1: *> \brief \b ZLAQGE 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
9: *> Download ZLAQGE + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqge.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqge.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqge.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
22: * EQUED )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER EQUED
26: * INTEGER LDA, M, N
27: * DOUBLE PRECISION AMAX, COLCND, ROWCND
28: * ..
29: * .. Array Arguments ..
30: * DOUBLE PRECISION C( * ), R( * )
31: * COMPLEX*16 A( LDA, * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZLAQGE 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*16 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 DOUBLE PRECISION array, dimension (M)
76: *> The row scale factors for A.
77: *> \endverbatim
78: *>
79: *> \param[in] C
80: *> \verbatim
81: *> C is DOUBLE PRECISION array, dimension (N)
82: *> The column scale factors for A.
83: *> \endverbatim
84: *>
85: *> \param[in] ROWCND
86: *> \verbatim
87: *> ROWCND is DOUBLE PRECISION
88: *> Ratio of the smallest R(i) to the largest R(i).
89: *> \endverbatim
90: *>
91: *> \param[in] COLCND
92: *> \verbatim
93: *> COLCND is DOUBLE PRECISION
94: *> Ratio of the smallest C(i) to the largest C(i).
95: *> \endverbatim
96: *>
97: *> \param[in] AMAX
98: *> \verbatim
99: *> AMAX is DOUBLE PRECISION
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 September 2012
139: *
140: *> \ingroup complex16GEauxiliary
141: *
142: * =====================================================================
143: SUBROUTINE ZLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
144: $ EQUED )
145: *
146: * -- LAPACK auxiliary routine (version 3.4.2) --
147: * -- LAPACK is a software package provided by Univ. of Tennessee, --
148: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149: * September 2012
150: *
151: * .. Scalar Arguments ..
152: CHARACTER EQUED
153: INTEGER LDA, M, N
154: DOUBLE PRECISION AMAX, COLCND, ROWCND
155: * ..
156: * .. Array Arguments ..
157: DOUBLE PRECISION C( * ), R( * )
158: COMPLEX*16 A( LDA, * )
159: * ..
160: *
161: * =====================================================================
162: *
163: * .. Parameters ..
164: DOUBLE PRECISION ONE, THRESH
165: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
166: * ..
167: * .. Local Scalars ..
168: INTEGER I, J
169: DOUBLE PRECISION CJ, LARGE, SMALL
170: * ..
171: * .. External Functions ..
172: DOUBLE PRECISION DLAMCH
173: EXTERNAL DLAMCH
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 = DLAMCH( 'Safe minimum' ) / DLAMCH( '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 ZLAQGE
237: *
238: END
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