LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
claqge.f
Go to the documentation of this file.
1 *> \brief \b CLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/claqge.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/claqge.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/claqge.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
22 * EQUED )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER EQUED
26 * INTEGER LDA, M, N
27 * REAL AMAX, COLCND, ROWCND
28 * ..
29 * .. Array Arguments ..
30 * REAL C( * ), R( * )
31 * COMPLEX A( LDA, * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> CLAQGE equilibrates a general M by N matrix A using the row and
41 *> column scaling factors in the vectors R and C.
42 *> \endverbatim
43 *
44 * Arguments:
45 * ==========
46 *
47 *> \param[in] M
48 *> \verbatim
49 *> M is INTEGER
50 *> The number of rows of the matrix A. M >= 0.
51 *> \endverbatim
52 *>
53 *> \param[in] N
54 *> \verbatim
55 *> N is INTEGER
56 *> The number of columns of the matrix A. N >= 0.
57 *> \endverbatim
58 *>
59 *> \param[in,out] A
60 *> \verbatim
61 *> A is COMPLEX array, dimension (LDA,N)
62 *> On entry, the M by N matrix A.
63 *> On exit, the equilibrated matrix. See EQUED for the form of
64 *> the equilibrated matrix.
65 *> \endverbatim
66 *>
67 *> \param[in] LDA
68 *> \verbatim
69 *> LDA is INTEGER
70 *> The leading dimension of the array A. LDA >= max(M,1).
71 *> \endverbatim
72 *>
73 *> \param[in] R
74 *> \verbatim
75 *> R is REAL array, dimension (M)
76 *> The row scale factors for A.
77 *> \endverbatim
78 *>
79 *> \param[in] C
80 *> \verbatim
81 *> C is REAL array, dimension (N)
82 *> The column scale factors for A.
83 *> \endverbatim
84 *>
85 *> \param[in] ROWCND
86 *> \verbatim
87 *> ROWCND is REAL
88 *> Ratio of the smallest R(i) to the largest R(i).
89 *> \endverbatim
90 *>
91 *> \param[in] COLCND
92 *> \verbatim
93 *> COLCND is REAL
94 *> Ratio of the smallest C(i) to the largest C(i).
95 *> \endverbatim
96 *>
97 *> \param[in] AMAX
98 *> \verbatim
99 *> AMAX is REAL
100 *> Absolute value of largest matrix entry.
101 *> \endverbatim
102 *>
103 *> \param[out] EQUED
104 *> \verbatim
105 *> EQUED is CHARACTER*1
106 *> Specifies the form of equilibration that was done.
107 *> = 'N': No equilibration
108 *> = 'R': Row equilibration, i.e., A has been premultiplied by
109 *> diag(R).
110 *> = 'C': Column equilibration, i.e., A has been postmultiplied
111 *> by diag(C).
112 *> = 'B': Both row and column equilibration, i.e., A has been
113 *> replaced by diag(R) * A * diag(C).
114 *> \endverbatim
115 *
116 *> \par Internal Parameters:
117 * =========================
118 *>
119 *> \verbatim
120 *> THRESH is a threshold value used to decide if row or column scaling
121 *> should be done based on the ratio of the row or column scaling
122 *> factors. If ROWCND < THRESH, row scaling is done, and if
123 *> COLCND < THRESH, column scaling is done.
124 *>
125 *> LARGE and SMALL are threshold values used to decide if row scaling
126 *> should be done based on the absolute size of the largest matrix
127 *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
128 *> \endverbatim
129 *
130 * Authors:
131 * ========
132 *
133 *> \author Univ. of Tennessee
134 *> \author Univ. of California Berkeley
135 *> \author Univ. of Colorado Denver
136 *> \author NAG Ltd.
137 *
138 *> \date December 2016
139 *
140 *> \ingroup complexGEauxiliary
141 *
142 * =====================================================================
143  SUBROUTINE claqge( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
144  \$ equed )
145 *
146 * -- LAPACK auxiliary routine (version 3.7.0) --
147 * -- LAPACK is a software package provided by Univ. of Tennessee, --
148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149 * December 2016
150 *
151 * .. Scalar Arguments ..
152  CHARACTER EQUED
153  INTEGER LDA, M, N
154  REAL AMAX, COLCND, ROWCND
155 * ..
156 * .. Array Arguments ..
157  REAL C( * ), R( * )
158  COMPLEX A( lda, * )
159 * ..
160 *
161 * =====================================================================
162 *
163 * .. Parameters ..
164  REAL ONE, THRESH
165  parameter ( one = 1.0e+0, thresh = 0.1e+0 )
166 * ..
167 * .. Local Scalars ..
168  INTEGER I, J
169  REAL CJ, LARGE, SMALL
170 * ..
171 * .. External Functions ..
172  REAL SLAMCH
173  EXTERNAL slamch
174 * ..
175 * .. Executable Statements ..
176 *
177 * Quick return if possible
178 *
179  IF( m.LE.0 .OR. n.LE.0 ) THEN
180  equed = 'N'
181  RETURN
182  END IF
183 *
184 * Initialize LARGE and SMALL.
185 *
186  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
187  large = one / small
188 *
189  IF( rowcnd.GE.thresh .AND. amax.GE.small .AND. amax.LE.large )
190  \$ THEN
191 *
192 * No row scaling
193 *
194  IF( colcnd.GE.thresh ) THEN
195 *
196 * No column scaling
197 *
198  equed = 'N'
199  ELSE
200 *
201 * Column scaling
202 *
203  DO 20 j = 1, n
204  cj = c( j )
205  DO 10 i = 1, m
206  a( i, j ) = cj*a( i, j )
207  10 CONTINUE
208  20 CONTINUE
209  equed = 'C'
210  END IF
211  ELSE IF( colcnd.GE.thresh ) THEN
212 *
213 * Row scaling, no column scaling
214 *
215  DO 40 j = 1, n
216  DO 30 i = 1, m
217  a( i, j ) = r( i )*a( i, j )
218  30 CONTINUE
219  40 CONTINUE
220  equed = 'R'
221  ELSE
222 *
223 * Row and column scaling
224 *
225  DO 60 j = 1, n
226  cj = c( j )
227  DO 50 i = 1, m
228  a( i, j ) = cj*r( i )*a( i, j )
229  50 CONTINUE
230  60 CONTINUE
231  equed = 'B'
232  END IF
233 *
234  RETURN
235 *
236 * End of CLAQGE
237 *
238  END
subroutine claqge(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, EQUED)
CLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ...
Definition: claqge.f:145