.TH "SRC/sgeev.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/sgeev.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBsgeev\fP (jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info)"
.br
.RI "\fB SGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sgeev (character jobvl, character jobvr, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr, integer ldvr, real, dimension( * ) work, integer lwork, integer info)"

.PP
\fB SGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SGEEV computes for an N-by-N real nonsymmetric matrix A, the
!> eigenvalues and, optionally, the left and/or right eigenvectors\&.
!>
!> The right eigenvector v(j) of A satisfies
!>                  A * v(j) = lambda(j) * v(j)
!> where lambda(j) is its eigenvalue\&.
!> The left eigenvector u(j) of A satisfies
!>               u(j)**H * A = lambda(j) * u(j)**H
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBVL\fP 
.PP
.nf
!>          JOBVL is CHARACTER*1
!>          = 'N': left eigenvectors of A are not computed;
!>          = 'V': left eigenvectors of A are computed\&.
!> 
.fi
.PP
.br
\fIJOBVR\fP 
.PP
.nf
!>          JOBVR is CHARACTER*1
!>          = 'N': right eigenvectors of A are not computed;
!>          = 'V': right eigenvectors of A are computed\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the N-by-N matrix A\&.
!>          On exit, A has been overwritten\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIWR\fP 
.PP
.nf
!>          WR is REAL array, dimension (N)
!> 
.fi
.PP
.br
\fIWI\fP 
.PP
.nf
!>          WI is 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\&.
!> 
.fi
.PP
.br
\fIVL\fP 
.PP
.nf
!>          VL is REAL array, dimension (LDVL,N)
!>          If JOBVL = 'V', the left eigenvectors u(j) are stored one
!>          after another in the columns of VL, in the same order
!>          as their eigenvalues\&.
!>          If JOBVL = 'N', VL is not referenced\&.
!>          If the j-th eigenvalue is real, then u(j) = VL(:,j),
!>          the j-th column of VL\&.
!>          If the j-th 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)\&.
!> 
.fi
.PP
.br
\fILDVL\fP 
.PP
.nf
!>          LDVL is INTEGER
!>          The leading dimension of the array VL\&.  LDVL >= 1; if
!>          JOBVL = 'V', LDVL >= N\&.
!> 
.fi
.PP
.br
\fIVR\fP 
.PP
.nf
!>          VR is REAL array, dimension (LDVR,N)
!>          If JOBVR = 'V', the right eigenvectors v(j) are stored one
!>          after another in the columns of VR, in the same order
!>          as their eigenvalues\&.
!>          If JOBVR = 'N', VR is not referenced\&.
!>          If the j-th eigenvalue is real, then v(j) = VR(:,j),
!>          the j-th column of VR\&.
!>          If the j-th 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)\&.
!> 
.fi
.PP
.br
\fILDVR\fP 
.PP
.nf
!>          LDVR is INTEGER
!>          The leading dimension of the array VR\&.  LDVR >= 1; if
!>          JOBVR = 'V', LDVR >= N\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The dimension of the array WORK\&.  LWORK >= max(1,3*N), and
!>          if JOBVL = 'V' or JOBVR = 'V', 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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB190\fP of file \fBsgeev\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.