LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dbdt02()

 subroutine dbdt02 ( integer M, integer N, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( ldu, * ) U, integer LDU, double precision, dimension( * ) WORK, double precision RESID )

DBDT02

Purpose:
``` DBDT02 tests the change of basis C = U' * 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDC,N) The m by n matrix C, assumed to contain U' * B.``` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).``` [in] U ``` U is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (M)` [out] RESID ``` RESID is DOUBLE PRECISION RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),```
Date
December 2016

Definition at line 113 of file dbdt02.f.

113 *
114 * -- LAPACK test routine (version 3.7.0) --
115 * -- LAPACK is a software package provided by Univ. of Tennessee, --
116 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117 * December 2016
118 *
119 * .. Scalar Arguments ..
120  INTEGER ldb, ldc, ldu, m, n
121  DOUBLE PRECISION resid
122 * ..
123 * .. Array Arguments ..
124  DOUBLE PRECISION b( ldb, * ), c( ldc, * ), u( ldu, * ),
125  \$ work( * )
126 * ..
127 *
128 * ======================================================================
129 *
130 * .. Parameters ..
131  DOUBLE PRECISION zero, one
132  parameter( zero = 0.0d+0, one = 1.0d+0 )
133 * ..
134 * .. Local Scalars ..
135  INTEGER j
136  DOUBLE PRECISION bnorm, eps, realmn
137 * ..
138 * .. External Functions ..
139  DOUBLE PRECISION dasum, dlamch, dlange
140  EXTERNAL dasum, dlamch, dlange
141 * ..
142 * .. External Subroutines ..
143  EXTERNAL dcopy, dgemv
144 * ..
145 * .. Intrinsic Functions ..
146  INTRINSIC dble, max, min
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 = dble( max( m, n ) )
156  eps = dlamch( 'Precision' )
157 *
158 * Compute norm( B - U * C )
159 *
160  DO 10 j = 1, n
161  CALL dcopy( m, b( 1, j ), 1, work, 1 )
162  CALL dgemv( 'No transpose', m, m, -one, u, ldu, c( 1, j ), 1,
163  \$ one, work, 1 )
164  resid = max( resid, dasum( m, work, 1 ) )
165  10 CONTINUE
166 *
167 * Compute norm of B.
168 *
169  bnorm = dlange( '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 DBDT02
189 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:84
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:158
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:116
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:73
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