sbdt05.f

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*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE SBDT05( M, N, A, LDA, S, NS, U, LDU, 
*                          VT, LDVT, WORK, RESID )                
* 
*       .. Scalar Arguments ..
*       INTEGER            LDA, LDU, LDVT, N, NS
*       REAL               RESID
*       ..
*       .. Array Arguments ..
*       REAL               D( * ), E( * ), S( * ), U( LDU, * ),
*      $                   VT( LDVT, * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrices A and U.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrices A and VT.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          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).
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*>          S is REAL array, dimension (NS)
*>          The singular values from the (partial) SVD of B, sorted in 
*>          decreasing order.
*> \endverbatim
*>
*> \param[in] NS
*> \verbatim
*>          NS is INTEGER
*>          The number of singular values/vectors from the (partial) 
*>          SVD of B.
*> \endverbatim
*>
*> \param[in] U
*> \verbatim
*>          U is REAL array, dimension (LDU,NS)
*>          The n by ns orthogonal matrix U in S = U' * B * V.
*> \endverbatim
*>
*> \param[in] LDU
*> \verbatim
*>          LDU is INTEGER
*>          The leading dimension of the array U.  LDU >= max(1,N)
*> \endverbatim
*>
*> \param[in] VT
*> \verbatim
*>          VT is REAL array, dimension (LDVT,N)
*>          The n by ns orthogonal matrix V in S = U' * B * V.
*> \endverbatim
*>
*> \param[in] LDVT
*> \verbatim
*>          LDVT is INTEGER
*>          The leading dimension of the array VT.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (M,N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is REAL
*>          The test ratio:  norm(S - U' * A * V) / ( n * norm(A) * EPS )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup double_eig
*
*  =====================================================================
      SUBROUTINE sbdt05( M, N, A, LDA, S, NS, U, LDU, 
     $                    vt, ldvt, work, resid )
*
*  -- LAPACK test routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      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
*
      END