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

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.ti -1c
.RI "subroutine \fBsgegv\fP (jobvl, jobvr, n, a, lda, b, ldb, alphar, alphai, beta, vl, ldvl, vr, ldvr, work, lwork, info)"
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.RI "\fB SGEGV computes the eigenvalues and, optionally, the left and/or right eigenvectors of a real matrix pair (A,B)\&.\fP "
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.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sgegv (character jobvl, character jobvr, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) alphar, real, dimension( * ) alphai, real, dimension( * ) beta, real, dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr, integer ldvr, real, dimension( * ) work, integer lwork, integer info)"

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\fB SGEGV computes the eigenvalues and, optionally, the left and/or right eigenvectors of a real matrix pair (A,B)\&.\fP  
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\fBPurpose:\fP
.RS 4

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!>
!> This routine is deprecated and has been replaced by routine SGGEV\&.
!>
!> SGEGV computes the eigenvalues and, optionally, the left and/or right
!> eigenvectors of a real matrix pair (A,B)\&.
!> Given two square matrices A and B,
!> the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
!> eigenvalues lambda and corresponding (non-zero) eigenvectors x such
!> that
!>
!>    A*x = lambda*B*x\&.
!>
!> An alternate form is to find the eigenvalues mu and corresponding
!> eigenvectors y such that
!>
!>    mu*A*y = B*y\&.
!>
!> These two forms are equivalent with mu = 1/lambda and x = y if
!> neither lambda nor mu is zero\&.  In order to deal with the case that
!> lambda or mu is zero or small, two values alpha and beta are returned
!> for each eigenvalue, such that lambda = alpha/beta and
!> mu = beta/alpha\&.
!>
!> The vectors x and y in the above equations are right eigenvectors of
!> the matrix pair (A,B)\&.  Vectors u and v satisfying
!>
!>    u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B
!>
!> are left eigenvectors of (A,B)\&.
!>
!> Note: this routine performs  on A and B
!> 
.fi
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.RE
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\fBParameters\fP
.RS 4
\fIJOBVL\fP 
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!>          JOBVL is CHARACTER*1
!>          = 'N':  do not compute the left generalized eigenvectors;
!>          = 'V':  compute the left generalized eigenvectors (returned
!>                  in VL)\&.
!> 
.fi
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\fIJOBVR\fP 
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!>          JOBVR is CHARACTER*1
!>          = 'N':  do not compute the right generalized eigenvectors;
!>          = 'V':  compute the right generalized eigenvectors (returned
!>                  in VR)\&.
!> 
.fi
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\fIN\fP 
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!>          N is INTEGER
!>          The order of the matrices A, B, VL, and VR\&.  N >= 0\&.
!> 
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\fIA\fP 
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!>          A is REAL array, dimension (LDA, N)
!>          On entry, the matrix A\&.
!>          If JOBVL = 'V' or JOBVR = 'V', then on exit A
!>          contains the real Schur form of A from the generalized Schur
!>          factorization of the pair (A,B) after balancing\&.
!>          If no eigenvectors were computed, then only the diagonal
!>          blocks from the Schur form will be correct\&.  See SGGHRD and
!>          SHGEQZ for details\&.
!> 
.fi
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.br
\fILDA\fP 
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!>          LDA is INTEGER
!>          The leading dimension of A\&.  LDA >= max(1,N)\&.
!> 
.fi
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\fIB\fP 
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!>          B is REAL array, dimension (LDB, N)
!>          On entry, the matrix B\&.
!>          If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
!>          upper triangular matrix obtained from B in the generalized
!>          Schur factorization of the pair (A,B) after balancing\&.
!>          If no eigenvectors were computed, then only those elements of
!>          B corresponding to the diagonal blocks from the Schur form of
!>          A will be correct\&.  See SGGHRD and SHGEQZ for details\&.
!> 
.fi
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\fILDB\fP 
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!>          LDB is INTEGER
!>          The leading dimension of B\&.  LDB >= max(1,N)\&.
!> 
.fi
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\fIALPHAR\fP 
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!>          ALPHAR is REAL array, dimension (N)
!>          The real parts of each scalar alpha defining an eigenvalue of
!>          GNEP\&.
!> 
.fi
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\fIALPHAI\fP 
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!>          ALPHAI is REAL array, dimension (N)
!>          The imaginary parts of each scalar alpha defining an
!>          eigenvalue of GNEP\&.  If ALPHAI(j) is zero, then the j-th
!>          eigenvalue is real; if positive, then the j-th and
!>          (j+1)-st eigenvalues are a complex conjugate pair, with
!>          ALPHAI(j+1) = -ALPHAI(j)\&.
!> 
.fi
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\fIBETA\fP 
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!>          BETA is REAL array, dimension (N)
!>          The scalars beta that define the eigenvalues of GNEP\&.
!>
!>          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
!>          beta = BETA(j) represent the j-th eigenvalue of the matrix
!>          pair (A,B), in one of the forms lambda = alpha/beta or
!>          mu = beta/alpha\&.  Since either lambda or mu may overflow,
!>          they should not, in general, be computed\&.
!> 
.fi
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.br
\fIVL\fP 
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!>          VL is REAL array, dimension (LDVL,N)
!>          If JOBVL = 'V', the left eigenvectors u(j) are stored
!>          in the columns of VL, in the same order as their eigenvalues\&.
!>          If the j-th eigenvalue is real, then u(j) = VL(:,j)\&.
!>          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)\&.
!>
!>          Each eigenvector is scaled so that its largest component has
!>          abs(real part) + abs(imag\&. part) = 1, except for eigenvectors
!>          corresponding to an eigenvalue with alpha = beta = 0, which
!>          are set to zero\&.
!>          Not referenced if JOBVL = 'N'\&.
!> 
.fi
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.br
\fILDVL\fP 
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!>          LDVL is INTEGER
!>          The leading dimension of the matrix VL\&. LDVL >= 1, and
!>          if JOBVL = 'V', LDVL >= N\&.
!> 
.fi
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.br
\fIVR\fP 
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!>          VR is REAL array, dimension (LDVR,N)
!>          If JOBVR = 'V', the right eigenvectors x(j) are stored
!>          in the columns of VR, in the same order as their eigenvalues\&.
!>          If the j-th eigenvalue is real, then x(j) = VR(:,j)\&.
!>          If the j-th and (j+1)-st eigenvalues form a complex conjugate
!>          pair, then
!>            x(j) = VR(:,j) + i*VR(:,j+1)
!>          and
!>            x(j+1) = VR(:,j) - i*VR(:,j+1)\&.
!>
!>          Each eigenvector is scaled so that its largest component has
!>          abs(real part) + abs(imag\&. part) = 1, except for eigenvalues
!>          corresponding to an eigenvalue with alpha = beta = 0, which
!>          are set to zero\&.
!>          Not referenced if JOBVR = 'N'\&.
!> 
.fi
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\fILDVR\fP 
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!>          LDVR is INTEGER
!>          The leading dimension of the matrix VR\&. LDVR >= 1, and
!>          if JOBVR = 'V', LDVR >= N\&.
!> 
.fi
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.br
\fIWORK\fP 
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.nf
!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
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\fILWORK\fP 
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!>          LWORK is INTEGER
!>          The dimension of the array WORK\&.  LWORK >= max(1,8*N)\&.
!>          For good performance, LWORK must generally be larger\&.
!>          To compute the optimal value of LWORK, call ILAENV to get
!>          blocksizes (for SGEQRF, SORMQR, and SORGQR\&.)  Then compute:
!>          NB  -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR;
!>          The optimal LWORK is:
!>              2*N + MAX( 6*N, N*(NB+1) )\&.
!>
!>          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
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.br
\fIINFO\fP 
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!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
!>          = 1,\&.\&.\&.,N:
!>                The QZ iteration failed\&.  No eigenvectors have been
!>                calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
!>                should be correct for j=INFO+1,\&.\&.\&.,N\&.
!>          > N:  errors that usually indicate LAPACK problems:
!>                =N+1: error return from SGGBAL
!>                =N+2: error return from SGEQRF
!>                =N+3: error return from SORMQR
!>                =N+4: error return from SORGQR
!>                =N+5: error return from SGGHRD
!>                =N+6: error return from SHGEQZ (other than failed
!>                                                iteration)
!>                =N+7: error return from STGEVC
!>                =N+8: error return from SGGBAK (computing VL)
!>                =N+9: error return from SGGBAK (computing VR)
!>                =N+10: error return from SLASCL (various calls)
!> 
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

