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

6       ZLAQGB  - 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 ZLAQGB( 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           DOUBLE         PRECISION AMAX, COLCND, ROWCND
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20           DOUBLE         PRECISION C( * ), R( * )
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22           COMPLEX*16     AB( LDAB, * )
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PURPOSE

25       ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals
26       and  KU superdiagonals using the row and scaling factors in the vectors
27       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)  On  exit,  the equilibrated matrix, in the
47               same storage format as A.  See EQUED for the form of the  equi‐
48               librated matrix.
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50       LDAB    (input) INTEGER
51               The leading dimension of the array AB.  LDA >= KL+KU+1.
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53       R       (input) DOUBLE PRECISION array, dimension (M)
54               The row scale factors for A.
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56       C       (input) DOUBLE PRECISION array, dimension (N)
57               The column scale factors for A.
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59       ROWCND  (input) DOUBLE PRECISION
60               Ratio of the smallest R(i) to the largest R(i).
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62       COLCND  (input) DOUBLE PRECISION
63               Ratio of the smallest C(i) to the largest C(i).
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65       AMAX    (input) DOUBLE PRECISION
66               Absolute value of largest matrix entry.
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68       EQUED   (output) CHARACTER*1
69               Specifies  the form of equilibration that was done.  = 'N':  No
70               equilibration
71               = 'R':  Row equilibration, i.e., A has  been  premultiplied  by
72               diag(R).   = 'C':  Column equilibration, i.e., A has been post‐
73               multiplied by diag(C).  = 'B':  Both row and column  equilibra‐
74               tion, i.e., A has been replaced by diag(R) * A * diag(C).
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PARAMETERS

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