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

```
_TRIDIB(3F)							   _TRIDIB(3F)

```

### NAME[Toc][Back]

```     TRIDIB, STRIDIB  -	 EISPACK routine.  This	subroutine finds those
eigenvalues of a TRIDIAGONAL SYMMETRIC matrix between specified boundary
indices, using bisection.

```

### SYNOPSYS[Toc][Back]

```	  subroutine  tridib(n,eps1,d,e,e2,lb,ub,m11,m,w,ind,ierr,rv4,rv5)
integer	   n, m11, m, ierr, ind(m)
double precision eps1, lb, ub
double precision d(n), e(n), e2(n), w(m), rv4(n), rv5(n)

subroutine stridib(n,eps1,d,e,e2,lb,ub,m11,m,w,ind,ierr,rv4,rv5)
integer	   n, m11, m, ierr, ind(m)
real		   eps1, lb, ub
real		   d(n), e(n), e2(n), w(m), rv4(n), rv5(n)

```

### DESCRIPTION[Toc][Back]

```     On	Input

N is the order of the matrix.

EPS1 is an	absolute error tolerance for the computed eigenvalues.	If the
input EPS1	is non-positive, it is reset for each submatrix	to a default
value, namely, minus the product of the relative machine precision	and
the 1-norm	of the submatrix.

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. E2(1) is
arbitrary.

M11 specifies the lower boundary index for	the desired eigenvalues.

M specifies the number of eigenvalues desired.  The upper boundary	index
M22 is then obtained as M22=M11+M-1.  On Output

EPS1 is unaltered unless it has been reset	to its (last) default value.

D and E are unaltered. ELEMENTS of	E2, corresponding to elements of E
regarded as negligible, have been replaced	by zero	causing	the matrix to
split into	a direct sum of	submatrices.  E2(1) is also set	to zero.

LB	and UB DEFINE an interval containing exactly the desired eigenvalues.

W contains, in its	first M	positions, the eigenvalues between indices M11
and M22 in	ascending order.

Page 1

_TRIDIB(3F)							   _TRIDIB(3F)

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.

IERR is set to Zero       for normal return, 3*N+1	     if	multiple
eigenvalues at index M11 make
unique selection impossible, 3*N+2	if multiple eigenvalues	at
index M22 make
unique selection impossible.

RV4 and RV5 are temporary storage arrays. Note that subroutine TQL1,
IMTQL1, or	TQLRAT is generally faster than	TRIDIB,	if more	than N/4
eigenvalues are to	be found.  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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