SUBROUTINE DLAVSY( UPLO, TRANS, DIAG, N, NRHS, A, LDA, 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, LDA, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * Purpose * ======= * * DLAVSY 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 DSYTRF. * * 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 (LDA,N) * The block diagonal matrix D and the multipliers used to * obtain the factor U or L as computed by DSYTRF. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * IPIV (input) INTEGER array, dimension (N) * The pivot indices from DSYTRF. * * 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, 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( 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( 'DLAVSY ', -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 DSCAL( 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 DGER( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ), \$ LDB, B( 1, 1 ), LDB ) * * Interchange if P(K) .ne. I. * KP = IPIV( K ) 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 * * 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 = 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( 1, K ), 1, B( K, 1 ), \$ LDB, B( 1, 1 ), LDB ) CALL DGER( K-1, NRHS, ONE, A( 1, K+1 ), 1, \$ B( K+1, 1 ), LDB, B( 1, 1 ), LDB ) * * Interchange if P(K) .ne. I. * KP = ABS( IPIV( K ) ) IF( KP.NE.K ) \$ CALL DSWAP( 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 DSCAL( 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 DGER( 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 DSWAP( 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 = 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( K+1, K ), 1, B( K, 1 ), \$ LDB, B( K+1, 1 ), LDB ) CALL DGER( 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 DSWAP( 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' * 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 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) .ne. 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( 1, K ), 1, ONE, B( K, 1 ), LDB ) END IF IF( NOUNIT ) \$ CALL DSCAL( 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) .ne. 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( 1, K ), 1, ONE, B( K, 1 ), LDB ) CALL DGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB, \$ A( 1, K-1 ), 1, ONE, 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 = 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'*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 = 1 100 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) .ne. 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( K+1, K ), 1, ONE, B( K, 1 ), LDB ) END IF IF( NOUNIT ) \$ CALL DSCAL( 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) .ne. 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( K+2, K+1 ), 1, ONE, \$ B( K+1, 1 ), LDB ) CALL DGEMV( 'Transpose', N-K-1, NRHS, ONE, \$ B( K+2, 1 ), LDB, A( K+2, K ), 1, ONE, \$ 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 = 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 DLAVSY * END