LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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claqge.f
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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*> \ingroup laqge
139*
140* =====================================================================
141 SUBROUTINE claqge( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
142 \$ EQUED )
143*
144* -- LAPACK auxiliary routine --
145* -- LAPACK is a software package provided by Univ. of Tennessee, --
146* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147*
148* .. Scalar Arguments ..
149 CHARACTER EQUED
150 INTEGER LDA, M, N
151 REAL AMAX, COLCND, ROWCND
152* ..
153* .. Array Arguments ..
154 REAL C( * ), R( * )
155 COMPLEX A( LDA, * )
156* ..
157*
158* =====================================================================
159*
160* .. Parameters ..
161 REAL ONE, THRESH
162 parameter( one = 1.0e+0, thresh = 0.1e+0 )
163* ..
164* .. Local Scalars ..
165 INTEGER I, J
166 REAL CJ, LARGE, SMALL
167* ..
168* .. External Functions ..
169 REAL SLAMCH
170 EXTERNAL slamch
171* ..
172* .. Executable Statements ..
173*
174* Quick return if possible
175*
176 IF( m.LE.0 .OR. n.LE.0 ) THEN
177 equed = 'N'
178 RETURN
179 END IF
180*
181* Initialize LARGE and SMALL.
182*
183 small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
184 large = one / small
185*
186 IF( rowcnd.GE.thresh .AND. amax.GE.small .AND. amax.LE.large )
187 \$ THEN
188*
189* No row scaling
190*
191 IF( colcnd.GE.thresh ) THEN
192*
193* No column scaling
194*
195 equed = 'N'
196 ELSE
197*
198* Column scaling
199*
200 DO 20 j = 1, n
201 cj = c( j )
202 DO 10 i = 1, m
203 a( i, j ) = cj*a( i, j )
204 10 CONTINUE
205 20 CONTINUE
206 equed = 'C'
207 END IF
208 ELSE IF( colcnd.GE.thresh ) THEN
209*
210* Row scaling, no column scaling
211*
212 DO 40 j = 1, n
213 DO 30 i = 1, m
214 a( i, j ) = r( i )*a( i, j )
215 30 CONTINUE
216 40 CONTINUE
217 equed = 'R'
218 ELSE
219*
220* Row and column scaling
221*
222 DO 60 j = 1, n
223 cj = c( j )
224 DO 50 i = 1, m
225 a( i, j ) = cj*r( i )*a( i, j )
226 50 CONTINUE
227 60 CONTINUE
228 equed = 'B'
229 END IF
230*
231 RETURN
232*
233* End of CLAQGE
234*
235 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:143