dggev.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 490 行 · 第 1/2 页

      SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
     $                  BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
*
*  -- LAPACK driver routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          JOBVL, JOBVR
      INTEGER            INFO, LDA, LDB, LDVL, LDVR, LWORK, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
     $                   B( LDB, * ), BETA( * ), VL( LDVL, * ),
     $                   VR( LDVR, * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
*  the generalized eigenvalues, and optionally, the left and/or right
*  generalized eigenvectors.
*
*  A generalized eigenvalue for a pair of matrices (A,B) is a scalar
*  lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
*  singular. It is usually represented as the pair (alpha,beta), as
*  there is a reasonable interpretation for beta=0, and even for both
*  being zero.
*
*  The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
*  of (A,B) satisfies
*
*                   A * v(j) = lambda(j) * B * v(j).
*
*  The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
*  of (A,B) satisfies
*
*                   u(j)**H * A  = lambda(j) * u(j)**H * B .
*
*  where u(j)**H is the conjugate-transpose of u(j).
*
*
*  Arguments
*  =========
*
*  JOBVL   (input) CHARACTER*1
*          = 'N':  do not compute the left generalized eigenvectors;
*          = 'V':  compute the left generalized eigenvectors.
*
*  JOBVR   (input) CHARACTER*1
*          = 'N':  do not compute the right generalized eigenvectors;
*          = 'V':  compute the right generalized eigenvectors.
*
*  N       (input) INTEGER
*          The order of the matrices A, B, VL, and VR.  N >= 0.
*
*  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
*          On entry, the matrix A in the pair (A,B).
*          On exit, A has been overwritten.
*
*  LDA     (input) INTEGER
*          The leading dimension of A.  LDA >= max(1,N).
*
*  B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)
*          On entry, the matrix B in the pair (A,B).
*          On exit, B has been overwritten.
*
*  LDB     (input) INTEGER
*          The leading dimension of B.  LDB >= max(1,N).
*
*  ALPHAR  (output) DOUBLE PRECISION array, dimension (N)
*  ALPHAI  (output) DOUBLE PRECISION array, dimension (N)
*  BETA    (output) DOUBLE PRECISION array, dimension (N)
*          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
*          be the generalized eigenvalues.  If ALPHAI(j) is zero, then
*          the j-th eigenvalue is real; if positive, then the j-th and
*          (j+1)-st eigenvalues are a complex conjugate pair, with
*          ALPHAI(j+1) negative.
*
*          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
*          may easily over- or underflow, and BETA(j) may even be zero.
*          Thus, the user should avoid naively computing the ratio
*          alpha/beta.  However, ALPHAR and ALPHAI will be always less
*          than and usually comparable with norm(A) in magnitude, and
*          BETA always less than and usually comparable with norm(B).
*
*  VL      (output) DOUBLE PRECISION array, dimension (LDVL,N)
*          If JOBVL = 'V', the left eigenvectors u(j) are stored one
*          after another in the columns of VL, in the same order as
*          their eigenvalues. If the j-th eigenvalue is real, then
*          u(j) = VL(:,j), the j-th column of VL. If the j-th and
*          (j+1)-th eigenvalues form a complex conjugate pair, then
*          u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).
*          Each eigenvector is scaled so the largest component has
*          abs(real part)+abs(imag. part)=1.
*          Not referenced if JOBVL = 'N'.
*
*  LDVL    (input) INTEGER
*          The leading dimension of the matrix VL. LDVL >= 1, and
*          if JOBVL = 'V', LDVL >= N.
*
*  VR      (output) DOUBLE PRECISION array, dimension (LDVR,N)
*          If JOBVR = 'V', the right eigenvectors v(j) are stored one
*          after another in the columns of VR, in the same order as
*          their eigenvalues. If the j-th eigenvalue is real, then
*          v(j) = VR(:,j), the j-th column of VR. If the j-th and
*          (j+1)-th eigenvalues form a complex conjugate pair, then
*          v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).
*          Each eigenvector is scaled so the largest component has
*          abs(real part)+abs(imag. part)=1.
*          Not referenced if JOBVR = 'N'.
*
*  LDVR    (input) INTEGER
*          The leading dimension of the matrix VR. LDVR >= 1, and
*          if JOBVR = 'V', LDVR >= N.
*
*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.  LWORK >= max(1,8*N).
*          For good performance, LWORK must generally be larger.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value.
*          = 1,...,N:
*                The QZ iteration failed.  No eigenvectors have been
*                calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
*                should be correct for j=INFO+1,...,N.
*          > N:  =N+1: other than QZ iteration failed in DHGEQZ.
*                =N+2: error return from DTGEVC.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY
      CHARACTER          CHTEMP
      INTEGER            ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO,
     $                   IN, IRIGHT, IROWS, ITAU, IWRK, JC, JR, MAXWRK,
     $                   MINWRK
      DOUBLE PRECISION   ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
     $                   SMLNUM, TEMP
*     ..
*     .. Local Arrays ..
      LOGICAL            LDUMMA( 1 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLABAD,
     $                   DLACPY,DLASCL, DLASET, DORGQR, DORMQR, DTGEVC,
     $                   XERBLA
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      DOUBLE PRECISION   DLAMCH, DLANGE
      EXTERNAL           LSAME, ILAENV, DLAMCH, DLANGE
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, MAX, SQRT
*     ..
*     .. Executable Statements ..
*
*     Decode the input arguments
*
      IF( LSAME( JOBVL, 'N' ) ) THEN
         IJOBVL = 1
         ILVL = .FALSE.
      ELSE IF( LSAME( JOBVL, 'V' ) ) THEN
         IJOBVL = 2
         ILVL = .TRUE.
      ELSE
         IJOBVL = -1
         ILVL = .FALSE.
      END IF
*
      IF( LSAME( JOBVR, 'N' ) ) THEN
         IJOBVR = 1
         ILVR = .FALSE.
      ELSE IF( LSAME( JOBVR, 'V' ) ) THEN
         IJOBVR = 2
         ILVR = .TRUE.
      ELSE
         IJOBVR = -1
         ILVR = .FALSE.
      END IF
      ILV = ILVL .OR. ILVR
*
*     Test the input arguments
*
      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      IF( IJOBVL.LE.0 ) THEN
         INFO = -1
      ELSE IF( IJOBVR.LE.0 ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -7
      ELSE IF( LDVL.LT.1 .OR. ( ILVL .AND. LDVL.LT.N ) ) THEN
         INFO = -12
      ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN
         INFO = -14
      END IF
*
*     Compute workspace
*      (Note: Comments in the code beginning "Workspace:" describe the
*       minimal amount of workspace needed at that point in the code,
*       as well as the preferred amount for good performance.
*       NB refers to the optimal block size for the immediately
*       following subroutine, as returned by ILAENV. The workspace is
*       computed assuming ILO = 1 and IHI = N, the worst case.)
*
      IF( INFO.EQ.0 ) THEN
         MINWRK = MAX( 1, 8*N )
         MAXWRK = MAX( 1, N*( 7 +
     $                 ILAENV( 1, 'DGEQRF', ' ', N, 1, N, 0 ) ) )
         MAXWRK = MAX( MAXWRK, N*( 7 +
     $                 ILAENV( 1, 'DORMQR', ' ', N, 1, N, 0 ) ) )
         IF( ILVL ) THEN
            MAXWRK = MAX( MAXWRK, N*( 7 +
     $                 ILAENV( 1, 'DORGQR', ' ', N, 1, N, -1 ) ) )
         END IF
         WORK( 1 ) = MAXWRK
*
         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
     $      INFO = -16
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DGGEV ', -INFO )
         RETURN