LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sbdt02()

subroutine sbdt02 ( integer  M,
integer  N,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( ldc, * )  C,
integer  LDC,
real, dimension( ldu, * )  U,
integer  LDU,
real, dimension( * )  WORK,
real  RESID 
)

SBDT02

Purpose:
 SBDT02 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 REAL 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 REAL 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 REAL 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 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 111 of file sbdt02.f.

112 *
113 * -- LAPACK test routine --
114 * -- LAPACK is a software package provided by Univ. of Tennessee, --
115 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116 *
117 * .. Scalar Arguments ..
118  INTEGER LDB, LDC, LDU, M, N
119  REAL RESID
120 * ..
121 * .. Array Arguments ..
122  REAL B( LDB, * ), C( LDC, * ), U( LDU, * ),
123  $ WORK( * )
124 * ..
125 *
126 * ======================================================================
127 *
128 * .. Parameters ..
129  REAL ZERO, ONE
130  parameter( zero = 0.0e+0, one = 1.0e+0 )
131 * ..
132 * .. Local Scalars ..
133  INTEGER J
134  REAL BNORM, EPS, REALMN
135 * ..
136 * .. External Functions ..
137  REAL SASUM, SLAMCH, SLANGE
138  EXTERNAL sasum, slamch, slange
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL scopy, sgemv
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC max, min, real
145 * ..
146 * .. Executable Statements ..
147 *
148 * Quick return if possible
149 *
150  resid = zero
151  IF( m.LE.0 .OR. n.LE.0 )
152  $ RETURN
153  realmn = real( max( m, n ) )
154  eps = slamch( 'Precision' )
155 *
156 * Compute norm(B - U * C)
157 *
158  DO 10 j = 1, n
159  CALL scopy( m, b( 1, j ), 1, work, 1 )
160  CALL sgemv( 'No transpose', m, m, -one, u, ldu, c( 1, j ), 1,
161  $ one, work, 1 )
162  resid = max( resid, sasum( m, work, 1 ) )
163  10 CONTINUE
164 *
165 * Compute norm of B.
166 *
167  bnorm = slange( '1', m, n, b, ldb, work )
168 *
169  IF( bnorm.LE.zero ) THEN
170  IF( resid.NE.zero )
171  $ resid = one / eps
172  ELSE
173  IF( bnorm.GE.resid ) THEN
174  resid = ( resid / bnorm ) / ( realmn*eps )
175  ELSE
176  IF( bnorm.LT.one ) THEN
177  resid = ( min( resid, realmn*bnorm ) / bnorm ) /
178  $ ( realmn*eps )
179  ELSE
180  resid = min( resid / bnorm, realmn ) / ( realmn*eps )
181  END IF
182  END IF
183  END IF
184  RETURN
185 *
186 * End of SBDT02
187 *
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
Definition: sgemv.f:156
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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