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zpbequ.f(3)				      LAPACK				      zpbequ.f(3)

NAME
       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.

Version 3.4.2				 Tue Sep 25 2012			      zpbequ.f(3)
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