clavhe.f

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*> \brief \b CLAVHE
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE CLAVHE( 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            A( LDA, * ), B( LDB, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CLAVHE 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 CHETRF.
*>
*> 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^H*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 array, dimension (LDA,N)
*>          The block diagonal matrix D and the multipliers used to
*>          obtain the factor U or L as computed by CHETRF_ROOK.
*>          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 CHETRF.
*>
*>          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 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 complex_lin
*
*  =====================================================================
      SUBROUTINE clavhe( 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            A( LDA, * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX            ONE
      parameter( one = ( 1.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOUNIT
      INTEGER            J, K, KP
      COMPLEX            D11, D12, D21, D22, T1, T2
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           cgemv, cgeru, clacgv, cscal, cswap, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, conjg, max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'l' ) ) THEN
         INFO = -1
.NOT.      ELSE IF( LSAME( TRANS, 'n.AND..NOT.' )  LSAME( TRANS, 'c' ) )
     $          THEN
         INFO = -2
.NOT.      ELSE IF( LSAME( DIAG, 'u.AND..NOT.' )  LSAME( DIAG, 'n' ) )
     $          THEN
         INFO = -3
.LT.      ELSE IF( N0 ) THEN
         INFO = -4
.LT.      ELSE IF( LDAMAX( 1, N ) ) THEN
         INFO = -6
.LT.      ELSE IF( LDBMAX( 1, N ) ) THEN
         INFO = -9
      END IF
.NE.      IF( INFO0 ) THEN
         CALL XERBLA( 'clavhe ', -INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
.EQ.      IF( N0 )
     $   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
.GT.            IF( KN )
     $         GO TO 30
.GT.            IF( IPIV( K )0 ) THEN
*
*              1 x 1 pivot block
*
*              Multiply by the diagonal element if forming U * D.
*
               IF( NOUNIT )
     $            CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB )
*
*              Multiply by  P(K) * inv(U(K))  if K > 1.
*
.GT.               IF( K1 ) THEN
*
*                 Apply the transformation.
*
                  CALL CGERU( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ),
     $                        LDB, B( 1, 1 ), LDB )
*
*                 Interchange if P(K) != I.
*
                  KP = IPIV( K )
.NE.                  IF( KPK )
     $               CALL CSWAP( 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 = CONJG( 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.
*
.GT.               IF( K1 ) THEN
*
*                 Apply the transformations.
*
                  CALL CGERU( K-1, NRHS, ONE, A( 1, K ), 1, B( K, 1 ),
     $                        LDB, B( 1, 1 ), LDB )
                  CALL CGERU( 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 ) )
.NE.                  IF( KPK )
     $               CALL CSWAP( 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
.LT.            IF( K1 )
     $         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.
*
.GT.            IF( IPIV( K )0 ) THEN
*
*              1 x 1 pivot block:
*
*              Multiply by the diagonal element if forming L * D.
*
               IF( NOUNIT )
     $            CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB )
*
*              Multiply by  P(K) * inv(L(K))  if K < N.
*
.NE.               IF( KN ) THEN
                  KP = IPIV( K )
*
*                 Apply the transformation.
*
                  CALL CGERU( 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.
*
.NE.                  IF( KPK )
     $               CALL CSWAP( 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 = CONJG( 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.
*
.NE.               IF( KN ) THEN
*
*                 Apply the transformation.
*
                  CALL CGERU( N-K, NRHS, ONE, A( K+1, K ), 1,
     $                        B( K, 1 ), LDB, B( K+1, 1 ), LDB )
                  CALL CGERU( 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 ) )
.NE.                  IF( KPK )
     $               CALL CSWAP( 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
.LT.   70       IF( K1 )
     $         GO TO 90
*
*           1 x 1 pivot block.
*
.GT.            IF( IPIV( K )0 ) THEN
.GT.               IF( K1 ) THEN
*
*                 Interchange if P(K) != I.
*
                  KP = IPIV( K )
.NE.                  IF( KPK )
     $               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 CLACGV( NRHS, B( K, 1 ), LDB )
                  CALL CGEMV( 'conjugate', K-1, NRHS, ONE, B, LDB,
     $                        A( 1, K ), 1, ONE, B( K, 1 ), LDB )
                  CALL CLACGV( NRHS, B( K, 1 ), LDB )
               END IF
               IF( NOUNIT )
     $            CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB )
               K = K - 1
*
*           2 x 2 pivot block.
*
            ELSE
.GT.               IF( K2 ) THEN
*
*                 Interchange if P(K) != I.
*
                  KP = ABS( IPIV( K ) )
.NE.                  IF( KPK-1 )
     $               CALL CSWAP( 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 CLACGV( NRHS, B( K, 1 ), LDB )
                  CALL CGEMV( 'conjugate', K-2, NRHS, ONE, B, LDB,
     $                        A( 1, K ), 1, ONE, B( K, 1 ), LDB )
                  CALL CLACGV( NRHS, B( K, 1 ), LDB )
*
                  CALL CLACGV( NRHS, B( K-1, 1 ), LDB )
                  CALL CGEMV( 'conjugate', K-2, NRHS, ONE, B, LDB,
     $                        A( 1, K-1 ), 1, ONE, B( K-1, 1 ), LDB )
                  CALL CLACGV( 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 = CONJG( 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
.GT.            IF( KN )
     $         GO TO 120
*
*           1 x 1 pivot block
*
.GT.            IF( IPIV( K )0 ) THEN
.LT.               IF( KN ) THEN
*
*                 Interchange if P(K) != I.
*
                  KP = IPIV( K )
.NE.                  IF( KPK )
     $               CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
*
*                 Apply the transformation
*
                  CALL CLACGV( NRHS, B( K, 1 ), LDB )
                  CALL CGEMV( 'conjugate', N-K, NRHS, ONE, B( K+1, 1 ),
     $                        LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
                  CALL CLACGV( NRHS, B( K, 1 ), LDB )
               END IF
               IF( NOUNIT )
     $            CALL CSCAL( NRHS, A( K, K ), B( K, 1 ), LDB )
               K = K + 1
*
*           2 x 2 pivot block.
*
            ELSE
.LT.               IF( KN-1 ) THEN
*
*              Interchange if P(K) != I.
*
                  KP = ABS( IPIV( K ) )
.NE.                  IF( KPK+1 )
     $               CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ),
     $                           LDB )
*
*                 Apply the transformation
*
                  CALL CLACGV( NRHS, B( K+1, 1 ), LDB )
                  CALL CGEMV( 'conjugate', N-K-1, NRHS, ONE,
     $                        B( K+2, 1 ), LDB, A( K+2, K+1 ), 1, ONE,
     $                        B( K+1, 1 ), LDB )
                  CALL CLACGV( NRHS, B( K+1, 1 ), LDB )
*
                  CALL CLACGV( NRHS, B( K, 1 ), LDB )
                  CALL CGEMV( 'conjugate', N-K-1, NRHS, ONE,
     $                        B( K+2, 1 ), LDB, A( K+2, K ), 1, ONE,
     $                        B( K, 1 ), LDB )
                  CALL CLACGV( 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 = CONJG( 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 CLAVHE
*
      END