_INVIT(3F)							    _INVIT(3F)

NAME    [Toc]    [Back]

     INVIT, SINVIT   -	EISPACK	routine.  This subroutine finds	those
     eigenvectors of a REAL UPPER Hessenberg matrix corresponding to specified
     eigenvalues, using	inverse	iteration.

SYNOPSYS    [Toc]    [Back]

	  subroutine  invit(nm,n,a,wr,wi,select,mm,m,z,ierr,rm1,rv1,rv2)
	  integer	   nm, n, mm, m, ierr
	  double precision a(nm,n), wr(n), wi(n), z(nm,mm)
	  double precision rm1(n,n), rv1(n), rv2(n)
	  logical	   select(n)

	  subroutine sinvit(nm,n,a,wr,wi,select,mm,m,z,ierr,rm1,rv1,rv2)
	  integer	   nm, n, mm, m, ierr
	  real		   a(nm,n), wr(n), wi(n), z(nm,mm)
	  real		   rm1(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.

     A contains	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  HQR, 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 columns required to
     store the eigenvectors to be found.  NOTE that two	columns	are required
     to	store the eigenvector corresponding to a complex eigenvalue.  On
     OUTPUT

     A and WI are unaltered.

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

     SELECT may	have been altered.  If the elements corresponding to a pair of
     conjugate complex eigenvalues were	each initially set to .TRUE., the



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_INVIT(3F)							    _INVIT(3F)



     program resets the	second of the two elements to .FALSE.

     M is the number of	columns	actually used to store the eigenvectors.

     Z contains	the real and imaginary parts of	the eigenvectors. If the next
     selected eigenvalue is real, the next column of Z contains	its
     eigenvector.  If the eigenvalue is	complex, the next two columns of Z
     contain the real and imaginary parts of its eigenvector.  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
     columns of	Z are necessary
	to store the eigenvectors corresponding	to
	the specified eigenvalues.  -K	       if the iteration	corresponding
     to	the K-th
	value fails, -(N+K)	if both	error situations occur.

     RM1 , RV1,	and RV2	are temporary storage arrays.  Note that RM1 is	square
     of	dimension N by N and, augmented	by two columns of Z, is	the transpose
     of	the corresponding ALGOL	B array.  The ALGOL procedure GUESSVEC appears
     in	INVIT 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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