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578 lines
17 KiB
578 lines
17 KiB
2 years ago
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*> \brief \b CLAVSY_ROOK
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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 CLAVSY_ROOK( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
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* LDB, 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, LDA, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* COMPLEX A( LDA, * ), 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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*> CLAVSY_ROOK 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 CSYTRF_ROOK.
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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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*> \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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*> \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 COMPLEX array, dimension (LDA,N)
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*> The block diagonal matrix D and the multipliers used to
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*> obtain the factor U or L as computed by CSYTRF_ROOK.
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*> Stored as a 2-D triangular matrix.
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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 >= max(1,N).
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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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*> Details of the interchanges and the block structure of D,
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*> as determined by CSYTRF_ROOK.
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*>
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*> If UPLO = 'U':
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*> If IPIV(k) > 0, then rows and columns k and IPIV(k)
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*> were interchanged and D(k,k) is a 1-by-1 diagonal block.
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*> (If IPIV( k ) = k, no interchange was done).
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*>
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*> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
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*> columns k and -IPIV(k) were interchanged and rows and
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*> columns k-1 and -IPIV(k-1) were inerchaged,
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*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
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*>
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*> If UPLO = 'L':
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*> If IPIV(k) > 0, then rows and columns k and IPIV(k)
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*> were interchanged and D(k,k) is a 1-by-1 diagonal block.
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*> (If IPIV( k ) = k, no interchange was done).
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*>
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*> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
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*> columns k and -IPIV(k) were interchanged and rows and
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*> columns k+1 and -IPIV(k+1) were inerchaged,
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*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
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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 COMPLEX 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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*> \ingroup complex_lin
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*
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* =====================================================================
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SUBROUTINE CLAVSY_ROOK( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV,
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$ B, LDB, INFO )
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*
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* -- LAPACK test routine --
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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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*
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* .. Scalar Arguments ..
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CHARACTER DIAG, TRANS, UPLO
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INTEGER INFO, LDA, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX A( LDA, * ), 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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COMPLEX CONE
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PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL NOUNIT
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INTEGER J, K, KP
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COMPLEX 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 CGEMV, CGERU, CSCAL, CSWAP, 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.LSAME( TRANS, 'T' ) )
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$ 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( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -6
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -9
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CLAVSY_ROOK ', -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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10 CONTINUE
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IF( K.GT.N )
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$ GO TO 30
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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 U * D.
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*
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IF( NOUNIT )
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$ CALL CSCAL( NRHS, A( K, K ), 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 CGERU( K-1, NRHS, CONE, A( 1, K ), 1, B( K, 1 ),
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$ 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 = IPIV( K )
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IF( KP.NE.K )
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$ CALL CSWAP( 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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ELSE
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*
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* 2 x 2 pivot block
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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( K, K )
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D22 = A( K+1, K+1 )
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D12 = A( K, 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 CGERU( K-1, NRHS, CONE, A( 1, K ), 1, B( K, 1 ),
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$ LDB, B( 1, 1 ), LDB )
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CALL CGERU( K-1, NRHS, CONE, A( 1, K+1 ), 1,
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$ B( K+1, 1 ), LDB, B( 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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* Swap the first of pair with IMAXth
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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 CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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*
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* NOW swap the first of pair with Pth
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*
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KP = ABS( IPIV( K+1 ) )
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IF( KP.NE.K+1 )
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$ CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ),
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$ LDB )
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END IF
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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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40 CONTINUE
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IF( K.LT.1 )
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$ GO TO 60
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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 CSCAL( NRHS, A( K, K ), 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 CGERU( N-K, NRHS, CONE, A( K+1, K ), 1,
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$ B( K, 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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IF( KP.NE.K )
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$ CALL CSWAP( 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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* 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( K-1, K-1 )
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D22 = A( K, K )
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D21 = A( K, K-1 )
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D12 = D21
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DO 50 J = 1, NRHS
|
||
|
|
T1 = B( K-1, J )
|
||
|
|
T2 = B( K, J )
|
||
|
|
B( K-1, J ) = D11*T1 + D12*T2
|
||
|
|
B( K, J ) = D21*T1 + D22*T2
|
||
|
|
50 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Multiply by P(K) * inv(L(K)) if K < N.
