SLATEC Routines --- SGEEV ---

*DECK SGEEV
      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