sormr3.f

Go to the documentation of this file.

      SUBROUTINE SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
     $                   WORK, INFO )
*
*  -- LAPACK routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, L, LDA, LDC, M, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  SORMR3 overwrites the general real m by n matrix C with
*
*        Q * C  if SIDE = 'L' and TRANS = 'N', or
*
*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
*
*        C * Q  if SIDE = 'R' and TRANS = 'N', or
*
*        C * Q' if SIDE = 'R' and TRANS = 'T',
*
*  where Q is a real orthogonal matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(1) H(2) . . . H(k)
*
*  as returned by STZRZF. Q is of order m if SIDE = 'L' and of order n
*  if SIDE = 'R'.
*
*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q' from the Left
*          = 'R': apply Q or Q' from the Right
*
*  TRANS   (input) CHARACTER*1
*          = 'N': apply Q  (No transpose)
*          = 'T': apply Q' (Transpose)
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  L       (input) INTEGER
*          The number of columns of the matrix A containing
*          the meaningful part of the Householder reflectors.
*          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*
*  A       (input) REAL array, dimension
*                               (LDA,M) if SIDE = 'L',
*                               (LDA,N) if SIDE = 'R'
*          The i-th row must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          STZRZF in the last k rows of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,K).
*
*  TAU     (input) REAL array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by STZRZF.
*
*  C       (input/output) REAL array, dimension (LDC,N)
*          On entry, the m-by-n matrix C.
*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace) REAL array, dimension
*                                   (N) if SIDE = 'L',
*                                   (M) if SIDE = 'R'
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*
*  Further Details
*  ===============
*
*  Based on contributions by
*    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LEFT, NOTRAN
      INTEGER            I, I1, I2, I3, IC, JA, JC, MI, NI, NQ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           SLARZ, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      LEFT = LSAME( SIDE, 'L' )
      NOTRAN = LSAME( TRANS, 'N' )
*
*     NQ is the order of Q
*
      IF( LEFT ) THEN
         NQ = M
      ELSE
         NQ = N
      END IF
      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
         INFO = -1
      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) 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( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
     $         ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
         INFO = -6
      ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
         INFO = -8
      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
         INFO = -11
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'SORMR3', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
     $   RETURN
*
      IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN
         I1 = 1
         I2 = K
         I3 = 1
      ELSE
         I1 = K
         I2 = 1
         I3 = -1
      END IF
*
      IF( LEFT ) THEN
         NI = N
         JA = M - L + 1
         JC = 1
      ELSE
         MI = M
         JA = N - L + 1
         IC = 1
      END IF
*
      DO 10 I = I1, I2, I3
         IF( LEFT ) THEN
*
*           H(i) or H(i)' is applied to C(i:m,1:n)
*
            MI = M - I + 1
            IC = I
         ELSE
*
*           H(i) or H(i)' is applied to C(1:m,i:n)
*
            NI = N - I + 1
            JC = I
         END IF
*
*        Apply H(i) or H(i)'
*
         CALL SLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ),
     $               C( IC, JC ), LDC, WORK )
*
   10 CONTINUE
*
      RETURN
*
*     End of SORMR3
*
      END