# zpbequ.f (3) - Linux Manuals

zpbequ.f -

## SYNOPSIS

### Functions/Subroutines

subroutine zpbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO)
ZPBEQU

## Function/Subroutine Documentation

### subroutine zpbequ (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, integerINFO)

ZPBEQU

Purpose:

ZPBEQU computes row and column scalings intended to equilibrate a
Hermitian 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 COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangle of the Hermitian 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 DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

SCOND is 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

AMAX is 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

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:

November 2011

Definition at line 131 of file zpbequ.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.