 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sbdt05()

 subroutine sbdt05 ( integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, integer NS, real, dimension( ldu, * ) U, integer LDU, real, dimension( ldvt, * ) VT, integer LDVT, real, dimension( * ) WORK, real RESID )

SBDT05

Purpose:
``` SBDT05 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 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] 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 (M,N)` [out] RESID ``` RESID is REAL The test ratio: norm(S - U' * A * V) / ( n * norm(A) * EPS )```

Definition at line 125 of file sbdt05.f.

127 *
128 * -- LAPACK test routine --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 *
132 * .. Scalar Arguments ..
133  INTEGER LDA, LDU, LDVT, M, N, NS
134  REAL RESID
135 * ..
136 * .. Array Arguments ..
137  REAL A( LDA, * ), S( * ), U( LDU, * ),
138  \$ VT( LDVT, * ), WORK( * )
139 * ..
140 *
141 * ======================================================================
142 *
143 * .. Parameters ..
144  REAL ZERO, ONE
145  parameter( zero = 0.0e+0, one = 1.0e+0 )
146 * ..
147 * .. Local Scalars ..
148  INTEGER I, J
149  REAL ANORM, EPS
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME
153  INTEGER ISAMAX
154  REAL SASUM, SLAMCH, SLANGE
155  EXTERNAL lsame, isamax, sasum, slamch, slange
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL sgemm
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC abs, real, max, min
162 * ..
163 * .. Executable Statements ..
164 *
165 * Quick return if possible.
166 *
167  resid = zero
168  IF( min( m, n ).LE.0 .OR. ns.LE.0 )
169  \$ RETURN
170 *
171  eps = slamch( 'Precision' )
172  anorm = slange( 'M', m, n, a, lda, work )
173 *
174 * Compute U' * A * V.
175 *
176  CALL sgemm( 'N', 'T', m, ns, n, one, a, lda, vt,
177  \$ ldvt, zero, work( 1+ns*ns ), m )
178  CALL sgemm( 'T', 'N', ns, ns, m, -one, u, ldu, work( 1+ns*ns ),
179  \$ m, zero, work, ns )
180 *
181 * norm(S - U' * B * V)
182 *
183  j = 0
184  DO 10 i = 1, ns
185  work( j+i ) = work( j+i ) + s( i )
186  resid = max( resid, sasum( ns, work( j+1 ), 1 ) )
187  j = j + ns
188  10 CONTINUE
189 *
190  IF( anorm.LE.zero ) THEN
191  IF( resid.NE.zero )
192  \$ resid = one / eps
193  ELSE
194  IF( anorm.GE.resid ) THEN
195  resid = ( resid / anorm ) / ( real( n )*eps )
196  ELSE
197  IF( anorm.LT.one ) THEN
198  resid = ( min( resid, real( n )*anorm ) / anorm ) /
199  \$ ( real( n )*eps )
200  ELSE
201  resid = min( resid / anorm, real( n ) ) /
202  \$ ( real( n )*eps )
203  END IF
204  END IF
205  END IF
206 *
207  RETURN
208 *
209 * End of SBDT05
210 *
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:114
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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