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SUBROUTINE DLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, |
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$ LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, |
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$ GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, |
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$ IWORK, INFO ) |
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* |
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* -- LAPACK routine (version 3.2) -- |
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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 2006 |
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* |
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* .. Scalar Arguments .. |
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INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, |
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$ SMLSIZ |
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* .. |
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* .. Array Arguments .. |
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INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), |
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$ K( * ), PERM( LDGCOL, * ) |
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DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), C( * ), |
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$ DIFL( LDU, * ), DIFR( LDU, * ), |
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$ GIVNUM( LDU, * ), POLES( LDU, * ), S( * ), |
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$ U( LDU, * ), VT( LDU, * ), WORK( * ), |
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$ Z( LDU, * ) |
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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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* DLALSA is an itermediate step in solving the least squares problem |
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* by computing the SVD of the coefficient matrix in compact form (The |
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* singular vectors are computed as products of simple orthorgonal |
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* matrices.). |
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* |
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* If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector |
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* matrix of an upper bidiagonal matrix to the right hand side; and if |
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* ICOMPQ = 1, DLALSA applies the right singular vector matrix to the |
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* right hand side. The singular vector matrices were generated in |
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* compact form by DLALSA. |
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* |
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* Arguments |
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* ========= |
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* |
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* |
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* ICOMPQ (input) INTEGER |
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* Specifies whether the left or the right singular vector |
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* matrix is involved. |
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* = 0: Left singular vector matrix |
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* = 1: Right singular vector matrix |
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* |
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* SMLSIZ (input) INTEGER |
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* The maximum size of the subproblems at the bottom of the |
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* computation tree. |
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* |
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* N (input) INTEGER |
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* The row and column dimensions of the upper bidiagonal matrix. |
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* |
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* NRHS (input) INTEGER |
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* The number of columns of B and BX. NRHS must be at least 1. |
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* |
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* B (input/output) DOUBLE PRECISION array, dimension ( LDB, NRHS ) |
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* On input, B contains the right hand sides of the least |
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* squares problem in rows 1 through M. |
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* On output, B contains the solution X in rows 1 through N. |
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* |
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* LDB (input) INTEGER |
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* The leading dimension of B in the calling subprogram. |
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* LDB must be at least max(1,MAX( M, N ) ). |
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* |
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* BX (output) DOUBLE PRECISION array, dimension ( LDBX, NRHS ) |
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* On exit, the result of applying the left or right singular |
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* vector matrix to B. |
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* |
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* LDBX (input) INTEGER |
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* The leading dimension of BX. |
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* |
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* U (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ). |
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* On entry, U contains the left singular vector matrices of all |
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* subproblems at the bottom level. |
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* |
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* LDU (input) INTEGER, LDU = > N. |
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* The leading dimension of arrays U, VT, DIFL, DIFR, |
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* POLES, GIVNUM, and Z. |
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* |
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* VT (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). |
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* On entry, VT' contains the right singular vector matrices of |
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* all subproblems at the bottom level. |
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* |
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* K (input) INTEGER array, dimension ( N ). |
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* |
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* DIFL (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ). |
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* where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. |
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* |
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* DIFR (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). |
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* On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record |
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* distances between singular values on the I-th level and |
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* singular values on the (I -1)-th level, and DIFR(*, 2 * I) |
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* record the normalizing factors of the right singular vectors |
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* matrices of subproblems on I-th level. |
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* |
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* Z (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ). |
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* On entry, Z(1, I) contains the components of the deflation- |
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* adjusted updating row vector for subproblems on the I-th |
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* level. |
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* |
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* POLES (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). |
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* On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old |
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* singular values involved in the secular equations on the I-th |
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* level. |
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* |
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* GIVPTR (input) INTEGER array, dimension ( N ). |
