Unix/Linux Go Back    


RedHat 9 (Linux i386) - man page for sgeevx (redhat section l)

Linux & Unix Commands - Search Man Pages
Man Page or Keyword Search:   man
Select Man Page Set:       apropos Keyword Search (sections above)


SGEEVX(l)					)					SGEEVX(l)

NAME
       SGEEVX  -  compute  for an N-by-N real nonsymmetric matrix A, the eigenvalues and, option-
       ally, the left and/or right eigenvectors

SYNOPSIS
       SUBROUTINE SGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI,  VL,	LDVL,  VR,  LDVR,
			  ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, WORK, LWORK, IWORK, INFO )

	   CHARACTER	  BALANC, JOBVL, JOBVR, SENSE

	   INTEGER	  IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N

	   REAL 	  ABNRM

	   INTEGER	  IWORK( * )

	   REAL 	  A(  LDA,  * ), RCONDE( * ), RCONDV( * ), SCALE( * ), VL( LDVL, * ), VR(
			  LDVR, * ), WI( * ), WORK( * ), WR( * )

PURPOSE
       SGEEVX computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally,
       the  left and/or right eigenvectors.  Optionally also, it computes a balancing transforma-
       tion to improve the conditioning of the eigenvalues and eigenvectors (ILO, IHI, SCALE, and
       ABNRM),	reciprocal  condition numbers for the eigenvalues (RCONDE), and reciprocal condi-
       tion numbers for the right
       eigenvectors (RCONDV).

       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.

       Balancing  a matrix means permuting the rows and columns to make it more nearly upper tri-
       angular, and applying a diagonal similarity transformation D * A * D**(-1), where D  is	a
       diagonal  matrix, to make its rows and columns closer in norm and the condition numbers of
       its eigenvalues and eigenvectors smaller.  The computed reciprocal condition numbers  cor-
       respond	to the balanced matrix.  Permuting rows and columns will not change the condition
       numbers (in exact arithmetic) but diagonal scaling will.  For further explanation of  bal-
       ancing, see section 4.10.2 of the LAPACK Users' Guide.

ARGUMENTS
       BALANC  (input) CHARACTER*1
	       Indicates  how  the  input  matrix  should be diagonally scaled and/or permuted to
	       improve the conditioning of its eigenvalues.  = 'N': Do not  diagonally	scale  or
	       permute;
	       =  'P':	Perform  permutations to make the matrix more nearly upper triangular. Do
	       not diagonally scale; = 'S': Diagonally	scale  the  matrix,  i.e.  replace  A  by
	       D*A*D**(-1), where D is a diagonal matrix chosen to make the rows and columns of A
	       more equal in norm. Do not permute; = 'B': Both diagonally scale and permute A.

	       Computed reciprocal condition numbers will  be  for  the  matrix  after	balancing
	       and/or  permuting.  Permuting  does  not change condition numbers (in exact arith-
	       metic), but balancing does.

       JOBVL   (input) CHARACTER*1
	       = 'N': left eigenvectors of A are not computed;
	       = 'V': left eigenvectors of A are computed.  If SENSE = 'E' or 'B', JOBVL  must	=
	       'V'.

       JOBVR   (input) CHARACTER*1
	       = 'N': right eigenvectors of A are not computed;
	       =  'V': right eigenvectors of A are computed.  If SENSE = 'E' or 'B', JOBVR must =
	       'V'.

       SENSE   (input) CHARACTER*1
	       Determines which reciprocal condition numbers are computed.  = 'N': None are  com-
	       puted;
	       = 'E': Computed for eigenvalues only;
	       = 'V': Computed for right eigenvectors only;
	       = 'B': Computed for eigenvalues and right eigenvectors.

	       If  SENSE  =  'E'  or  'B', both left and right eigenvectors must also be computed
	       (JOBVL = 'V' and JOBVR = 'V').

       N       (input) INTEGER
	       The order of the matrix A. N >= 0.

       A       (input/output) REAL array, dimension (LDA,N)
	       On entry, the N-by-N matrix A.  On exit, A has been overwritten.  If JOBVL  =  'V'
	       or  JOBVR  =  'V',  A  contains the real Schur form of the balanced version of the
	       input matrix A.

       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  imagi-
	       nary parts, respectively, of the computed eigenvalues.  Complex conjugate pairs of
	       eigenvalues will appear consecutively with  the	eigenvalue  having  the  positive
	       imaginary part first.

       VL      (output) 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).

       LDVL    (input) INTEGER
	       The leading dimension of the array VL.  LDVL >= 1; if JOBVL = 'V', LDVL >= N.

       VR      (output) 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).

       LDVR    (input) INTEGER
	       The leading dimension of the array VR.  LDVR >= 1, and if JOBVR = 'V', LDVR >= N.

	       ILO,IHI (output) INTEGER ILO and IHI are integer values determined when A was bal-
	       anced.  The balanced A(i,j) = 0 if I > J and J = 1,...,ILO-1 or I = IHI+1,...,N.

       SCALE   (output) REAL array, dimension (N)
	       Details of the permutations and scaling factors applied when balancing A.  If P(j)
	       is the index of the row and column interchanged with row and column j, and D(j) is
	       the scaling factor applied to row and column j, then SCALE(J) = P(J),	for  J	=
	       1,...,ILO-1  =  D(J),	 for J = ILO,...,IHI = P(J)	for J = IHI+1,...,N.  The
	       order in which the interchanges are made is N to IHI+1, then 1 to ILO-1.

       ABNRM   (output) REAL
	       The one-norm of the balanced matrix (the maximum of the sum of absolute values  of
	       elements of any column).

       RCONDE  (output) REAL array, dimension (N)
	       RCONDE(j) is the reciprocal condition number of the j-th eigenvalue.

       RCONDV  (output) REAL array, dimension (N)
	       RCONDV(j) is the reciprocal condition number of the j-th right eigenvector.

       WORK    (workspace/output) REAL array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The dimension of the array WORK.   If SENSE = 'N' or 'E', LWORK >= max(1,2*N), and
	       if JOBVL = 'V' or JOBVR = 'V', LWORK >= 3*N.  If SENSE =  'V'  or  'B',	LWORK  >=
	       N*(N+6).  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.

       IWORK   (workspace) INTEGER array, dimension (2*N-2)
	       If SENSE = 'N' or 'E', not referenced.

       INFO    (output) 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 or condition numbers have been computed; elements 1:ILO-1  and  i+1:N
	       of WR and WI contain eigenvalues which have converged.

LAPACK version 3.0			   15 June 2000 				SGEEVX(l)
Unix & Linux Commands & Man Pages : ©2000 - 2018 Unix and Linux Forums


All times are GMT -4. The time now is 11:35 AM.