196 lines
6.2 KiB
FortranFixed
196 lines
6.2 KiB
FortranFixed
SUBROUTINE SLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
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$ INFO )
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*
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* -- LAPACK 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 CUTPNT, INFO, LDQ, N
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REAL RHO
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* ..
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* .. Array Arguments ..
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INTEGER INDXQ( * ), IWORK( * )
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REAL D( * ), Q( LDQ, * ), 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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* SLAED1 computes the updated eigensystem of a diagonal
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* matrix after modification by a rank-one symmetric matrix. This
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* routine is used only for the eigenproblem which requires all
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* eigenvalues and eigenvectors of a tridiagonal matrix. SLAED7 handles
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* the case in which eigenvalues only or eigenvalues and eigenvectors
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* of a full symmetric matrix (which was reduced to tridiagonal form)
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* are desired.
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*
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* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
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*
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* where Z = Q'u, u is a vector of length N with ones in the
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* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
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*
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* The eigenvectors of the original matrix are stored in Q, and the
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* eigenvalues are in D. The algorithm consists of three stages:
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*
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* The first stage consists of deflating the size of the problem
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* when there are multiple eigenvalues or if there is a zero in
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* the Z vector. For each such occurence the dimension of the
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* secular equation problem is reduced by one. This stage is
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* performed by the routine SLAED2.
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*
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* The second stage consists of calculating the updated
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* eigenvalues. This is done by finding the roots of the secular
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* equation via the routine SLAED4 (as called by SLAED3).
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* This routine also calculates the eigenvectors of the current
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* problem.
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*
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* The final stage consists of computing the updated eigenvectors
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* directly using the updated eigenvalues. The eigenvectors for
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* the current problem are multiplied with the eigenvectors from
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* the overall problem.
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*
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* Arguments
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* =========
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*
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* N (input) INTEGER
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* The dimension of the symmetric tridiagonal matrix. N >= 0.
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*
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* D (input/output) REAL array, dimension (N)
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* On entry, the eigenvalues of the rank-1-perturbed matrix.
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* On exit, the eigenvalues of the repaired matrix.
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*
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* Q (input/output) REAL array, dimension (LDQ,N)
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* On entry, the eigenvectors of the rank-1-perturbed matrix.
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* On exit, the eigenvectors of the repaired tridiagonal matrix.
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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,N).
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*
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* INDXQ (input/output) INTEGER array, dimension (N)
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* On entry, the permutation which separately sorts the two
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* subproblems in D into ascending order.
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* On exit, the permutation which will reintegrate the
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* subproblems back into sorted order,
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* i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
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*
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* RHO (input) REAL
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* The subdiagonal entry used to create the rank-1 modification.
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*
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* CUTPNT (input) INTEGER
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* The location of the last eigenvalue in the leading sub-matrix.
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* min(1,N) <= CUTPNT <= N/2.
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*
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* WORK (workspace) REAL array, dimension (4*N + N**2)
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*
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* IWORK (workspace) INTEGER array, dimension (4*N)
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*
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* INFO (output) INTEGER
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* = 0: successful exit.
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* < 0: if INFO = -i, the i-th argument had an illegal value.
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* > 0: if INFO = 1, an eigenvalue did not converge
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*
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* Further Details
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* ===============
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*
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* Based on contributions by
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* Jeff Rutter, Computer Science Division, University of California
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* at Berkeley, USA
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* Modified by Francoise Tisseur, University of Tennessee.
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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INTEGER COLTYP, CPP1, I, IDLMDA, INDX, INDXC, INDXP,
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$ IQ2, IS, IW, IZ, K, N1, N2
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* ..
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* .. External Subroutines ..
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EXTERNAL SCOPY, SLAED2, SLAED3, SLAMRG, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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*
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
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INFO = -4
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ELSE IF( MIN( 1, N / 2 ).GT.CUTPNT .OR. ( N / 2 ).LT.CUTPNT ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SLAED1', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* The following values are integer pointers which indicate
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* the portion of the workspace
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* used by a particular array in SLAED2 and SLAED3.
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*
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IZ = 1
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IDLMDA = IZ + N
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IW = IDLMDA + N
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IQ2 = IW + N
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*
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INDX = 1
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INDXC = INDX + N
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COLTYP = INDXC + N
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INDXP = COLTYP + N
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*
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*
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* Form the z-vector which consists of the last row of Q_1 and the
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* first row of Q_2.
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*
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CALL SCOPY( CUTPNT, Q( CUTPNT, 1 ), LDQ, WORK( IZ ), 1 )
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CPP1 = CUTPNT + 1
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CALL SCOPY( N-CUTPNT, Q( CPP1, CPP1 ), LDQ, WORK( IZ+CUTPNT ), 1 )
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*
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* Deflate eigenvalues.
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*
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CALL SLAED2( K, N, CUTPNT, D, Q, LDQ, INDXQ, RHO, WORK( IZ ),
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$ WORK( IDLMDA ), WORK( IW ), WORK( IQ2 ),
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$ IWORK( INDX ), IWORK( INDXC ), IWORK( INDXP ),
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$ IWORK( COLTYP ), INFO )
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*
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IF( INFO.NE.0 )
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$ GO TO 20
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*
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* Solve Secular Equation.
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*
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IF( K.NE.0 ) THEN
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IS = ( IWORK( COLTYP )+IWORK( COLTYP+1 ) )*CUTPNT +
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$ ( IWORK( COLTYP+1 )+IWORK( COLTYP+2 ) )*( N-CUTPNT ) + IQ2
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CALL SLAED3( K, N, CUTPNT, D, Q, LDQ, RHO, WORK( IDLMDA ),
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$ WORK( IQ2 ), IWORK( INDXC ), IWORK( COLTYP ),
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$ WORK( IW ), WORK( IS ), INFO )
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IF( INFO.NE.0 )
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$ GO TO 20
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*
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* Prepare the INDXQ sorting permutation.
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*
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N1 = K
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N2 = N - K
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CALL SLAMRG( N1, N2, D, 1, -1, INDXQ )
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ELSE
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DO 10 I = 1, N
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INDXQ( I ) = I
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10 CONTINUE
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END IF
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*
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20 CONTINUE
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RETURN
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*
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* End of SLAED1
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*
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END
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