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  • 12/20/2021
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ZGEEV 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. * ============================================================================= * * ZGEEV Example. * ============== * * Program computes the eigenvalues and left and right eigenvectors of a general * rectangular matrix A: * * ( -3.84, 2.25) ( -8.94, -4.75) ( 8.95, -6.53) ( -9.87, 4.82) * ( -0.66, 0.83) ( -4.40, -3.82) ( -3.50, -4.26) ( -3.15, 7.36) * ( -3.99, -4.73) ( -5.88, -6.60) ( -3.36, -0.40) ( -0.75, 5.23) * ( 7.74, 4.18) ( 3.66, -7.53) ( 2.58, 3.60) ( 4.59, 5.41) * * Description. * ============ * * The routine computes for an n-by-n complex nonsymmetric matrix A, the * eigenvalues and, optionally, the left and/or right eigenvectors. The right * eigenvector v(j) of A satisfies * * A*v(j)= lambda(j)*v(j) * * where lambda(j) is its eigenvalue. The left eigenvector u(j) of A satisfies * * u(j)H*A = lambda(j)*u(j)H * * where u(j)H denotes the conjugate transpose of u(j). The computed * eigenvectors are normalized to have Euclidean norm equal to 1 and * largest component real. * * Example Program Results. * ======================== * * ZGEEV Example Program Results * * Eigenvalues * ( -9.43,-12.98) ( -3.44, 12.69) ( 0.11, -3.40) ( 5.76, 7.13) * * Left eigenvectors * ( 0.24, -0.18) ( 0.61, 0.00) ( -0.18, -0.33) ( 0.28, 0.09) * ( 0.79, 0.00) ( -0.05, -0.27) ( 0.82, 0.00) ( -0.55, 0.16) * ( 0.22, -0.27) ( -0.21, 0.53) ( -0.37, 0.15) ( 0.45, 0.09) * ( -0.02, 0.41) ( 0.40, -0.24) ( 0.06, 0.12) ( 0.62, 0.00) * * Right eigenvectors * ( 0.43, 0.33) ( 0.83, 0.00) ( 0.60, 0.00) ( -0.31, 0.03) * ( 0.51, -0.03) ( 0.08, -0.25) ( -0.40, -0.20) ( 0.04, 0.34) * ( 0.62, 0.00) ( -0.25, 0.28) ( -0.09, -0.48) ( 0.36, 0.06) * ( -0.23, 0.11) ( -0.10, -0.32) ( -0.43, 0.13) ( 0.81, 0.00) * ============================================================================= * * .. Parameters .. INTEGER N PARAMETER ( N = 4 ) INTEGER LDA, LDVL, LDVR PARAMETER ( LDA = N, LDVL = N, LDVR = N ) INTEGER LWMAX PARAMETER ( LWMAX = 1000 ) * * .. Local Scalars .. INTEGER INFO, LWORK * * .. Local Arrays .. * RWORK dimension should be at least 2*N DOUBLE PRECISION RWORK( 2*N ) COMPLEX*16 A( LDA, N ), VL( LDVL, N ), VR( LDVR, N ), $ W( N ), WORK( LWMAX ) DATA A/ $ (-3.84, 2.25),(-0.66, 0.83),(-3.99,-4.73),( 7.74, 4.18), $ (-8.94,-4.75),(-4.40,-3.82),(-5.88,-6.60),( 3.66,-7.53), $ ( 8.95,-6.53),(-3.50,-4.26),(-3.36,-0.40),( 2.58, 3.60), $ (-9.87, 4.82),(-3.15, 7.36),(-0.75, 5.23),( 4.59, 5.41) $ / * * .. External Subroutines .. EXTERNAL ZGEEV EXTERNAL PRINT_MATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'ZGEEV Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL ZGEEV( 'Vectors', 'Vectors', N, A, LDA, W, VL, LDVL, $ VR, LDVR, WORK, LWORK, RWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Solve eigenproblem. * CALL ZGEEV( 'Vectors', 'Vectors', N, A, LDA, W, VL, LDVL, $ VR, LDVR, WORK, LWORK, RWORK, INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm failed to compute eigenvalues.' STOP END IF * * Print eigenvalues. * CALL PRINT_MATRIX( 'Eigenvalues', 1, N, W, 1 ) * * Print left eigenvectors. * CALL PRINT_MATRIX( 'Left eigenvectors', N, N, VL, LDVL ) * * Print right eigenvectors. * CALL PRINT_MATRIX( 'Right eigenvectors', N, N, VR, LDVR ) STOP END * * End of ZGEEV 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

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