sgeev (l)  Linux Manuals
sgeev: computes for an NbyN real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
NAME
SGEEV  computes for an NbyN real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectorsSYNOPSIS
 SUBROUTINE SGEEV(
 JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
 CHARACTER JOBVL, JOBVR
 INTEGER INFO, LDA, LDVL, LDVR, LWORK, N
 REAL A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), WI( * ), WORK( * ), WR( * )
PURPOSE
SGEEV computes for an NbyN real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. The right eigenvector v(j) of A satisfieswhere lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.
ARGUMENTS
 JOBVL (input) CHARACTER*1

= aqNaq: left eigenvectors of A are not computed;
= aqVaq: left eigenvectors of A are computed.  JOBVR (input) CHARACTER*1

= aqNaq: right eigenvectors of A are not computed;
= aqVaq: right eigenvectors of A are computed.  N (input) INTEGER
 The order of the matrix A. N >= 0.
 A (input/output) REAL array, dimension (LDA,N)
 On entry, the NbyN matrix A. On exit, A has been overwritten.
 LDA (input) INTEGER
 The leading dimension of the array A. LDA >= max(1,N).
 WR (output) REAL array, dimension (N)
 WI (output) REAL array, dimension (N) WR and WI contain the real and imaginary parts, respectively, of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue having the positive imaginary part first.
 VL (output) REAL array, dimension (LDVL,N)

If JOBVL = aqVaq, the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = aqNaq, VL is not referenced.
If the jth eigenvalue is real, then u(j) = VL(:,j),
the jth column of VL.
If the jth and (j+1)st 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).  LDVL (input) INTEGER
 The leading dimension of the array VL. LDVL >= 1; if JOBVL = aqVaq, LDVL >= N.
 VR (output) REAL array, dimension (LDVR,N)

If JOBVR = aqVaq, the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = aqNaq, VR is not referenced.
If the jth eigenvalue is real, then v(j) = VR(:,j),
the jth column of VR.
If the jth and (j+1)st 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).  LDVR (input) INTEGER
 The leading dimension of the array VR. LDVR >= 1; if JOBVR = aqVaq, LDVR >= N.
 WORK (workspace/output) REAL 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(1,3*N), and if JOBVL = aqVaq or JOBVR = aqVaq, LWORK >= 4*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 ith argument had an illegal value.
> 0: if INFO = i, the QR algorithm failed to compute all the eigenvalues, and no eigenvectors have been computed; elements i+1:N of WR and WI contain eigenvalues which have converged.