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SUBROUTINE DBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
$ RESID )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER KD, LDA, LDPT, LDQ, M, N
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), PT( LDPT, * ),
$ Q( LDQ, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DBDT01 reconstructs a general matrix A from its bidiagonal form
* A = Q * B * P'
* where Q (m by min(m,n)) and P' (min(m,n) by n) are orthogonal
* matrices and B is bidiagonal.
*
* The test ratio to test the reduction is
* RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
* where PT = P' and EPS is the machine precision.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrices A and Q.
*
* N (input) INTEGER
* The number of columns of the matrices A and P'.
*
* KD (input) 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.
*
* A (input) DOUBLE PRECISION array, dimension (LDA,N)
* The m by n matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,M).
*
* Q (input) DOUBLE PRECISION array, dimension (LDQ,N)
* The m by min(m,n) orthogonal matrix Q in the reduction
* A = Q * B * P'.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. LDQ >= max(1,M).
*
* D (input) DOUBLE PRECISION array, dimension (min(M,N))
* The diagonal elements of the bidiagonal matrix B.
*
* E (input) 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.
*
* PT (input) DOUBLE PRECISION array, dimension (LDPT,N)
* The min(m,n) by n orthogonal matrix P' in the reduction
* A = Q * B * P'.
*
* LDPT (input) INTEGER
* The leading dimension of the array PT.
* LDPT >= max(1,min(M,N)).
*
* WORK (workspace) DOUBLE PRECISION array, dimension (M+N)
*
* RESID (output) DOUBLE PRECISION
* The test ratio: norm(A - Q * B * P') / ( n * norm(A) * EPS )
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
DOUBLE PRECISION ANORM, EPS
* ..
* .. External Functions ..
DOUBLE PRECISION DASUM, DLAMCH, DLANGE
EXTERNAL DASUM, DLAMCH, DLANGE
* ..
* .. External Subroutines ..
EXTERNAL DCOPY, DGEMV
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( M.LE.0 .OR. N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Compute A - Q * B * P' one column at a time.
*
RESID = ZERO
IF( KD.NE.0 ) THEN
*
* B is bidiagonal.
*
IF( KD.NE.0 .AND. M.GE.N ) THEN
*
* B is upper bidiagonal and M >= N.
*
DO 20 J = 1, N
CALL DCOPY( M, A( 1, J ), 1, WORK, 1 )
DO 10 I = 1, N - 1
WORK( M+I ) = D( I )*PT( I, J ) + E( I )*PT( I+1, J )
10 CONTINUE
WORK( M+N ) = D( N )*PT( N, J )
CALL DGEMV( 'No transpose', M, N, -ONE, Q, LDQ,
$ WORK( M+1 ), 1, ONE, WORK, 1 )
RESID = MAX( RESID, DASUM( M, WORK, 1 ) )
20 CONTINUE
ELSE IF( KD.LT.0 ) THEN
*
* B is upper bidiagonal and M < N.
*
DO 40 J = 1, N
CALL DCOPY( M, A( 1, J ), 1, WORK, 1 )
DO 30 I = 1, M - 1
WORK( M+I ) = D( I )*PT( I, J ) + E( I )*PT( I+1, J )
30 CONTINUE
WORK( M+M ) = D( M )*PT( M, J )
CALL DGEMV( 'No transpose', M, M, -ONE, Q, LDQ,
$ WORK( M+1 ), 1, ONE, WORK, 1 )
RESID = MAX( RESID, DASUM( M, WORK, 1 ) )
40 CONTINUE
ELSE
*
* B is lower bidiagonal.
*
DO 60 J = 1, N
CALL DCOPY( M, A( 1, J ), 1, WORK, 1 )
WORK( M+1 ) = D( 1 )*PT( 1, J )
DO 50 I = 2, M
WORK( M+I ) = E( I-1 )*PT( I-1, J ) +
$ D( I )*PT( I, J )
50 CONTINUE
CALL DGEMV( 'No transpose', M, M, -ONE, Q, LDQ,
$ WORK( M+1 ), 1, ONE, WORK, 1 )
RESID = MAX( RESID, DASUM( M, WORK, 1 ) )
60 CONTINUE
END IF
ELSE
*
* B is diagonal.
*
IF( M.GE.N ) THEN
DO 80 J = 1, N
CALL DCOPY( M, A( 1, J ), 1, WORK, 1 )
DO 70 I = 1, N
WORK( M+I ) = D( I )*PT( I, J )
70 CONTINUE
CALL DGEMV( 'No transpose', M, N, -ONE, Q, LDQ,
$ WORK( M+1 ), 1, ONE, WORK, 1 )
RESID = MAX( RESID, DASUM( M, WORK, 1 ) )
80 CONTINUE
ELSE
DO 100 J = 1, N
CALL DCOPY( M, A( 1, J ), 1, WORK, 1 )
DO 90 I = 1, M
WORK( M+I ) = D( I )*PT( I, J )
90 CONTINUE
CALL DGEMV( 'No transpose', M, M, -ONE, Q, LDQ,
$ WORK( M+1 ), 1, ONE, WORK, 1 )
RESID = MAX( RESID, DASUM( M, WORK, 1 ) )
100 CONTINUE
END IF
END IF
*
* Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
*
ANORM = DLANGE( '1', M, N, A, LDA, WORK )
EPS = DLAMCH( 'Precision' )
*
IF( ANORM.LE.ZERO ) THEN
IF( RESID.NE.ZERO )
$ RESID = ONE / EPS
ELSE
IF( ANORM.GE.RESID ) THEN
RESID = ( RESID / ANORM ) / ( DBLE( N )*EPS )
ELSE
IF( ANORM.LT.ONE ) THEN
RESID = ( MIN( RESID, DBLE( N )*ANORM ) / ANORM ) /
$ ( DBLE( N )*EPS )
ELSE
RESID = MIN( RESID / ANORM, DBLE( N ) ) /
$ ( DBLE( N )*EPS )
END IF
END IF
END IF
*
RETURN
*
* End of DBDT01
*
END
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