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

```
_BQR(3F)							      _BQR(3F)

```

### NAME[Toc][Back]

```     BQR, SBQR	   -  EISPACK routine.	This subroutine	finds the eigenvalue
of	smallest (usually) magnitude of	a REAL SYMMETRIC BAND matrix using the
QR	algorithm with shifts of origin.  Consecutive calls can	be made	to
find further eigenvalues.

```

### SYNOPSYS[Toc][Back]

```	  subroutine  bqr(nm, n, mb, a,	t, r, ierr, nv,	rv)
integer	   nm, n, mb, ierr, nv
double precision t, r
double precision a(nm,mb), rv(nv)

subroutine sbqr(nm, n, mb, a,	t, r, ierr, nv,	rv)
integer	   nm, n, mb, ierr, nv
real		   t, r
real		   a(nm,mb), rv(nv)

```

### 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.

MB	is the (half) band width of the	matrix,	defined	as the number of
adjacent diagonals, including the principal diagonal, required to specify
the non-zero portion of the lower triangle	of the matrix.

A contains	the lower triangle of the symmetric band input matrix stored
as	an N by	MB array.  Its lowest subdiagonal is stored in the last	N+1-MB
positions of the first column, its	next subdiagonal in the	last N+2-MB
positions of the second column, further subdiagonals similarly, and
finally its principal diagonal in the N positions of the last column.
Contents of storages not part of the matrix are arbitrary.	 On a
subsequent	call, its output contents from the previous call should	be
passed.

T specifies the shift (of eigenvalues) applied to the diagonal of A in
forming the input matrix. What is actually	determined is the eigenvalue
of	A+TI (I	is the identity	matrix)	nearest	to T.  On a subsequent call,
the output	value of T from	the previous call should be passed if the next
nearest eigenvalue	is sought.

R should be specified as zero on the first	call, and as its output	value
from the previous call on a subsequent call.  It is used to determine
when the last row and column of the transformed band matrix can be
regarded as negligible.

Page 1

_BQR(3F)							      _BQR(3F)

NV	must be	set to the dimension of	the array parameter RV as declared in
the calling program dimension statement.  On OUTPUT

A contains	the transformed	band matrix.  The matrix A+TI derived from the
output parameters is similar to the input A+TI to within rounding errors.
Its last row and column are null (if IERR is zero).

T contains	the computed eigenvalue	of A+TI	(if IERR is zero).

R contains	the maximum of its input value and the norm of the last	column
of	the input matrix A.

IERR is set to Zero       for normal return, N	     if	the eigenvalue
has not been
determined after 30 iterations.

RV	is a temporary storage array of	dimension at least (2*MB**2+4*MB-3).
The first (3*MB-2)	locations correspond to	the ALGOL array	B, the next
(2*MB-1) locations	correspond to the ALGOL	array H, and the final
(2*MB**2-MB) locations correspond to the MB by (2*MB-1) ALGOL array U.
NOTE. For a subsequent call, N should be replaced by N-1, but

MB	should not be altered even when	it exceeds the current N. Calls
PYTHAG(A,B) for SQRT(A**2 + B**2).	 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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