# spbequ.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine spbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO)
SPBEQU

## Function/Subroutine Documentation

### subroutine spbequ (character UPLO, integer N, integer KD, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) S, real SCOND, real AMAX, integer INFO)

SPBEQU

Purpose:

``` SPBEQU computes row and column scalings intended to equilibrate a
symmetric positive definite band matrix A and reduce its condition
number (with respect to the two-norm).  S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.```
Parameters:

UPLO

```          UPLO is CHARACTER*1
= 'U':  Upper triangular of A is stored;
= 'L':  Lower triangular of A is stored.```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.```

KD

```          KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KD >= 0.```

AB

```          AB is REAL array, dimension (LDAB,N)
The upper or lower triangle of the symmetric band matrix A,
stored in the first KD+1 rows of the array.  The j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).```

LDAB

```          LDAB is INTEGER
The leading dimension of the array A.  LDAB >= KD+1.```

S

```          S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.```

SCOND

```          SCOND is REAL
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.```

AMAX

```          AMAX is REAL
Absolute value of largest matrix element.  If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.```

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  if INFO = i, the i-th diagonal element is nonpositive.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 131 of file spbequ.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page spbequ(3) is an alias of spbequ.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK