LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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zbdt02.f
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1*> \brief \b ZBDT02
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 ZBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK,
12* RESID )
13*
14* .. Scalar Arguments ..
15* INTEGER LDB, LDC, LDU, M, N
16* DOUBLE PRECISION RESID
17* ..
18* .. Array Arguments ..
19* DOUBLE PRECISION RWORK( * )
20* COMPLEX*16 B( LDB, * ), C( LDC, * ), U( LDU, * ),
21* $ WORK( * )
22* ..
23*
24*
25*> \par Purpose:
26* =============
27*>
28*> \verbatim
29*>
30*> ZBDT02 tests the change of basis C = U**H * B by computing the
31*> residual
32*>
33*> RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
34*>
35*> where B and C are M by N matrices, U is an M by M orthogonal matrix,
36*> and EPS is the machine precision.
37*> \endverbatim
38*
39* Arguments:
40* ==========
41*
42*> \param[in] M
43*> \verbatim
44*> M is INTEGER
45*> The number of rows of the matrices B and C and the order of
46*> the matrix Q.
47*> \endverbatim
48*>
49*> \param[in] N
50*> \verbatim
51*> N is INTEGER
52*> The number of columns of the matrices B and C.
53*> \endverbatim
54*>
55*> \param[in] B
56*> \verbatim
57*> B is COMPLEX*16 array, dimension (LDB,N)
58*> The m by n matrix B.
59*> \endverbatim
60*>
61*> \param[in] LDB
62*> \verbatim
63*> LDB is INTEGER
64*> The leading dimension of the array B. LDB >= max(1,M).
65*> \endverbatim
66*>
67*> \param[in] C
68*> \verbatim
69*> C is COMPLEX*16 array, dimension (LDC,N)
70*> The m by n matrix C, assumed to contain U**H * B.
71*> \endverbatim
72*>
73*> \param[in] LDC
74*> \verbatim
75*> LDC is INTEGER
76*> The leading dimension of the array C. LDC >= max(1,M).
77*> \endverbatim
78*>
79*> \param[in] U
80*> \verbatim
81*> U is COMPLEX*16 array, dimension (LDU,M)
82*> The m by m orthogonal matrix U.
83*> \endverbatim
84*>
85*> \param[in] LDU
86*> \verbatim
87*> LDU is INTEGER
88*> The leading dimension of the array U. LDU >= max(1,M).
89*> \endverbatim
90*>
91*> \param[out] WORK
92*> \verbatim
93*> WORK is COMPLEX*16 array, dimension (M)
94*> \endverbatim
95*>
96*> \param[out] RWORK
97*> \verbatim
98*> RWORK is DOUBLE PRECISION array, dimension (M)
99*> \endverbatim
100*>
101*> \param[out] RESID
102*> \verbatim
103*> RESID is DOUBLE PRECISION
104*> RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
105*> \endverbatim
106*
107* Authors:
108* ========
109*
110*> \author Univ. of Tennessee
111*> \author Univ. of California Berkeley
112*> \author Univ. of Colorado Denver
113*> \author NAG Ltd.
114*
115*> \ingroup complex16_eig
116*
117* =====================================================================
118 SUBROUTINE zbdt02( M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK,
119 $ RESID )
120*
121* -- LAPACK test routine --
122* -- LAPACK is a software package provided by Univ. of Tennessee, --
123* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124*
125* .. Scalar Arguments ..
126 INTEGER LDB, LDC, LDU, M, N
127 DOUBLE PRECISION RESID
128* ..
129* .. Array Arguments ..
130 DOUBLE PRECISION RWORK( * )
131 COMPLEX*16 B( LDB, * ), C( LDC, * ), U( LDU, * ),
132 $ work( * )
133* ..
134*
135* ======================================================================
136*
137* .. Parameters ..
138 DOUBLE PRECISION ZERO, ONE
139 parameter( zero = 0.0d+0, one = 1.0d+0 )
140* ..
141* .. Local Scalars ..
142 INTEGER J
143 DOUBLE PRECISION BNORM, EPS, REALMN
144* ..
145* .. External Functions ..
146 DOUBLE PRECISION DLAMCH, DZASUM, ZLANGE
147 EXTERNAL dlamch, dzasum, zlange
148* ..
149* .. External Subroutines ..
150 EXTERNAL zcopy, zgemv
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC dble, dcmplx, max, min
154* ..
155* .. Executable Statements ..
156*
157* Quick return if possible
158*
159 resid = zero
160 IF( m.LE.0 .OR. n.LE.0 )
161 $ RETURN
162 realmn = dble( max( m, n ) )
163 eps = dlamch( 'Precision' )
164*
165* Compute norm(B - U * C)
166*
167 DO 10 j = 1, n
168 CALL zcopy( m, b( 1, j ), 1, work, 1 )
169 CALL zgemv( 'No transpose', m, m, -dcmplx( one ), u, ldu,
170 $ c( 1, j ), 1, dcmplx( one ), work, 1 )
171 resid = max( resid, dzasum( m, work, 1 ) )
172 10 CONTINUE
173*
174* Compute norm of B.
175*
176 bnorm = zlange( '1', m, n, b, ldb, rwork )
177*
178 IF( bnorm.LE.zero ) THEN
179 IF( resid.NE.zero )
180 $ resid = one / eps
181 ELSE
182 IF( bnorm.GE.resid ) THEN
183 resid = ( resid / bnorm ) / ( realmn*eps )
184 ELSE
185 IF( bnorm.LT.one ) THEN
186 resid = ( min( resid, realmn*bnorm ) / bnorm ) /
187 $ ( realmn*eps )
188 ELSE
189 resid = min( resid / bnorm, realmn ) / ( realmn*eps )
190 END IF
191 END IF
192 END IF
193 RETURN
194*
195* End of ZBDT02
196*
197 END
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:158
subroutine zbdt02(M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK, RESID)
ZBDT02
Definition: zbdt02.f:120