sorm2l()

subroutine sorm2l	(	character	side,
		character	trans,
		integer	m,
		integer	n,
		integer	k,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( * )	tau,
		real, dimension( ldc, * )	c,
		integer	ldc,
		real, dimension( * )	work,
		integer	info )

SORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).

Download SORM2L + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> SORM2L 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 SGEQLF. 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 REAL 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 !> SGEQLF 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 REAL array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by SGEQLF. !>
[in,out]	C	!> C is REAL 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 REAL 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 155 of file sorm2l.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 ..
      REAL               A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LEFT, NOTRAN
      INTEGER            I, I1, I2, I3, MI, NI, NQ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           slarf1l, 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( 'SORM2L', -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)
*
         CALL slarf1l( side, mi, ni, a( 1, i ), 1, tau( i ), c, ldc,
     $               work )
   10 CONTINUE
      RETURN
*
*     End of SORM2L
*

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