Annotation of rpl/lapack/lapack/dlaqge.f, revision 1.17
1.11 bertrand 1: *> \brief \b DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download DLAQGE + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqge.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqge.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqge.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
22: * EQUED )
1.15 bertrand 23: *
1.8 bertrand 24: * .. Scalar Arguments ..
25: * CHARACTER EQUED
26: * INTEGER LDA, M, N
27: * DOUBLE PRECISION AMAX, COLCND, ROWCND
28: * ..
29: * .. Array Arguments ..
30: * DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
31: * ..
1.15 bertrand 32: *
1.8 bertrand 33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> DLAQGE equilibrates a general M by N matrix A using the row and
40: *> column scaling factors in the vectors R and C.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] M
47: *> \verbatim
48: *> M is INTEGER
49: *> The number of rows of the matrix A. M >= 0.
50: *> \endverbatim
51: *>
52: *> \param[in] N
53: *> \verbatim
54: *> N is INTEGER
55: *> The number of columns of the matrix A. N >= 0.
56: *> \endverbatim
57: *>
58: *> \param[in,out] A
59: *> \verbatim
60: *> A is DOUBLE PRECISION array, dimension (LDA,N)
61: *> On entry, the M by N matrix A.
62: *> On exit, the equilibrated matrix. See EQUED for the form of
63: *> the equilibrated matrix.
64: *> \endverbatim
65: *>
66: *> \param[in] LDA
67: *> \verbatim
68: *> LDA is INTEGER
69: *> The leading dimension of the array A. LDA >= max(M,1).
70: *> \endverbatim
71: *>
72: *> \param[in] R
73: *> \verbatim
74: *> R is DOUBLE PRECISION array, dimension (M)
75: *> The row scale factors for A.
76: *> \endverbatim
77: *>
78: *> \param[in] C
79: *> \verbatim
80: *> C is DOUBLE PRECISION array, dimension (N)
81: *> The column scale factors for A.
82: *> \endverbatim
83: *>
84: *> \param[in] ROWCND
85: *> \verbatim
86: *> ROWCND is DOUBLE PRECISION
87: *> Ratio of the smallest R(i) to the largest R(i).
88: *> \endverbatim
89: *>
90: *> \param[in] COLCND
91: *> \verbatim
92: *> COLCND is DOUBLE PRECISION
93: *> Ratio of the smallest C(i) to the largest C(i).
94: *> \endverbatim
95: *>
96: *> \param[in] AMAX
97: *> \verbatim
98: *> AMAX is DOUBLE PRECISION
99: *> Absolute value of largest matrix entry.
100: *> \endverbatim
101: *>
102: *> \param[out] EQUED
103: *> \verbatim
104: *> EQUED is CHARACTER*1
105: *> Specifies the form of equilibration that was done.
106: *> = 'N': No equilibration
107: *> = 'R': Row equilibration, i.e., A has been premultiplied by
108: *> diag(R).
109: *> = 'C': Column equilibration, i.e., A has been postmultiplied
110: *> by diag(C).
111: *> = 'B': Both row and column equilibration, i.e., A has been
112: *> replaced by diag(R) * A * diag(C).
113: *> \endverbatim
114: *
115: *> \par Internal Parameters:
116: * =========================
117: *>
118: *> \verbatim
119: *> THRESH is a threshold value used to decide if row or column scaling
120: *> should be done based on the ratio of the row or column scaling
121: *> factors. If ROWCND < THRESH, row scaling is done, and if
122: *> COLCND < THRESH, column scaling is done.
123: *>
124: *> LARGE and SMALL are threshold values used to decide if row scaling
125: *> should be done based on the absolute size of the largest matrix
126: *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
127: *> \endverbatim
128: *
129: * Authors:
130: * ========
131: *
1.15 bertrand 132: *> \author Univ. of Tennessee
133: *> \author Univ. of California Berkeley
134: *> \author Univ. of Colorado Denver
135: *> \author NAG Ltd.
1.8 bertrand 136: *
1.15 bertrand 137: *> \date December 2016
1.8 bertrand 138: *
139: *> \ingroup doubleGEauxiliary
140: *
141: * =====================================================================
1.1 bertrand 142: SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
143: $ EQUED )
144: *
1.15 bertrand 145: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 146: * -- LAPACK is a software package provided by Univ. of Tennessee, --
147: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 bertrand 148: * December 2016
1.1 bertrand 149: *
150: * .. Scalar Arguments ..
151: CHARACTER EQUED
152: INTEGER LDA, M, N
153: DOUBLE PRECISION AMAX, COLCND, ROWCND
154: * ..
155: * .. Array Arguments ..
156: DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
157: * ..
158: *
159: * =====================================================================
160: *
161: * .. Parameters ..
162: DOUBLE PRECISION ONE, THRESH
163: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
164: * ..
165: * .. Local Scalars ..
166: INTEGER I, J
167: DOUBLE PRECISION CJ, LARGE, SMALL
168: * ..
169: * .. External Functions ..
170: DOUBLE PRECISION DLAMCH
171: EXTERNAL DLAMCH
172: * ..
173: * .. Executable Statements ..
174: *
175: * Quick return if possible
176: *
177: IF( M.LE.0 .OR. N.LE.0 ) THEN
178: EQUED = 'N'
179: RETURN
180: END IF
181: *
182: * Initialize LARGE and SMALL.
183: *
184: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
185: LARGE = ONE / SMALL
186: *
187: IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
188: $ THEN
189: *
190: * No row scaling
191: *
192: IF( COLCND.GE.THRESH ) THEN
193: *
194: * No column scaling
195: *
196: EQUED = 'N'
197: ELSE
198: *
199: * Column scaling
200: *
201: DO 20 J = 1, N
202: CJ = C( J )
203: DO 10 I = 1, M
204: A( I, J ) = CJ*A( I, J )
205: 10 CONTINUE
206: 20 CONTINUE
207: EQUED = 'C'
208: END IF
209: ELSE IF( COLCND.GE.THRESH ) THEN
210: *
211: * Row scaling, no column scaling
212: *
213: DO 40 J = 1, N
214: DO 30 I = 1, M
215: A( I, J ) = R( I )*A( I, J )
216: 30 CONTINUE
217: 40 CONTINUE
218: EQUED = 'R'
219: ELSE
220: *
221: * Row and column scaling
222: *
223: DO 60 J = 1, N
224: CJ = C( J )
225: DO 50 I = 1, M
226: A( I, J ) = CJ*R( I )*A( I, J )
227: 50 CONTINUE
228: 60 CONTINUE
229: EQUED = 'B'
230: END IF
231: *
232: RETURN
233: *
234: * End of DLAQGE
235: *
236: END
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