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## zgeequb()

subroutine zgeequb | ( | integer | m,
|  | integer | n,
|  | complex*16, dimension( lda, * ) | a,
|  | integer | lda,
|  | double precision, dimension( * ) | r,
|  | double precision, dimension( * ) | c,
|  | double precision | rowcnd,
|  | double precision | colcnd,
|  | double precision | amax,
|  | integer | info )

ZGEEQUB

Download ZGEEQUB + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> ZGEEQUB computes row and column scalings intended to equilibrate an
      !> M-by-N matrix A and reduce its condition number.  R returns the row
      !> scale factors and C the column scale factors, chosen to try to make
      !> the largest element in each row and column of the matrix B with
      !> elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
      !> the radix.
      !>
      !> R(i) and C(j) are restricted to be a power of the radix between
      !> SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use
      !> of these scaling factors is not guaranteed to reduce the condition
      !> number of A but works well in practice.
      !>
      !> This routine differs from ZGEEQU by restricting the scaling factors
      !> to a power of the radix.  Barring over- and underflow, scaling by
      !> these factors introduces no additional rounding errors.  However, the
      !> scaled entries' magnitudes are no longer approximately 1 but lie
      !> between sqrt(radix) and 1/sqrt(radix).
      !>

Parameters

  [in]

  M

      !>          M is INTEGER
      !>          The number of rows of the matrix A.  M >= 0.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The number of columns of the matrix A.  N >= 0.
      !>

  [in]

  A

      !>          A is COMPLEX*16 array, dimension (LDA,N)
      !>          The M-by-N matrix whose equilibration factors are
      !>          to be computed.
      !>

  [in]

  LDA

      !>          LDA is INTEGER
      !>          The leading dimension of the array A.  LDA >= max(1,M).
      !>

  [out]

  R

      !>          R is DOUBLE PRECISION array, dimension (M)
      !>          If INFO = 0 or INFO > M, R contains the row scale factors
      !>          for A.
      !>

  [out]

  C

      !>          C is DOUBLE PRECISION array, dimension (N)
      !>          If INFO = 0,  C contains the column scale factors for A.
      !>

  [out]

  ROWCND

      !>          ROWCND is DOUBLE PRECISION
      !>          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
      !>          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
      !>          AMAX is neither too large nor too small, it is not worth
      !>          scaling by R.
      !>

  [out]

  COLCND

      !>          COLCND is DOUBLE PRECISION
      !>          If INFO = 0, COLCND contains the ratio of the smallest
      !>          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
      !>          worth scaling by C.
      !>

  [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,  and i is
      !>                <= M:  the i-th row of A is exactly zero
      !>                >  M:  the (i-M)-th column of A is exactly zero
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.