548 lines
16 KiB
Fortran
548 lines
16 KiB
Fortran
*> \brief \b CLAVSP
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
|
|
* INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER DIAG, TRANS, UPLO
|
|
* INTEGER INFO, LDB, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* INTEGER IPIV( * )
|
|
* COMPLEX A( * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CLAVSP performs one of the matrix-vector operations
|
|
*> x := A*x or x := A^T*x,
|
|
*> where x is an N element vector and A is one of the factors
|
|
*> from the symmetric factorization computed by CSPTRF.
|
|
*> CSPTRF produces a factorization of the form
|
|
*> U * D * U^T or L * D * L^T,
|
|
*> where U (or L) is a product of permutation and unit upper (lower)
|
|
*> triangular matrices, U^T (or L^T) is the transpose of
|
|
*> U (or L), and D is symmetric and block diagonal with 1 x 1 and
|
|
*> 2 x 2 diagonal blocks. The multipliers for the transformations
|
|
*> and the upper or lower triangular parts of the diagonal blocks
|
|
*> are stored columnwise in packed format in the linear array A.
|
|
*>
|
|
*> If TRANS = 'N' or 'n', CLAVSP multiplies either by U or U * D
|
|
*> (or L or L * D).
|
|
*> If TRANS = 'C' or 'c', CLAVSP multiplies either by U^T or D * U^T
|
|
*> (or L^T or D * L^T ).
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \verbatim
|
|
*> UPLO - CHARACTER*1
|
|
*> On entry, UPLO specifies whether the triangular matrix
|
|
*> stored in A is upper or lower triangular.
|
|
*> UPLO = 'U' or 'u' The matrix is upper triangular.
|
|
*> UPLO = 'L' or 'l' The matrix is lower triangular.
|
|
*> Unchanged on exit.
|
|
*>
|
|
*> TRANS - CHARACTER*1
|
|
*> On entry, TRANS specifies the operation to be performed as
|
|
*> follows:
|
|
*> TRANS = 'N' or 'n' x := A*x.
|
|
*> TRANS = 'T' or 't' x := A^T*x.
|
|
*> Unchanged on exit.
|
|
*>
|
|
*> DIAG - CHARACTER*1
|
|
*> On entry, DIAG specifies whether the diagonal blocks are
|
|
*> assumed to be unit matrices, as follows:
|
|
*> DIAG = 'U' or 'u' Diagonal blocks are unit matrices.
|
|
*> DIAG = 'N' or 'n' Diagonal blocks are non-unit.
|
|
*> Unchanged on exit.
|
|
*>
|
|
*> N - INTEGER
|
|
*> On entry, N specifies the order of the matrix A.
|
|
*> N must be at least zero.
|
|
*> Unchanged on exit.
|
|
*>
|
|
*> NRHS - INTEGER
|
|
*> On entry, NRHS specifies the number of right hand sides,
|
|
*> i.e., the number of vectors x to be multiplied by A.
|
|
*> NRHS must be at least zero.
|
|
*> Unchanged on exit.
|
|
*>
|
|
*> A - COMPLEX array, dimension( N*(N+1)/2 )
|
|
*> On entry, A contains a block diagonal matrix and the
|
|
*> multipliers of the transformations used to obtain it,
|
|
*> stored as a packed triangular matrix.
|
|
*> Unchanged on exit.
|
|
*>
|
|
*> IPIV - INTEGER array, dimension( N )
|
|
*> On entry, IPIV contains the vector of pivot indices as
|
|
*> determined by CSPTRF.
|
|
*> If IPIV( K ) = K, no interchange was done.
|
|
*> If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter-
|
|
*> changed with row IPIV( K ) and a 1 x 1 pivot block was used.
|
|
*> If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged
|
|
*> with row | IPIV( K ) | and a 2 x 2 pivot block was used.
|
|
*> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged
|
|
*> with row | IPIV( K ) | and a 2 x 2 pivot block was used.
