SRC/cpbequ.f(3)

NAME
SRC/cpbequ.f

SYNOPSIS

  Functions/Subroutines
subroutine cpbequ (uplo, n, kd, ab, ldab, s, scond, amax, info)
CPBEQU

Function/Subroutine Documentation

  subroutine cpbequ (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real amax, integer info)

CPBEQU

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.
    !>

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

    SCOND

    !>          SCOND is 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

    !>          AMAX is 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

    !>          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.

Definition at line 129 of file cpbequ.f.

Author

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