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

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

10       SUBROUTINE SGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,  AMAX,
11                          INFO )
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13           INTEGER        INFO, KL, KU, LDAB, M, N
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15           REAL           AMAX, COLCND, ROWCND
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17           REAL           AB( LDAB, * ), C( * ), R( * )
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PURPOSE

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

31       M       (input) INTEGER
32               The number of rows of the matrix A.  M >= 0.
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34       N       (input) INTEGER
35               The number of columns of the matrix A.  N >= 0.
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37       KL      (input) INTEGER
38               The number of subdiagonals within the band of A.  KL >= 0.
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40       KU      (input) INTEGER
41               The number of superdiagonals within the band of A.  KU >= 0.
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43       AB      (input) REAL array, dimension (LDAB,N)
44               The band matrix A, stored in rows 1 to KL+KU+1.  The j-th  col‐
45               umn  of  A is stored in the j-th column of the array AB as fol‐
46               lows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
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48       LDAB    (input) INTEGER
49               The leading dimension of the array AB.  LDAB >= KL+KU+1.
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51       R       (output) REAL array, dimension (M)
52               If INFO = 0, or INFO > M, R contains the row scale factors  for
53               A.
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55       C       (output) REAL array, dimension (N)
56               If INFO = 0, C contains the column scale factors for A.
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58       ROWCND  (output) REAL
59               If  INFO  =  0  or  INFO  > M, ROWCND contains the ratio of the
60               smallest R(i) to the largest R(i).  If ROWCND >= 0.1  and  AMAX
61               is  neither too large nor too small, it is not worth scaling by
62               R.
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64       COLCND  (output) REAL
65               If INFO = 0, COLCND contains the ratio of the smallest C(i)  to
66               the largest C(i).  If COLCND >= 0.1, it is not worth scaling by
67               C.
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69       AMAX    (output) REAL
70               Absolute value of largest matrix  element.   If  AMAX  is  very
71               close to overflow or very close to underflow, the matrix should
72               be scaled.
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74       INFO    (output) INTEGER
75               = 0:  successful exit
76               < 0:  if INFO = -i, the i-th argument had an illegal value
77               > 0:  if INFO = i, and i is
78               <= M:  the i-th row of A is exactly zero
79               >  M:  the (i-M)-th column of A is exactly zero
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83 LAPACK routine (version 3.2)    November 2008                       SGBEQU(1)