 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cbdt02()

 subroutine cbdt02 ( integer M, integer N, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldc, * ) C, integer LDC, complex, dimension( ldu, * ) U, integer LDU, complex, dimension( * ) WORK, real, dimension( * ) RWORK, real RESID )

CBDT02

Purpose:
``` CBDT02 tests the change of basis C = U**H * B by computing the
residual

RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),

where B and C are M by N matrices, U is an M by M orthogonal matrix,
and EPS is the machine precision.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrices B and C and the order of the matrix Q.``` [in] N ``` N is INTEGER The number of columns of the matrices B and C.``` [in] B ``` B is COMPLEX array, dimension (LDB,N) The m by n matrix B.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).``` [in] C ``` C is COMPLEX array, dimension (LDC,N) The m by n matrix C, assumed to contain U**H * B.``` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).``` [in] U ``` U is COMPLEX array, dimension (LDU,M) The m by m orthogonal matrix U.``` [in] LDU ``` LDU is INTEGER The leading dimension of the array U. LDU >= max(1,M).``` [out] WORK ` WORK is COMPLEX array, dimension (M)` [out] RWORK ` RWORK is REAL array, dimension (M)` [out] RESID ``` RESID is REAL RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),```

Definition at line 118 of file cbdt02.f.

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 REAL RESID
128* ..
129* .. Array Arguments ..
130 REAL RWORK( * )
131 COMPLEX B( LDB, * ), C( LDC, * ), U( LDU, * ),
132 \$ WORK( * )
133* ..
134*
135* ======================================================================
136*
137* .. Parameters ..
138 REAL ZERO, ONE
139 parameter( zero = 0.0e+0, one = 1.0e+0 )
140* ..
141* .. Local Scalars ..
142 INTEGER J
143 REAL BNORM, EPS, REALMN
144* ..
145* .. External Functions ..
146 REAL CLANGE, SCASUM, SLAMCH
147 EXTERNAL clange, scasum, slamch
148* ..
149* .. External Subroutines ..
150 EXTERNAL ccopy, cgemv
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC cmplx, max, min, real
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 = real( max( m, n ) )
163 eps = slamch( 'Precision' )
164*
165* Compute norm(B - U * C)
166*
167 DO 10 j = 1, n
168 CALL ccopy( m, b( 1, j ), 1, work, 1 )
169 CALL cgemv( 'No transpose', m, m, -cmplx( one ), u, ldu,
170 \$ c( 1, j ), 1, cmplx( one ), work, 1 )
171 resid = max( resid, scasum( m, work, 1 ) )
172 10 CONTINUE
173*
174* Compute norm of B.
175*
176 bnorm = clange( '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 CBDT02
196*
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:81
subroutine cgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV
Definition: cgemv.f:158
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:72
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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