|
|
*>
|
|
*> B - COMPLEX array, dimension( LDB, NRHS )
|
|
*> On entry, B contains NRHS vectors of length N.
|
|
*> On exit, B is overwritten with the product A * B.
|
|
*>
|
|
*> LDB - INTEGER
|
|
*> On entry, LDB contains the leading dimension of B as
|
|
*> declared in the calling program. LDB must be at least
|
|
*> max( 1, N ).
|
|
*> Unchanged on exit.
|
|
*>
|
|
*> INFO - INTEGER
|
|
*> INFO is the error flag.
|
|
*> On exit, a value of 0 indicates a successful exit.
|
|
*> A negative value, say -K, indicates that the K-th argument
|
|
*> has an illegal value.
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \date November 2011
|
|
*
|
|
*> \ingroup complex_lin
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE CLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
|
|
$ INFO )
|
|
*
|
|
* -- LAPACK test routine (version 3.4.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2011
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER DIAG, TRANS, UPLO
|
|
INTEGER INFO, LDB, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IPIV( * )
|
|
COMPLEX A( * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX ONE
|
|
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL NOUNIT
|
|
INTEGER J, K, KC, KCNEXT, KP
|
|
COMPLEX D11, D12, D21, D22, T1, T2
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CGEMV, CGERU, CSCAL, CSWAP, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, 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, 'T' ) )
|
|
$ 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( LDB.LT.MAX( 1, N ) ) THEN
|
|
INFO = -8
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'CLAVSP ', -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
|
|
KC = 1
|
|
10 CONTINUE
|
|
IF( K.GT.N )
|
|
$ GO TO 30
|
|
*
|
|
* 1 x 1 pivot block
|
|
*
|
|
IF( IPIV( K ).GT.0 ) THEN
|
|
*
|
|
* Multiply by the diagonal element if forming U * D.
|
|
*
|
|
IF( NOUNIT )
|
|
$ CALL CSCAL( NRHS, A( KC+K-1 ), 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( KC ), 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
|
|
KC = KC + K
|
|
K = K + 1
|
|
ELSE
|
|
*
|
|
* 2 x 2 pivot block
|
|
*
|
|
KCNEXT = KC + K
|
|
*
|
|
* Multiply by the diagonal block if forming U * D.
|
|
*
|
|
IF( NOUNIT ) THEN
|
|
D11 = A( KCNEXT-1 )
|
|
D22 = A( KCNEXT+K )
|
|
D12 = A( KCNEXT+K-1 )
|
|
D21 = 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( KC ), 1, B( K, 1 ),
|
|
$ LDB, B( 1, 1 ), LDB )
|
|
CALL CGERU( K-1, NRHS, ONE, A( KCNEXT ), 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
|
|
KC = KCNEXT + K + 1
|
|
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
|
|
KC = N*( N+1 ) / 2 + 1
|
|
40 CONTINUE
|
|
IF( K.LT.1 )
|
|
$ GO TO 60
|
|
KC = KC - ( N-K+1 )
|
|
*
|
|
* 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( KC ), 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( KC+1 ), 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:
|
|
*
|
|
KCNEXT = KC - ( N-K+2 )
|
|
*
|
|
* Multiply by the diagonal block if forming L * D.
|
|
*
|
|
IF( NOUNIT ) THEN
|
|
D11 = A( KCNEXT )
|
|
D22 = A( KC )
|
|
D21 = A( KCNEXT+1 )
|
|
D12 = 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( KC+1 ), 1, B( K, 1 ),
|
|
$ LDB, B( K+1, 1 ), LDB )
|
|
CALL CGERU( N-K, NRHS, ONE, A( KCNEXT+2 ), 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
|
|
KC = KCNEXT
|
|
K = K - 2
|
|
END IF
|
|
GO TO 40
|
|
60 CONTINUE
|
|
END IF
|
|
*-------------------------------------------------
|
|
*
|
|
* Compute B := A^T * B (transpose)
|
|
*
|
|
*-------------------------------------------------
|
|
ELSE
|
|
*
|
|
* Form B := U^T*B
|
|
* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
|
|
* and U^T = inv(U^T(1))*P(1)* ... *inv(U^T(m))*P(m)
|
|
*
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
|
*
|
|
* Loop backward applying the transformations.
