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|
*> \brief \b CLAVHE
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CLAVHE( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
* LDB, INFO )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, TRANS, UPLO
* INTEGER INFO, LDA, LDB, N, NRHS
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLAVHE performs one of the matrix-vector operations
*> x := A*x or x := A^H*x,
*> where x is an N element vector and A is one of the factors
*> from the block U*D*U' or L*D*L' factorization computed by CHETRF.
*>
*> If TRANS = 'N', multiplies by U or U * D (or L or L * D)
*> If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the factor stored in A is upper or lower
*> triangular.
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> Specifies the operation to be performed:
*> = 'N': x := A*x
*> = 'C': x := A^H*x
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> Specifies whether or not the diagonal blocks are unit
*> matrices. If the diagonal blocks are assumed to be unit,
*> then A = U or A = L, otherwise A = U*D or A = L*D.
*> = 'U': Diagonal blocks are assumed to be unit matrices.
*> = 'N': Diagonal blocks are assumed to be non-unit matrices.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows and columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of vectors
*> x to be multiplied by A. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> The block diagonal matrix D and the multipliers used to
*> obtain the factor U or L as computed by CHETRF_ROOK.
*> Stored as a 2-D triangular matrix.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> Details of the interchanges and the block structure of D,
*> as determined by CHETRF.
*>
*> If UPLO = 'U':
*> If IPIV(k) > 0, then rows and columns k and IPIV(k)
*> were interchanged and D(k,k) is a 1-by-1 diagonal block.
*> (If IPIV( k ) = k, no interchange was done).
*>
*> If IPIV(k) = IPIV(k-1) < 0, then rows and
*> columns k-1 and -IPIV(k) were interchanged,
*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
*>
*> If UPLO = 'L':
*> If IPIV(k) > 0, then rows and columns k and IPIV(k)
*> were interchanged and D(k,k) is a 1-by-1 diagonal block.
*> (If IPIV( k ) = k, no interchange was done).
*>
*> If IPIV(k) = IPIV(k+1) < 0, then rows and
*> columns k+1 and -IPIV(k) were interchanged,
*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB,NRHS)
*> On entry, B contains NRHS vectors of length N.
*> On exit, B is overwritten with the product A * B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_lin
*
* =====================================================================
SUBROUTINE CLAVHE( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
$ LDB, INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, LDA, LDB, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT
INTEGER J, K, KP
COMPLEX D11, D12, D21, D22, T1, T2
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CGEMV, CGERU, CLACGV, CSCAL, CSWAP, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, CONJG, MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'C' ) )
$ THEN
INFO = -2
ELSE IF( .NOT.LSAME( DIAG, 'U' ) .AND. .NOT.LSAME( DIAG, 'N' ) )
$ THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -6
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CLAVHE ', -INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( N.EQ.0 )
$ RETURN
*
NOUNIT = LSAME( DIAG, 'N' )
*------------------------------------------
*
* Compute B := A * B (No transpose)
*
*------------------------------------------
IF( LSAME( TRANS, 'N' ) ) THEN
*
* Compute B := U*B
* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Loop forward applying the transformations.
*
K = 1
10 CONTINUE
IF( K.GT.N )
$ GO TO 30
IF( IPIV( K ).GT.0 ) THEN
*
* 1 x 1 pivot block
*
* Multiply by the diagonal element if forming U * D.
*
IF( NOUNIT )
$ CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB )
*
* Multiply by P(K) * inv(U(K)) if K > 1.
*
IF( K.GT.1 ) THEN
*
* Apply the transformation.
*
CALL CGERU( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ),
$ LDB, B( 1, 1 ), LDB )
*
* Interchange if P(K) != I.
*
KP = IPIV( K )
IF( KP.NE.K )
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
END IF
K = K + 1
ELSE
*
* 2 x 2 pivot block
*
* Multiply by the diagonal block if forming U * D.
*
IF( NOUNIT ) THEN
D11 = A( K, K )
D22 = A( K+1, K+1 )
D12 = A( K, K+1 )
D21 = CONJG( D12 )
DO 20 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
20 CONTINUE
END IF
*
* Multiply by P(K) * inv(U(K)) if K > 1.
*
IF( K.GT.1 ) THEN
*
* Apply the transformations.
*
CALL CGERU( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ),
$ LDB, B( 1, 1 ), LDB )
CALL CGERU( K-1, NRHS, ONE, A( 1, K+1 ), 1,
$ B( K+1, 1 ), LDB, B( 1, 1 ), LDB )
*
* Interchange if P(K) != I.
