544 lines
15 KiB
Fortran
544 lines
15 KiB
Fortran
*> \brief \b SLAVSP
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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 SLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
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* INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, TRANS, UPLO
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* INTEGER INFO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* REAL A( * ), B( LDB, * )
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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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*> SLAVSP performs one of the matrix-vector operations
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*> x := A*x or x := A'*x,
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*> where x is an N element vector and A is one of the factors
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*> from the block U*D*U' or L*D*L' factorization computed by SSPTRF.
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*>
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*> If TRANS = 'N', multiplies by U or U * D (or L or L * D)
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*> If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L' )
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*> If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L' )
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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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the factor stored in A is upper or lower
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*> triangular.
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> Specifies the operation to be performed:
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*> = 'N': x := A*x
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*> = 'T': x := A'*x
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*> = 'C': x := A'*x
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*> \endverbatim
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*>
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*> \param[in] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> Specifies whether or not the diagonal blocks are unit
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*> matrices. If the diagonal blocks are assumed to be unit,
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*> then A = U or A = L, otherwise A = U*D or A = L*D.
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*> = 'U': Diagonal blocks are assumed to be unit matrices.
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*> = 'N': Diagonal blocks are assumed to be non-unit matrices.
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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 rows and columns of the matrix A. N >= 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 right hand sides, i.e., the number of vectors
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*> x to be multiplied by A. 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 (N*(N+1)/2)
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*> The block diagonal matrix D and the multipliers used to
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*> obtain the factor U or L, stored as a packed triangular
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*> matrix as computed by SSPTRF.
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices from SSPTRF.
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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, B contains NRHS vectors of length N.
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*> On exit, B is overwritten with the product A * 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] 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 = -k, the k-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 SLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
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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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CHARACTER DIAG, TRANS, UPLO
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INTEGER INFO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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REAL A( * ), B( LDB, * )
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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 ONE
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PARAMETER ( ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL NOUNIT
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INTEGER J, K, KC, KCNEXT, KP
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REAL D11, D12, D21, D22, T1, T2
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEMV, SGER, SSCAL, SSWAP, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, 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( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
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$ LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
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INFO = -2
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ELSE IF( .NOT.LSAME( DIAG, 'U' ) .AND. .NOT.LSAME( DIAG, 'N' ) )
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$ THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -8
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SLAVSP ', -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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NOUNIT = LSAME( DIAG, 'N' )
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*------------------------------------------
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*
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* Compute B := A * B (No transpose)
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*
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*------------------------------------------
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IF( LSAME( TRANS, 'N' ) ) THEN
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*
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* Compute B := U*B
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* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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*
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* Loop forward applying the transformations.
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*
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K = 1
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KC = 1
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10 CONTINUE
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IF( K.GT.N )
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$ GO TO 30
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*
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* 1 x 1 pivot block
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*
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IF( IPIV( K ).GT.0 ) THEN
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*
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* Multiply by the diagonal element if forming U * D.
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*
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IF( NOUNIT )
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$ CALL SSCAL( NRHS, A( KC+K-1 ), B( K, 1 ), LDB )
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*
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* Multiply by P(K) * inv(U(K)) if K > 1.
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*
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IF( K.GT.1 ) THEN
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*
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* Apply the transformation.
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*
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CALL SGER( K-1, NRHS, ONE, A( KC ), 1, B( K, 1 ), LDB,
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$ B( 1, 1 ), LDB )
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*
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* Interchange if P(K) != I.
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*
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KP = IPIV( K )
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IF( KP.NE.K )
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$ CALL SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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END IF
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KC = KC + K
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K = K + 1
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ELSE
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*
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* 2 x 2 pivot block
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*
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KCNEXT = KC + K
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*
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* Multiply by the diagonal block if forming U * D.
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*
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IF( NOUNIT ) THEN
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D11 = A( KCNEXT-1 )
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D22 = A( KCNEXT+K )
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D12 = A( KCNEXT+K-1 )
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D21 = D12
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DO 20 J = 1, NRHS
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T1 = B( K, J )
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T2 = B( K+1, J )
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B( K, J ) = D11*T1 + D12*T2
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B( K+1, J ) = D21*T1 + D22*T2
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20 CONTINUE
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END IF
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*
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* Multiply by P(K) * inv(U(K)) if K > 1.
