554 lines
17 KiB
Fortran
554 lines
17 KiB
Fortran
*> \brief \b ZLAVHE
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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 ZLAVHE( 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*16 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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*> ZLAVHE performs one of the matrix-vector operations
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*> x := A*x or x := A^H*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 symmetric factorization computed by ZHETRF.
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*> ZHETRF produces a factorization of the form
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*> U * D * U^H or L * D * L^H,
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*> where U (or L) is a product of permutation and unit upper (lower)
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*> triangular matrices, U^H (or L^H) is the conjugate transpose of
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*> U (or L), and D is Hermitian and block diagonal with 1 x 1 and
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*> 2 x 2 diagonal blocks. The multipliers for the transformations
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*> and the upper or lower triangular parts of the diagonal blocks
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*> are stored in the leading upper or lower triangle of the 2-D
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*> array A.
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*>
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*> If TRANS = 'N' or 'n', ZLAVHE multiplies either by U or U * D
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*> (or L or L * D).
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*> If TRANS = 'C' or 'c', ZLAVHE multiplies either by U^H or D * U^H
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*> (or L^H or D * L^H ).
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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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*> \verbatim
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*> UPLO - CHARACTER*1
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*> On entry, UPLO specifies whether the triangular matrix
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*> stored in A is upper or lower triangular.
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*> UPLO = 'U' or 'u' The matrix is upper triangular.
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*> UPLO = 'L' or 'l' The matrix is lower triangular.
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*> Unchanged on exit.
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*>
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*> TRANS - CHARACTER*1
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*> On entry, TRANS specifies the operation to be performed as
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*> follows:
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*> TRANS = 'N' or 'n' x := A*x.
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*> TRANS = 'C' or 'c' x := A^H*x.
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*> Unchanged on exit.
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*>
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*> DIAG - CHARACTER*1
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*> On entry, DIAG specifies whether the diagonal blocks are
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*> assumed to be unit matrices:
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*> DIAG = 'U' or 'u' Diagonal blocks are unit matrices.
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*> DIAG = 'N' or 'n' Diagonal blocks are non-unit.
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*> Unchanged on exit.
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*>
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*> N - INTEGER
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*> On entry, N specifies the order of the matrix A.
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*> N must be at least zero.
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*> Unchanged on exit.
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*>
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*> NRHS - INTEGER
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*> On entry, NRHS specifies the number of right hand sides,
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*> i.e., the number of vectors x to be multiplied by A.
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*> NRHS must be at least zero.
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*> Unchanged on exit.
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*>
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*> A - COMPLEX*16 array, dimension( LDA, N )
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*> On entry, A contains a block diagonal matrix and the
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*> multipliers of the transformations used to obtain it,
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*> stored as a 2-D triangular matrix.
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*> Unchanged on exit.
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*>
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*> LDA - INTEGER
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*> On entry, LDA specifies the first dimension of A as declared
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*> in the calling ( sub ) program. LDA must be at least
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*> max( 1, N ).
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*> Unchanged on exit.
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*>
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*> IPIV - INTEGER array, dimension( N )
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*> On entry, IPIV contains the vector of pivot indices as
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*> determined by ZSYTRF or ZHETRF.
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*> If IPIV( K ) = K, no interchange was done.
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*> If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter-
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*> changed with row IPIV( K ) and a 1 x 1 pivot block was used.
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*> If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged
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*> with row | IPIV( K ) | and a 2 x 2 pivot block was used.
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*> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged
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*> with row | IPIV( K ) | and a 2 x 2 pivot block was used.
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*>
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*> B - COMPLEX*16 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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*>
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*> LDB - INTEGER
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*> On entry, LDB contains the leading dimension of B as
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*> declared in the calling program. LDB must be at least
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*> max( 1, N ).
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*> Unchanged on exit.
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*>
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*> INFO - INTEGER
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*> INFO is the error flag.
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*> On exit, a value of 0 indicates a successful exit.
