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
	)

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. \param[in] LDA \verbatim 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 )

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

December 2016

Definition at line 126 of file sbdt05.f.

*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      INTEGER            lda, ldu, ldvt, m, n, ns
      REAL               resid
*     ..
*     .. Array Arguments ..
      REAL               a( lda, * ), s( * ), u( ldu, * ),
     $                   vt( ldvt, * ), work( * )
*     ..
*
* ======================================================================
*
*     .. Parameters ..
      REAL               zero, one
      parameter                ( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            i, j
      REAL               anorm, eps
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      INTEGER            isamax
      REAL               sasum, slamch, slange
      EXTERNAL           lsame, isamax, sasum, slamch, slange
*     ..
*     .. External Subroutines ..
      EXTERNAL           sgemm
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, REAL, max, min
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible.
*
      resid = zero
      IF( min( m, n ).LE.0 .OR. ns.LE.0 )
     $   RETURN
*
      eps = slamch( 'Precision' )
      anorm = slange( 'M', m, n, a, lda, work )
*
*     Compute U' * A * V.
*
      CALL sgemm( 'N', 'T', m, ns, n, one, a, lda, vt,
     $            ldvt, zero, work( 1+ns*ns ), m )
      CALL sgemm( 'T', 'N', ns, ns, m, -one, u, ldu, work( 1+ns*ns ),
     $            m, zero, work, ns )
*
*     norm(S - U' * B * V)
*
      j = 0
      DO 10 i = 1, ns
         work( j+i ) =  work( j+i ) + s( i )
         resid = max( resid, sasum( ns, work( j+1 ), 1 ) )
         j = j + ns
   10 CONTINUE
*
      IF( anorm.LE.zero ) THEN
         IF( resid.NE.zero )
     $      resid = one / eps
      ELSE
         IF( anorm.GE.resid ) THEN
            resid = ( resid / anorm ) / ( REAL( n )*eps )
         ELSE
            IF( anorm.LT.one ) THEN
               resid = ( min( resid, REAL( n )*anorm ) / anorm ) /
     $                 ( REAL( n )*eps )
            ELSE
               resid = min( resid / anorm, REAL( N ) ) /
     $                 ( REAL( n )*eps )
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of SBDT05
*

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