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*
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IF( K.GT.1 ) THEN
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*
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* Apply the transformations.
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*
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CALL SGER( K-1, NRHS, ONE, A( KC ), 1, B( K, 1 ), LDB,
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$ B( 1, 1 ), LDB )
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CALL SGER( K-1, NRHS, ONE, A( KCNEXT ), 1,
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$ B( K+1, 1 ), LDB, B( 1, 1 ), LDB )
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*
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* Interchange if P(K) != I.
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*
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KP = ABS( IPIV( K ) )
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IF( KP.NE.K )
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$ CALL SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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END IF
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KC = KCNEXT + K + 1
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K = K + 2
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END IF
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GO TO 10
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30 CONTINUE
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*
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* Compute B := L*B
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* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) .
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*
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ELSE
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*
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* Loop backward applying the transformations to B.
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*
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K = N
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KC = N*( N+1 ) / 2 + 1
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40 CONTINUE
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IF( K.LT.1 )
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$ GO TO 60
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KC = KC - ( N-K+1 )
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*
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* Test the pivot index. If greater than zero, a 1 x 1
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* pivot was used, otherwise a 2 x 2 pivot was used.
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*
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IF( IPIV( K ).GT.0 ) THEN
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*
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* 1 x 1 pivot block:
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*
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* Multiply by the diagonal element if forming L * D.
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*
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IF( NOUNIT )
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$ CALL SSCAL( NRHS, A( KC ), B( K, 1 ), LDB )
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*
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* Multiply by P(K) * inv(L(K)) if K < N.
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*
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IF( K.NE.N ) THEN
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KP = IPIV( K )
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*
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* Apply the transformation.
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*
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CALL SGER( N-K, NRHS, ONE, A( KC+1 ), 1, B( K, 1 ),
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$ LDB, B( K+1, 1 ), LDB )
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*
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* Interchange if a permutation was applied at the
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* K-th step of the factorization.
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*
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IF( KP.NE.K )
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$ CALL SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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END IF
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K = K - 1
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*
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ELSE
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*
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* 2 x 2 pivot block:
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*
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KCNEXT = KC - ( N-K+2 )
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*
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* Multiply by the diagonal block if forming L * D.
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*
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IF( NOUNIT ) THEN
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D11 = A( KCNEXT )
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D22 = A( KC )
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D21 = A( KCNEXT+1 )
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D12 = D21
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DO 50 J = 1, NRHS
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T1 = B( K-1, J )
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T2 = B( K, J )
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B( K-1, J ) = D11*T1 + D12*T2
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B( K, J ) = D21*T1 + D22*T2
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50 CONTINUE
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END IF
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*
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* Multiply by P(K) * inv(L(K)) if K < N.
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*
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IF( K.NE.N ) THEN
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*
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* Apply the transformation.
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*
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CALL SGER( N-K, NRHS, ONE, A( KC+1 ), 1, B( K, 1 ),
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$ LDB, B( K+1, 1 ), LDB )
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CALL SGER( N-K, NRHS, ONE, A( KCNEXT+2 ), 1,
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$ B( K-1, 1 ), LDB, B( K+1, 1 ), LDB )
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*
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* Interchange if a permutation was applied at the
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* K-th step of the factorization.
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*
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KP = ABS( IPIV( K ) )
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IF( KP.NE.K )
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$ CALL SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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END IF
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KC = KCNEXT
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K = K - 2
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END IF
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GO TO 40
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60 CONTINUE
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END IF
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*----------------------------------------
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*
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* Compute B := A' * B (transpose)
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*
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*----------------------------------------
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ELSE
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*
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* Form B := U'*B
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* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
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* and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m)
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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*
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* Loop backward applying the transformations.
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*
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K = N
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KC = N*( N+1 ) / 2 + 1
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70 CONTINUE
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IF( K.LT.1 )
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$ GO TO 90
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KC = KC - K
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*
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* 1 x 1 pivot block.
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*
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IF( IPIV( K ).GT.0 ) THEN
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IF( K.GT.1 ) THEN
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*
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* Interchange if P(K) != I.
