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man pages->IRIX man pages -> complib/TINVIT (3)
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### Contents

```
_TINVIT(3F)							   _TINVIT(3F)

```

### NAME[Toc][Back]

```     TINVIT, STINVIT  -	 EISPACK routine.  This	subroutine finds those
eigenvectors of a TRIDIAGONAL SYMMETRIC matrix corresponding to specified
eigenvalues, using	inverse	iteration.

```

### SYNOPSYS[Toc][Back]

```	  subroutine  tinvit(nm,n,d,e,e2,m,w,ind,z,ierr,rv1,rv2,rv3,rv4,rv6)
integer	    nm,	n, m, ierr, ind(m)
double precision d(n), e(n), e2(n), w(m), z(nm,m)
double precision rv1(n), rv2(n), rv3(n), rv4(n), rv6(n)

subroutine stinvit(nm,n,d,e,e2,m,w,ind,z,ierr,rv1,rv2,rv3,rv4,rv6)
integer	    nm,	n, m, ierr, ind(m)
real		   d(n), e(n), e2(n), w(m), z(nm,m)
real		   rv1(n), rv2(n), rv3(n), rv4(n), rv6(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.

D contains	the diagonal elements of the input matrix.

E contains	the subdiagonal	elements of the	input matrix in	its last N-1
positions.	 E(1) is arbitrary.

E2	contains the squares of	the corresponding elements of E, with zeros
corresponding to negligible elements of E.	 E(I) is considered negligible
if	it is not larger than the product of the relative machine precision
and the sum of the	magnitudes of D(I) and D(I-1).	E2(1) must contain
0.0e0 if the eigenvalues are in ascending order, or 2.0e0 if the
eigenvalues are in	descending order.  If  BISECT, TRIDIB, or  IMTQLV  has
been used to find the eigenvalues,	their output E2	array is exactly what
is	expected here.

M is the number of	specified eigenvalues.

W CONTAINS	the M eigenvalues in ascending or descending order.

IND contains in its first M positions the submatrix indices associated
with the corresponding eigenvalues	in W --	1 for eigenvalues belonging to
the first submatrix from the top, 2 for those belonging to	the second
submatrix,	etc.  On Output

Z contains	the associated set of orthonormal eigenvectors.	any vector
which fails to converge is	set to zero.

Page 1

_TINVIT(3F)							   _TINVIT(3F)

IERR is set to Zero       for normal return, -R	     if	the
eigenvector corresponding to the R-th
eigenvalue fails to converge in	5 iterations.

RV1 , RV2,	RV3, RV4, and RV6 are temporary	storage	arrays.	Questions and
comments should be	directed to B. S. Garbow, APPLIED MATHEMATICS
DIVISION, ARGONNE NATIONAL	LABORATORY

PPPPaaaaggggeeee 2222```
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