1: *> \brief \b DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLAQGB + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqgb.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqgb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqgb.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
22: * AMAX, EQUED )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER EQUED
26: * INTEGER KL, KU, LDAB, M, N
27: * DOUBLE PRECISION AMAX, COLCND, ROWCND
28: * ..
29: * .. Array Arguments ..
30: * DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> DLAQGB equilibrates a general M by N band matrix A with KL
40: *> subdiagonals and KU superdiagonals using the row and scaling factors
41: *> 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] KL
60: *> \verbatim
61: *> KL is INTEGER
62: *> The number of subdiagonals within the band of A. KL >= 0.
63: *> \endverbatim
64: *>
65: *> \param[in] KU
66: *> \verbatim
67: *> KU is INTEGER
68: *> The number of superdiagonals within the band of A. KU >= 0.
69: *> \endverbatim
70: *>
71: *> \param[in,out] AB
72: *> \verbatim
73: *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
74: *> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
75: *> The j-th column of A is stored in the j-th column of the
76: *> array AB as follows:
77: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
78: *>
79: *> On exit, the equilibrated matrix, in the same storage format
80: *> as A. See EQUED for the form of the equilibrated matrix.
81: *> \endverbatim
82: *>
83: *> \param[in] LDAB
84: *> \verbatim
85: *> LDAB is INTEGER
86: *> The leading dimension of the array AB. LDA >= KL+KU+1.
87: *> \endverbatim
88: *>
89: *> \param[in] R
90: *> \verbatim
91: *> R is DOUBLE PRECISION array, dimension (M)
92: *> The row scale factors for A.
93: *> \endverbatim
94: *>
95: *> \param[in] C
96: *> \verbatim
97: *> C is DOUBLE PRECISION array, dimension (N)
98: *> The column scale factors for A.
99: *> \endverbatim
100: *>
101: *> \param[in] ROWCND
102: *> \verbatim
103: *> ROWCND is DOUBLE PRECISION
104: *> Ratio of the smallest R(i) to the largest R(i).
105: *> \endverbatim
106: *>
107: *> \param[in] COLCND
108: *> \verbatim
109: *> COLCND is DOUBLE PRECISION
110: *> Ratio of the smallest C(i) to the largest C(i).
111: *> \endverbatim
112: *>
113: *> \param[in] AMAX
114: *> \verbatim
115: *> AMAX is DOUBLE PRECISION
116: *> Absolute value of largest matrix entry.
117: *> \endverbatim
118: *>
119: *> \param[out] EQUED
120: *> \verbatim
121: *> EQUED is CHARACTER*1
122: *> Specifies the form of equilibration that was done.
123: *> = 'N': No equilibration
124: *> = 'R': Row equilibration, i.e., A has been premultiplied by
125: *> diag(R).
126: *> = 'C': Column equilibration, i.e., A has been postmultiplied
127: *> by diag(C).
128: *> = 'B': Both row and column equilibration, i.e., A has been
129: *> replaced by diag(R) * A * diag(C).
130: *> \endverbatim
131: *
132: *> \par Internal Parameters:
133: * =========================
134: *>
135: *> \verbatim
136: *> THRESH is a threshold value used to decide if row or column scaling
137: *> should be done based on the ratio of the row or column scaling
138: *> factors. If ROWCND < THRESH, row scaling is done, and if
139: *> COLCND < THRESH, column scaling is done.
140: *>
141: *> LARGE and SMALL are threshold values used to decide if row scaling
142: *> should be done based on the absolute size of the largest matrix
143: *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
144: *> \endverbatim
145: *
146: * Authors:
147: * ========
148: *
149: *> \author Univ. of Tennessee
150: *> \author Univ. of California Berkeley
151: *> \author Univ. of Colorado Denver
152: *> \author NAG Ltd.
153: *
154: *> \ingroup doubleGBauxiliary
155: *
156: * =====================================================================
157: SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
158: $ AMAX, EQUED )
159: *
160: * -- LAPACK auxiliary routine --
161: * -- LAPACK is a software package provided by Univ. of Tennessee, --
162: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163: *
164: * .. Scalar Arguments ..
165: CHARACTER EQUED
166: INTEGER KL, KU, LDAB, M, N
167: DOUBLE PRECISION AMAX, COLCND, ROWCND
168: * ..
169: * .. Array Arguments ..
170: DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
171: * ..
172: *
173: * =====================================================================
174: *
175: * .. Parameters ..
176: DOUBLE PRECISION ONE, THRESH
177: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
178: * ..
179: * .. Local Scalars ..
180: INTEGER I, J
181: DOUBLE PRECISION CJ, LARGE, SMALL
182: * ..
183: * .. External Functions ..
184: DOUBLE PRECISION DLAMCH
185: EXTERNAL DLAMCH
186: * ..
187: * .. Intrinsic Functions ..
188: INTRINSIC MAX, MIN
189: * ..
190: * .. Executable Statements ..
191: *
192: * Quick return if possible
193: *
194: IF( M.LE.0 .OR. N.LE.0 ) THEN
195: EQUED = 'N'
196: RETURN
197: END IF
198: *
199: * Initialize LARGE and SMALL.
200: *
201: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
202: LARGE = ONE / SMALL
203: *
204: IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
205: $ THEN
206: *
207: * No row scaling
208: *
209: IF( COLCND.GE.THRESH ) THEN
210: *
211: * No column scaling
212: *
213: EQUED = 'N'
214: ELSE
215: *
216: * Column scaling
217: *
218: DO 20 J = 1, N
219: CJ = C( J )
220: DO 10 I = MAX( 1, J-KU ), MIN( M, J+KL )
221: AB( KU+1+I-J, J ) = CJ*AB( KU+1+I-J, J )
222: 10 CONTINUE
223: 20 CONTINUE
224: EQUED = 'C'
225: END IF
226: ELSE IF( COLCND.GE.THRESH ) THEN
227: *
228: * Row scaling, no column scaling
229: *
230: DO 40 J = 1, N
231: DO 30 I = MAX( 1, J-KU ), MIN( M, J+KL )
232: AB( KU+1+I-J, J ) = R( I )*AB( KU+1+I-J, J )
233: 30 CONTINUE
234: 40 CONTINUE
235: EQUED = 'R'
236: ELSE
237: *
238: * Row and column scaling
239: *
240: DO 60 J = 1, N
241: CJ = C( J )
242: DO 50 I = MAX( 1, J-KU ), MIN( M, J+KL )
243: AB( KU+1+I-J, J ) = CJ*R( I )*AB( KU+1+I-J, J )
244: 50 CONTINUE
245: 60 CONTINUE
246: EQUED = 'B'
247: END IF
248: *
249: RETURN
250: *
251: * End of DLAQGB
252: *
253: END
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