_CINVIT(3F)							   _CINVIT(3F)

NAME    [Toc]    [Back]

     CINVIT, SCINVIT  -	 EISPACK routine.  This	subroutine finds those
     eigenvectors of A COMPLEX UPPER Hessenberg	matrix corresponding to
     specified eigenvalues, using inverse iteration.

SYNOPSYS    [Toc]    [Back]

	  subroutine  cinvit(nm, n, ar,	ai, wr,	wi, select, mm,	m, zr, zi,
	  1	       ierr, rm1, rm2, rv1, rv2)
	  integer	   nm, n, mm, m, ierr
	  double precision ar(nm,n),  ai(nm,n),	wr(n), wi(n)
	  double precision zr(nm,mm), zi(nm,mm)
	  double precision rm1(n,n),  rm2(n,n),	rv1(n),	rv2(n)
	  logical	   select(n)

	  subroutine scinvit(nm, n, ar,	ai, wr,	wi, select, mm,	m, zr, zi,
	  1	       ierr, rm1, rm2, rv1, rv2)
	  integer	   nm, n, mm, m, ierr
	  real		   ar(nm,n),  ai(nm,n),	wr(n), wi(n)
	  real		   zr(nm,mm), zi(nm,mm)
	  real		   rm1(n,n),  rm2(n,n),	rv1(n),	rv2(n)
	  logical	   select(n)

DESCRIPTION    [Toc]    [Back]

     On	INPUT

     NM	must be	set to the row dimension of two-dimensional array parameters
     as	declared in the	calling	program	dimension statement.

     N is the order of the matrix.

     AR	and AI contain the real	and imaginary parts, respectively, of the
     Hessenberg	matrix.

     WR	and WI contain the real	and imaginary parts, respectively, of the
     eigenvalues of the	matrix.	 The eigenvalues must be stored	in a manner
     identical to that of subroutine  COMLR, which recognizes possible
     splitting of the matrix.

     SELECT specifies the eigenvectors to be found.  The eigenvector
     corresponding to the J-th eigenvalue is specified by setting SELECT(J) to
     .TRUE.

     MM	should be set to an upper bound	for the	number of eigenvectors to be
     found.  On	OUTPUT

     AR	, AI, WI, and SELECT are unaltered.

     WR	may have been altered since close eigenvalues are perturbed slightly
     in	searching for independent eigenvectors.



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_CINVIT(3F)							   _CINVIT(3F)



     M is the number of	eigenvectors actually found.

     ZR	and ZI contain the real	and imaginary parts, respectively, of the
     eigenvectors.  The	eigenvectors are normalized so that the	component of
     largest magnitude is 1.  Any vector which fails the acceptance test is
     set to zero.

     IERR is set to Zero       for normal return, -(2*N+1)   if	more than MM
     eigenvectors have been specified, -K	  if the iteration
     corresponding to the K-th
	value fails, -(N+K)	if both	error situations occur.

     RM1 , RM2,	RV1, and RV2 are temporary storage arrays. The ALGOL procedure
     GUESSVEC appears in CINVIT	in line.  Calls	PYTHAG(A,B) for	sqrt(A**2 +
     B**2).  Calls CDIV	for complex division.  Questions and comments should
     be	directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION,	ARGONNE
     NATIONAL LABORATORY


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