Annotation of rpl/lapack/lapack/dlaqsp.f, revision 1.18
1.11 bertrand 1: *> \brief \b DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
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 DLAQSP + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsp.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqsp.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqsp.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
1.15 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER EQUED, UPLO
25: * INTEGER N
26: * DOUBLE PRECISION AMAX, SCOND
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION AP( * ), S( * )
30: * ..
1.15 bertrand 31: *
1.8 bertrand 32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DLAQSP 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] AP
61: *> \verbatim
62: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
63: *> On entry, the upper or lower triangle of the symmetric matrix
64: *> A, packed columnwise in a linear array. The j-th column of A
65: *> is stored in the array AP as follows:
66: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
67: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
68: *>
69: *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in
70: *> the same storage format as A.
71: *> \endverbatim
72: *>
73: *> \param[in] S
74: *> \verbatim
75: *> S is DOUBLE PRECISION array, dimension (N)
76: *> The scale factors for A.
77: *> \endverbatim
78: *>
79: *> \param[in] SCOND
80: *> \verbatim
81: *> SCOND is DOUBLE PRECISION
82: *> Ratio of the smallest S(i) to the largest S(i).
83: *> \endverbatim
84: *>
85: *> \param[in] AMAX
86: *> \verbatim
87: *> AMAX is DOUBLE PRECISION
88: *> Absolute value of largest matrix entry.
89: *> \endverbatim
90: *>
91: *> \param[out] EQUED
92: *> \verbatim
93: *> EQUED is CHARACTER*1
94: *> Specifies whether or not equilibration was done.
95: *> = 'N': No equilibration.
96: *> = 'Y': Equilibration was done, i.e., A has been replaced by
97: *> diag(S) * A * diag(S).
98: *> \endverbatim
99: *
100: *> \par Internal Parameters:
101: * =========================
102: *>
103: *> \verbatim
104: *> THRESH is a threshold value used to decide if scaling should be done
105: *> based on the ratio of the scaling factors. If SCOND < THRESH,
106: *> scaling is done.
107: *>
108: *> LARGE and SMALL are threshold values used to decide if scaling should
109: *> be done based on the absolute size of the largest matrix element.
110: *> If AMAX > LARGE or AMAX < SMALL, scaling is done.
111: *> \endverbatim
112: *
113: * Authors:
114: * ========
115: *
1.15 bertrand 116: *> \author Univ. of Tennessee
117: *> \author Univ. of California Berkeley
118: *> \author Univ. of Colorado Denver
119: *> \author NAG Ltd.
1.8 bertrand 120: *
121: *> \ingroup doubleOTHERauxiliary
122: *
123: * =====================================================================
1.1 bertrand 124: SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
125: *
1.18 ! bertrand 126: * -- LAPACK auxiliary routine --
1.1 bertrand 127: * -- LAPACK is a software package provided by Univ. of Tennessee, --
128: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129: *
130: * .. Scalar Arguments ..
131: CHARACTER EQUED, UPLO
132: INTEGER N
133: DOUBLE PRECISION AMAX, SCOND
134: * ..
135: * .. Array Arguments ..
136: DOUBLE PRECISION AP( * ), S( * )
137: * ..
138: *
139: * =====================================================================
140: *
141: * .. Parameters ..
142: DOUBLE PRECISION ONE, THRESH
143: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
144: * ..
145: * .. Local Scalars ..
146: INTEGER I, J, JC
147: DOUBLE PRECISION CJ, LARGE, SMALL
148: * ..
149: * .. External Functions ..
150: LOGICAL LSAME
151: DOUBLE PRECISION DLAMCH
152: EXTERNAL LSAME, DLAMCH
153: * ..
154: * .. Executable Statements ..
155: *
156: * Quick return if possible
157: *
158: IF( N.LE.0 ) THEN
159: EQUED = 'N'
160: RETURN
161: END IF
162: *
163: * Initialize LARGE and SMALL.
164: *
165: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
166: LARGE = ONE / SMALL
167: *
168: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
169: *
170: * No equilibration
171: *
172: EQUED = 'N'
173: ELSE
174: *
175: * Replace A by diag(S) * A * diag(S).
176: *
177: IF( LSAME( UPLO, 'U' ) ) THEN
178: *
179: * Upper triangle of A is stored.
180: *
181: JC = 1
182: DO 20 J = 1, N
183: CJ = S( J )
184: DO 10 I = 1, J
185: AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
186: 10 CONTINUE
187: JC = JC + J
188: 20 CONTINUE
189: ELSE
190: *
191: * Lower triangle of A is stored.
192: *
193: JC = 1
194: DO 40 J = 1, N
195: CJ = S( J )
196: DO 30 I = J, N
197: AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
198: 30 CONTINUE
199: JC = JC + N - J + 1
200: 40 CONTINUE
201: END IF
202: EQUED = 'Y'
203: END IF
204: *
205: RETURN
206: *
207: * End of DLAQSP
208: *
209: END
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