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SUBROUTINE DBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
$ RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. 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 |