1ZLAQGB(1)           LAPACK auxiliary routine (version 3.1)           ZLAQGB(1)
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NAME

6       ZLAQGB  -  a  general  M by N band matrix A with KL subdiagonals and KU
7       superdiagonals using the row and scaling factors in the vectors R and C
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SYNOPSIS

10       SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,  AMAX,
11                          EQUED )
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13           CHARACTER      EQUED
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15           INTEGER        KL, KU, LDAB, M, N
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17           DOUBLE         PRECISION AMAX, COLCND, ROWCND
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19           DOUBLE         PRECISION C( * ), R( * )
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21           COMPLEX*16     AB( LDAB, * )
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PURPOSE

24       ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals
25       and KU superdiagonals using the row and scaling factors in the  vectors
26       R and C.
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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       KL      (input) INTEGER
37               The number of subdiagonals within the band of A.  KL >= 0.
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39       KU      (input) INTEGER
40               The number of superdiagonals within the band of A.  KU >= 0.
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42       AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
43               On  entry,  the matrix A in band storage, in rows 1 to KL+KU+1.
44               The j-th column of A is stored in the j-th column of the  array
45               AB   as   follows:   AB(ku+1+i-j,j)   =   A(i,j)  for  max(1,j-
46               ku)<=i<=min(m,j+kl)
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48               On exit, the equilibrated matrix, in the same storage format as
49               A.  See EQUED for the form of the equilibrated matrix.
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51       LDAB    (input) INTEGER
52               The leading dimension of the array AB.  LDA >= KL+KU+1.
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54       R       (input) DOUBLE PRECISION array, dimension (M)
55               The row scale factors for A.
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57       C       (input) DOUBLE PRECISION array, dimension (N)
58               The column scale factors for A.
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60       ROWCND  (input) DOUBLE PRECISION
61               Ratio of the smallest R(i) to the largest R(i).
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63       COLCND  (input) DOUBLE PRECISION
64               Ratio of the smallest C(i) to the largest C(i).
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66       AMAX    (input) DOUBLE PRECISION
67               Absolute value of largest matrix entry.
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69       EQUED   (output) CHARACTER*1
70               Specifies  the form of equilibration that was done.  = 'N':  No
71               equilibration
72               = 'R':  Row equilibration, i.e., A has  been  premultiplied  by
73               diag(R).   = 'C':  Column equilibration, i.e., A has been post‐
74               multiplied by diag(C).  = 'B':  Both row and column  equilibra‐
75               tion, i.e., A has been replaced by diag(R) * A * diag(C).
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PARAMETERS

78       THRESH  is  a  threshold  value used to decide if row or column scaling
79       should be done based on the ratio of the row or column scaling factors.
80       If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column
81       scaling is done.
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83       LARGE and SMALL are threshold values used  to  decide  if  row  scaling
84       should  be  done  based on the absolute size of the largest matrix ele‐
85       ment.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
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89 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLAQGB(1)