zpbequ()

subroutine zpbequ	(	character	uplo,
		integer	n,
		integer	kd,
		complex*16, dimension( ldab, * )	ab,
		integer	ldab,
		double precision, dimension( * )	s,
		double precision	scond,
		double precision	amax,
		integer	info )

ZPBEQU

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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

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangular of A is stored; !> = 'L': Lower triangular of A is stored. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	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. !>
[in]	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). !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array A. LDAB >= KD+1. !>
[out]	S	!> S is DOUBLE PRECISION array, dimension (N) !> If INFO = 0, S contains the scale factors for A. !>
[out]	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. !>
[out]	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. !>
[out]	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.