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* On entry, GIVPTR( I ) records the number of Givens |
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* rotations performed on the I-th problem on the computation |
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* tree. |
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* |
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* GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ). |
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* On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the |
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* locations of Givens rotations performed on the I-th level on |
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* the computation tree. |
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* |
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* LDGCOL (input) INTEGER, LDGCOL = > N. |
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* The leading dimension of arrays GIVCOL and PERM. |
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* |
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* PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ). |
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* On entry, PERM(*, I) records permutations done on the I-th |
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* level of the computation tree. |
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* |
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* GIVNUM (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). |
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* On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- |
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* values of Givens rotations performed on the I-th level on the |
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* computation tree. |
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* |
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* C (input) DOUBLE PRECISION array, dimension ( N ). |
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* On entry, if the I-th subproblem is not square, |
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* C( I ) contains the C-value of a Givens rotation related to |
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* the right null space of the I-th subproblem. |
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* |
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* S (input) DOUBLE PRECISION array, dimension ( N ). |
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* On entry, if the I-th subproblem is not square, |
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* S( I ) contains the S-value of a Givens rotation related to |
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* the right null space of the I-th subproblem. |
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* |
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* WORK (workspace) DOUBLE PRECISION array. |
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* The dimension must be at least N. |
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* |
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* IWORK (workspace) INTEGER array. |
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* The dimension must be at least 3 * 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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* |
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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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* Ming Gu and Ren-Cang Li, Computer Science Division, University of |
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* California at Berkeley, USA |
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* Osni Marques, LBNL/NERSC, USA |
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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 = 0.0D0, ONE = 1.0D0 ) |
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* .. |
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* .. Local Scalars .. |
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INTEGER I, I1, IC, IM1, INODE, J, LF, LL, LVL, LVL2, |
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$ ND, NDB1, NDIML, NDIMR, NL, NLF, NLP1, NLVL, |
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$ NR, NRF, NRP1, SQRE |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL DCOPY, DGEMM, DLALS0, DLASDT, XERBLA |
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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( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN |
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INFO = -1 |
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ELSE IF( SMLSIZ.LT.3 ) THEN |
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INFO = -2 |
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ELSE IF( N.LT.SMLSIZ ) THEN |
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INFO = -3 |
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ELSE IF( NRHS.LT.1 ) THEN |
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INFO = -4 |
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ELSE IF( LDB.LT.N ) THEN |
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INFO = -6 |
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ELSE IF( LDBX.LT.N ) THEN |
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INFO = -8 |
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ELSE IF( LDU.LT.N ) THEN |
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INFO = -10 |
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ELSE IF( LDGCOL.LT.N ) THEN |
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INFO = -19 |
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END IF |
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IF( INFO.NE.0 ) THEN |
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CALL XERBLA( 'DLALSA', -INFO ) |
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RETURN |
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END IF |
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* |
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* Book-keeping and setting up the computation tree. |
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* |
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INODE = 1 |
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NDIML = INODE + N |
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NDIMR = NDIML + N |
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* |
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CALL DLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ), |
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$ IWORK( NDIMR ), SMLSIZ ) |
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* |
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* The following code applies back the left singular vector factors. |
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* For applying back the right singular vector factors, go to 50. |
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* |
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IF( ICOMPQ.EQ.1 ) THEN |
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GO TO 50 |
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END IF |
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* |
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* The nodes on the bottom level of the tree were solved |
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* by DLASDQ. The corresponding left and right singular vector |
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* matrices are in explicit form. First apply back the left |
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* singular vector matrices. |
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* |
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NDB1 = ( ND+1 ) / 2 |
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DO 10 I = NDB1, ND |
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* |
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* IC : center row of each node |
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* NL : number of rows of left subproblem |
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* NR : number of rows of right subproblem |
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* NLF: starting row of the left subproblem |
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* NRF: starting row of the right subproblem |
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* |
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I1 = I - 1 |
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IC = IWORK( INODE+I1 ) |
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NL = IWORK( NDIML+I1 ) |
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NR = IWORK( NDIMR+I1 ) |
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NLF = IC - NL |
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NRF = IC + 1 |
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CALL DGEMM( 'T', 'N', NL, NRHS, NL, ONE, U( NLF, 1 ), LDU, |
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$ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) |
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CALL DGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU, |
