LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zbdt01()

 subroutine zbdt01 ( integer M, integer N, integer KD, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldq, * ) Q, integer LDQ, double precision, dimension( * ) D, double precision, dimension( * ) E, complex*16, dimension( ldpt, * ) PT, integer LDPT, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, double precision RESID )

ZBDT01

Purpose:
``` ZBDT01 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 unitary
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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDQ,N) The m by min(m,n) unitary 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 DOUBLE PRECISION array, dimension (min(M,N)) The diagonal elements of the bidiagonal matrix B.``` [in] E ``` E is DOUBLE PRECISION 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 COMPLEX*16 array, dimension (LDPT,N) The min(m,n) by n unitary 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 COMPLEX*16 array, dimension (M+N)` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (M)` [out] RESID ``` RESID is DOUBLE PRECISION The test ratio: norm(A - Q * B * P') / ( n * norm(A) * EPS )```
Date
December 2016

Definition at line 148 of file zbdt01.f.

148 *
149 * -- LAPACK test routine (version 3.7.0) --
150 * -- LAPACK is a software package provided by Univ. of Tennessee, --
151 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
152 * December 2016
153 *
154 * .. Scalar Arguments ..
155  INTEGER kd, lda, ldpt, ldq, m, n
156  DOUBLE PRECISION resid
157 * ..
158 * .. Array Arguments ..
159  DOUBLE PRECISION d( * ), e( * ), rwork( * )
160  COMPLEX*16 a( lda, * ), pt( ldpt, * ), q( ldq, * ),
161  \$ work( * )
162 * ..
163 *
164 * =====================================================================
165 *
166 * .. Parameters ..
167  DOUBLE PRECISION zero, one
168  parameter( zero = 0.0d+0, one = 1.0d+0 )
169 * ..
170 * .. Local Scalars ..
171  INTEGER i, j
172  DOUBLE PRECISION anorm, eps
173 * ..
174 * .. External Functions ..
175  DOUBLE PRECISION dlamch, dzasum, zlange
176  EXTERNAL dlamch, dzasum, zlange
177 * ..
178 * .. External Subroutines ..
179  EXTERNAL zcopy, zgemv
180 * ..
181 * .. Intrinsic Functions ..
182  INTRINSIC dble, dcmplx, max, min
183 * ..
184 * .. Executable Statements ..
185 *
186 * Quick return if possible
187 *
188  IF( m.LE.0 .OR. n.LE.0 ) THEN
189  resid = zero
190  RETURN
191  END IF
192 *
193 * Compute A - Q * B * P' one column at a time.
194 *
195  resid = zero
196  IF( kd.NE.0 ) THEN
197 *
198 * B is bidiagonal.
199 *
200  IF( kd.NE.0 .AND. m.GE.n ) THEN
201 *
202 * B is upper bidiagonal and M >= N.
203 *
204  DO 20 j = 1, n
205  CALL zcopy( m, a( 1, j ), 1, work, 1 )
206  DO 10 i = 1, n - 1
207  work( m+i ) = d( i )*pt( i, j ) + e( i )*pt( i+1, j )
208  10 CONTINUE
209  work( m+n ) = d( n )*pt( n, j )
210  CALL zgemv( 'No transpose', m, n, -dcmplx( one ), q, ldq,
211  \$ work( m+1 ), 1, dcmplx( one ), work, 1 )
212  resid = max( resid, dzasum( m, work, 1 ) )
213  20 CONTINUE
214  ELSE IF( kd.LT.0 ) THEN
215 *
216 * B is upper bidiagonal and M < N.
217 *
218  DO 40 j = 1, n
219  CALL zcopy( m, a( 1, j ), 1, work, 1 )
220  DO 30 i = 1, m - 1
221  work( m+i ) = d( i )*pt( i, j ) + e( i )*pt( i+1, j )
222  30 CONTINUE
223  work( m+m ) = d( m )*pt( m, j )
224  CALL zgemv( 'No transpose', m, m, -dcmplx( one ), q, ldq,
225  \$ work( m+1 ), 1, dcmplx( one ), work, 1 )
226  resid = max( resid, dzasum( m, work, 1 ) )
227  40 CONTINUE
228  ELSE
229 *
230 * B is lower bidiagonal.
231 *
232  DO 60 j = 1, n
233  CALL zcopy( m, a( 1, j ), 1, work, 1 )
234  work( m+1 ) = d( 1 )*pt( 1, j )
235  DO 50 i = 2, m
236  work( m+i ) = e( i-1 )*pt( i-1, j ) +
237  \$ d( i )*pt( i, j )
238  50 CONTINUE
239  CALL zgemv( 'No transpose', m, m, -dcmplx( one ), q, ldq,
240  \$ work( m+1 ), 1, dcmplx( one ), work, 1 )
241  resid = max( resid, dzasum( m, work, 1 ) )
242  60 CONTINUE
243  END IF
244  ELSE
245 *
246 * B is diagonal.
247 *
248  IF( m.GE.n ) THEN
249  DO 80 j = 1, n
250  CALL zcopy( m, a( 1, j ), 1, work, 1 )
251  DO 70 i = 1, n
252  work( m+i ) = d( i )*pt( i, j )
253  70 CONTINUE
254  CALL zgemv( 'No transpose', m, n, -dcmplx( one ), q, ldq,
255  \$ work( m+1 ), 1, dcmplx( one ), work, 1 )
256  resid = max( resid, dzasum( m, work, 1 ) )
257  80 CONTINUE
258  ELSE
259  DO 100 j = 1, n
260  CALL zcopy( m, a( 1, j ), 1, work, 1 )
261  DO 90 i = 1, m
262  work( m+i ) = d( i )*pt( i, j )
263  90 CONTINUE
264  CALL zgemv( 'No transpose', m, m, -dcmplx( one ), q, ldq,
265  \$ work( m+1 ), 1, dcmplx( one ), work, 1 )
266  resid = max( resid, dzasum( m, work, 1 ) )
267  100 CONTINUE
268  END IF
269  END IF
270 *
271 * Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
272 *
273  anorm = zlange( '1', m, n, a, lda, rwork )
274  eps = dlamch( 'Precision' )
275 *
276  IF( anorm.LE.zero ) THEN
277  IF( resid.NE.zero )
278  \$ resid = one / eps
279  ELSE
280  IF( anorm.GE.resid ) THEN
281  resid = ( resid / anorm ) / ( dble( n )*eps )
282  ELSE
283  IF( anorm.LT.one ) THEN
284  resid = ( min( resid, dble( n )*anorm ) / anorm ) /
285  \$ ( dble( n )*eps )
286  ELSE
287  resid = min( resid / anorm, dble( n ) ) /
288  \$ ( dble( n )*eps )
289  END IF
290  END IF
291  END IF
292 *
293  RETURN
294 *
295 * End of ZBDT01
296 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:83
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:160
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:117
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:74
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