CPBEQU man page on IRIX

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CPBEQU(3F)							    CPBEQU(3F)

NAME
     CPBEQU - compute 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.

									Page 1

CPBEQU(3F)							    CPBEQU(3F)

     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.

									Page 2

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