Annotation of rpl/lapack/lapack/zlaqge.f, revision 1.18
1.11 bertrand 1: *> \brief \b ZLAQGE 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 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">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLAQGE( 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 C( * ), R( * )
31: * COMPLEX*16 A( LDA, * )
32: * ..
1.15 bertrand 33: *
1.8 bertrand 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: *
1.15 bertrand 133: *> \author Univ. of Tennessee
134: *> \author Univ. of California Berkeley
135: *> \author Univ. of Colorado Denver
136: *> \author NAG Ltd.
1.8 bertrand 137: *
138: *> \ingroup complex16GEauxiliary
139: *
140: * =====================================================================
1.1 bertrand 141: SUBROUTINE ZLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
142: $ EQUED )
143: *
1.18 ! bertrand 144: * -- LAPACK auxiliary routine --
1.1 bertrand 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: DOUBLE PRECISION AMAX, COLCND, ROWCND
152: * ..
153: * .. Array Arguments ..
154: DOUBLE PRECISION C( * ), R( * )
155: COMPLEX*16 A( LDA, * )
156: * ..
157: *
158: * =====================================================================
159: *
160: * .. Parameters ..
161: DOUBLE PRECISION ONE, THRESH
162: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
163: * ..
164: * .. Local Scalars ..
165: INTEGER I, J
166: DOUBLE PRECISION CJ, LARGE, SMALL
167: * ..
168: * .. External Functions ..
169: DOUBLE PRECISION DLAMCH
170: EXTERNAL DLAMCH
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 = DLAMCH( 'Safe minimum' ) / DLAMCH( '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 ZLAQGE
234: *
235: END
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