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      SUBROUTINE <a name="DLARFB.1"></a><a href="dlarfb.f.html#DLARFB.1">DLARFB</a>( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
     $                   T, LDT, C, LDC, WORK, LDWORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          DIRECT, SIDE, STOREV, TRANS
      INTEGER            K, LDC, LDT, LDV, LDWORK, M, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   C( LDC, * ), T( LDT, * ), V( LDV, * ),
     $                   WORK( LDWORK, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DLARFB.20"></a><a href="dlarfb.f.html#DLARFB.1">DLARFB</a> applies a real block reflector H or its transpose H' to a
</span><span class="comment">*</span><span class="comment">  real m by n matrix C, from either the left or the right.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SIDE    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'L': apply H or H' from the Left
</span><span class="comment">*</span><span class="comment">          = 'R': apply H or H' from the Right
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TRANS   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N': apply H (No transpose)
</span><span class="comment">*</span><span class="comment">          = 'T': apply H' (Transpose)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DIRECT  (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Indicates how H is formed from a product of elementary
</span><span class="comment">*</span><span class="comment">          reflectors
</span><span class="comment">*</span><span class="comment">          = 'F': H = H(1) H(2) . . . H(k) (Forward)
</span><span class="comment">*</span><span class="comment">          = 'B': H = H(k) . . . H(2) H(1) (Backward)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  STOREV  (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Indicates how the vectors which define the elementary
</span><span class="comment">*</span><span class="comment">          reflectors are stored:
</span><span class="comment">*</span><span class="comment">          = 'C': Columnwise
</span><span class="comment">*</span><span class="comment">          = 'R': Rowwise
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of the matrix C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns of the matrix C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  K       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix T (= the number of elementary
</span><span class="comment">*</span><span class="comment">          reflectors whose product defines the block reflector).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  V       (input) DOUBLE PRECISION array, dimension
</span><span class="comment">*</span><span class="comment">                                (LDV,K) if STOREV = 'C'
</span><span class="comment">*</span><span class="comment">                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
</span><span class="comment">*</span><span class="comment">                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
</span><span class="comment">*</span><span class="comment">          The matrix V. See further details.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDV     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array V.
</span><span class="comment">*</span><span class="comment">          If STOREV = 'C' and SIDE = 'L', LDV &gt;= max(1,M);
</span><span class="comment">*</span><span class="comment">          if STOREV = 'C' and SIDE = 'R', LDV &gt;= max(1,N);
</span><span class="comment">*</span><span class="comment">          if STOREV = 'R', LDV &gt;= K.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  T       (input) DOUBLE PRECISION array, dimension (LDT,K)
</span><span class="comment">*</span><span class="comment">          The triangular k by k matrix T in the representation of the
</span><span class="comment">*</span><span class="comment">          block reflector.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDT     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array T. LDT &gt;= K.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
</span><span class="comment">*</span><span class="comment">          On entry, the m by n matrix C.
</span><span class="comment">*</span><span class="comment">          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDC     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array C. LDA &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) DOUBLE PRECISION array, dimension (LDWORK,K)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDWORK  (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array WORK.
</span><span class="comment">*</span><span class="comment">          If SIDE = 'L', LDWORK &gt;= max(1,N);
</span><span class="comment">*</span><span class="comment">          if SIDE = 'R', LDWORK &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      CHARACTER          TRANST
      INTEGER            I, J
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.100"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.101"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DCOPY, DGEMM, DTRMM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( M.LE.0 .OR. N.LE.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.113"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> ) ) THEN
         TRANST = <span class="string">'T'</span>
      ELSE
         TRANST = <span class="string">'N'</span>
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( STOREV, <span class="string">'C'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span>         IF( <a name="LSAME.121"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIRECT, <span class="string">'F'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Let  V =  ( V1 )    (first K rows)
</span><span class="comment">*</span><span class="comment">                     ( V2 )
</span><span class="comment">*</span><span class="comment">           where  V1  is unit lower triangular.
</span><span class="comment">*</span><span class="comment">
</span>            IF( <a name="LSAME.127"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'L'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Form  H * C  or  H' * C  where  C = ( C1 )
</span><span class="comment">*</span><span class="comment">                                                  ( C2 )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              W := C1'
</span><span class="comment">*</span><span class="comment">
</span>               DO 10 J = 1, K
                  CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
   10          CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              W := W * V1
</span><span class="comment">*</span><span class="comment">
</span>               CALL DTRMM( <span class="string">'Right'</span>, <span class="string">'Lower'</span>, <span class="string">'No transpose'</span>, <span class="string">'Unit'</span>, N,
     $                     K, ONE, V, LDV, WORK, LDWORK )
               IF( M.GT.K ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 W := W + C2'*V2
</span><span class="comment">*</span><span class="comment">
</span>                  CALL DGEMM( <span class="string">'Transpose'</span>, <span class="string">'No transpose'</span>, N, K, M-K,
     $                        ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV,
     $                        ONE, WORK, LDWORK )
               END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              W := W * T'  or  W * T
</span><span class="comment">*</span><span class="comment">
</span>               CALL DTRMM( <span class="string">'Right'</span>, <span class="string">'Upper'</span>, TRANST, <span class="string">'Non-unit'</span>, N, K,
     $                     ONE, T, LDT, WORK, LDWORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              C := C - V * W'
</span><span class="comment">*</span><span class="comment">
</span>               IF( M.GT.K ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 C2 := C2 - V2 * W'
</span><span class="comment">*</span><span class="comment">
</span>                  CALL DGEMM( <span class="string">'No transpose'</span>, <span class="string">'Transpose'</span>, M-K, N, K,
     $                        -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE,
     $                        C( K+1, 1 ), LDC )
               END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              W := W * V1'
</span><span class="comment">*</span><span class="comment">
</span>               CALL DTRMM( <span class="string">'Right'</span>, <span class="string">'Lower'</span>, <span class="string">'Transpose'</span>, <span class="string">'Unit'</span>, N, K,
     $                     ONE, V, LDV, WORK, LDWORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              C1 := C1 - W'
</span><span class="comment">*</span><span class="comment">
</span>               DO 30 J = 1, K
                  DO 20 I = 1, N
                     C( J, I ) = C( J, I ) - WORK( I, J )
   20             CONTINUE
   30          CONTINUE
<span class="comment">*</span><span class="comment">
</span>            ELSE IF( <a name="LSAME.182"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'R'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Form  C * H  or  C * H'  where  C = ( C1  C2 )
</span><span class="comment">*</span><span class="comment">
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