You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
565 lines
17 KiB
565 lines
17 KiB
*> \brief \b ZLAVHE
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE ZLAVHE( 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*16 A( LDA, * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> ZLAVHE 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 ZHETRF.
|
|
*>
|
|
*> 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'*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*16 array, dimension (LDA,N)
|
|
*> The block diagonal matrix D and the multipliers used to
|
|
*> obtain the factor U or L as computed by ZHETRF.
|
|
*> 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 ZHETRF.
|
|
*>
|
|
*> 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*16 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 complex16_lin
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE ZLAVHE( 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*16 A( LDA, * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX*16 ONE
|
|
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL NOUNIT
|
|
INTEGER J, K, KP
|
|
COMPLEX*16 D11, D12, D21, D22, T1, T2
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL XERBLA, ZGEMV, ZGERU, ZLACGV, ZSCAL, ZSWAP
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, DCONJG, 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( 'ZLAVHE ', -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 ZSCAL( 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 ZGERU( 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 ZSWAP( 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 = DCONJG( 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 ZGERU( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ),
|
|
$ LDB, B( 1, 1 ), LDB )
|
|
CALL ZGERU( 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 ZSWAP( 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 ZSCAL( 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 ZGERU( 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 ZSWAP( 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 = DCONJG( 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 ZGERU( N-K, NRHS, ONE, A( K+1, K ), 1, B( K, 1 ),
|
|
$ LDB, B( K+1, 1 ), LDB )
|
|
CALL ZGERU( 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 ZSWAP( 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 CONTINUE
|
|
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 ZSWAP( 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 ZLACGV( NRHS, B( K, 1 ), LDB )
|
|
CALL ZGEMV( 'Conjugate', K-1, NRHS, ONE, B, LDB,
|
|
$ A( 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.GT.2 ) 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 transformations
|
|
* y = y - B' conjg(x),
|
|
* where x is a block column of A and y is a block
|
|
* row of B.
|
|
*
|
|
CALL ZLACGV( NRHS, B( K, 1 ), LDB )
|
|
CALL ZGEMV( 'Conjugate', K-2, NRHS, ONE, B, LDB,
|
|
$ A( 1, K ), 1, ONE, B( K, 1 ), LDB )
|
|
CALL ZLACGV( NRHS, B( K, 1 ), LDB )
|
|
*
|
|
CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
|
|
CALL ZGEMV( 'Conjugate', K-2, NRHS, ONE, B, LDB,
|
|
$ A( 1, K-1 ), 1, ONE, B( K-1, 1 ), LDB )
|
|
CALL ZLACGV( 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 = DCONJG( 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 ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
*
|
|
* Apply the transformation
|
|
*
|
|
CALL ZLACGV( NRHS, B( K, 1 ), LDB )
|
|
CALL ZGEMV( 'Conjugate', N-K, NRHS, ONE, B( K+1, 1 ),
|
|
$ 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
|
|
|