dorm2l()

subroutine dorm2l	(	character	side,
		character	trans,
		integer	m,
		integer	n,
		integer	k,
		double precision, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( * )	tau,
		double precision, dimension( ldc, * )	c,
		integer	ldc,
		double precision, dimension( * )	work,
		integer	info
	)

DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).

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Purpose:

 DORM2L overwrites the general real m by n matrix C with

       Q * C  if SIDE = 'L' and TRANS = 'N', or

       Q**T * C  if SIDE = 'L' and TRANS = 'T', or

       C * Q  if SIDE = 'R' and TRANS = 'N', or

       C * Q**T if SIDE = 'R' and TRANS = 'T',

 where Q is a real orthogonal matrix defined as the product of k
 elementary reflectors

       Q = H(k) . . . H(2) H(1)

 as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n
 if SIDE = 'R'.

Parameters

[in]	SIDE	SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left = 'R': apply Q or Q**T from the Right
[in]	TRANS	TRANS is CHARACTER*1 = 'N': apply Q (No transpose) = 'T': apply Q**T (Transpose)
[in]	M	M is INTEGER The number of rows of the matrix C. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix C. N >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQLF in the last k columns of its array argument A. A is modified by the routine but restored on exit.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N).
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEQLF.
[in,out]	C	C is DOUBLE PRECISION array, dimension (LDC,N) On entry, the m by n matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
[in]	LDC	LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N) if SIDE = 'L', (M) if SIDE = 'R'
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 157 of file dorm2l.f.

*
*  -- LAPACK computational 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          SIDE, TRANS
      INTEGER            INFO, K, LDA, LDC, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE
      parameter( one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LEFT, NOTRAN
      INTEGER            I, I1, I2, I3, MI, NI, NQ
      DOUBLE PRECISION   AII
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlarf, 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( 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 xerbla( 'DORM2L', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
     $   RETURN
*
      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
*
      IF( left ) THEN
         ni = n
      ELSE
         mi = m
      END IF
*
      DO 10 i = i1, i2, i3
         IF( left ) THEN
*
*           H(i) is applied to C(1:m-k+i,1:n)
*
            mi = m - k + i
         ELSE
*
*           H(i) is applied to C(1:m,1:n-k+i)
*
            ni = n - k + i
         END IF
*
*        Apply H(i)
*
         aii = a( nq-k+i, i )
         a( nq-k+i, i ) = one
         CALL dlarf( side, mi, ni, a( 1, i ), 1, tau( i ), c, ldc,
     $               work )
         a( nq-k+i, i ) = aii
   10 CONTINUE
      RETURN
*
*     End of DORM2L
*

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