Annotation of rpl/lapack/lapack/dlaqsb.f, revision 1.10
1.9 bertrand 1: *> \brief \b DLAQSB
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLAQSB + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsb.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqsb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqsb.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER EQUED, UPLO
25: * INTEGER KD, LDAB, N
26: * DOUBLE PRECISION AMAX, SCOND
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION AB( LDAB, * ), S( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DLAQSB equilibrates a symmetric band matrix A using the scaling
39: *> factors 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] KD
61: *> \verbatim
62: *> KD is INTEGER
63: *> The number of super-diagonals of the matrix A if UPLO = 'U',
64: *> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
65: *> \endverbatim
66: *>
67: *> \param[in,out] AB
68: *> \verbatim
69: *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
70: *> On entry, the upper or lower triangle of the symmetric band
71: *> matrix A, stored in the first KD+1 rows of the array. The
72: *> j-th column of A is stored in the j-th column of the array AB
73: *> as follows:
74: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
75: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
76: *>
77: *> On exit, if INFO = 0, the triangular factor U or L from the
78: *> Cholesky factorization A = U**T*U or A = L*L**T of the band
79: *> matrix A, in the same storage format as A.
80: *> \endverbatim
81: *>
82: *> \param[in] LDAB
83: *> \verbatim
84: *> LDAB is INTEGER
85: *> The leading dimension of the array AB. LDAB >= KD+1.
86: *> \endverbatim
87: *>
88: *> \param[in] S
89: *> \verbatim
90: *> S is DOUBLE PRECISION array, dimension (N)
91: *> The scale factors for A.
92: *> \endverbatim
93: *>
94: *> \param[in] SCOND
95: *> \verbatim
96: *> SCOND is DOUBLE PRECISION
97: *> Ratio of the smallest S(i) to the largest S(i).
98: *> \endverbatim
99: *>
100: *> \param[in] AMAX
101: *> \verbatim
102: *> AMAX is DOUBLE PRECISION
103: *> Absolute value of largest matrix entry.
104: *> \endverbatim
105: *>
106: *> \param[out] EQUED
107: *> \verbatim
108: *> EQUED is CHARACTER*1
109: *> Specifies whether or not equilibration was done.
110: *> = 'N': No equilibration.
111: *> = 'Y': Equilibration was done, i.e., A has been replaced by
112: *> diag(S) * A * diag(S).
113: *> \endverbatim
114: *
115: *> \par Internal Parameters:
116: * =========================
117: *>
118: *> \verbatim
119: *> THRESH is a threshold value used to decide if scaling should be done
120: *> based on the ratio of the scaling factors. If SCOND < THRESH,
121: *> scaling is done.
122: *>
123: *> LARGE and SMALL are threshold values used to decide if scaling should
124: *> be done based on the absolute size of the largest matrix element.
125: *> If AMAX > LARGE or AMAX < SMALL, scaling is done.
126: *> \endverbatim
127: *
128: * Authors:
129: * ========
130: *
131: *> \author Univ. of Tennessee
132: *> \author Univ. of California Berkeley
133: *> \author Univ. of Colorado Denver
134: *> \author NAG Ltd.
135: *
136: *> \date November 2011
137: *
138: *> \ingroup doubleOTHERauxiliary
139: *
140: * =====================================================================
1.1 bertrand 141: SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
142: *
1.9 bertrand 143: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 144: * -- LAPACK is a software package provided by Univ. of Tennessee, --
145: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 146: * November 2011
1.1 bertrand 147: *
148: * .. Scalar Arguments ..
149: CHARACTER EQUED, UPLO
150: INTEGER KD, LDAB, N
151: DOUBLE PRECISION AMAX, SCOND
152: * ..
153: * .. Array Arguments ..
154: DOUBLE PRECISION AB( LDAB, * ), S( * )
155: * ..
156: *
157: * =====================================================================
158: *
159: * .. Parameters ..
160: DOUBLE PRECISION ONE, THRESH
161: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
162: * ..
163: * .. Local Scalars ..
164: INTEGER I, J
165: DOUBLE PRECISION CJ, LARGE, SMALL
166: * ..
167: * .. External Functions ..
168: LOGICAL LSAME
169: DOUBLE PRECISION DLAMCH
170: EXTERNAL LSAME, DLAMCH
171: * ..
172: * .. Intrinsic Functions ..
173: INTRINSIC MAX, MIN
174: * ..
175: * .. Executable Statements ..
176: *
177: * Quick return if possible
178: *
179: IF( N.LE.0 ) THEN
180: EQUED = 'N'
181: RETURN
182: END IF
183: *
184: * Initialize LARGE and SMALL.
185: *
186: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
187: LARGE = ONE / SMALL
188: *
189: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
190: *
191: * No equilibration
192: *
193: EQUED = 'N'
194: ELSE
195: *
196: * Replace A by diag(S) * A * diag(S).
197: *
198: IF( LSAME( UPLO, 'U' ) ) THEN
199: *
200: * Upper triangle of A is stored in band format.
201: *
202: DO 20 J = 1, N
203: CJ = S( J )
204: DO 10 I = MAX( 1, J-KD ), J
205: AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
206: 10 CONTINUE
207: 20 CONTINUE
208: ELSE
209: *
210: * Lower triangle of A is stored.
211: *
212: DO 40 J = 1, N
213: CJ = S( J )
214: DO 30 I = J, MIN( N, J+KD )
215: AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
216: 30 CONTINUE
217: 40 CONTINUE
218: END IF
219: EQUED = 'Y'
220: END IF
221: *
222: RETURN
223: *
224: * End of DLAQSB
225: *
226: END
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