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

```
_BISECT(3F)							   _BISECT(3F)

```

### NAME[Toc][Back]

```     BISECT, SBISECT  -	 EISPACK routine.  This	subroutine finds those
eigenvalues of a TRIDIAGONAL SYMMETRIC matrix which lie in	a specified
interval, using bisection.

```

### SYNOPSYS[Toc][Back]

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

subroutine sbisect(n,eps1,d,e,e2,lb,ub,mm,m,w,ind,ierr,rv4,rv5)
integer	   n, mm, m, ierr
integer	   ind(mm)
real		   eps1, lb, ub
real		   d(n), e(n), e2(n), w(mm), 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.

LB	and UB define the interval to be searched for eigenvalues. If LB is
not less than UB, no eigenvalues will be found.

MM	should be set to an upper bound	for the	number of eigenvalues in the
interval.	WARNING. If more than MM eigenvalues are determined to lie in
the interval, an error return is made with	no eigenvalues found.  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regarded as negligible, have been replaced	by zero	causing	the matrix to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.

Page 1

_BISECT(3F)							   _BISECT(3F)

M is the number of	eigenvalues determined to lie in (LB,UB).

W contains	the M eigenvalues in ascending 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.

IERR is set to Zero       for normal return, 3*N+1	     if	M exceeds MM.

RV4 and RV5 are temporary storage arrays. The ALGOL procedure STURMCNT
contained in TRISTURM appears in BISECT in-line.  Note that subroutine
TQL1 or IMTQL1 is generally faster	than

BISECT , 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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