|
||
|
|
*
|
||
|
|
IF( K.NE.N ) THEN
|
||
|
|
*
|
||
|
|
* Apply the transformation.
|
||
|
|
*
|
||
|
|
CALL CGERU( N-K, NRHS, CONE, A( K+1, K ), 1,
|
||
|
|
$ B( K, 1 ), LDB, B( K+1, 1 ), LDB )
|
||
|
|
CALL CGERU( N-K, NRHS, CONE, A( K+1, K-1 ), 1,
|
||
|
|
$ B( K-1, 1 ), LDB, B( K+1, 1 ), LDB )
|
||
|
|
*
|
||
|
|
* Interchange if a permutation was applied at the
|
||
|
|
* K-th step of the factorization.
|
||
|
|
*
|
||
|
|
* Swap the second of pair with IMAXth
|
||
|
|
*
|
||
|
|
KP = ABS( IPIV( K ) )
|
||
|
|
IF( KP.NE.K )
|
||
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
||
|
|
*
|
||
|
|
* NOW swap the first of pair with Pth
|
||
|
|
*
|
||
|
|
KP = ABS( IPIV( K-1 ) )
|
||
|
|
IF( KP.NE.K-1 )
|
||
|
|
$ CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ),
|
||
|
|
$ LDB )
|
||
|
|
END IF
|
||
|
|
K = K - 2
|
||
|
|
END IF
|
||
|
|
GO TO 40
|
||
|
|
60 CONTINUE
|
||
|
|
END IF
|
||
|
|
*----------------------------------------
|
||
|
|
*
|
||
|
|
* Compute B := A' * B (transpose)
|
||
|
|
*
|
||
|
|
*----------------------------------------
|
||
|
|
ELSE IF( LSAME( TRANS, 'T' ) ) THEN
|
||
|
|
*
|
||
|
|
* Form B := U'*B
|
||
|
|
* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
|
||
|
|
* and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m)
|
||
|
|
*
|
||
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
||
|
|
*
|
||
|
|
* Loop backward applying the transformations.
|
||
|
|
*
|
||
|
|
K = N
|
||
|
|
70 IF( K.LT.1 )
|
||
|
|
$ GO TO 90
|
||
|
|
*
|
||
|
|
* 1 x 1 pivot block.
|
||
|
|
*
|
||
|
|
IF( IPIV( K ).GT.0 ) THEN
|
||
|
|
IF( K.GT.1 ) THEN
|
||
|
|
*
|
||
|
|
* Interchange if P(K) != I.
|
||
|
|
*
|
||
|
|
KP = IPIV( K )
|
||
|
|
IF( KP.NE.K )
|
||
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
||
|
|
*
|
||
|
|
* Apply the transformation
|
||
|
|
*
|
||
|
|
CALL CGEMV( 'Transpose', K-1, NRHS, CONE, B, LDB,
|
||
|
|
$ A( 1, K ), 1, CONE, B( K, 1 ), LDB )
|
||
|
|
END IF
|
||
|
|
IF( NOUNIT )
|
||
|
|
$ CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB )
|
||
|
|
K = K - 1
|
||
|
|
*
|
||
|
|
* 2 x 2 pivot block.
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
IF( K.GT.2 ) THEN
|
||
|
|
*
|
||
|
|
* Swap the second of pair with Pth
|
||
|
|
*
|
||
|
|
KP = ABS( IPIV( K ) )
|
||
|
|
IF( KP.NE.K )
|
||
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
||
|
|
*
|
||
|
|
* Now swap the first of pair with IMAX(r)th
|
||
|
|
*
|
||
|
|
KP = ABS( IPIV( K-1 ) )
|
||
|
|
IF( KP.NE.K-1 )
|
||
|
|
$ CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ),
|
||
|
|
$ LDB )
|
||
|
|
*
|
||
|
|
* Apply the transformations
|
||
|
|
*
|
||
|
|
CALL CGEMV( 'Transpose', K-2, NRHS, CONE, B, LDB,
|
||
|
|
$ A( 1, K ), 1, CONE, B( K, 1 ), LDB )
|
||
|
|
CALL CGEMV( 'Transpose', K-2, NRHS, CONE, B, LDB,
|
||
|
|
$ A( 1, K-1 ), 1, CONE, B( K-1, 1 ), LDB )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Multiply by the diagonal block if non-unit.
