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RedHat 9 (Linux i386) - man page for spbequ (redhat section l)

SPBEQU(l)					)					SPBEQU(l)

NAME
       SPBEQU - compute row and column scalings intended to equilibrate a symmetric positive def-
       inite band matrix A and reduce its condition number (with respect to the two-norm)

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

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   REAL 	  AMAX, SCOND

	   REAL 	  AB( LDAB, * ), S( * )

PURPOSE
       SPBEQU computes row and column scalings intended to equilibrate a symmetric positive defi-
       nite  band matrix A and reduce its condition number (with respect to the two-norm). S con-
       tains 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 sub-
	       diagonals if UPLO = 'L'.  KD >= 0.

       AB      (input) REAL 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) 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 version 3.0			   15 June 2000 				SPBEQU(l)


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