LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
slaqsb.f
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1 *> \brief \b SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SLAQSB( 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 AB( LDAB, * ), S( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> SLAQSB 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 REAL 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 REAL array, dimension (N)
91 *> The scale factors for A.
92 *> \endverbatim
93 *>
94 *> \param[in] SCOND
95 *> \verbatim
96 *> SCOND is REAL
97 *> Ratio of the smallest S(i) to the largest S(i).
98 *> \endverbatim
99 *>
100 *> \param[in] AMAX
101 *> \verbatim
102 *> AMAX is REAL
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 *> \ingroup realOTHERauxiliary
137 *
138 * =====================================================================
139  SUBROUTINE slaqsb( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
140 *
141 * -- LAPACK auxiliary routine --
142 * -- LAPACK is a software package provided by Univ. of Tennessee, --
143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144 *
145 * .. Scalar Arguments ..
146  CHARACTER EQUED, UPLO
147  INTEGER KD, LDAB, N
148  REAL AMAX, SCOND
149 * ..
150 * .. Array Arguments ..
151  REAL AB( LDAB, * ), S( * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157  REAL ONE, THRESH
158  parameter( one = 1.0e+0, thresh = 0.1e+0 )
159 * ..
160 * .. Local Scalars ..
161  INTEGER I, J
162  REAL CJ, LARGE, SMALL
163 * ..
164 * .. External Functions ..
165  LOGICAL LSAME
166  REAL SLAMCH
167  EXTERNAL lsame, slamch
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC max, min
171 * ..
172 * .. Executable Statements ..
173 *
174 * Quick return if possible
175 *
176  IF( n.LE.0 ) THEN
177  equed = 'N'
178  RETURN
179  END IF
180 *
181 * Initialize LARGE and SMALL.
182 *
183  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
184  large = one / small
185 *
186  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
187 *
188 * No equilibration
189 *
190  equed = 'N'
191  ELSE
192 *
193 * Replace A by diag(S) * A * diag(S).
194 *
195  IF( lsame( uplo, 'U' ) ) THEN
196 *
197 * Upper triangle of A is stored in band format.
198 *
199  DO 20 j = 1, n
200  cj = s( j )
201  DO 10 i = max( 1, j-kd ), j
202  ab( kd+1+i-j, j ) = cj*s( i )*ab( kd+1+i-j, j )
203  10 CONTINUE
204  20 CONTINUE
205  ELSE
206 *
207 * Lower triangle of A is stored.
208 *
209  DO 40 j = 1, n
210  cj = s( j )
211  DO 30 i = j, min( n, j+kd )
212  ab( 1+i-j, j ) = cj*s( i )*ab( 1+i-j, j )
213  30 CONTINUE
214  40 CONTINUE
215  END IF
216  equed = 'Y'
217  END IF
218 *
219  RETURN
220 *
221 * End of SLAQSB
222 *
223  END
subroutine slaqsb(UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
Definition: slaqsb.f:140