215 lines
6.8 KiB
FortranFixed
215 lines
6.8 KiB
FortranFixed
SUBROUTINE ZBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
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$ RWORK, RESID )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER KD, LDA, LDPT, LDQ, M, N
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DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION D( * ), E( * ), RWORK( * )
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COMPLEX*16 A( LDA, * ), PT( LDPT, * ), Q( LDQ, * ),
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$ WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* ZBDT01 reconstructs a general matrix A from its bidiagonal form
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* A = Q * B * P'
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* where Q (m by min(m,n)) and P' (min(m,n) by n) are unitary
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* matrices and B is bidiagonal.
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*
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* The test ratio to test the reduction is
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* RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
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* where PT = P' and EPS is the machine precision.
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*
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* Arguments
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* =========
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*
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* M (input) INTEGER
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* The number of rows of the matrices A and Q.
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*
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* N (input) INTEGER
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* The number of columns of the matrices A and P'.
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*
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* KD (input) INTEGER
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* If KD = 0, B is diagonal and the array E is not referenced.
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* If KD = 1, the reduction was performed by xGEBRD; B is upper
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* bidiagonal if M >= N, and lower bidiagonal if M < N.
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* If KD = -1, the reduction was performed by xGBBRD; B is
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* always upper bidiagonal.
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*
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* A (input) COMPLEX*16 array, dimension (LDA,N)
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* The m by n matrix A.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,M).
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*
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* Q (input) COMPLEX*16 array, dimension (LDQ,N)
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* The m by min(m,n) unitary matrix Q in the reduction
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* A = Q * B * P'.
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*
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* LDQ (input) INTEGER
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* The leading dimension of the array Q. LDQ >= max(1,M).
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*
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* D (input) DOUBLE PRECISION array, dimension (min(M,N))
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* The diagonal elements of the bidiagonal matrix B.
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*
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* E (input) DOUBLE PRECISION array, dimension (min(M,N)-1)
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* The superdiagonal elements of the bidiagonal matrix B if
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* m >= n, or the subdiagonal elements of B if m < n.
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*
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* PT (input) COMPLEX*16 array, dimension (LDPT,N)
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* The min(m,n) by n unitary matrix P' in the reduction
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* A = Q * B * P'.
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*
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* LDPT (input) INTEGER
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* The leading dimension of the array PT.
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* LDPT >= max(1,min(M,N)).
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*
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* WORK (workspace) COMPLEX*16 array, dimension (M+N)
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*
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* RWORK (workspace) DOUBLE PRECISION array, dimension (M)
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*
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* RESID (output) DOUBLE PRECISION
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* The test ratio: norm(A - Q * B * P') / ( n * norm(A) * EPS )
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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DOUBLE PRECISION ANORM, EPS
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, DZASUM, ZLANGE
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EXTERNAL DLAMCH, DZASUM, ZLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL ZCOPY, ZGEMV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, DCMPLX, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( M.LE.0 .OR. N.LE.0 ) THEN
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RESID = ZERO
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RETURN
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END IF
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*
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* Compute A - Q * B * P' one column at a time.
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*
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RESID = ZERO
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IF( KD.NE.0 ) THEN
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*
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* B is bidiagonal.
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*
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IF( KD.NE.0 .AND. M.GE.N ) THEN
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*
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* B is upper bidiagonal and M >= N.
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*
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DO 20 J = 1, N
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CALL ZCOPY( M, A( 1, J ), 1, WORK, 1 )
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DO 10 I = 1, N - 1
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WORK( M+I ) = D( I )*PT( I, J ) + E( I )*PT( I+1, J )
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10 CONTINUE
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WORK( M+N ) = D( N )*PT( N, J )
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CALL ZGEMV( 'No transpose', M, N, -DCMPLX( ONE ), Q, LDQ,
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$ WORK( M+1 ), 1, DCMPLX( ONE ), WORK, 1 )
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RESID = MAX( RESID, DZASUM( M, WORK, 1 ) )
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20 CONTINUE
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ELSE IF( KD.LT.0 ) THEN
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*
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* B is upper bidiagonal and M < N.
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*
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DO 40 J = 1, N
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CALL ZCOPY( M, A( 1, J ), 1, WORK, 1 )
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DO 30 I = 1, M - 1
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WORK( M+I ) = D( I )*PT( I, J ) + E( I )*PT( I+1, J )
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30 CONTINUE
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WORK( M+M ) = D( M )*PT( M, J )
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CALL ZGEMV( 'No transpose', M, M, -DCMPLX( ONE ), Q, LDQ,
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$ WORK( M+1 ), 1, DCMPLX( ONE ), WORK, 1 )
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RESID = MAX( RESID, DZASUM( M, WORK, 1 ) )
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40 CONTINUE
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ELSE
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*
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* B is lower bidiagonal.
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*
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DO 60 J = 1, N
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CALL ZCOPY( M, A( 1, J ), 1, WORK, 1 )
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WORK( M+1 ) = D( 1 )*PT( 1, J )
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DO 50 I = 2, M
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WORK( M+I ) = E( I-1 )*PT( I-1, J ) +
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$ D( I )*PT( I, J )
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50 CONTINUE
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CALL ZGEMV( 'No transpose', M, M, -DCMPLX( ONE ), Q, LDQ,
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$ WORK( M+1 ), 1, DCMPLX( ONE ), WORK, 1 )
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RESID = MAX( RESID, DZASUM( M, WORK, 1 ) )
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60 CONTINUE
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END IF
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ELSE
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*
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* B is diagonal.
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*
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IF( M.GE.N ) THEN
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DO 80 J = 1, N
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CALL ZCOPY( M, A( 1, J ), 1, WORK, 1 )
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DO 70 I = 1, N
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WORK( M+I ) = D( I )*PT( I, J )
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70 CONTINUE
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CALL ZGEMV( 'No transpose', M, N, -DCMPLX( ONE ), Q, LDQ,
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$ WORK( M+1 ), 1, DCMPLX( ONE ), WORK, 1 )
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RESID = MAX( RESID, DZASUM( M, WORK, 1 ) )
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80 CONTINUE
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ELSE
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DO 100 J = 1, N
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CALL ZCOPY( M, A( 1, J ), 1, WORK, 1 )
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DO 90 I = 1, M
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WORK( M+I ) = D( I )*PT( I, J )
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90 CONTINUE
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CALL ZGEMV( 'No transpose', M, M, -DCMPLX( ONE ), Q, LDQ,
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$ WORK( M+1 ), 1, DCMPLX( ONE ), WORK, 1 )
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RESID = MAX( RESID, DZASUM( M, WORK, 1 ) )
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100 CONTINUE
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END IF
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END IF
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*
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* Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
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*
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ANORM = ZLANGE( '1', M, N, A, LDA, RWORK )
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EPS = DLAMCH( 'Precision' )
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*
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IF( ANORM.LE.ZERO ) THEN
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IF( RESID.NE.ZERO )
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$ RESID = ONE / EPS
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ELSE
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IF( ANORM.GE.RESID ) THEN
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RESID = ( RESID / ANORM ) / ( DBLE( N )*EPS )
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ELSE
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IF( ANORM.LT.ONE ) THEN
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RESID = ( MIN( RESID, DBLE( N )*ANORM ) / ANORM ) /
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$ ( DBLE( N )*EPS )
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ELSE
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RESID = MIN( RESID / ANORM, DBLE( N ) ) /
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$ ( DBLE( N )*EPS )
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END IF
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END IF
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END IF
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*
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RETURN
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*
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* End of ZBDT01
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*
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END
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