Annotation of rpl/lapack/lapack/zlaqsb.f, revision 1.13
1.12 bertrand 1: *> \brief \b ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLAQSB + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqsb.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqsb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqsb.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLAQSB( 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 S( * )
30: * COMPLEX*16 AB( LDAB, * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZLAQSB equilibrates a symmetric band matrix A using the scaling
40: *> factors 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] KD
62: *> \verbatim
63: *> KD is INTEGER
64: *> The number of super-diagonals of the matrix A if UPLO = 'U',
65: *> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
66: *> \endverbatim
67: *>
68: *> \param[in,out] AB
69: *> \verbatim
70: *> AB is COMPLEX*16 array, dimension (LDAB,N)
71: *> On entry, the upper or lower triangle of the symmetric band
72: *> matrix A, stored in the first KD+1 rows of the array. The
73: *> j-th column of A is stored in the j-th column of the array AB
74: *> as follows:
75: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
76: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
77: *>
78: *> On exit, if INFO = 0, the triangular factor U or L from the
79: *> Cholesky factorization A = U**H *U or A = L*L**H of the band
80: *> matrix A, in the same storage format as A.
81: *> \endverbatim
82: *>
83: *> \param[in] LDAB
84: *> \verbatim
85: *> LDAB is INTEGER
86: *> The leading dimension of the array AB. LDAB >= KD+1.
87: *> \endverbatim
88: *>
89: *> \param[in] S
90: *> \verbatim
91: *> S is DOUBLE PRECISION array, dimension (N)
92: *> The scale factors for A.
93: *> \endverbatim
94: *>
95: *> \param[in] SCOND
96: *> \verbatim
97: *> SCOND is DOUBLE PRECISION
98: *> Ratio of the smallest S(i) to the largest S(i).
99: *> \endverbatim
100: *>
101: *> \param[in] AMAX
102: *> \verbatim
103: *> AMAX is DOUBLE PRECISION
104: *> Absolute value of largest matrix entry.
105: *> \endverbatim
106: *>
107: *> \param[out] EQUED
108: *> \verbatim
109: *> EQUED is CHARACTER*1
110: *> Specifies whether or not equilibration was done.
111: *> = 'N': No equilibration.
112: *> = 'Y': Equilibration was done, i.e., A has been replaced by
113: *> diag(S) * A * diag(S).
114: *> \endverbatim
115: *
116: *> \par Internal Parameters:
117: * =========================
118: *>
119: *> \verbatim
120: *> THRESH is a threshold value used to decide if scaling should be done
121: *> based on the ratio of the scaling factors. If SCOND < THRESH,
122: *> scaling is done.
123: *>
124: *> LARGE and SMALL are threshold values used to decide if scaling should
125: *> be done based on the absolute size of the largest matrix element.
126: *> If AMAX > LARGE or AMAX < SMALL, scaling is done.
127: *> \endverbatim
128: *
129: * Authors:
130: * ========
131: *
132: *> \author Univ. of Tennessee
133: *> \author Univ. of California Berkeley
134: *> \author Univ. of Colorado Denver
135: *> \author NAG Ltd.
136: *
1.12 bertrand 137: *> \date September 2012
1.9 bertrand 138: *
139: *> \ingroup complex16OTHERauxiliary
140: *
141: * =====================================================================
1.1 bertrand 142: SUBROUTINE ZLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
143: *
1.12 bertrand 144: * -- LAPACK auxiliary routine (version 3.4.2) --
1.1 bertrand 145: * -- LAPACK is a software package provided by Univ. of Tennessee, --
146: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.12 bertrand 147: * September 2012
1.1 bertrand 148: *
149: * .. Scalar Arguments ..
150: CHARACTER EQUED, UPLO
151: INTEGER KD, LDAB, N
152: DOUBLE PRECISION AMAX, SCOND
153: * ..
154: * .. Array Arguments ..
155: DOUBLE PRECISION S( * )
156: COMPLEX*16 AB( LDAB, * )
157: * ..
158: *
159: * =====================================================================
160: *
161: * .. Parameters ..
162: DOUBLE PRECISION ONE, THRESH
163: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
164: * ..
165: * .. Local Scalars ..
166: INTEGER I, J
167: DOUBLE PRECISION CJ, LARGE, SMALL
168: * ..
169: * .. External Functions ..
170: LOGICAL LSAME
171: DOUBLE PRECISION DLAMCH
172: EXTERNAL LSAME, DLAMCH
173: * ..
174: * .. Intrinsic Functions ..
175: INTRINSIC MAX, MIN
176: * ..
177: * .. Executable Statements ..
178: *
179: * Quick return if possible
180: *
181: IF( N.LE.0 ) THEN
182: EQUED = 'N'
183: RETURN
184: END IF
185: *
186: * Initialize LARGE and SMALL.
187: *
188: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
189: LARGE = ONE / SMALL
190: *
191: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
192: *
193: * No equilibration
194: *
195: EQUED = 'N'
196: ELSE
197: *
198: * Replace A by diag(S) * A * diag(S).
199: *
200: IF( LSAME( UPLO, 'U' ) ) THEN
201: *
202: * Upper triangle of A is stored in band format.
203: *
204: DO 20 J = 1, N
205: CJ = S( J )
206: DO 10 I = MAX( 1, J-KD ), J
207: AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
208: 10 CONTINUE
209: 20 CONTINUE
210: ELSE
211: *
212: * Lower triangle of A is stored.
213: *
214: DO 40 J = 1, N
215: CJ = S( J )
216: DO 30 I = J, MIN( N, J+KD )
217: AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
218: 30 CONTINUE
219: 40 CONTINUE
220: END IF
221: EQUED = 'Y'
222: END IF
223: *
224: RETURN
225: *
226: * End of ZLAQSB
227: *
228: END
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