Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3  -  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)

SYNOPSIS

SUBROUTINE DPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )

CHARACTER      UPLO

INTEGER        INFO, KD, LDAB, N

DOUBLE         PRECISION AMAX, SCOND

DOUBLE         PRECISION AB( LDAB, * ), S( * )

PURPOSE

DPBEQU 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.

ARGUMENTS

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

N       (input) INTEGER
The order of the matrix A.  N >= 0.

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

AB      (input) DOUBLE PRECISION 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    (input) INTEGER
The leading dimension of the array A.  LDAB >= KD+1.

S       (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND   (output) DOUBLE PRECISION
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    (output) DOUBLE PRECISION
Absolute value of largest matrix element.  If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.

INFO    (output) 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.

LAPACK routine (version 3.2.2)             April 2011                            DPBEQU(3lapack)