Annotation of rpl/lapack/lapack/dlaqsy.f, revision 1.11
1.11 ! bertrand 1: *> \brief \b DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLAQSY + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsy.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqsy.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqsy.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER EQUED, UPLO
25: * INTEGER LDA, N
26: * DOUBLE PRECISION AMAX, SCOND
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION A( LDA, * ), S( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DLAQSY equilibrates a symmetric matrix A using the scaling factors
39: *> in the vector S.
40: *> \endverbatim
41: *
42: * Arguments:
43: * ==========
44: *
45: *> \param[in] UPLO
46: *> \verbatim
47: *> UPLO is CHARACTER*1
48: *> Specifies whether the upper or lower triangular part of the
49: *> symmetric matrix A is stored.
50: *> = 'U': Upper triangular
51: *> = 'L': Lower triangular
52: *> \endverbatim
53: *>
54: *> \param[in] N
55: *> \verbatim
56: *> N is INTEGER
57: *> The order of the matrix A. N >= 0.
58: *> \endverbatim
59: *>
60: *> \param[in,out] A
61: *> \verbatim
62: *> A is DOUBLE PRECISION array, dimension (LDA,N)
63: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
64: *> n by n upper triangular part of A contains the upper
65: *> triangular part of the matrix A, and the strictly lower
66: *> triangular part of A is not referenced. If UPLO = 'L', the
67: *> leading n by n lower triangular part of A contains the lower
68: *> triangular part of the matrix A, and the strictly upper
69: *> triangular part of A is not referenced.
70: *>
71: *> On exit, if EQUED = 'Y', the equilibrated matrix:
72: *> diag(S) * A * diag(S).
73: *> \endverbatim
74: *>
75: *> \param[in] LDA
76: *> \verbatim
77: *> LDA is INTEGER
78: *> The leading dimension of the array A. LDA >= max(N,1).
79: *> \endverbatim
80: *>
81: *> \param[in] S
82: *> \verbatim
83: *> S is DOUBLE PRECISION array, dimension (N)
84: *> The scale factors for A.
85: *> \endverbatim
86: *>
87: *> \param[in] SCOND
88: *> \verbatim
89: *> SCOND is DOUBLE PRECISION
90: *> Ratio of the smallest S(i) to the largest S(i).
91: *> \endverbatim
92: *>
93: *> \param[in] AMAX
94: *> \verbatim
95: *> AMAX is DOUBLE PRECISION
96: *> Absolute value of largest matrix entry.
97: *> \endverbatim
98: *>
99: *> \param[out] EQUED
100: *> \verbatim
101: *> EQUED is CHARACTER*1
102: *> Specifies whether or not equilibration was done.
103: *> = 'N': No equilibration.
104: *> = 'Y': Equilibration was done, i.e., A has been replaced by
105: *> diag(S) * A * diag(S).
106: *> \endverbatim
107: *
108: *> \par Internal Parameters:
109: * =========================
110: *>
111: *> \verbatim
112: *> THRESH is a threshold value used to decide if scaling should be done
113: *> based on the ratio of the scaling factors. If SCOND < THRESH,
114: *> scaling is done.
115: *>
116: *> LARGE and SMALL are threshold values used to decide if scaling should
117: *> be done based on the absolute size of the largest matrix element.
118: *> If AMAX > LARGE or AMAX < SMALL, scaling is done.
119: *> \endverbatim
120: *
121: * Authors:
122: * ========
123: *
124: *> \author Univ. of Tennessee
125: *> \author Univ. of California Berkeley
126: *> \author Univ. of Colorado Denver
127: *> \author NAG Ltd.
128: *
1.11 ! bertrand 129: *> \date September 2012
1.8 bertrand 130: *
131: *> \ingroup doubleSYauxiliary
132: *
133: * =====================================================================
1.1 bertrand 134: SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
135: *
1.11 ! bertrand 136: * -- LAPACK auxiliary routine (version 3.4.2) --
1.1 bertrand 137: * -- LAPACK is a software package provided by Univ. of Tennessee, --
138: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.11 ! bertrand 139: * September 2012
1.1 bertrand 140: *
141: * .. Scalar Arguments ..
142: CHARACTER EQUED, UPLO
143: INTEGER LDA, N
144: DOUBLE PRECISION AMAX, SCOND
145: * ..
146: * .. Array Arguments ..
147: DOUBLE PRECISION A( LDA, * ), S( * )
148: * ..
149: *
150: * =====================================================================
151: *
152: * .. Parameters ..
153: DOUBLE PRECISION ONE, THRESH
154: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
155: * ..
156: * .. Local Scalars ..
157: INTEGER I, J
158: DOUBLE PRECISION CJ, LARGE, SMALL
159: * ..
160: * .. External Functions ..
161: LOGICAL LSAME
162: DOUBLE PRECISION DLAMCH
163: EXTERNAL LSAME, DLAMCH
164: * ..
165: * .. Executable Statements ..
166: *
167: * Quick return if possible
168: *
169: IF( N.LE.0 ) THEN
170: EQUED = 'N'
171: RETURN
172: END IF
173: *
174: * Initialize LARGE and SMALL.
175: *
176: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
177: LARGE = ONE / SMALL
178: *
179: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
180: *
181: * No equilibration
182: *
183: EQUED = 'N'
184: ELSE
185: *
186: * Replace A by diag(S) * A * diag(S).
187: *
188: IF( LSAME( UPLO, 'U' ) ) THEN
189: *
190: * Upper triangle of A is stored.
191: *
192: DO 20 J = 1, N
193: CJ = S( J )
194: DO 10 I = 1, J
195: A( I, J ) = CJ*S( I )*A( I, J )
196: 10 CONTINUE
197: 20 CONTINUE
198: ELSE
199: *
200: * Lower triangle of A is stored.
201: *
202: DO 40 J = 1, N
203: CJ = S( J )
204: DO 30 I = J, N
205: A( I, J ) = CJ*S( I )*A( I, J )
206: 30 CONTINUE
207: 40 CONTINUE
208: END IF
209: EQUED = 'Y'
210: END IF
211: *
212: RETURN
213: *
214: * End of DLAQSY
215: *
216: END
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