sorm2l.f.html

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      SUBROUTINE <a name="SORM2L.1"></a><a href="sorm2l.f.html#SORM2L.1">SORM2L</a>( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK 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          SIDE, TRANS
      INTEGER            INFO, K, LDA, LDC, M, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
<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="SORM2L.19"></a><a href="sorm2l.f.html#SORM2L.1">SORM2L</a> overwrites the general real m by n matrix C with
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Q * C  if SIDE = 'L' and TRANS = 'N', or
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Q'* C  if SIDE = 'L' and TRANS = 'T', or
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        C * Q  if SIDE = 'R' and TRANS = 'N', or
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        C * Q' if SIDE = 'R' and TRANS = 'T',
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where Q is a real orthogonal matrix defined as the product of k
</span><span class="comment">*</span><span class="comment">  elementary reflectors
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Q = H(k) . . . H(2) H(1)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  as returned by <a name="SGEQLF.34"></a><a href="sgeqlf.f.html#SGEQLF.1">SGEQLF</a>. Q is of order m if SIDE = 'L' and of order n
</span><span class="comment">*</span><span class="comment">  if SIDE = 'R'.
</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 Q or Q' from the Left
</span><span class="comment">*</span><span class="comment">          = 'R': apply Q or Q' 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 Q  (No transpose)
</span><span class="comment">*</span><span class="comment">          = 'T': apply Q' (Transpose)
</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. M &gt;= 0.
</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. N &gt;= 0.
</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 number of elementary reflectors whose product defines
</span><span class="comment">*</span><span class="comment">          the matrix Q.
</span><span class="comment">*</span><span class="comment">          If SIDE = 'L', M &gt;= K &gt;= 0;
</span><span class="comment">*</span><span class="comment">          if SIDE = 'R', N &gt;= K &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input) REAL array, dimension (LDA,K)
</span><span class="comment">*</span><span class="comment">          The i-th column must contain the vector which defines the
</span><span class="comment">*</span><span class="comment">          elementary reflector H(i), for i = 1,2,...,k, as returned by
</span><span class="comment">*</span><span class="comment">          <a name="SGEQLF.63"></a><a href="sgeqlf.f.html#SGEQLF.1">SGEQLF</a> in the last k columns of its array argument A.
</span><span class="comment">*</span><span class="comment">          A is modified by the routine but restored on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.
</span><span class="comment">*</span><span class="comment">          If SIDE = 'L', LDA &gt;= max(1,M);
</span><span class="comment">*</span><span class="comment">          if SIDE = 'R', LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TAU     (input) REAL array, dimension (K)
</span><span class="comment">*</span><span class="comment">          TAU(i) must contain the scalar factor of the elementary
</span><span class="comment">*</span><span class="comment">          reflector H(i), as returned by <a name="SGEQLF.73"></a><a href="sgeqlf.f.html#SGEQLF.1">SGEQLF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  C       (input/output) REAL 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 Q*C or Q'*C or C*Q' or C*Q.
</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. LDC &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) REAL array, dimension
</span><span class="comment">*</span><span class="comment">                                   (N) if SIDE = 'L',
</span><span class="comment">*</span><span class="comment">                                   (M) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0: successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0: if INFO = -i, the i-th argument had an illegal value
</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>      REAL               ONE
      PARAMETER          ( ONE = 1.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LEFT, NOTRAN
      INTEGER            I, I1, I2, I3, MI, NI, NQ
      REAL               AII
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.102"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.103"></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           <a name="SLARF.106"></a><a href="slarf.f.html#SLARF.1">SLARF</a>, <a name="XERBLA.106"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX
<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">     Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      LEFT = <a name="LSAME.116"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'L'</span> )
      NOTRAN = <a name="LSAME.117"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     NQ is the order of Q
</span><span class="comment">*</span><span class="comment">
</span>      IF( LEFT ) THEN
         NQ = M
      ELSE
         NQ = N
      END IF
      IF( .NOT.LEFT .AND. .NOT.<a name="LSAME.126"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'R'</span> ) ) THEN
         INFO = -1
      ELSE IF( .NOT.NOTRAN .AND. .NOT.<a name="LSAME.128"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'T'</span> ) ) THEN
         INFO = -2
      ELSE IF( M.LT.0 ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
         INFO = -5
      ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
         INFO = -7
      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
         INFO = -10
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.142"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SORM2L.142"></a><a href="sorm2l.f.html#SORM2L.1">SORM2L</a>'</span>, -INFO )
         RETURN
      END IF
<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.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) )
     $     THEN
         I1 = 1
         I2 = K
         I3 = 1
      ELSE
         I1 = K
         I2 = 1
         I3 = -1
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( LEFT ) THEN
         NI = N
      ELSE
         MI = M
      END IF
<span class="comment">*</span><span class="comment">
</span>      DO 10 I = I1, I2, I3
         IF( LEFT ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           H(i) is applied to C(1:m-k+i,1:n)
</span><span class="comment">*</span><span class="comment">
</span>            MI = M - K + I
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           H(i) is applied to C(1:m,1:n-k+i)
</span><span class="comment">*</span><span class="comment">
</span>            NI = N - K + I
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Apply H(i)
</span><span class="comment">*</span><span class="comment">
</span>         AII = A( NQ-K+I, I )
         A( NQ-K+I, I ) = ONE
         CALL <a name="SLARF.185"></a><a href="slarf.f.html#SLARF.1">SLARF</a>( SIDE, MI, NI, A( 1, I ), 1, TAU( I ), C, LDC,
     $               WORK )
         A( NQ-K+I, I ) = AII
   10 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SORM2L.191"></a><a href="sorm2l.f.html#SORM2L.1">SORM2L</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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