--- 
:name: dgegv
:md5sum: 155f15d8861adb20fd687c0f414a941d
:category: :subroutine
:arguments: 
- jobvl: 
    :type: char
    :intent: input
- jobvr: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- a: 
    :type: doublereal
    :intent: input/output
    :dims: 
    - lda
    - n
- lda: 
    :type: integer
    :intent: input
- b: 
    :type: doublereal
    :intent: input/output
    :dims: 
    - ldb
    - n
- ldb: 
    :type: integer
    :intent: input
- alphar: 
    :type: doublereal
    :intent: output
    :dims: 
    - n
- alphai: 
    :type: doublereal
    :intent: output
    :dims: 
    - n
- beta: 
    :type: doublereal
    :intent: output
    :dims: 
    - n
- vl: 
    :type: doublereal
    :intent: output
    :dims: 
    - ldvl
    - n
- ldvl: 
    :type: integer
    :intent: input
- vr: 
    :type: doublereal
    :intent: output
    :dims: 
    - ldvr
    - n
- ldvr: 
    :type: integer
    :intent: input
- work: 
    :type: doublereal
    :intent: output
    :dims: 
    - MAX(1,lwork)
- lwork: 
    :type: integer
    :intent: input
    :option: true
    :default: 8*n
- info: 
    :type: integer
    :intent: output
:substitutions: 
  ldvr: "lsame_(&jobvr,\"V\") ? n : 1"
  ldvl: "lsame_(&jobvl,\"V\") ? n : 1"
:fortran_help: "      SUBROUTINE DGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  This routine is deprecated and has been replaced by routine DGGEV.\n\
  *\n\
  *  DGEGV computes the eigenvalues and, optionally, the left and/or right\n\
  *  eigenvectors of a real matrix pair (A,B).\n\
  *  Given two square matrices A and B,\n\
  *  the generalized nonsymmetric eigenvalue problem (GNEP) is to find the\n\
  *  eigenvalues lambda and corresponding (non-zero) eigenvectors x such\n\
  *  that\n\
  *\n\
  *     A*x = lambda*B*x.\n\
  *\n\
  *  An alternate form is to find the eigenvalues mu and corresponding\n\
  *  eigenvectors y such that\n\
  *\n\
  *     mu*A*y = B*y.\n\
  *\n\
  *  These two forms are equivalent with mu = 1/lambda and x = y if\n\
  *  neither lambda nor mu is zero.  In order to deal with the case that\n\
  *  lambda or mu is zero or small, two values alpha and beta are returned\n\
  *  for each eigenvalue, such that lambda = alpha/beta and\n\
  *  mu = beta/alpha.\n\
  *\n\
  *  The vectors x and y in the above equations are right eigenvectors of\n\
  *  the matrix pair (A,B).  Vectors u and v satisfying\n\
  *\n\
  *     u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B\n\
  *\n\
  *  are left eigenvectors of (A,B).\n\
  *\n\
  *  Note: this routine performs \"full balancing\" on A and B -- see\n\
  *  \"Further Details\", below.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  JOBVL   (input) CHARACTER*1\n\
  *          = 'N':  do not compute the left generalized eigenvectors;\n\
  *          = 'V':  compute the left generalized eigenvectors (returned\n\
  *                  in VL).\n\
  *\n\
  *  JOBVR   (input) CHARACTER*1\n\
  *          = 'N':  do not compute the right generalized eigenvectors;\n\
  *          = 'V':  compute the right generalized eigenvectors (returned\n\
  *                  in VR).\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrices A, B, VL, and VR.  N >= 0.\n\
  *\n\
  *  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)\n\
  *          On entry, the matrix A.\n\
  *          If JOBVL = 'V' or JOBVR = 'V', then on exit A\n\
  *          contains the real Schur form of A from the generalized Schur\n\
  *          factorization of the pair (A,B) after balancing.\n\
  *          If no eigenvectors were computed, then only the diagonal\n\
  *          blocks from the Schur form will be correct.  See DGGHRD and\n\