*
KP = ABS( IPIV( K ) )
IF( KP.NE.K )
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
END IF
K = K + 2
END IF
GO TO 10
30 CONTINUE
*
* Compute B := L*B
* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) .
*
ELSE
*
* Loop backward applying the transformations to B.
*
K = N
40 CONTINUE
IF( K.LT.1 )
$ GO TO 60
*
* Test the pivot index. If greater than zero, a 1 x 1
* pivot was used, otherwise a 2 x 2 pivot was used.
*
IF( IPIV( K ).GT.0 ) THEN
*
* 1 x 1 pivot block:
*
* Multiply by the diagonal element if forming L * D.
*
IF( NOUNIT )
$ CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB )
*
* Multiply by P(K) * inv(L(K)) if K < N.
*
IF( K.NE.N ) THEN
KP = IPIV( K )
*
* Apply the transformation.
*
CALL CGERU( N-K, NRHS, ONE, A( K+1, K ), 1,
$ B( K, 1 ), LDB, B( K+1, 1 ), LDB )
*
* Interchange if a permutation was applied at the
* K-th step of the factorization.
*
IF( KP.NE.K )
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
END IF
K = K - 1
*
ELSE
*
* 2 x 2 pivot block:
*
* Multiply by the diagonal block if forming L * D.
*
IF( NOUNIT ) THEN
D11 = A( K-1, K-1 )
D22 = A( K, K )
D21 = A( K, K-1 )
D12 = CONJG( D21 )
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, ONE, A( K+1, K ), 1,
$ B( K, 1 ), LDB, B( K+1, 1 ), LDB )
CALL CGERU( N-K, NRHS, ONE, 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.
*
KP = ABS( IPIV( K ) )
IF( KP.NE.K )
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
END IF
K = K - 2
END IF
GO TO 40
60 CONTINUE
END IF
*--------------------------------------------------
*
* Compute B := A^H * B (conjugate transpose)
*
*--------------------------------------------------
ELSE
*
* Form B := U^H*B
* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
* and U^H = inv(U^H(1))*P(1)* ... *inv(U^H(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
* y = y - B' conjg(x),
* where x is a column of A and y is a row of B.
*
CALL CLACGV( NRHS, B( K, 1 ), LDB )
CALL CGEMV( 'Conjugate', K-1, NRHS, ONE, B, LDB,
$ A( 1, K ), 1, ONE, B( K, 1 ), LDB )
CALL CLACGV( NRHS, 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
*
* Interchange if P(K) != I.
*
KP = ABS( IPIV( K ) )
IF( KP.NE.K-1 )
$ CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ),
$ LDB )
*
* Apply the transformations
* y = y - B' conjg(x),
* where x is a block column of A and y is a block
* row of B.
*
CALL CLACGV( NRHS, B( K, 1 ), LDB )
CALL CGEMV( 'Conjugate', K-2, NRHS, ONE, B, LDB,
$ A( 1, K ), 1, ONE, B( K, 1 ), LDB )
CALL CLACGV( NRHS, B( K, 1 ), LDB )
*
CALL CLACGV( NRHS, B( K-1, 1 ), LDB )
CALL CGEMV( 'Conjugate', K-2, NRHS, ONE, B, LDB,
$ A( 1, K-1 ), 1, ONE, B( K-1, 1 ), LDB )
CALL CLACGV( NRHS, 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 = CONJG( 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^H*B
* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
* and L^H = inv(L^H(m))*P(m)* ... *inv(L^H(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 CLACGV( NRHS, B( K, 1 ), LDB )
CALL CGEMV( 'Conjugate', N-K, NRHS, ONE, B( K+1, 1 ),
$ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
CALL CLACGV( NRHS, 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
*
* Interchange if P(K) != I.
*
KP = ABS( IPIV( K ) )
IF( KP.NE.K+1 )
$ CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ),
$ LDB )
*
* Apply the transformation
*
CALL CLACGV( NRHS, B( K+1, 1 ), LDB )
CALL CGEMV( 'Conjugate', N-K-1, NRHS, ONE,
$ B( K+2, 1 ), LDB, A( K+2, K+1 ), 1, ONE,
$ B( K+1, 1 ), LDB )
CALL CLACGV( NRHS, B( K+1, 1 ), LDB )
*
CALL CLACGV( NRHS, B( K, 1 ), LDB )
CALL CGEMV( 'Conjugate', N-K-1, NRHS, ONE,
$ B( K+2, 1 ), LDB, A( K+2, K ), 1, ONE,
$ B( K, 1 ), LDB )
CALL CLACGV( 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 = CONJG( 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 CLAVHE
*
END
|
