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  • 12/20/2021
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DGEEV Example Program in Fortran

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Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ============================================================================= * * DGEEV Example. * ============== * * Program computes the eigenvalues and left and right eigenvectors of a general * rectangular matrix A: * * -1.01 0.86 -4.60 3.31 -4.81 * 3.98 0.53 -7.04 5.29 3.55 * 3.30 8.26 -3.89 8.20 -1.51 * 4.43 4.96 -7.66 -7.33 6.18 * 7.31 -6.43 -6.16 2.47 5.58 * * Description. * ============ * * The routine computes for an n-by-n real 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. * ======================== * * DGEEV Example Program Results * * Eigenvalues * ( 2.86, 10.76) ( 2.86,-10.76) ( -0.69, 4.70) ( -0.69, -4.70) -10.46 * * Left eigenvectors * ( 0.04, 0.29) ( 0.04, -0.29) ( -0.13, -0.33) ( -0.13, 0.33) 0.04 * ( 0.62, 0.00) ( 0.62, 0.00) ( 0.69, 0.00) ( 0.69, 0.00) 0.56 * ( -0.04, -0.58) ( -0.04, 0.58) ( -0.39, -0.07) ( -0.39, 0.07) -0.13 * ( 0.28, 0.01) ( 0.28, -0.01) ( -0.02, -0.19) ( -0.02, 0.19) -0.80 * ( -0.04, 0.34) ( -0.04, -0.34) ( -0.40, 0.22) ( -0.40, -0.22) 0.18 * * Right eigenvectors * ( 0.11, 0.17) ( 0.11, -0.17) ( 0.73, 0.00) ( 0.73, 0.00) 0.46 * ( 0.41, -0.26) ( 0.41, 0.26) ( -0.03, -0.02) ( -0.03, 0.02) 0.34 * ( 0.10, -0.51) ( 0.10, 0.51) ( 0.19, -0.29) ( 0.19, 0.29) 0.31 * ( 0.40, -0.09) ( 0.40, 0.09) ( -0.08, -0.08) ( -0.08, 0.08) -0.74 * ( 0.54, 0.00) ( 0.54, 0.00) ( -0.29, -0.49) ( -0.29, 0.49) 0.16 * ============================================================================= * * .. Parameters .. INTEGER N PARAMETER ( N = 5 ) INTEGER LDA, LDVL, LDVR PARAMETER ( LDA = N, LDVL = N, LDVR = N ) INTEGER LWMAX PARAMETER ( LWMAX = 1000 ) * * .. Local Scalars .. INTEGER INFO, LWORK * * .. Local Arrays .. DOUBLE PRECISION A( LDA, N ), VL( LDVL, N ), VR( LDVR, N ), $ WR( N ), WI( N ), WORK( LWMAX ) DATA A/ $ -1.01, 3.98, 3.30, 4.43, 7.31, $ 0.86, 0.53, 8.26, 4.96,-6.43, $ -4.60,-7.04,-3.89,-7.66,-6.16, $ 3.31, 5.29, 8.20,-7.33, 2.47, $ -4.81, 3.55,-1.51, 6.18, 5.58 $ / * * .. External Subroutines .. EXTERNAL DGEEV EXTERNAL PRINT_EIGENVALUES, PRINT_EIGENVECTORS * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'DGEEV Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL DGEEV( 'Vectors', 'Vectors', N, A, LDA, WR, WI, VL, LDVL, $ VR, LDVR, WORK, LWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Solve eigenproblem. * CALL DGEEV( 'Vectors', 'Vectors', N, A, LDA, WR, WI, VL, LDVL, $ VR, LDVR, WORK, LWORK, INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm failed to compute eigenvalues.' STOP END IF * * Print eigenvalues. * CALL PRINT_EIGENVALUES( 'Eigenvalues', N, WR, WI ) * * Print left eigenvectors. * CALL PRINT_EIGENVECTORS( 'Left eigenvectors', N, WI, VL, LDVL ) * * Print right eigenvectors. * CALL PRINT_EIGENVECTORS( 'Right eigenvectors', N, WI, VR, LDVR ) STOP END * * End of DGEEV Example. * * ============================================================================= * * Auxiliary routine: printing eigenvalues. * SUBROUTINE PRINT_EIGENVALUES( DESC, N, WR, WI ) CHARACTER*(*) DESC INTEGER N DOUBLE PRECISION WR( * ), WI( * ) * DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0 ) INTEGER J * WRITE(*,*) WRITE(*,*) DESC DO J = 1, N IF( WI( J ).EQ.ZERO ) THEN WRITE(*,9998,ADVANCE='NO') WR( J ) ELSE WRITE(*,9999,ADVANCE='NO') WR( J ), WI( J ) END IF END DO WRITE(*,*) * 9998 FORMAT( 11(:,1X,F6.2) ) 9999 FORMAT( 11(:,1X,'(',F6.2,',',F6.2,')') ) RETURN END * * Auxiliary routine: printing eigenvectors. * SUBROUTINE PRINT_EIGENVECTORS( DESC, N, WI, V, LDV ) CHARACTER*(*) DESC INTEGER N, LDV DOUBLE PRECISION WI( * ), V( LDV, * ) * DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0 ) INTEGER I, J * WRITE(*,*) WRITE(*,*) DESC DO I = 1, N J = 1 DO WHILE( J.LE.N ) IF( WI( J ).EQ.ZERO ) THEN WRITE(*,9998,ADVANCE='NO') V( I, J ) J = J + 1 ELSE WRITE(*,9999,ADVANCE='NO') V( I, J ), V( I, J+1 ) WRITE(*,9999,ADVANCE='NO') V( I, J ), -V( I, J+1 ) J = J + 2 END IF END DO WRITE(*,*) END DO * 9998 FORMAT( 11(:,1X,F6.2) ) 9999 FORMAT( 11(:,1X,'(',F6.2,',',F6.2,')') ) RETURN END

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