  *          DHGEQZ for details.\n\
  *\n\
  *  LDA     (input) INTEGER\n\
  *          The leading dimension of A.  LDA >= max(1,N).\n\
  *\n\
  *  B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)\n\
  *          On entry, the matrix B.\n\
  *          If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the\n\
  *          upper triangular matrix obtained from B in the generalized\n\
  *          Schur factorization of the pair (A,B) after balancing.\n\
  *          If no eigenvectors were computed, then only those elements of\n\
  *          B corresponding to the diagonal blocks from the Schur form of\n\
  *          A will be correct.  See DGGHRD and DHGEQZ for details.\n\
  *\n\
  *  LDB     (input) INTEGER\n\
  *          The leading dimension of B.  LDB >= max(1,N).\n\
  *\n\
  *  ALPHAR  (output) DOUBLE PRECISION array, dimension (N)\n\
  *          The real parts of each scalar alpha defining an eigenvalue of\n\
  *          GNEP.\n\
  *\n\
  *  ALPHAI  (output) DOUBLE PRECISION array, dimension (N)\n\
  *          The imaginary parts of each scalar alpha defining an\n\
  *          eigenvalue of GNEP.  If ALPHAI(j) is zero, then the j-th\n\
  *          eigenvalue is real; if positive, then the j-th and\n\
  *          (j+1)-st eigenvalues are a complex conjugate pair, with\n\
  *          ALPHAI(j+1) = -ALPHAI(j).\n\
  *\n\
  *  BETA    (output) DOUBLE PRECISION array, dimension (N)\n\
  *          The scalars beta that define the eigenvalues of GNEP.\n\
  *          \n\
  *          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and\n\
  *          beta = BETA(j) represent the j-th eigenvalue of the matrix\n\
  *          pair (A,B), in one of the forms lambda = alpha/beta or\n\
  *          mu = beta/alpha.  Since either lambda or mu may overflow,\n\
  *          they should not, in general, be computed.\n\
  *\n\
  *  VL      (output) DOUBLE PRECISION array, dimension (LDVL,N)\n\
  *          If JOBVL = 'V', the left eigenvectors u(j) are stored\n\
  *          in the columns of VL, in the same order as their eigenvalues.\n\
  *          If the j-th eigenvalue is real, then u(j) = VL(:,j).\n\
  *          If the j-th and (j+1)-st eigenvalues form a complex conjugate\n\
  *          pair, then\n\
  *             u(j) = VL(:,j) + i*VL(:,j+1)\n\
  *          and\n\
  *            u(j+1) = VL(:,j) - i*VL(:,j+1).\n\
  *\n\
  *          Each eigenvector is scaled so that its largest component has\n\
  *          abs(real part) + abs(imag. part) = 1, except for eigenvectors\n\
  *          corresponding to an eigenvalue with alpha = beta = 0, which\n\
  *          are set to zero.\n\
  *          Not referenced if JOBVL = 'N'.\n\
  *\n\
  *  LDVL    (input) INTEGER\n\
  *          The leading dimension of the matrix VL. LDVL >= 1, and\n\
  *          if JOBVL = 'V', LDVL >= N.\n\
  *\n\
  *  VR      (output) DOUBLE PRECISION array, dimension (LDVR,N)\n\
  *          If JOBVR = 'V', the right eigenvectors x(j) are stored\n\
  *          in the columns of VR, in the same order as their eigenvalues.\n\
  *          If the j-th eigenvalue is real, then x(j) = VR(:,j).\n\
  *          If the j-th and (j+1)-st eigenvalues form a complex conjugate\n\
  *          pair, then\n\
  *            x(j) = VR(:,j) + i*VR(:,j+1)\n\
  *          and\n\
  *            x(j+1) = VR(:,j) - i*VR(:,j+1).\n\
  *\n\
  *          Each eigenvector is scaled so that its largest component has\n\
  *          abs(real part) + abs(imag. part) = 1, except for eigenvalues\n\
  *          corresponding to an eigenvalue with alpha = beta = 0, which\n\
  *          are set to zero.\n\
  *          Not referenced if JOBVR = 'N'.\n\
