LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
claqhb.f
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1 *> \brief \b CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER EQUED, UPLO
25 * INTEGER KD, LDAB, N
26 * REAL AMAX, SCOND
27 * ..
28 * .. Array Arguments ..
29 * REAL S( * )
30 * COMPLEX AB( LDAB, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> CLAQHB equilibrates an Hermitian 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 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[out] S
90 *> \verbatim
91 *> S is REAL array, dimension (N)
92 *> The scale factors for A.
93 *> \endverbatim
94 *>
95 *> \param[in] SCOND
96 *> \verbatim
97 *> SCOND is REAL
98 *> Ratio of the smallest S(i) to the largest S(i).
99 *> \endverbatim
100 *>
101 *> \param[in] AMAX
102 *> \verbatim
103 *> AMAX is REAL
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 *
137 *> \ingroup complexOTHERauxiliary
138 *
139 * =====================================================================
140  SUBROUTINE claqhb( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
141 *
142 * -- LAPACK auxiliary routine --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 *
146 * .. Scalar Arguments ..
147  CHARACTER EQUED, UPLO
148  INTEGER KD, LDAB, N
149  REAL AMAX, SCOND
150 * ..
151 * .. Array Arguments ..
152  REAL S( * )
153  COMPLEX AB( LDAB, * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  REAL ONE, THRESH
160  parameter( one = 1.0e+0, thresh = 0.1e+0 )
161 * ..
162 * .. Local Scalars ..
163  INTEGER I, J
164  REAL CJ, LARGE, SMALL
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  REAL SLAMCH
169  EXTERNAL lsame, slamch
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC max, min, real
173 * ..
174 * .. Executable Statements ..
175 *
176 * Quick return if possible
177 *
178  IF( n.LE.0 ) THEN
179  equed = 'N'
180  RETURN
181  END IF
182 *
183 * Initialize LARGE and SMALL.
184 *
185  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
186  large = one / small
187 *
188  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
189 *
190 * No equilibration
191 *
192  equed = 'N'
193  ELSE
194 *
195 * Replace A by diag(S) * A * diag(S).
196 *
197  IF( lsame( uplo, 'U' ) ) THEN
198 *
199 * Upper triangle of A is stored in band format.
200 *
201  DO 20 j = 1, n
202  cj = s( j )
203  DO 10 i = max( 1, j-kd ), j - 1
204  ab( kd+1+i-j, j ) = cj*s( i )*ab( kd+1+i-j, j )
205  10 CONTINUE
206  ab( kd+1, j ) = cj*cj*real( ab( kd+1, j ) )
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  ab( 1, j ) = cj*cj*real( ab( 1, j ) )
215  DO 30 i = j + 1, min( n, j+kd )
216  ab( 1+i-j, j ) = cj*s( i )*ab( 1+i-j, j )
217  30 CONTINUE
218  40 CONTINUE
219  END IF
220  equed = 'Y'
221  END IF
222 *
223  RETURN
224 *
225 * End of CLAQHB
226 *
227  END
subroutine claqhb(UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.
Definition: claqhb.f:141