LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ sbdt04()

 subroutine sbdt04 ( character UPLO, integer N, real, dimension( * ) D, real, dimension( * ) E, real, dimension( * ) S, integer NS, real, dimension( ldu, * ) U, integer LDU, real, dimension( ldvt, * ) VT, integer LDVT, real, dimension( * ) WORK, real RESID )

SBDT04

Purpose:
``` SBDT04 reconstructs a bidiagonal matrix B from its (partial) SVD:
S = U' * B * V
where U and V are orthogonal matrices and S is diagonal.

The test ratio to test the singular value decomposition is
RESID = norm( S - U' * B * V ) / ( n * norm(B) * EPS )
where VT = V' and EPS is the machine precision.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the matrix B is upper or lower bidiagonal. = 'U': Upper bidiagonal = 'L': Lower bidiagonal``` [in] N ``` N is INTEGER The order of the matrix B.``` [in] D ``` D is REAL array, dimension (N) The n diagonal elements of the bidiagonal matrix B.``` [in] E ``` E is REAL array, dimension (N-1) The (n-1) superdiagonal elements of the bidiagonal matrix B if UPLO = 'U', or the (n-1) subdiagonal elements of B if UPLO = 'L'.``` [in] S ``` S is REAL array, dimension (NS) The singular values from the (partial) SVD of B, sorted in decreasing order.``` [in] NS ``` NS is INTEGER The number of singular values/vectors from the (partial) SVD of B.``` [in] U ``` U is REAL array, dimension (LDU,NS) The n by ns orthogonal matrix U in S = U' * B * V.``` [in] LDU ``` LDU is INTEGER The leading dimension of the array U. LDU >= max(1,N)``` [in] VT ``` VT is REAL array, dimension (LDVT,N) The n by ns orthogonal matrix V in S = U' * B * V.``` [in] LDVT ``` LDVT is INTEGER The leading dimension of the array VT.``` [out] WORK ` WORK is REAL array, dimension (2*N)` [out] RESID ``` RESID is REAL The test ratio: norm(S - U' * B * V) / ( n * norm(B) * EPS )```
Date
December 2016

Definition at line 133 of file sbdt04.f.

133 *
134 * -- LAPACK test routine (version 3.7.0) --
135 * -- LAPACK is a software package provided by Univ. of Tennessee, --
136 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137 * December 2016
138 *
139 * .. Scalar Arguments ..
140  CHARACTER uplo
141  INTEGER ldu, ldvt, n, ns
142  REAL resid
143 * ..
144 * .. Array Arguments ..
145  REAL d( * ), e( * ), s( * ), u( ldu, * ),
146  \$ vt( ldvt, * ), work( * )
147 * ..
148 *
149 * ======================================================================
150 *
151 * .. Parameters ..
152  REAL zero, one
153  parameter( zero = 0.0e+0, one = 1.0e+0 )
154 * ..
155 * .. Local Scalars ..
156  INTEGER i, j, k
157  REAL bnorm, eps
158 * ..
159 * .. External Functions ..
160  LOGICAL lsame
161  INTEGER isamax
162  REAL sasum, slamch
163  EXTERNAL lsame, isamax, sasum, slamch
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL sgemm
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC abs, REAL, max, min
170 * ..
171 * .. Executable Statements ..
172 *
173 * Quick return if possible.
174 *
175  resid = zero
176  IF( n.LE.0 .OR. ns.LE.0 )
177  \$ RETURN
178 *
179  eps = slamch( 'Precision' )
180 *
181 * Compute S - U' * B * V.
182 *
183  bnorm = zero
184 *
185  IF( lsame( uplo, 'U' ) ) THEN
186 *
187 * B is upper bidiagonal.
188 *
189  k = 0
190  DO 20 i = 1, ns
191  DO 10 j = 1, n-1
192  k = k + 1
193  work( k ) = d( j )*vt( i, j ) + e( j )*vt( i, j+1 )
194  10 CONTINUE
195  k = k + 1
196  work( k ) = d( n )*vt( i, n )
197  20 CONTINUE
198  bnorm = abs( d( 1 ) )
199  DO 30 i = 2, n
200  bnorm = max( bnorm, abs( d( i ) )+abs( e( i-1 ) ) )
201  30 CONTINUE
202  ELSE
203 *
204 * B is lower bidiagonal.
205 *
206  k = 0
207  DO 50 i = 1, ns
208  k = k + 1
209  work( k ) = d( 1 )*vt( i, 1 )
210  DO 40 j = 1, n-1
211  k = k + 1
212  work( k ) = e( j )*vt( i, j ) + d( j+1 )*vt( i, j+1 )
213  40 CONTINUE
214  50 CONTINUE
215  bnorm = abs( d( n ) )
216  DO 60 i = 1, n-1
217  bnorm = max( bnorm, abs( d( i ) )+abs( e( i ) ) )
218  60 CONTINUE
219  END IF
220 *
221  CALL sgemm( 'T', 'N', ns, ns, n, -one, u, ldu, work( 1 ),
222  \$ n, zero, work( 1+n*ns ), ns )
223 *
224 * norm(S - U' * B * V)
225 *
226  k = n*ns
227  DO 70 i = 1, ns
228  work( k+i ) = work( k+i ) + s( i )
229  resid = max( resid, sasum( ns, work( k+1 ), 1 ) )
230  k = k + ns
231  70 CONTINUE
232 *
233  IF( bnorm.LE.zero ) THEN
234  IF( resid.NE.zero )
235  \$ resid = one / eps
236  ELSE
237  IF( bnorm.GE.resid ) THEN
238  resid = ( resid / bnorm ) / ( REAL( n )*eps )
239  ELSE
240  IF( bnorm.LT.one ) THEN
241  resid = ( min( resid, REAL( n )*bnorm ) / bnorm ) /
242  \$ ( REAL( n )*eps )
243  ELSE
244  resid = min( resid / bnorm, REAL( N ) ) /
245  \$ ( REAL( n )*eps )
246  END IF
247  END IF
248  END IF
249 *
250  RETURN
251 *
252 * End of SBDT04
253 *
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:73
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:74
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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