  *\n\
  *  LDVR    (input) INTEGER\n\
  *          The leading dimension of the matrix VR. LDVR >= 1, and\n\
  *          if JOBVR = 'V', LDVR >= N.\n\
  *\n\
  *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))\n\
  *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
  *\n\
  *  LWORK   (input) INTEGER\n\
  *          The dimension of the array WORK.  LWORK >= max(1,8*N).\n\
  *          For good performance, LWORK must generally be larger.\n\
  *          To compute the optimal value of LWORK, call ILAENV to get\n\
  *          blocksizes (for DGEQRF, DORMQR, and DORGQR.)  Then compute:\n\
  *          NB  -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR;\n\
  *          The optimal LWORK is:\n\
  *              2*N + MAX( 6*N, N*(NB+1) ).\n\
  *\n\
  *          If LWORK = -1, then a workspace query is assumed; the routine\n\
  *          only calculates the optimal size of the WORK array, returns\n\
  *          this value as the first entry of the WORK array, and no error\n\
  *          message related to LWORK is issued by XERBLA.\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *          = 0:  successful exit\n\
  *          < 0:  if INFO = -i, the i-th argument had an illegal value.\n\
  *          = 1,...,N:\n\
  *                The QZ iteration failed.  No eigenvectors have been\n\
  *                calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)\n\
  *                should be correct for j=INFO+1,...,N.\n\
  *          > N:  errors that usually indicate LAPACK problems:\n\
  *                =N+1: error return from DGGBAL\n\
  *                =N+2: error return from DGEQRF\n\
  *                =N+3: error return from DORMQR\n\
  *                =N+4: error return from DORGQR\n\
  *                =N+5: error return from DGGHRD\n\
  *                =N+6: error return from DHGEQZ (other than failed\n\
  *                                                iteration)\n\
  *                =N+7: error return from DTGEVC\n\
  *                =N+8: error return from DGGBAK (computing VL)\n\
  *                =N+9: error return from DGGBAK (computing VR)\n\
  *                =N+10: error return from DLASCL (various calls)\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  Balancing\n\
  *  ---------\n\
  *\n\
  *  This driver calls DGGBAL to both permute and scale rows and columns\n\
  *  of A and B.  The permutations PL and PR are chosen so that PL*A*PR\n\
  *  and PL*B*R will be upper triangular except for the diagonal blocks\n\
  *  A(i:j,i:j) and B(i:j,i:j), with i and j as close together as\n\
  *  possible.  The diagonal scaling matrices DL and DR are chosen so\n\
  *  that the pair  DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to\n\
  *  one (except for the elements that start out zero.)\n\
  *\n\
  *  After the eigenvalues and eigenvectors of the balanced matrices\n\
  *  have been computed, DGGBAK transforms the eigenvectors back to what\n\
  *  they would have been (in perfect arithmetic) if they had not been\n\
  *  balanced.\n\
  *\n\
  *  Contents of A and B on Exit\n\
  *  -------- -- - --- - -- ----\n\
  *\n\
  *  If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or\n\
  *  both), then on exit the arrays A and B will contain the real Schur\n\
  *  form[*] of the \"balanced\" versions of A and B.  If no eigenvectors\n\
  *  are computed, then only the diagonal blocks will be correct.\n\
  *\n\
  *  [*] See DHGEQZ, DGEGS, or read the book \"Matrix Computations\",\n\
  *      by Golub & van Loan, pub. by Johns Hopkins U. Press.\n\
  *\n\
  *  =====================================================================\n\
  *\n"