
spbequ.f(3) LAPACK spbequ.f(3)
NAME
spbequ.f 
SYNOPSIS
Functions/Subroutines
subroutine spbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO)
SPBEQU
Function/Subroutine Documentation
subroutine spbequ (characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB,
integerLDAB, real, dimension( * )S, realSCOND, realAMAX, integerINFO)
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 twonorm). 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 jth column
of A is stored in the jth column of the array AB as follows:
if UPLO = 'U', AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j;
if UPLO = 'L', AB(1+ij,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 ith argument had an illegal value.
> 0: if INFO = i, the ith diagonal element is nonpositive.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 130 of file spbequ.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 spbequ.f(3) 
