Annotation of rpl/lapack/lapack/zlaqsp.f, revision 1.18
1.11 bertrand 1: *> \brief \b ZLAQSP 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 ZLAQSP + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqsp.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqsp.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqsp.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLAQSP( 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 S( * )
30: * COMPLEX*16 AP( * )
31: * ..
1.15 bertrand 32: *
1.8 bertrand 33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZLAQSP equilibrates a symmetric matrix A using the scaling factors
40: *> in the vector S.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] UPLO
47: *> \verbatim
48: *> UPLO is CHARACTER*1
49: *> Specifies whether the upper or lower triangular part of the
50: *> symmetric matrix A is stored.
51: *> = 'U': Upper triangular
52: *> = 'L': Lower triangular
53: *> \endverbatim
54: *>
55: *> \param[in] N
56: *> \verbatim
57: *> N is INTEGER
58: *> The order of the matrix A. N >= 0.
59: *> \endverbatim
60: *>
61: *> \param[in,out] AP
62: *> \verbatim
63: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
64: *> On entry, the upper or lower triangle of the symmetric matrix
65: *> A, packed columnwise in a linear array. The j-th column of A
66: *> is stored in the array AP as follows:
67: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
68: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
69: *>
70: *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in
71: *> the same storage format as A.
72: *> \endverbatim
73: *>
74: *> \param[in] S
75: *> \verbatim
76: *> S is DOUBLE PRECISION array, dimension (N)
77: *> The scale factors for A.
78: *> \endverbatim
79: *>
80: *> \param[in] SCOND
81: *> \verbatim
82: *> SCOND is DOUBLE PRECISION
83: *> Ratio of the smallest S(i) to the largest S(i).
84: *> \endverbatim
85: *>
86: *> \param[in] AMAX
87: *> \verbatim
88: *> AMAX is DOUBLE PRECISION
89: *> Absolute value of largest matrix entry.
90: *> \endverbatim
91: *>
92: *> \param[out] EQUED
93: *> \verbatim
94: *> EQUED is CHARACTER*1
95: *> Specifies whether or not equilibration was done.
96: *> = 'N': No equilibration.
97: *> = 'Y': Equilibration was done, i.e., A has been replaced by
98: *> diag(S) * A * diag(S).
99: *> \endverbatim
100: *
101: *> \par Internal Parameters:
102: * =========================
103: *>
104: *> \verbatim
105: *> THRESH is a threshold value used to decide if scaling should be done
106: *> based on the ratio of the scaling factors. If SCOND < THRESH,
107: *> scaling is done.
108: *>
109: *> LARGE and SMALL are threshold values used to decide if scaling should
110: *> be done based on the absolute size of the largest matrix element.
111: *> If AMAX > LARGE or AMAX < SMALL, scaling is done.
112: *> \endverbatim
113: *
114: * Authors:
115: * ========
116: *
1.15 bertrand 117: *> \author Univ. of Tennessee
118: *> \author Univ. of California Berkeley
119: *> \author Univ. of Colorado Denver
120: *> \author NAG Ltd.
1.8 bertrand 121: *
122: *> \ingroup complex16OTHERauxiliary
123: *
124: * =====================================================================
1.1 bertrand 125: SUBROUTINE ZLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
126: *
1.18 ! bertrand 127: * -- LAPACK auxiliary routine --
1.1 bertrand 128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130: *
131: * .. Scalar Arguments ..
132: CHARACTER EQUED, UPLO
133: INTEGER N
134: DOUBLE PRECISION AMAX, SCOND
135: * ..
136: * .. Array Arguments ..
137: DOUBLE PRECISION S( * )
138: COMPLEX*16 AP( * )
139: * ..
140: *
141: * =====================================================================
142: *
143: * .. Parameters ..
144: DOUBLE PRECISION ONE, THRESH
145: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
146: * ..
147: * .. Local Scalars ..
148: INTEGER I, J, JC
149: DOUBLE PRECISION CJ, LARGE, SMALL
150: * ..
151: * .. External Functions ..
152: LOGICAL LSAME
153: DOUBLE PRECISION DLAMCH
154: EXTERNAL LSAME, DLAMCH
155: * ..
156: * .. Executable Statements ..
157: *
158: * Quick return if possible
159: *
160: IF( N.LE.0 ) THEN
161: EQUED = 'N'
162: RETURN
163: END IF
164: *
165: * Initialize LARGE and SMALL.
166: *
167: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
168: LARGE = ONE / SMALL
169: *
170: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
171: *
172: * No equilibration
173: *
174: EQUED = 'N'
175: ELSE
176: *
177: * Replace A by diag(S) * A * diag(S).
178: *
179: IF( LSAME( UPLO, 'U' ) ) THEN
180: *
181: * Upper triangle of A is stored.
182: *
183: JC = 1
184: DO 20 J = 1, N
185: CJ = S( J )
186: DO 10 I = 1, J
187: AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
188: 10 CONTINUE
189: JC = JC + J
190: 20 CONTINUE
191: ELSE
192: *
193: * Lower triangle of A is stored.
194: *
195: JC = 1
196: DO 40 J = 1, N
197: CJ = S( J )
198: DO 30 I = J, N
199: AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
200: 30 CONTINUE
201: JC = JC + N - J + 1
202: 40 CONTINUE
203: END IF
204: EQUED = 'Y'
205: END IF
206: *
207: RETURN
208: *
209: * End of ZLAQSP
210: *
211: END
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