 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sbdt01 ( integer M, integer N, integer KD, real, dimension( lda, * ) A, integer LDA, real, dimension( ldq, * ) Q, integer LDQ, real, dimension( * ) D, real, dimension( * ) E, real, dimension( ldpt, * ) PT, integer LDPT, real, dimension( * ) WORK, real RESID )

SBDT01

Purpose:
``` SBDT01 reconstructs a general matrix A from its bidiagonal form
A = Q * B * P'
where Q (m by min(m,n)) and P' (min(m,n) by n) are orthogonal
matrices and B is bidiagonal.

The test ratio to test the reduction is
RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
where PT = P' and EPS is the machine precision.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrices A and Q.``` [in] N ``` N is INTEGER The number of columns of the matrices A and P'.``` [in] KD ``` KD is INTEGER If KD = 0, B is diagonal and the array E is not referenced. If KD = 1, the reduction was performed by xGEBRD; B is upper bidiagonal if M >= N, and lower bidiagonal if M < N. If KD = -1, the reduction was performed by xGBBRD; B is always upper bidiagonal.``` [in] A ``` A is REAL array, dimension (LDA,N) The m by n matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).``` [in] Q ``` Q is REAL array, dimension (LDQ,N) The m by min(m,n) orthogonal matrix Q in the reduction A = Q * B * P'.``` [in] LDQ ``` LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,M).``` [in] D ``` D is REAL array, dimension (min(M,N)) The diagonal elements of the bidiagonal matrix B.``` [in] E ``` E is REAL array, dimension (min(M,N)-1) The superdiagonal elements of the bidiagonal matrix B if m >= n, or the subdiagonal elements of B if m < n.``` [in] PT ``` PT is REAL array, dimension (LDPT,N) The min(m,n) by n orthogonal matrix P' in the reduction A = Q * B * P'.``` [in] LDPT ``` LDPT is INTEGER The leading dimension of the array PT. LDPT >= max(1,min(M,N)).``` [out] WORK ` WORK is REAL array, dimension (M+N)` [out] RESID ``` RESID is REAL The test ratio: norm(A - Q * B * P') / ( n * norm(A) * EPS )```
Date
November 2011

Definition at line 142 of file sbdt01.f.

142 *
143 * -- LAPACK test routine (version 3.4.0) --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 * November 2011
147 *
148 * .. Scalar Arguments ..
149  INTEGER kd, lda, ldpt, ldq, m, n
150  REAL resid
151 * ..
152 * .. Array Arguments ..
153  REAL a( lda, * ), d( * ), e( * ), pt( ldpt, * ),
154  \$ q( ldq, * ), work( * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. Parameters ..
160  REAL zero, one
161  parameter ( zero = 0.0e+0, one = 1.0e+0 )
162 * ..
163 * .. Local Scalars ..
164  INTEGER i, j
165  REAL anorm, eps
166 * ..
167 * .. External Functions ..
168  REAL sasum, slamch, slange
169  EXTERNAL sasum, slamch, slange
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL scopy, sgemv
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC max, min, real
176 * ..
177 * .. Executable Statements ..
178 *
179 * Quick return if possible
180 *
181  IF( m.LE.0 .OR. n.LE.0 ) THEN
182  resid = zero
183  RETURN
184  END IF
185 *
186 * Compute A - Q * B * P' one column at a time.
187 *
188  resid = zero
189  IF( kd.NE.0 ) THEN
190 *
191 * B is bidiagonal.
192 *
193  IF( kd.NE.0 .AND. m.GE.n ) THEN
194 *
195 * B is upper bidiagonal and M >= N.
196 *
197  DO 20 j = 1, n
198  CALL scopy( m, a( 1, j ), 1, work, 1 )
199  DO 10 i = 1, n - 1
200  work( m+i ) = d( i )*pt( i, j ) + e( i )*pt( i+1, j )
201  10 CONTINUE
202  work( m+n ) = d( n )*pt( n, j )
203  CALL sgemv( 'No transpose', m, n, -one, q, ldq,
204  \$ work( m+1 ), 1, one, work, 1 )
205  resid = max( resid, sasum( m, work, 1 ) )
206  20 CONTINUE
207  ELSE IF( kd.LT.0 ) THEN
208 *
209 * B is upper bidiagonal and M < N.
210 *
211  DO 40 j = 1, n
212  CALL scopy( m, a( 1, j ), 1, work, 1 )
213  DO 30 i = 1, m - 1
214  work( m+i ) = d( i )*pt( i, j ) + e( i )*pt( i+1, j )
215  30 CONTINUE
216  work( m+m ) = d( m )*pt( m, j )
217  CALL sgemv( 'No transpose', m, m, -one, q, ldq,
218  \$ work( m+1 ), 1, one, work, 1 )
219  resid = max( resid, sasum( m, work, 1 ) )
220  40 CONTINUE
221  ELSE
222 *
223 * B is lower bidiagonal.
224 *
225  DO 60 j = 1, n
226  CALL scopy( m, a( 1, j ), 1, work, 1 )
227  work( m+1 ) = d( 1 )*pt( 1, j )
228  DO 50 i = 2, m
229  work( m+i ) = e( i-1 )*pt( i-1, j ) +
230  \$ d( i )*pt( i, j )
231  50 CONTINUE
232  CALL sgemv( 'No transpose', m, m, -one, q, ldq,
233  \$ work( m+1 ), 1, one, work, 1 )
234  resid = max( resid, sasum( m, work, 1 ) )
235  60 CONTINUE
236  END IF
237  ELSE
238 *
239 * B is diagonal.
240 *
241  IF( m.GE.n ) THEN
242  DO 80 j = 1, n
243  CALL scopy( m, a( 1, j ), 1, work, 1 )
244  DO 70 i = 1, n
245  work( m+i ) = d( i )*pt( i, j )
246  70 CONTINUE
247  CALL sgemv( 'No transpose', m, n, -one, q, ldq,
248  \$ work( m+1 ), 1, one, work, 1 )
249  resid = max( resid, sasum( m, work, 1 ) )
250  80 CONTINUE
251  ELSE
252  DO 100 j = 1, n
253  CALL scopy( m, a( 1, j ), 1, work, 1 )
254  DO 90 i = 1, m
255  work( m+i ) = d( i )*pt( i, j )
256  90 CONTINUE
257  CALL sgemv( 'No transpose', m, m, -one, q, ldq,
258  \$ work( m+1 ), 1, one, work, 1 )
259  resid = max( resid, sasum( m, work, 1 ) )
260  100 CONTINUE
261  END IF
262  END IF
263 *
264 * Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
265 *
266  anorm = slange( '1', m, n, a, lda, work )
267  eps = slamch( 'Precision' )
268 *
269  IF( anorm.LE.zero ) THEN
270  IF( resid.NE.zero )
271  \$ resid = one / eps
272  ELSE
273  IF( anorm.GE.resid ) THEN
274  resid = ( resid / anorm ) / ( REAL( n )*eps )
275  ELSE
276  IF( anorm.LT.one ) THEN
277  resid = ( min( resid, REAL( n )*anorm ) / anorm ) /
278  \$ ( REAL( n )*eps )
279  ELSE
280  resid = min( resid / anorm, REAL( N ) ) /
281  \$ ( REAL( n )*eps )
282  END IF
283  END IF
284  END IF
285 *
286  RETURN
287 *
288 * End of SBDT01
289 *
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
Definition: sgemv.f:158
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:116
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:54
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:53

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