, 1 ) * * Print eigenvectors. * CALL PRINT_MATRIX( 'Eigenvectors (stored columnwise)', N, N, A, $ LDA ) STOP END * * End of ZHEEVD 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

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