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)