ZGEEQU (3lapack)

compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number

SYNOPSIS

  SUBROUTINE ZGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )

      INTEGER        INFO, LDA, M, N

      DOUBLE         PRECISION AMAX, COLCND, ROWCND

      DOUBLE         PRECISION C( * ), R( * )

      COMPLEX*16     A( LDA, * )

PURPOSE

  ZGEEQU 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 absolute value 1.

  R(i) and C(j) are restricted to be 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.

ARGUMENTS

  M       (input) INTEGER
          The number of rows of the matrix A.  M >= 0.

  N       (input) INTEGER
          The number of columns of the matrix A.  N >= 0.

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

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

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

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

  ROWCND  (output) 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.

  COLCND  (output) 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.

  AMAX    (output) 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.

  INFO    (output) 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