1SLAQGB(1)           LAPACK auxiliary routine (version 3.2)           SLAQGB(1)
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NAME

6       SLAQGB  - equilibrates a general M by N band matrix A with KL subdiago‐
7       nals and KU superdiagonals using the row and  scaling  factors  in  the
8       vectors R and C
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SYNOPSIS

11       SUBROUTINE SLAQGB( M,  N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
12                          EQUED )
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14           CHARACTER      EQUED
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16           INTEGER        KL, KU, LDAB, M, N
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18           REAL           AMAX, COLCND, ROWCND
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20           REAL           AB( LDAB, * ), C( * ), R( * )
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PURPOSE

23       SLAQGB equilibrates a general M by N band matrix A with KL subdiagonals
24       and  KU superdiagonals using the row and scaling factors in the vectors
25       R and C.
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ARGUMENTS

28       M       (input) INTEGER
29               The number of rows of the matrix A.  M >= 0.
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31       N       (input) INTEGER
32               The number of columns of the matrix A.  N >= 0.
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34       KL      (input) INTEGER
35               The number of subdiagonals within the band of A.  KL >= 0.
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37       KU      (input) INTEGER
38               The number of superdiagonals within the band of A.  KU >= 0.
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40       AB      (input/output) REAL array, dimension (LDAB,N)
41               On entry, the matrix A in band storage, in rows 1  to  KL+KU+1.
42               The  j-th column of A is stored in the j-th column of the array
43               AB  as  follows:   AB(ku+1+i-j,j)   =   A(i,j)   for   max(1,j-
44               ku)<=i<=min(m,j+kl)  On  exit,  the equilibrated matrix, in the
45               same storage format as A.  See EQUED for the form of the  equi‐
46               librated matrix.
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48       LDAB    (input) INTEGER
49               The leading dimension of the array AB.  LDA >= KL+KU+1.
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51       R       (input) REAL array, dimension (M)
52               The row scale factors for A.
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54       C       (input) REAL array, dimension (N)
55               The column scale factors for A.
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57       ROWCND  (input) REAL
58               Ratio of the smallest R(i) to the largest R(i).
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60       COLCND  (input) REAL
61               Ratio of the smallest C(i) to the largest C(i).
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63       AMAX    (input) REAL
64               Absolute value of largest matrix entry.
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66       EQUED   (output) CHARACTER*1
67               Specifies  the form of equilibration that was done.  = 'N':  No
68               equilibration
69               = 'R':  Row equilibration, i.e., A has  been  premultiplied  by
70               diag(R).   = 'C':  Column equilibration, i.e., A has been post‐
71               multiplied by diag(C).  = 'B':  Both row and column  equilibra‐
72               tion, i.e., A has been replaced by diag(R) * A * diag(C).
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PARAMETERS

75       THRESH  is  a  threshold  value used to decide if row or column scaling
76       should be done based on the ratio of the row or column scaling factors.
77       If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column
78       scaling is done.  LARGE and SMALL are threshold values used  to  decide
79       if row scaling should be done based on the absolute size of the largest
80       matrix element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
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84 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLAQGB(1)