# sgeev.f

          SUBROUTINE SGEEV (A, LDA, N, E, V, LDV, WORK, JOB, INFO)
    C***BEGIN PROLOGUE  SGEEV
    C***PURPOSE  Compute the eigenvalues and, optionally, the eigenvectors
    C            of a real general matrix.
    C***LIBRARY   SLATEC
    C***CATEGORY  D4A2
    C***TYPE      SINGLE PRECISION (SGEEV-S, CGEEV-C)
    C***KEYWORDS  EIGENVALUES, EIGENVECTORS, GENERAL MATRIX
    C***AUTHOR  Kahaner, D. K., (NBS)
    C           Moler, C. B., (U. of New Mexico)
    C           Stewart, G. W., (U. of Maryland)
    C***DESCRIPTION
    C
    C     Abstract
    C      SGEEV computes the eigenvalues and, optionally,
    C      the eigenvectors of a general real matrix.
    C
    C     Call Sequence Parameters-
    C       (The values of parameters marked with * (star) will be changed
    C         by SGEEV.)
    C
    C        A*      REAL(LDA,N)
    C                real nonsymmetric input matrix.
    C
    C        LDA     INTEGER
    C                set by the user to
    C                the leading dimension of the real array A.
    C
    C        N       INTEGER
    C                set by the user to
    C                the order of the matrices A and V, and
    C                the number of elements in E.
    C
    C        E*      COMPLEX(N)
    C                on return from SGEEV, E contains the eigenvalues of A.
    C                See also INFO below.
    C
    C        V*      COMPLEX(LDV,N)
    C                on return from SGEEV, if the user has set JOB
    C                = 0        V is not referenced.
    C                = nonzero  the N eigenvectors of A are stored in the
    C                first N columns of V.  See also INFO below.
    C                (Note that if the input matrix A is nearly degenerate,
    C                 V may be badly conditioned, i.e., may have nearly
    C                 dependent columns.)
    C
    C        LDV     INTEGER
    C                set by the user to
    C                the leading dimension of the array V if JOB is also
    C                set nonzero.  In that case, N must be .LE. LDV.
    C                If JOB is set to zero, LDV is not referenced.
    C
    C        WORK*   REAL(2N)
    C                temporary storage vector.  Contents changed by SGEEV.
    C
    C        JOB     INTEGER
    C                set by the user to
    C                = 0        eigenvalues only to be calculated by SGEEV.
    C                           Neither V nor LDV is referenced.
    C                = nonzero  eigenvalues and vectors to be calculated.
    C                           In this case, A & V must be distinct arrays.
    C                           Also, if LDA .GT. LDV, SGEEV changes all the
    C                           elements of A thru column N.  If LDA < LDV,
    C                           SGEEV changes all the elements of V through
    C                           column N. If LDA = LDV, only A(I,J) and V(I,
    C                           J) for I,J = 1,...,N are changed by SGEEV.
    C
    C        INFO*   INTEGER
    C                on return from SGEEV the value of INFO is
    C                = 0  normal return, calculation successful.
    C                = K  if the eigenvalue iteration fails to converge,
    C                     eigenvalues K+1 through N are correct, but
    C                     no eigenvectors were computed even if they were
    C                     requested (JOB nonzero).
    C
    C      Error Messages
    C           No. 1  recoverable  N is greater than LDA
    C           No. 2  recoverable  N is less than one.
    C           No. 3  recoverable  JOB is nonzero and N is greater than LDV
    C           No. 4  warning      LDA > LDV, elements of A other than the
    C                               N by N input elements have been changed.
    C           No. 5  warning      LDA < LDV, elements of V other than the
    C                               N x N output elements have been changed.
    C
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  BALANC, BALBAK, HQR, HQR2, ORTHES, ORTRAN, SCOPY,
    C                    SCOPYM, XERMSG
    C***REVISION HISTORY  (YYMMDD)
    C   800808  DATE WRITTEN
    C   890531  Changed all specific intrinsics to generic.  (WRB)
    C   890531  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
    C   900326  Removed duplicate information from DESCRIPTION section.
    C           (WRB)
    C***END PROLOGUE  SGEEV