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*
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KP = IPIV( K )
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IF( KP.NE.K )
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$ CALL SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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*
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* Apply the transformation
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*
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CALL SGEMV( 'Transpose', K-1, NRHS, ONE, B, LDB,
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$ A( KC ), 1, ONE, B( K, 1 ), LDB )
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END IF
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IF( NOUNIT )
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$ CALL SSCAL( NRHS, A( KC+K-1 ), B( K, 1 ), LDB )
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K = K - 1
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*
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* 2 x 2 pivot block.
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*
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ELSE
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KCNEXT = KC - ( K-1 )
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IF( K.GT.2 ) THEN
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*
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* Interchange if P(K) != I.
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*
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KP = ABS( IPIV( K ) )
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IF( KP.NE.K-1 )
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$ CALL SSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ),
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$ LDB )
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*
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* Apply the transformations
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*
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CALL SGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB,
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$ A( KC ), 1, ONE, B( K, 1 ), LDB )
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CALL SGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB,
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$ A( KCNEXT ), 1, ONE, B( K-1, 1 ), LDB )
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END IF
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*
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* Multiply by the diagonal block if non-unit.
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*
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IF( NOUNIT ) THEN
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D11 = A( KC-1 )
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D22 = A( KC+K-1 )
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D12 = A( KC+K-2 )
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D21 = D12
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DO 80 J = 1, NRHS
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T1 = B( K-1, J )
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T2 = B( K, J )
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B( K-1, J ) = D11*T1 + D12*T2
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B( K, J ) = D21*T1 + D22*T2
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80 CONTINUE
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END IF
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KC = KCNEXT
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K = K - 2
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END IF
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GO TO 70
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90 CONTINUE
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*
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* Form B := L'*B
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* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
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* and L' = inv(L(m))*P(m)* ... *inv(L(1))*P(1)
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*
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ELSE
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*
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* Loop forward applying the L-transformations.
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*
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K = 1
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KC = 1
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100 CONTINUE
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IF( K.GT.N )
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$ GO TO 120
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*
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* 1 x 1 pivot block
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*
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IF( IPIV( K ).GT.0 ) THEN
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IF( K.LT.N ) THEN
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*
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* Interchange if P(K) != I.
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*
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KP = IPIV( K )
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IF( KP.NE.K )
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$ CALL SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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*
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* Apply the transformation
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*
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CALL SGEMV( 'Transpose', N-K, NRHS, ONE, B( K+1, 1 ),
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$ LDB, A( KC+1 ), 1, ONE, B( K, 1 ), LDB )
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END IF
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IF( NOUNIT )
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$ CALL SSCAL( NRHS, A( KC ), B( K, 1 ), LDB )
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KC = KC + N - K + 1
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K = K + 1
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*
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* 2 x 2 pivot block.
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*
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ELSE
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KCNEXT = KC + N - K + 1
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IF( K.LT.N-1 ) THEN
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*
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* Interchange if P(K) != I.
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*
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KP = ABS( IPIV( K ) )
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IF( KP.NE.K+1 )
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$ CALL SSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ),
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$ LDB )
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*
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* Apply the transformation
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*
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CALL SGEMV( 'Transpose', N-K-1, NRHS, ONE,
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$ B( K+2, 1 ), LDB, A( KCNEXT+1 ), 1, ONE,
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$ B( K+1, 1 ), LDB )
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CALL SGEMV( 'Transpose', N-K-1, NRHS, ONE,
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$ B( K+2, 1 ), LDB, A( KC+2 ), 1, ONE,
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$ B( K, 1 ), LDB )
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END IF
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*
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* Multiply by the diagonal block if non-unit.
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|
*
|
|
IF( NOUNIT ) THEN
|
|
D11 = A( KC )
|
|
D22 = A( KCNEXT )
|
|
D21 = A( KC+1 )
|
|
D12 = D21
|
|
DO 110 J = 1, NRHS
|
|
T1 = B( K, J )
|
|
T2 = B( K+1, J )
|
|
B( K, J ) = D11*T1 + D12*T2
|
|
B( K+1, J ) = D21*T1 + D22*T2
|
|
110 CONTINUE
|
|
END IF
|
|
KC = KCNEXT + ( N-K )
|
|
K = K + 2
|
|
END IF
|
|
GO TO 100
|
|
120 CONTINUE
|
|
END IF
|
|
*
|
|
END IF
|
|
RETURN
|
|
*
|
|
* End of SLAVSP
|
|
*
|
|
END
|