SRC/dpbequ.f(3)            Library Functions Manual            SRC/dpbequ.f(3)

NAME
       SRC/dpbequ.f

SYNOPSIS
   Functions/Subroutines
       subroutine dpbequ (uplo, n, kd, ab, ldab, s, scond, amax, info)
           DPBEQU

Function/Subroutine Documentation
   subroutine dpbequ (character uplo, integer n, integer kd, double precision,
       dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
       s, double precision scond, double precision amax, integer info)
       DPBEQU

       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.

       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 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

                     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.

       Definition at line 128 of file dpbequ.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/dpbequ.f(3)