198 lines
4.9 KiB
Fortran
198 lines
4.9 KiB
Fortran
*> \brief \b SGERQS
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
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* INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), B( LDB, * ), TAU( * ),
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* $ WORK( LWORK )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> Compute a minimum-norm solution
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*> min || A*X - B ||
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*> using the RQ factorization
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*> A = R*Q
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*> computed by SGERQF.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix A. N >= M >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of columns of B. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> Details of the RQ factorization of the original matrix A as
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*> returned by SGERQF.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= M.
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is REAL array, dimension (M)
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*> Details of the orthogonal matrix Q.
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is REAL array, dimension (LDB,NRHS)
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*> On entry, the right hand side vectors for the linear system.
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*> On exit, the solution vectors X. Each solution vector
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*> is contained in rows 1:N of a column of B.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The length of the array WORK. LWORK must be at least NRHS,
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*> and should be at least NRHS*NB, where NB is the block size
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*> for this environment.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is 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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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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SUBROUTINE SGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
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$ INFO )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), B( LDB, * ), TAU( * ),
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$ WORK( LWORK )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. External Subroutines ..
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EXTERNAL SLASET, SORMRQ, STRSM, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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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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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 .OR. M.GT.N ) THEN
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INFO = -2
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -5
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -8
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ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
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$ THEN
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INFO = -10
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SGERQS', -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 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
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$ RETURN
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*
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* Solve R*X = B(n-m+1:n,:)
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*
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CALL STRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS,
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$ ONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB )
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*
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* Set B(1:n-m,:) to zero
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*
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CALL SLASET( 'Full', N-M, NRHS, ZERO, ZERO, B, LDB )
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*
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* B := Q' * B
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*
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CALL SORMRQ( 'Left', 'Transpose', N, NRHS, M, A, LDA, TAU, B, LDB,
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$ WORK, LWORK, INFO )
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*
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RETURN
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*
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* End of SGERQS
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*
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END
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