 LAPACK  3.10.1 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**H
where Q (m by min(m,n)) and P**H (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 * P**H) / ( n * norm(A) * EPS )
where 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**H.``` [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**H.``` [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**H in the reduction A = Q * B * P**H.``` [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**H) / ( n * norm(A) * EPS )```

Definition at line 145 of file zbdt01.f.

147 *
148 * -- LAPACK test routine --
149 * -- LAPACK is a software package provided by Univ. of Tennessee, --
150 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151 *
152 * .. Scalar Arguments ..
153  INTEGER KD, LDA, LDPT, LDQ, M, N
154  DOUBLE PRECISION RESID
155 * ..
156 * .. Array Arguments ..
157  DOUBLE PRECISION D( * ), E( * ), RWORK( * )
158  COMPLEX*16 A( LDA, * ), PT( LDPT, * ), Q( LDQ, * ),
159  \$ WORK( * )
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Parameters ..
165  DOUBLE PRECISION ZERO, ONE
166  parameter( zero = 0.0d+0, one = 1.0d+0 )
167 * ..
168 * .. Local Scalars ..
169  INTEGER I, J
170  DOUBLE PRECISION ANORM, EPS
171 * ..
172 * .. External Functions ..
173  DOUBLE PRECISION DLAMCH, DZASUM, ZLANGE
174  EXTERNAL dlamch, dzasum, zlange
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL zcopy, zgemv
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC dble, dcmplx, max, min
181 * ..
182 * .. Executable Statements ..
183 *
184 * Quick return if possible
185 *
186  IF( m.LE.0 .OR. n.LE.0 ) THEN
187  resid = zero
188  RETURN
189  END IF
190 *
191 * Compute A - Q * B * P**H one column at a time.
192 *
193  resid = zero
194  IF( kd.NE.0 ) THEN
195 *
196 * B is bidiagonal.
197 *
198  IF( kd.NE.0 .AND. m.GE.n ) THEN
199 *
200 * B is upper bidiagonal and M >= N.
201 *
202  DO 20 j = 1, n
203  CALL zcopy( m, a( 1, j ), 1, work, 1 )
204  DO 10 i = 1, n - 1
205  work( m+i ) = d( i )*pt( i, j ) + e( i )*pt( i+1, j )
206  10 CONTINUE
207  work( m+n ) = d( n )*pt( n, j )
208  CALL zgemv( 'No transpose', m, n, -dcmplx( one ), q, ldq,
209  \$ work( m+1 ), 1, dcmplx( one ), work, 1 )
210  resid = max( resid, dzasum( m, work, 1 ) )
211  20 CONTINUE
212  ELSE IF( kd.LT.0 ) THEN
213 *
214 * B is upper bidiagonal and M < N.
215 *
216  DO 40 j = 1, n
217  CALL zcopy( m, a( 1, j ), 1, work, 1 )
218  DO 30 i = 1, m - 1
219  work( m+i ) = d( i )*pt( i, j ) + e( i )*pt( i+1, j )
220  30 CONTINUE
221  work( m+m ) = d( m )*pt( m, j )
222  CALL zgemv( 'No transpose', m, m, -dcmplx( one ), q, ldq,
223  \$ work( m+1 ), 1, dcmplx( one ), work, 1 )
224  resid = max( resid, dzasum( m, work, 1 ) )
225  40 CONTINUE
226  ELSE
227 *
228 * B is lower bidiagonal.
229 *
230  DO 60 j = 1, n
231  CALL zcopy( m, a( 1, j ), 1, work, 1 )
232  work( m+1 ) = d( 1 )*pt( 1, j )
233  DO 50 i = 2, m
234  work( m+i ) = e( i-1 )*pt( i-1, j ) +
235  \$ d( i )*pt( i, j )
236  50 CONTINUE
237  CALL zgemv( 'No transpose', m, m, -dcmplx( one ), q, ldq,
238  \$ work( m+1 ), 1, dcmplx( one ), work, 1 )
239  resid = max( resid, dzasum( m, work, 1 ) )
240  60 CONTINUE
241  END IF
242  ELSE
243 *
244 * B is diagonal.
245 *
246  IF( m.GE.n ) THEN
247  DO 80 j = 1, n
248  CALL zcopy( m, a( 1, j ), 1, work, 1 )
249  DO 70 i = 1, n
250  work( m+i ) = d( i )*pt( i, j )
251  70 CONTINUE
252  CALL zgemv( 'No transpose', m, n, -dcmplx( one ), q, ldq,
253  \$ work( m+1 ), 1, dcmplx( one ), work, 1 )
254  resid = max( resid, dzasum( m, work, 1 ) )
255  80 CONTINUE
256  ELSE
257  DO 100 j = 1, n
258  CALL zcopy( m, a( 1, j ), 1, work, 1 )
259  DO 90 i = 1, m
260  work( m+i ) = d( i )*pt( i, j )
261  90 CONTINUE
262  CALL zgemv( 'No transpose', m, m, -dcmplx( one ), q, ldq,
263  \$ work( m+1 ), 1, dcmplx( one ), work, 1 )
264  resid = max( resid, dzasum( m, work, 1 ) )
265  100 CONTINUE
266  END IF
267  END IF
268 *
269 * Compute norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
270 *
271  anorm = zlange( '1', m, n, a, lda, rwork )
272  eps = dlamch( 'Precision' )
273 *
274  IF( anorm.LE.zero ) THEN
275  IF( resid.NE.zero )
276  \$ resid = one / eps
277  ELSE
278  IF( anorm.GE.resid ) THEN
279  resid = ( resid / anorm ) / ( dble( n )*eps )
280  ELSE
281  IF( anorm.LT.one ) THEN
282  resid = ( min( resid, dble( n )*anorm ) / anorm ) /
283  \$ ( dble( n )*eps )
284  ELSE
285  resid = min( resid / anorm, dble( n ) ) /
286  \$ ( dble( n )*eps )
287  END IF
288  END IF
289  END IF
290 *
291  RETURN
292 *
293 * End of ZBDT01
294 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:158
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:115
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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