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*> A negative value, say -K, indicates that the K-th argument
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*> has 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 complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZLAVHE( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
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$ LDB, 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, 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*16 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*16 ONE
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PARAMETER ( ONE = ( 1.0D+0, 0.0D+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*16 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 XERBLA, ZGEMV, ZGERU, ZLACGV, ZSCAL, ZSWAP
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DCONJG, 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, 'C' ) )
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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( 'ZLAVHE ', -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 ZSCAL( 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 ZGERU( K-1, NRHS, ONE, 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 ZSWAP( 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 = DCONJG( 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 ZGERU( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ),
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$ LDB, B( 1, 1 ), LDB )
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CALL ZGERU( K-1, NRHS, ONE, 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 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 ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), 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 ZSCAL( 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 ZGERU( N-K, NRHS, ONE, A( K+1, K ), 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 ZSWAP( 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 = DCONJG( 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 ZGERU( N-K, NRHS, ONE, A( K+1, K ), 1, B( K, 1 ),
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$ LDB, B( K+1, 1 ), LDB )
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CALL ZGERU( N-K, NRHS, ONE, A( K+1, K-1 ), 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 ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), 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 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^H * B (conjugate 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^H*B
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* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
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* and U^H = inv(U^H(1))*P(1)* ... *inv(U^H(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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70 CONTINUE
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IF( K.LT.1 )
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$ GO TO 90
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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 ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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*
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* Apply the transformation
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* y = y - B' conjg(x),
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* where x is a column of A and y is a row of B.
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*
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CALL ZLACGV( NRHS, B( K, 1 ), LDB )
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CALL ZGEMV( 'Conjugate', K-1, NRHS, ONE, B, LDB,
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$ A( 1, K ), 1, ONE, B( K, 1 ), LDB )
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CALL ZLACGV( NRHS, B( K, 1 ), LDB )
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END IF
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IF( NOUNIT )
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$ CALL ZSCAL( NRHS, A( K, K ), 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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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 ZSWAP( 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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* y = y - B' conjg(x),
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* where x is a block column of A and y is a block
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* row of B.
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*
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CALL ZLACGV( NRHS, B( K, 1 ), LDB )
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CALL ZGEMV( 'Conjugate', K-2, NRHS, ONE, B, LDB,
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$ A( 1, K ), 1, ONE, B( K, 1 ), LDB )
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CALL ZLACGV( NRHS, B( K, 1 ), LDB )
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*
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CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
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CALL ZGEMV( 'Conjugate', K-2, NRHS, ONE, B, LDB,
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$ A( 1, K-1 ), 1, ONE, B( K-1, 1 ), LDB )
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CALL ZLACGV( NRHS, 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( K-1, K-1 )
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D22 = A( K, K )
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D12 = A( K-1, K )
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D21 = DCONJG( 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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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^H*B
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* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
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* and L^H = inv(L^H(m))*P(m)* ... *inv(L^H(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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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 ZSWAP( 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 ZLACGV( NRHS, B( K, 1 ), LDB )
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CALL ZGEMV( 'Conjugate', N-K, NRHS, ONE, B( K+1, 1 ),
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$ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
|
|
CALL ZLACGV( NRHS, B( K, 1 ), LDB )
|
|
END IF
|
|
IF( NOUNIT )
|
|
$ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB )
|
|
K = K + 1
|
|
*
|
|
* 2 x 2 pivot block.
|
|
*
|
|
ELSE
|
|
IF( K.LT.N-1 ) THEN
|
|
*
|
|
* Interchange if P(K) != I.
|
|
*
|
|
KP = ABS( IPIV( K ) )
|
|
IF( KP.NE.K+1 )
|
|
$ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ),
|
|
$ LDB )
|
|
*
|
|
* Apply the transformation
|
|
*
|
|
CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
|
|
CALL ZGEMV( 'Conjugate', N-K-1, NRHS, ONE,
|
|
$ B( K+2, 1 ), LDB, A( K+2, K+1 ), 1, ONE,
|
|
$ B( K+1, 1 ), LDB )
|
|
CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
|
|
*
|
|
CALL ZLACGV( NRHS, B( K, 1 ), LDB )
|
|
CALL ZGEMV( 'Conjugate', N-K-1, NRHS, ONE,
|
|
$ B( K+2, 1 ), LDB, A( K+2, K ), 1, ONE,
|
|
$ B( K, 1 ), LDB )
|
|
CALL ZLACGV( NRHS, 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 = DCONJG( 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 ZLAVHE
|
|
*
|
|
END
|