206 lines
6.8 KiB
FortranFixed
206 lines
6.8 KiB
FortranFixed
SUBROUTINE DGBT05( TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X,
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$ LDX, XACT, LDXACT, FERR, BERR, RESLTS )
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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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CHARACTER TRANS
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INTEGER KL, KU, LDAB, LDB, LDX, LDXACT, N, NRHS
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ), BERR( * ),
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$ FERR( * ), RESLTS( * ), X( LDX, * ),
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$ XACT( LDXACT, * )
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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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* DGBT05 tests the error bounds from iterative refinement for the
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* computed solution to a system of equations op(A)*X = B, where A is a
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* general band matrix of order n with kl subdiagonals and ku
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* superdiagonals and op(A) = A or A**T, depending on TRANS.
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*
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* RESLTS(1) = test of the error bound
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* = norm(X - XACT) / ( norm(X) * FERR )
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*
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* A large value is returned if this ratio is not less than one.
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*
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* RESLTS(2) = residual from the iterative refinement routine
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* = the maximum of BERR / ( NZ*EPS + (*) ), where
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* (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
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* and NZ = max. number of nonzeros in any row of A, plus 1
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*
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* Arguments
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* =========
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*
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* TRANS (input) CHARACTER*1
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* Specifies the form of the system of equations.
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* = 'N': A * X = B (No transpose)
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* = 'T': A**T * X = B (Transpose)
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* = 'C': A**H * X = B (Conjugate transpose = Transpose)
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*
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* N (input) INTEGER
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* The number of rows of the matrices X, B, and XACT, and the
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* order of the matrix A. N >= 0.
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*
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* KL (input) INTEGER
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* The number of subdiagonals within the band of A. KL >= 0.
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*
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* KU (input) INTEGER
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* The number of superdiagonals within the band of A. KU >= 0.
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*
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* NRHS (input) INTEGER
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* The number of columns of the matrices X, B, and XACT.
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* NRHS >= 0.
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*
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* AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
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* The original band matrix A, stored in rows 1 to KL+KU+1.
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* The j-th column of A is stored in the j-th column of the
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* array AB as follows:
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* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
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*
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* LDAB (input) INTEGER
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* The leading dimension of the array AB. LDAB >= KL+KU+1.
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*
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* B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
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* The right hand side vectors for the system of linear
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* equations.
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*
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* LDB (input) INTEGER
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* The leading dimension of the array B. LDB >= max(1,N).
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*
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* X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
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* The computed solution vectors. Each vector is stored as a
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* column of the matrix X.
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*
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* LDX (input) INTEGER
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* The leading dimension of the array X. LDX >= max(1,N).
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*
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* XACT (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
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* The exact solution vectors. Each vector is stored as a
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* column of the matrix XACT.
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*
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* LDXACT (input) INTEGER
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* The leading dimension of the array XACT. LDXACT >= max(1,N).
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*
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* FERR (input) DOUBLE PRECISION array, dimension (NRHS)
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* The estimated forward error bounds for each solution vector
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* X. If XTRUE is the true solution, FERR bounds the magnitude
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* of the largest entry in (X - XTRUE) divided by the magnitude
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* of the largest entry in X.
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*
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* BERR (input) DOUBLE PRECISION array, dimension (NRHS)
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* The componentwise relative backward error of each solution
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* vector (i.e., the smallest relative change in any entry of A
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* or B that makes X an exact solution).
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*
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* RESLTS (output) DOUBLE PRECISION array, dimension (2)
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* The maximum over the NRHS solution vectors of the ratios:
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* RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
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* RESLTS(2) = BERR / ( NZ*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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LOGICAL NOTRAN
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INTEGER I, IMAX, J, K, NZ
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DOUBLE PRECISION AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER IDAMAX
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DOUBLE PRECISION DLAMCH
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EXTERNAL LSAME, IDAMAX, DLAMCH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0 or NRHS = 0.
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*
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IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
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RESLTS( 1 ) = ZERO
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RESLTS( 2 ) = ZERO
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RETURN
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END IF
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*
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EPS = DLAMCH( 'Epsilon' )
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UNFL = DLAMCH( 'Safe minimum' )
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OVFL = ONE / UNFL
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NOTRAN = LSAME( TRANS, 'N' )
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NZ = MIN( KL+KU+2, N+1 )
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*
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* Test 1: Compute the maximum of
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* norm(X - XACT) / ( norm(X) * FERR )
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* over all the vectors X and XACT using the infinity-norm.
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*
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ERRBND = ZERO
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DO 30 J = 1, NRHS
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IMAX = IDAMAX( N, X( 1, J ), 1 )
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XNORM = MAX( ABS( X( IMAX, J ) ), UNFL )
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DIFF = ZERO
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DO 10 I = 1, N
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DIFF = MAX( DIFF, ABS( X( I, J )-XACT( I, J ) ) )
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10 CONTINUE
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*
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IF( XNORM.GT.ONE ) THEN
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GO TO 20
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ELSE IF( DIFF.LE.OVFL*XNORM ) THEN
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GO TO 20
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ELSE
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ERRBND = ONE / EPS
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GO TO 30
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END IF
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*
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20 CONTINUE
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IF( DIFF / XNORM.LE.FERR( J ) ) THEN
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ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) )
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ELSE
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ERRBND = ONE / EPS
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END IF
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30 CONTINUE
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RESLTS( 1 ) = ERRBND
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*
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* Test 2: Compute the maximum of BERR / ( NZ*EPS + (*) ), where
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* (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
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*
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DO 70 K = 1, NRHS
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DO 60 I = 1, N
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TMP = ABS( B( I, K ) )
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IF( NOTRAN ) THEN
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DO 40 J = MAX( I-KL, 1 ), MIN( I+KU, N )
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TMP = TMP + ABS( AB( KU+1+I-J, J ) )*ABS( X( J, K ) )
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40 CONTINUE
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ELSE
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DO 50 J = MAX( I-KU, 1 ), MIN( I+KL, N )
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TMP = TMP + ABS( AB( KU+1+J-I, I ) )*ABS( X( J, K ) )
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50 CONTINUE
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END IF
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IF( I.EQ.1 ) THEN
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AXBI = TMP
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ELSE
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AXBI = MIN( AXBI, TMP )
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END IF
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60 CONTINUE
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TMP = BERR( K ) / ( NZ*EPS+NZ*UNFL / MAX( AXBI, NZ*UNFL ) )
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IF( K.EQ.1 ) THEN
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RESLTS( 2 ) = TMP
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ELSE
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RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP )
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END IF
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70 CONTINUE
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*
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RETURN
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*
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* End of DGBT05
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*
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END
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