LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cbdt05.f
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1 *> \brief \b CBDT05
2 * =========== DOCUMENTATION ===========
3 *
4 * Online html documentation available at
5 * http://www.netlib.org/lapack/explore-html/
6 *
7 * Definition:
8 * ===========
9 *
10 * SUBROUTINE CBDT05( M, N, A, LDA, S, NS, U, LDU,
11 * VT, LDVT, WORK, RESID )
12 *
13 * .. Scalar Arguments ..
14 * INTEGER LDA, LDU, LDVT, N, NS
15 * REAL RESID
16 * ..
17 * .. Array Arguments ..
18 * REAL S( * )
19 * COMPLEX A( LDA, * ), U( * ), VT( LDVT, * ), WORK( * )
20 * ..
21 *
22 *> \par Purpose:
23 * =============
24 *>
25 *> \verbatim
26 *>
27 *> CBDT05 reconstructs a bidiagonal matrix B from its (partial) SVD:
28 *> S = U' * B * V
29 *> where U and V are orthogonal matrices and S is diagonal.
30 *>
31 *> The test ratio to test the singular value decomposition is
32 *> RESID = norm( S - U' * B * V ) / ( n * norm(B) * EPS )
33 *> where VT = V' 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 A and U.
43 *> \endverbatim
44 *>
45 *> \param[in] N
46 *> \verbatim
47 *> N is INTEGER
48 *> The number of columns of the matrices A and VT.
49 *> \endverbatim
50 *>
51 *> \param[in] A
52 *> \verbatim
53 *> A is COMPLEX array, dimension (LDA,N)
54 *> The m by n matrix A.
55 *> \endverbatim
56 *>
57 *> \param[in] LDA
58 *> \verbatim
59 *> LDA is INTEGER
60 *> The leading dimension of the array A. LDA >= max(1,M).
61 *> \endverbatim
62 *>
63 *> \param[in] S
64 *> \verbatim
65 *> S is REAL array, dimension (NS)
66 *> The singular values from the (partial) SVD of B, sorted in
67 *> decreasing order.
68 *> \endverbatim
69 *>
70 *> \param[in] NS
71 *> \verbatim
72 *> NS is INTEGER
73 *> The number of singular values/vectors from the (partial)
74 *> SVD of B.
75 *> \endverbatim
76 *>
77 *> \param[in] U
78 *> \verbatim
79 *> U is COMPLEX array, dimension (LDU,NS)
80 *> The n by ns orthogonal matrix U in S = U' * B * V.
81 *> \endverbatim
82 *>
83 *> \param[in] LDU
84 *> \verbatim
85 *> LDU is INTEGER
86 *> The leading dimension of the array U. LDU >= max(1,N)
87 *> \endverbatim
88 *>
89 *> \param[in] VT
90 *> \verbatim
91 *> VT is COMPLEX array, dimension (LDVT,N)
92 *> The n by ns orthogonal matrix V in S = U' * B * V.
93 *> \endverbatim
94 *>
95 *> \param[in] LDVT
96 *> \verbatim
97 *> LDVT is INTEGER
98 *> The leading dimension of the array VT.
99 *> \endverbatim
100 *>
101 *> \param[out] WORK
102 *> \verbatim
103 *> WORK is COMPLEX array, dimension (M,N)
104 *> \endverbatim
105 *>
106 *> \param[out] RESID
107 *> \verbatim
108 *> RESID is REAL
109 *> The test ratio: norm(S - U' * A * V) / ( n * norm(A) * EPS )
110 *> \endverbatim
111 *
112 * Authors:
113 * ========
114 *
115 *> \author Univ. of Tennessee
116 *> \author Univ. of California Berkeley
117 *> \author Univ. of Colorado Denver
118 *> \author NAG Ltd.
119 *
120 *> \ingroup double_eig
121 *
122 * =====================================================================
123  SUBROUTINE cbdt05( M, N, A, LDA, S, NS, U, LDU,
124  $ VT, LDVT, WORK, RESID )
125 *
126 * -- LAPACK test routine --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 *
130 * .. Scalar Arguments ..
131  INTEGER LDA, LDU, LDVT, M, N, NS
132  REAL RESID
133 * ..
134 * .. Array Arguments ..
135  REAL S( * )
136  COMPLEX A( LDA, * ), U( * ), VT( LDVT, * ), WORK( * )
137 * ..
138 *
139 * ======================================================================
140 *
141 * .. Parameters ..
142  REAL ZERO, ONE
143  parameter( zero = 0.0e+0, one = 1.0e+0 )
144  COMPLEX CZERO, CONE
145  parameter( czero = ( 0.0e+0, 0.0e+0 ),
146  $ cone = ( 1.0e+0, 0.0e+0 ) )
147 * ..
148 * .. Local Scalars ..
149  INTEGER I, J
150  REAL ANORM, EPS
151 * ..
152 * .. Local Arrays ..
153  REAL DUM( 1 )
154 * ..
155 * .. External Functions ..
156  LOGICAL LSAME
157  INTEGER ISAMAX
158  REAL SASUM, SCASUM, SLAMCH, CLANGE
159  EXTERNAL lsame, isamax, sasum, scasum, slamch, clange
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL cgemm
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC abs, real, max, min
166 * ..
167 * .. Executable Statements ..
168 *
169 * Quick return if possible.
170 *
171  resid = zero
172  IF( min( m, n ).LE.0 .OR. ns.LE.0 )
173  $ RETURN
174 *
175  eps = slamch( 'Precision' )
176  anorm = clange( 'M', m, n, a, lda, dum )
177 *
178 * Compute U' * A * V.
179 *
180  CALL cgemm( 'N', 'C', m, ns, n, cone, a, lda, vt,
181  $ ldvt, czero, work( 1+ns*ns ), m )
182  CALL cgemm( 'C', 'N', ns, ns, m, -cone, u, ldu, work( 1+ns*ns ),
183  $ m, czero, work, ns )
184 *
185 * norm(S - U' * B * V)
186 *
187  j = 0
188  DO 10 i = 1, ns
189  work( j+i ) = work( j+i ) + cmplx( s( i ), zero )
190  resid = max( resid, scasum( ns, work( j+1 ), 1 ) )
191  j = j + ns
192  10 CONTINUE
193 *
194  IF( anorm.LE.zero ) THEN
195  IF( resid.NE.zero )
196  $ resid = one / eps
197  ELSE
198  IF( anorm.GE.resid ) THEN
199  resid = ( resid / anorm ) / ( real( n )*eps )
200  ELSE
201  IF( anorm.LT.one ) THEN
202  resid = ( min( resid, real( n )*anorm ) / anorm ) /
203  $ ( real( n )*eps )
204  ELSE
205  resid = min( resid / anorm, real( n ) ) /
206  $ ( real( n )*eps )
207  END IF
208  END IF
209  END IF
210 *
211  RETURN
212 *
213 * End of CBDT05
214 *
215  END
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine cbdt05(M, N, A, LDA, S, NS, U, LDU, VT, LDVT, WORK, RESID)
CBDT05
Definition: cbdt05.f:125