## Developer Reference

• 2022.1
• 12/20/2021
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# DGEEV 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
*  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.
*  =============================================================================
*
*  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
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
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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