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Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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\fBFurther Details:\fP
.RS 4

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!>
!>  Balancing
!>  ---------
!>
!>  This driver calls SGGBAL to both permute and scale rows and columns
!>  of A and B\&.  The permutations PL and PR are chosen so that PL*A*PR
!>  and PL*B*R will be upper triangular except for the diagonal blocks
!>  A(i:j,i:j) and B(i:j,i:j), with i and j as close together as
!>  possible\&.  The diagonal scaling matrices DL and DR are chosen so
!>  that the pair  DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to
!>  one (except for the elements that start out zero\&.)
!>
!>  After the eigenvalues and eigenvectors of the balanced matrices
!>  have been computed, SGGBAK transforms the eigenvectors back to what
!>  they would have been (in perfect arithmetic) if they had not been
!>  balanced\&.
!>
!>  Contents of A and B on Exit
!>  -------- -- - --- - -- ----
!>
!>  If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or
!>  both), then on exit the arrays A and B will contain the real Schur
!>  form[*] of the  versions of A and B\&.  If no eigenvectors
!>  are computed, then only the diagonal blocks will be correct\&.
!>
!>  [*] See SHGEQZ, SGEGS, or read the book ,
!>      by Golub & van Loan, pub\&. by Johns Hopkins U\&. Press\&.
!> 
.fi
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.RE
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Definition at line \fB304\fP of file \fBsgegv\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.