dormqr()

subroutine dormqr	(	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	lwork,
		integer	info )

DORMQR

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Purpose:

!>
!> DORMQR overwrites the general real M-by-N matrix C with
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'T':      Q**T * C       C * Q**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 DGEQRF. 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': No transpose, apply Q; !> = 'T': Transpose, apply Q**T. !>
[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 !> DGEQRF in the first k columns of its array argument A. !>
[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 DGEQRF. !>
[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 (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. !> If SIDE = 'L', LWORK >= max(1,N); !> if SIDE = 'R', LWORK >= max(1,M). !> For good performance, LWORK should generally be larger. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !>
[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 163 of file dormqr.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, LWORK, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            NBMAX, LDT, TSIZE
      parameter( nbmax = 64, ldt = nbmax+1,
     $                     tsize = ldt*nbmax )
*     ..
*     .. Local Scalars ..
      LOGICAL            LEFT, LQUERY, NOTRAN
      INTEGER            I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK,
     $                   LWKOPT, MI, NB, NBMIN, NI, NQ, NW
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           lsame, ilaenv
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlarfb, dlarft, dorm2r, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      left = lsame( side, 'L' )
      notran = lsame( trans, 'N' )
      lquery = ( lwork.EQ.-1 )
*
*     NQ is the order of Q and NW is the minimum dimension of WORK
*
      IF( left ) THEN
         nq = m
         nw = max( 1, n )
      ELSE
         nq = n
         nw = max( 1, m )
      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
      ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
         info = -12
      END IF
*
      IF( info.EQ.0 ) THEN
*
*        Compute the workspace requirements
*
         nb = min( nbmax, ilaenv( 1, 'DORMQR', side // trans, m, n,
     $             k,
     $        -1 ) )
         lwkopt = nw*nb + tsize
         work( 1 ) = lwkopt
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DORMQR', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
         work( 1 ) = 1
         RETURN
      END IF
*
      nbmin = 2
      ldwork = nw
      IF( nb.GT.1 .AND. nb.LT.k ) THEN
         IF( lwork.LT.lwkopt ) THEN
            nb = (lwork-tsize) / ldwork
            nbmin = max( 2, ilaenv( 2, 'DORMQR', side // trans, m, n,
     $                   k,
     $              -1 ) )
         END IF
      END IF
*
      IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
*
*        Use unblocked code
*
         CALL dorm2r( side, trans, m, n, k, a, lda, tau, c, ldc,
     $                work,
     $                iinfo )
      ELSE
*
*        Use blocked code
*
         iwt = 1 + nw*nb
         IF( ( left .AND. .NOT.notran ) .OR.
     $       ( .NOT.left .AND. notran ) ) THEN
            i1 = 1
            i2 = k
            i3 = nb
         ELSE
            i1 = ( ( k-1 ) / nb )*nb + 1
            i2 = 1
            i3 = -nb
         END IF
*
         IF( left ) THEN
            ni = n
            jc = 1
         ELSE
            mi = m
            ic = 1
         END IF
*
         DO 10 i = i1, i2, i3
            ib = min( nb, k-i+1 )
*
*           Form the triangular factor of the block reflector
*           H = H(i) H(i+1) . . . H(i+ib-1)
*
            CALL dlarft( 'Forward', 'Columnwise', nq-i+1, ib, a( i,
     $                   i ),
     $                   lda, tau( i ), work( iwt ), ldt )
            IF( left ) THEN
*
*              H or H**T is applied to C(i:m,1:n)
*
               mi = m - i + 1
               ic = i
            ELSE
*
*              H or H**T is applied to C(1:m,i:n)
*
               ni = n - i + 1
               jc = i
            END IF
*
*           Apply H or H**T
*
            CALL dlarfb( side, trans, 'Forward', 'Columnwise', mi,
     $                   ni,
     $                   ib, a( i, i ), lda, work( iwt ), ldt,
     $                   c( ic, jc ), ldc, work, ldwork )
   10    CONTINUE
      END IF
      work( 1 ) = lwkopt
      RETURN
*
*     End of DORMQR
*

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