|
|
*
|
|
K = N
|
|
KC = N*( N+1 ) / 2 + 1
|
|
70 IF( K.LT.1 )
|
|
$ GO TO 90
|
|
KC = KC - K
|
|
*
|
|
* 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 CGEMV( 'Transpose', K-1, NRHS, ONE, B, LDB,
|
|
$ A( KC ), 1, ONE, B( K, 1 ), LDB )
|
|
END IF
|
|
IF( NOUNIT )
|
|
$ CALL CSCAL( NRHS, A( KC+K-1 ), B( K, 1 ), LDB )
|
|
K = K - 1
|
|
*
|
|
* 2 x 2 pivot block.
|
|
*
|
|
ELSE
|
|
KCNEXT = KC - ( K-1 )
|
|
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.
|
|
*
|
|
CALL CGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB,
|
|
$ A( KC ), 1, ONE, B( K, 1 ), LDB )
|
|
*
|
|
CALL CGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB,
|
|
$ A( KCNEXT ), 1, ONE, B( K-1, 1 ), LDB )
|
|
END IF
|
|
*
|
|
* Multiply by the diagonal block if non-unit.
|
|
*
|
|
IF( NOUNIT ) THEN
|
|
D11 = A( KC-1 )
|
|
D22 = A( KC+K-1 )
|
|
D12 = A( KC+K-2 )
|
|
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
|
|
KC = KCNEXT
|
|
K = K - 2
|
|
END IF
|
|
GO TO 70
|
|
90 CONTINUE
|
|
*
|
|
* Form B := L^T*B
|
|
* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
|
|
* and L^T = inv(L(m))*P(m)* ... *inv(L(1))*P(1)
|
|
*
|
|
ELSE
|
|
*
|
|
* Loop forward applying the L-transformations.
|
|
*
|
|
K = 1
|
|
KC = 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, ONE, B( K+1, 1 ),
|
|
$ LDB, A( KC+1 ), 1, ONE, B( K, 1 ), LDB )
|
|
END IF
|
|
IF( NOUNIT )
|
|
$ CALL CSCAL( NRHS, A( KC ), B( K, 1 ), LDB )
|
|
KC = KC + N - K + 1
|
|
K = K + 1
|
|
*
|
|
* 2 x 2 pivot block.
|
|
*
|
|
ELSE
|
|
KCNEXT = KC + N - K + 1
|
|
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 CGEMV( 'Transpose', N-K-1, NRHS, ONE,
|
|
$ B( K+2, 1 ), LDB, A( KCNEXT+1 ), 1, ONE,
|
|
$ B( K+1, 1 ), LDB )
|
|
*
|
|
CALL CGEMV( 'Transpose', N-K-1, NRHS, ONE,
|
|
$ B( K+2, 1 ), LDB, A( KC+2 ), 1, ONE,
|
|
$ B( K, 1 ), LDB )
|
|
END IF
|
|
*
|
|
* Multiply by the diagonal block if non-unit.
|
|
*
|
|
IF( NOUNIT ) THEN
|
|
D11 = A( KC )
|
|
D22 = A( KCNEXT )
|
|
D21 = A( KC+1 )
|
|
D12 = D21
|
|
DO 110 J = 1, NRHS
|
|
T1 = B( K, J )
|
|
T2 = B( K+1, J )
|
|
B( K, J ) = D11*T1 + D12*T2
|
|
B( K+1, J ) = D21*T1 + D22*T2
|
|
110 CONTINUE
|
|
END IF
|
|
KC = KCNEXT + ( N-K )
|
|
K = K + 2
|
|
END IF
|
|
GO TO 100
|
|
120 CONTINUE
|
|
END IF
|
|
*
|
|
END IF
|
|
RETURN
|
|
*
|
|
* End of CLAVSP
|
|
*
|
|
END
|