LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zbdt05()

 subroutine zbdt05 ( integer M, integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) S, integer NS, complex*16, dimension( * ) U, integer LDU, complex*16, dimension( ldvt, * ) VT, integer LDVT, complex*16, dimension( * ) WORK, double precision RESID )

ZBDT05

Purpose:
``` ZBDT05 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] M ``` M is INTEGER The number of rows of the matrices A and U.``` [in] N ``` N is INTEGER The number of columns of the matrices A and VT.``` [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] S ``` S is DOUBLE PRECISION 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (M,N)` [out] RESID ``` RESID is DOUBLE PRECISION The test ratio: norm(S - U' * A * V) / ( n * norm(A) * EPS )```

Definition at line 123 of file zbdt05.f.

125 *
126 * -- LAPACK test routine --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 *
130 * .. Scalar Arguments ..
131  INTEGER LDA, LDU, LDVT, M, N, NS
132  DOUBLE PRECISION RESID
133 * ..
134 * .. Array Arguments ..
135  DOUBLE PRECISION S( * )
136  COMPLEX*16 A( LDA, * ), U( * ), VT( LDVT, * ), WORK( * )
137 * ..
138 *
139 * ======================================================================
140 *
141 * .. Parameters ..
142  DOUBLE PRECISION ZERO, ONE
143  parameter( zero = 0.0d+0, one = 1.0d+0 )
144  COMPLEX*16 CZERO, CONE
145  parameter( czero = ( 0.0d+0, 0.0d+0 ),
146  \$ cone = ( 1.0d+0, 0.0d+0 ) )
147 * ..
148 * .. Local Scalars ..
149  INTEGER I, J
150  DOUBLE PRECISION ANORM, EPS
151 * ..
152 * .. Local Arrays ..
153  DOUBLE PRECISION DUM( 1 )
154 * ..
155 * .. External Functions ..
156  LOGICAL LSAME
157  INTEGER IDAMAX
158  DOUBLE PRECISION DASUM, DZASUM, DLAMCH, ZLANGE
159  EXTERNAL lsame, idamax, dasum, dzasum, dlamch, zlange
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL zgemm
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC abs, dble, max, min
166 * ..
167 * .. Executable Statements ..
168 *
169 * Quick return if possible.
170 *
171  resid = zero
172  IF( min( m, n ).LE.0 .OR. ns.LE.0 )
173  \$ RETURN
174 *
175  eps = dlamch( 'Precision' )
176  anorm = zlange( 'M', m, n, a, lda, dum )
177 *
178 * Compute U' * A * V.
179 *
180  CALL zgemm( 'N', 'C', m, ns, n, cone, a, lda, vt,
181  \$ ldvt, czero, work( 1+ns*ns ), m )
182  CALL zgemm( 'C', 'N', ns, ns, m, -cone, u, ldu, work( 1+ns*ns ),
183  \$ m, czero, work, ns )
184 *
185 * norm(S - U' * B * V)
186 *
187  j = 0
188  DO 10 i = 1, ns
189  work( j+i ) = work( j+i ) + dcmplx( s( i ), zero )
190  resid = max( resid, dzasum( ns, work( j+1 ), 1 ) )
191  j = j + ns
192  10 CONTINUE
193 *
194  IF( anorm.LE.zero ) THEN
195  IF( resid.NE.zero )
196  \$ resid = one / eps
197  ELSE
198  IF( anorm.GE.resid ) THEN
199  resid = ( resid / anorm ) / ( dble( n )*eps )
200  ELSE
201  IF( anorm.LT.one ) THEN
202  resid = ( min( resid, dble( n )*anorm ) / anorm ) /
203  \$ ( dble( n )*eps )
204  ELSE
205  resid = min( resid / anorm, dble( n ) ) /
206  \$ ( dble( n )*eps )
207  END IF
208  END IF
209  END IF
210 *
211  RETURN
212 *
213 * End of ZBDT05
214 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
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
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
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