|
||
|
|
*
|
||
|
|
IF( NOUNIT ) THEN
|
||
|
|
D11 = A( K-1, K-1 )
|
||
|
|
D22 = A( K, K )
|
||
|
|
D12 = A( K-1, K )
|
||
|
|
D21 = D12
|
||
|
|
DO 80 J = 1, NRHS
|
||
|
|
T1 = B( K-1, J )
|
||
|
|
T2 = B( K, J )
|
||
|
|
B( K-1, J ) = D11*T1 + D12*T2
|
||
|
|
B( K, J ) = D21*T1 + D22*T2
|
||
|
|
80 CONTINUE
|
||
|
|
END IF
|
||
|
|
K = K - 2
|
||
|
|
END IF
|
||
|
|
GO TO 70
|
||
|
|
90 CONTINUE
|
||
|
|
*
|
||
|
|
* Form B := L'*B
|
||
|
|
* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
|
||
|
|
* and L' = inv(L'(m))*P(m)* ... *inv(L'(1))*P(1)
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Loop forward applying the L-transformations.
|
||
|
|
*
|
||
|
|
K = 1
|
||
|
|
100 CONTINUE
|
||
|
|
IF( K.GT.N )
|
||
|
|
$ GO TO 120
|
||
|
|
*
|
||
|
|
* 1 x 1 pivot block
|
||
|
|
*
|
||
|
|
IF( IPIV( K ).GT.0 ) THEN
|
||
|
|
IF( K.LT.N ) THEN
|
||
|
|
*
|
||
|
|
* Interchange if P(K) != I.
|
||
|
|
*
|
||
|
|
KP = IPIV( K )
|
||
|
|
IF( KP.NE.K )
|
||
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
||
|
|
*
|
||
|
|
* Apply the transformation
|
||
|
|
*
|
||
|
|
CALL CGEMV( 'Transpose', N-K, NRHS, CONE, B( K+1, 1 ),
|
||
|
|
$ LDB, A( K+1, K ), 1, CONE, B( K, 1 ), LDB )
|
||
|
|
END IF
|
||
|
|
IF( NOUNIT )
|
||
|
|
$ CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB )
|
||
|
|
K = K + 1
|
||
|
|
*
|
||
|
|
* 2 x 2 pivot block.
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
IF( K.LT.N-1 ) THEN
|
||
|
|
*
|
||
|
|
* Swap the first of pair with Pth
|
||
|
|
*
|
||
|
|
KP = ABS( IPIV( K ) )
|
||
|
|
IF( KP.NE.K )
|
||
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
||
|
|
*
|
||
|
|
* Now swap the second of pair with IMAX(r)th
|
||
|
|
*
|
||
|
|
KP = ABS( IPIV( K+1 ) )
|
||
|
|
IF( KP.NE.K+1 )
|
||
|
|
$ CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ),
|
||
|
|
$ LDB )
|
||
|
|
*
|
||
|
|
* Apply the transformation
|
||
|
|
*
|
||
|
|
CALL CGEMV( 'Transpose', N-K-1, NRHS, CONE,
|
||
|
|
$ B( K+2, 1 ), LDB, A( K+2, K+1 ), 1, CONE,
|
||
|
|
$ B( K+1, 1 ), LDB )
|
||
|
|
CALL CGEMV( 'Transpose', N-K-1, NRHS, CONE,
|
||
|
|
$ B( K+2, 1 ), LDB, A( K+2, K ), 1, CONE,
|
||
|
|
$ B( K, 1 ), LDB )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Multiply by the diagonal block if non-unit.
|
||
|
|
*
|
||
|
|
IF( NOUNIT ) THEN
|
||
|
|
D11 = A( K, K )
|
||
|
|
D22 = A( K+1, K+1 )
|
||
|
|
D21 = A( K+1, K )
|
||
|
|
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
|
||
|
|
K = K + 2
|
||
|
|
END IF
|
||
|
|
GO TO 100
|
||
|
|
120 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of CLAVSY_ROOK
|
||
|
|
*
|
||
|
|
END
|