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SUBROUTINE DLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
$ INFO )
*
* -- LAPACK auxiliary routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION A( * ), B( LDB, * )
* ..
*
* Purpose
* =======
*
* DLAVSP performs one of the matrix-vector operations
* x := A*x or x := A'*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 DSPTRF.
*
* If TRANS = 'N', multiplies by U or U * D (or L or L * D)
* If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L' )
* If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L' )
*
* Arguments
* ==========
*
* UPLO (input) CHARACTER*1
* Specifies whether the factor stored in A is upper or lower
* triangular.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* TRANS (input) CHARACTER*1
* Specifies the operation to be performed:
* = 'N': x := A*x
* = 'T': x := A'*x
* = 'C': x := A'*x
*
* DIAG (input) 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.
*
* N (input) INTEGER
* The number of rows and columns of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of vectors
* x to be multiplied by A. NRHS >= 0.
*
* A (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
* The block diagonal matrix D and the multipliers used to
* obtain the factor U or L, stored as a packed triangular
* matrix as computed by DSPTRF.
*
* IPIV (input) INTEGER array, dimension (N)
* The pivot indices from DSPTRF.
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* On entry, B contains NRHS vectors of length N.
* On exit, B is overwritten with the product A * B.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -k, the k-th argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT
INTEGER J, K, KC, KCNEXT, KP
DOUBLE PRECISION D11, D12, D21, D22, T1, T2
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DGEMV, DGER, DSCAL, DSWAP, 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' ) .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( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLAVSP ', -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 DSCAL( 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 DGER( 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 DSWAP( 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 DGER( K-1, NRHS, ONE, A( KC ), 1, B( K, 1 ), LDB,
$ B( 1, 1 ), LDB )
CALL DGER( 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 DSWAP( 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 DSCAL( 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 DGER( 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 DSWAP( 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 DGER( N-K, NRHS, ONE, A( KC+1 ), 1, B( K, 1 ),
$ LDB, B( K+1, 1 ), LDB )
CALL DGER( 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 DSWAP( 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' * B (transpose)
*
*----------------------------------------
ELSE
*
* 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
KC = N*( N+1 ) / 2 + 1
70 CONTINUE
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 DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
*
* Apply the transformation
*
CALL DGEMV( 'Transpose', K-1, NRHS, ONE, B, LDB,
$ A( KC ), 1, ONE, B( K, 1 ), LDB )
END IF
IF( NOUNIT )
$ CALL DSCAL( 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 DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ),
$ LDB )
*
* Apply the transformations
*
CALL DGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB,
$ A( KC ), 1, ONE, B( K, 1 ), LDB )
CALL DGEMV( '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'*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
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 DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
*
* Apply the transformation
*
CALL DGEMV( 'Transpose', N-K, NRHS, ONE, B( K+1, 1 ),
$ LDB, A( KC+1 ), 1, ONE, B( K, 1 ), LDB )
END IF
IF( NOUNIT )
$ CALL DSCAL( 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 DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ),
$ LDB )
*
* Apply the transformation
*
CALL DGEMV( 'Transpose', N-K-1, NRHS, ONE,
$ B( K+2, 1 ), LDB, A( KCNEXT+1 ), 1, ONE,
$ B( K+1, 1 ), LDB )
CALL DGEMV( '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 DLAVSP
*
END
|
