LAPACK  3.6.1 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 *
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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 *> \date September 2012
137 *
138 *> \ingroup realOTHERauxiliary
139 *
140 * =====================================================================
141  SUBROUTINE slaqsb( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
142 *
143 * -- LAPACK auxiliary routine (version 3.4.2) --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 * September 2012
147 *
148 * .. Scalar Arguments ..
149  CHARACTER EQUED, UPLO
150  INTEGER KD, LDAB, N
151  REAL AMAX, SCOND
152 * ..
153 * .. Array Arguments ..
154  REAL AB( ldab, * ), S( * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. Parameters ..
160  REAL ONE, THRESH
161  parameter ( one = 1.0e+0, thresh = 0.1e+0 )
162 * ..
163 * .. Local Scalars ..
164  INTEGER I, J
165  REAL CJ, LARGE, SMALL
166 * ..
167 * .. External Functions ..
168  LOGICAL LSAME
169  REAL SLAMCH
170  EXTERNAL lsame, slamch
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 = slamch( 'Safe minimum' ) / slamch( '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 SLAQSB
225 *
226  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:142