--- 
:name: sggev
:md5sum: c8f02404add51e664f048466e576c7d2
:category: :subroutine
:arguments: 
- jobvl: 
    :type: char
    :intent: input
- jobvr: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- a: 
    :type: real
    :intent: input/output
    :dims: 
    - lda
    - n
- lda: 
    :type: integer
    :intent: input
- b: 
    :type: real
    :intent: input/output
    :dims: 
    - ldb
    - n
- ldb: 
    :type: integer
    :intent: input
- alphar: 
    :type: real
    :intent: output
    :dims: 
    - n
- alphai: 
    :type: real
    :intent: output
    :dims: 
    - n
- beta: 
    :type: real
    :intent: output
    :dims: 
    - n
- vl: 
    :type: real
    :intent: output
    :dims: 
    - ldvl
    - n
- ldvl: 
    :type: integer
    :intent: input
- vr: 
    :type: real
    :intent: output
    :dims: 
    - ldvr
    - n
- ldvr: 
    :type: integer
    :intent: input
- work: 
    :type: real
    :intent: output
    :dims: 
    - MAX(1,lwork)
- lwork: 
    :type: integer
    :intent: input
    :option: true
    :default: MAX(1,8*n)
- info: 
    :type: integer
    :intent: output
:substitutions: 
  ldvr: "lsame_(&jobvr,\"V\") ? n : 1"
  ldvl: "lsame_(&jobvl,\"V\") ? n : 1"
:fortran_help: "      SUBROUTINE SGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  SGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)\n\
  *  the generalized eigenvalues, and optionally, the left and/or right\n\
  *  generalized eigenvectors.\n\
  *\n\
  *  A generalized eigenvalue for a pair of matrices (A,B) is a scalar\n\
  *  lambda or a ratio alpha/beta = lambda, such that A - lambda*B is\n\
  *  singular. It is usually represented as the pair (alpha,beta), as\n\
  *  there is a reasonable interpretation for beta=0, and even for both\n\
  *  being zero.\n\
  *\n\
  *  The right eigenvector v(j) corresponding to the eigenvalue lambda(j)\n\
  *  of (A,B) satisfies\n\
  *\n\
  *                   A * v(j) = lambda(j) * B * v(j).\n\
  *\n\
  *  The left eigenvector u(j) corresponding to the eigenvalue lambda(j)\n\
  *  of (A,B) satisfies\n\
  *\n\
  *                   u(j)**H * A  = lambda(j) * u(j)**H * B .\n\
  *\n\
  *  where u(j)**H is the conjugate-transpose of u(j).\n\
  *\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.\n\
  *\n\
  *  JOBVR   (input) CHARACTER*1\n\
  *          = 'N':  do not compute the right generalized eigenvectors;\n\
  *          = 'V':  compute the right generalized eigenvectors.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrices A, B, VL, and VR.  N >= 0.\n\
  *\n\
  *  A       (input/output) REAL array, dimension (LDA, N)\n\
  *          On entry, the matrix A in the pair (A,B).\n\
  *          On exit, A has been overwritten.\n\
  *\n\
  *  LDA     (input) INTEGER\n\
  *          The leading dimension of A.  LDA >= max(1,N).\n\
  *\n\
  *  B       (input/output) REAL array, dimension (LDB, N)\n\
  *          On entry, the matrix B in the pair (A,B).\n\
  *          On exit, B has been overwritten.\n\
  *\n\
  *  LDB     (input) INTEGER\n\
  *          The leading dimension of B.  LDB >= max(1,N).\n\
  *\n\
  *  ALPHAR  (output) REAL array, dimension (N)\n\
  *  ALPHAI  (output) REAL array, dimension (N)\n\
  *  BETA    (output) REAL array, dimension (N)\n\
  *          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will\n\
  *          be the generalized eigenvalues.  If ALPHAI(j) is zero, then\n\
  *          the j-th 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) negative.\n\
  *\n\
  *          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)\n\
  *          may easily over- or underflow, and BETA(j) may even be zero.\n\
  *          Thus, the user should avoid naively computing the ratio\n\
  *          alpha/beta.  However, ALPHAR and ALPHAI will be always less\n\
  *          than and usually comparable with norm(A) in magnitude, and\n\
  *          BETA always less than and usually comparable with norm(B).\n\
  *\n\
  *  VL      (output) REAL array, dimension (LDVL,N)\n\
  *          If JOBVL = 'V', the left eigenvectors u(j) are stored one\n\
  *          after another in the columns of VL, in the same order as\n\
  *          their eigenvalues. If the j-th eigenvalue is real, then\n\
  *          u(j) = VL(:,j), the j-th column of VL. If the j-th and\n\
  *          (j+1)-th eigenvalues form a complex conjugate pair, then\n\
  *          u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).\n\
  *          Each eigenvector is scaled so the largest component has\n\
  *          abs(real part)+abs(imag. part)=1.\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) REAL array, dimension (LDVR,N)\n\
  *          If JOBVR = 'V', the right eigenvectors v(j) are stored one\n\
  *          after another in the columns of VR, in the same order as\n\
  *          their eigenvalues. If the j-th eigenvalue is real, then\n\
  *          v(j) = VR(:,j), the j-th column of VR. If the j-th and\n\
  *          (j+1)-th eigenvalues form a complex conjugate pair, then\n\
  *          v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).\n\
  *          Each eigenvector is scaled so the largest component has\n\
  *          abs(real part)+abs(imag. part)=1.\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) REAL 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\
  *\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:  =N+1: other than QZ iteration failed in SHGEQZ.\n\
  *                =N+2: error return from STGEVC.\n\
  *\n\n\
  *  =====================================================================\n\
  *\n"
