1SGEEQU(1)                LAPACK routine (version 3.2)                SGEEQU(1)
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NAME

6       SGEEQU - computes row and column scalings intended to equilibrate an M-
7       by-N matrix A and reduce its condition number
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SYNOPSIS

10       SUBROUTINE SGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )
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12           INTEGER        INFO, LDA, M, N
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14           REAL           AMAX, COLCND, ROWCND
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16           REAL           A( LDA, * ), C( * ), R( * )
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PURPOSE

19       SGEEQU computes row and column scalings intended to equilibrate  an  M-
20       by-N matrix A and reduce its condition number.  R returns the row scale
21       factors and C the column scale factors,  chosen  to  try  to  make  the
22       largest  element  in  each row and column of the matrix B with elements
23       B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
24       R(i) and C(j) are restricted to be between SMLNUM = smallest safe  num‐
25       ber  and BIGNUM = largest safe number.  Use of these scaling factors is
26       not guaranteed to reduce the condition number of A but  works  well  in
27       practice.
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ARGUMENTS

30       M       (input) INTEGER
31               The number of rows of the matrix A.  M >= 0.
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33       N       (input) INTEGER
34               The number of columns of the matrix A.  N >= 0.
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36       A       (input) REAL array, dimension (LDA,N)
37               The  M-by-N  matrix  whose equilibration factors are to be com‐
38               puted.
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40       LDA     (input) INTEGER
41               The leading dimension of the array A.  LDA >= max(1,M).
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43       R       (output) REAL array, dimension (M)
44               If INFO = 0 or INFO > M, R contains the row scale  factors  for
45               A.
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47       C       (output) REAL array, dimension (N)
48               If INFO = 0,  C contains the column scale factors for A.
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50       ROWCND  (output) REAL
51               If  INFO  =  0  or  INFO  > M, ROWCND contains the ratio of the
52               smallest R(i) to the largest R(i).  If ROWCND >= 0.1  and  AMAX
53               is  neither too large nor too small, it is not worth scaling by
54               R.
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56       COLCND  (output) REAL
57               If INFO = 0, COLCND contains the ratio of the smallest C(i)  to
58               the largest C(i).  If COLCND >= 0.1, it is not worth scaling by
59               C.
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61       AMAX    (output) REAL
62               Absolute value of largest matrix  element.   If  AMAX  is  very
63               close to overflow or very close to underflow, the matrix should
64               be scaled.
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66       INFO    (output) INTEGER
67               = 0:  successful exit
68               < 0:  if INFO = -i, the i-th argument had an illegal value
69               > 0:  if INFO = i,  and i is
70               <= M:  the i-th row of A is exactly zero
71               >  M:  the (i-M)-th column of A is exactly zero
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75 LAPACK routine (version 3.2)    November 2008                       SGEEQU(1)