LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ 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 ),
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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