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

NAME

       LAPACK-3  -  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)

SYNOPSIS

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

           CHARACTER      UPLO

           INTEGER        INFO, KD, LDAB, N

           REAL           AMAX, SCOND

           REAL           S( * )

           COMPLEX        AB( LDAB, * )

PURPOSE

       CPBEQU 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.

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

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

        SCOND   (output) REAL
                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) REAL
                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)               April 2011                            CPBEQU(3lapack)