LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
sbdt02.f
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1 *> \brief \b SBDT02
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE SBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID )
12 *
13 * .. Scalar Arguments ..
14 * INTEGER LDB, LDC, LDU, M, N
15 * REAL RESID
16 * ..
17 * .. Array Arguments ..
18 * REAL B( LDB, * ), C( LDC, * ), U( LDU, * ),
19 * \$ WORK( * )
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> SBDT02 tests the change of basis C = U' * B by computing the residual
29 *>
30 *> RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
31 *>
32 *> where B and C are M by N matrices, U is an M by M orthogonal matrix,
33 *> and EPS is the machine precision.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] M
40 *> \verbatim
41 *> M is INTEGER
42 *> The number of rows of the matrices B and C and the order of
43 *> the matrix Q.
44 *> \endverbatim
45 *>
46 *> \param[in] N
47 *> \verbatim
48 *> N is INTEGER
49 *> The number of columns of the matrices B and C.
50 *> \endverbatim
51 *>
52 *> \param[in] B
53 *> \verbatim
54 *> B is REAL array, dimension (LDB,N)
55 *> The m by n matrix B.
56 *> \endverbatim
57 *>
58 *> \param[in] LDB
59 *> \verbatim
60 *> LDB is INTEGER
61 *> The leading dimension of the array B. LDB >= max(1,M).
62 *> \endverbatim
63 *>
64 *> \param[in] C
65 *> \verbatim
66 *> C is REAL array, dimension (LDC,N)
67 *> The m by n matrix C, assumed to contain U' * B.
68 *> \endverbatim
69 *>
70 *> \param[in] LDC
71 *> \verbatim
72 *> LDC is INTEGER
73 *> The leading dimension of the array C. LDC >= max(1,M).
74 *> \endverbatim
75 *>
76 *> \param[in] U
77 *> \verbatim
78 *> U is REAL array, dimension (LDU,M)
79 *> The m by m orthogonal matrix U.
80 *> \endverbatim
81 *>
82 *> \param[in] LDU
83 *> \verbatim
84 *> LDU is INTEGER
85 *> The leading dimension of the array U. LDU >= max(1,M).
86 *> \endverbatim
87 *>
88 *> \param[out] WORK
89 *> \verbatim
90 *> WORK is REAL array, dimension (M)
91 *> \endverbatim
92 *>
93 *> \param[out] RESID
94 *> \verbatim
95 *> RESID is REAL
96 *> RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
97 *> \endverbatim
98 *
99 * Authors:
100 * ========
101 *
102 *> \author Univ. of Tennessee
103 *> \author Univ. of California Berkeley
104 *> \author Univ. of Colorado Denver
105 *> \author NAG Ltd.
106 *
107 *> \date November 2011
108 *
109 *> \ingroup single_eig
110 *
111 * =====================================================================
112  SUBROUTINE sbdt02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID )
113 *
114 * -- LAPACK test routine (version 3.4.0) --
115 * -- LAPACK is a software package provided by Univ. of Tennessee, --
116 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117 * November 2011
118 *
119 * .. Scalar Arguments ..
120  INTEGER LDB, LDC, LDU, M, N
121  REAL RESID
122 * ..
123 * .. Array Arguments ..
124  REAL B( ldb, * ), C( ldc, * ), U( ldu, * ),
125  \$ work( * )
126 * ..
127 *
128 * ======================================================================
129 *
130 * .. Parameters ..
131  REAL ZERO, ONE
132  parameter ( zero = 0.0e+0, one = 1.0e+0 )
133 * ..
134 * .. Local Scalars ..
135  INTEGER J
136  REAL BNORM, EPS, REALMN
137 * ..
138 * .. External Functions ..
139  REAL SASUM, SLAMCH, SLANGE
140  EXTERNAL sasum, slamch, slange
141 * ..
142 * .. External Subroutines ..
143  EXTERNAL scopy, sgemv
144 * ..
145 * .. Intrinsic Functions ..
146  INTRINSIC max, min, real
147 * ..
148 * .. Executable Statements ..
149 *
150 * Quick return if possible
151 *
152  resid = zero
153  IF( m.LE.0 .OR. n.LE.0 )
154  \$ RETURN
155  realmn = REAL( MAX( M, N ) )
156  eps = slamch( 'Precision' )
157 *
158 * Compute norm( B - U * C )
159 *
160  DO 10 j = 1, n
161  CALL scopy( m, b( 1, j ), 1, work, 1 )
162  CALL sgemv( 'No transpose', m, m, -one, u, ldu, c( 1, j ), 1,
163  \$ one, work, 1 )
164  resid = max( resid, sasum( m, work, 1 ) )
165  10 CONTINUE
166 *
167 * Compute norm of B.
168 *
169  bnorm = slange( '1', m, n, b, ldb, work )
170 *
171  IF( bnorm.LE.zero ) THEN
172  IF( resid.NE.zero )
173  \$ resid = one / eps
174  ELSE
175  IF( bnorm.GE.resid ) THEN
176  resid = ( resid / bnorm ) / ( realmn*eps )
177  ELSE
178  IF( bnorm.LT.one ) THEN
179  resid = ( min( resid, realmn*bnorm ) / bnorm ) /
180  \$ ( realmn*eps )
181  ELSE
182  resid = min( resid / bnorm, realmn ) / ( realmn*eps )
183  END IF
184  END IF
185  END IF
186  RETURN
187 *
188 * End of SBDT02
189 *
190  END
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
Definition: sgemv.f:158
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:53
subroutine sbdt02(M, N, B, LDB, C, LDC, U, LDU, WORK, RESID)
SBDT02
Definition: sbdt02.f:113