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$ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) |
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10 CONTINUE |
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* |
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* Next copy the rows of B that correspond to unchanged rows |
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* in the bidiagonal matrix to BX. |
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* |
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DO 20 I = 1, ND |
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IC = IWORK( INODE+I-1 ) |
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CALL DCOPY( NRHS, B( IC, 1 ), LDB, BX( IC, 1 ), LDBX ) |
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20 CONTINUE |
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* |
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* Finally go through the left singular vector matrices of all |
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* the other subproblems bottom-up on the tree. |
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* |
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J = 2**NLVL |
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SQRE = 0 |
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* |
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DO 40 LVL = NLVL, 1, -1 |
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LVL2 = 2*LVL - 1 |
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* |
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* find the first node LF and last node LL on |
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* the current level LVL |
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* |
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IF( LVL.EQ.1 ) THEN |
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LF = 1 |
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LL = 1 |
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ELSE |
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LF = 2**( LVL-1 ) |
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LL = 2*LF - 1 |
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END IF |
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DO 30 I = LF, LL |
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IM1 = I - 1 |
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IC = IWORK( INODE+IM1 ) |
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NL = IWORK( NDIML+IM1 ) |
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NR = IWORK( NDIMR+IM1 ) |
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NLF = IC - NL |
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NRF = IC + 1 |
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J = J - 1 |
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CALL DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, BX( NLF, 1 ), LDBX, |
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$ B( NLF, 1 ), LDB, PERM( NLF, LVL ), |
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$ GIVPTR( J ), GIVCOL( NLF, LVL2 ), LDGCOL, |
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$ GIVNUM( NLF, LVL2 ), LDU, POLES( NLF, LVL2 ), |
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$ DIFL( NLF, LVL ), DIFR( NLF, LVL2 ), |
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$ Z( NLF, LVL ), K( J ), C( J ), S( J ), WORK, |
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$ INFO ) |
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30 CONTINUE |
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40 CONTINUE |
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GO TO 90 |
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* |
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* ICOMPQ = 1: applying back the right singular vector factors. |
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* |
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50 CONTINUE |
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* |
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* First now go through the right singular vector matrices of all |
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* the tree nodes top-down. |
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* |
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J = 0 |
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DO 70 LVL = 1, NLVL |
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LVL2 = 2*LVL - 1 |
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* |
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* Find the first node LF and last node LL on |
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* the current level LVL. |
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* |
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IF( LVL.EQ.1 ) THEN |
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LF = 1 |
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LL = 1 |
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ELSE |
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LF = 2**( LVL-1 ) |
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LL = 2*LF - 1 |
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END IF |
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DO 60 I = LL, LF, -1 |
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IM1 = I - 1 |
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IC = IWORK( INODE+IM1 ) |
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NL = IWORK( NDIML+IM1 ) |
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NR = IWORK( NDIMR+IM1 ) |
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NLF = IC - NL |
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NRF = IC + 1 |
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IF( I.EQ.LL ) THEN |
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SQRE = 0 |
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ELSE |
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SQRE = 1 |
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END IF |
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J = J + 1 |
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CALL DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B( NLF, 1 ), LDB, |
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$ BX( NLF, 1 ), LDBX, PERM( NLF, LVL ), |
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$ GIVPTR( J ), GIVCOL( NLF, LVL2 ), LDGCOL, |
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$ GIVNUM( NLF, LVL2 ), LDU, POLES( NLF, LVL2 ), |
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$ DIFL( NLF, LVL ), DIFR( NLF, LVL2 ), |
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$ Z( NLF, LVL ), K( J ), C( J ), S( J ), WORK, |
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$ INFO ) |
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60 CONTINUE |
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70 CONTINUE |
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* |
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* The nodes on the bottom level of the tree were solved |
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* by DLASDQ. The corresponding right singular vector |
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* matrices are in explicit form. Apply them back. |
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* |
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NDB1 = ( ND+1 ) / 2 |
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DO 80 I = NDB1, ND |
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I1 = I - 1 |
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IC = IWORK( INODE+I1 ) |
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NL = IWORK( NDIML+I1 ) |
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NR = IWORK( NDIMR+I1 ) |
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NLP1 = NL + 1 |
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IF( I.EQ.ND ) THEN |
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NRP1 = NR |
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ELSE |
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NRP1 = NR + 1 |
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END IF |
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NLF = IC - NL |
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NRF = IC + 1 |
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CALL DGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU, |
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$ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) |
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CALL DGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU, |
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$ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) |
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80 CONTINUE |
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* |
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90 CONTINUE |
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* |
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RETURN |
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* |
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* End of DLALSA |
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* |
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END |