SUBROUTINE ZLAVSY( 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( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * Purpose * ======= * * ZLAVSY 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 symmetric factorization computed by ZSYTRF. * ZSYTRF produces a factorization of the form * U * D * U' or L * D * L' , * where U (or L) is a product of permutation and unit upper (lower) * triangular matrices, U' (or L') 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 in the leading upper or lower triangle of the 2-D * array A. * * If TRANS = 'N' or 'n', ZLAVSY multiplies either by U or U * D * (or L or L * D). * If TRANS = 'T' or 't', ZLAVSY multiplies either by U' or D * U' * (or L' or D * L' ). * * Arguments * ========== * * 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'*x. * Unchanged on exit. * * DIAG - CHARACTER*1 * On entry, DIAG specifies whether the diagonal blocks are * assumed to be unit matrices: * 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*16 array, dimension( LDA, N ) * On entry, A contains a block diagonal matrix and the * multipliers of the transformations used to obtain it, * stored as a 2-D triangular matrix. * Unchanged on exit. * * LDA - INTEGER * On entry, LDA specifies the first dimension of A as declared * in the calling ( sub ) program. LDA must be at least * max( 1, N ). * Unchanged on exit. * * IPIV - INTEGER array, dimension( N ) * On entry, IPIV contains the vector of pivot indices as * determined by ZSYTRF or ZHETRF. * 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*16 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. * * ===================================================================== * * .. 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, ZSCAL, ZSWAP * .. * .. 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( 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( 'ZLAVSY ', -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 = 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 = 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' * B (transpose) * *---------------------------------------- ELSE IF( LSAME( TRANS, 'T' ) ) THEN * * 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) != I. * KP = IPIV( K ) IF( KP.NE.K ) \$ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * * Apply the transformation * CALL ZGEMV( 'Transpose', K-1, NRHS, ONE, B, LDB, \$ A( 1, K ), 1, ONE, 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 * CALL ZGEMV( 'Transpose', K-2, NRHS, ONE, B, LDB, \$ A( 1, K ), 1, ONE, B( K, 1 ), LDB ) CALL ZGEMV( '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) != I. * KP = IPIV( K ) IF( KP.NE.K ) \$ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * * Apply the transformation * CALL ZGEMV( '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 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 ZGEMV( 'Transpose', N-K-1, NRHS, ONE, \$ B( K+2, 1 ), LDB, A( K+2, K+1 ), 1, ONE, \$ B( K+1, 1 ), LDB ) CALL ZGEMV( '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 ZLAVSY * END