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

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)