sgelqt()

subroutine sgelqt	(	integer	m,
		integer	n,
		integer	mb,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( ldt, * )	t,
		integer	ldt,
		real, dimension( * )	work,
		integer	info
	)

SGELQT

Purpose:

 DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
 using the compact WY representation of Q.

Parameters

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	MB	MB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
[in,out]	A	A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is lower triangular if M <= N); the elements above the diagonal are the rows of V.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]	T	T is REAL array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.
[in]	LDT	LDT is INTEGER The leading dimension of the array T. LDT >= MB.
[out]	WORK	WORK is REAL array, dimension (MB*N)
[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.

Further Details:

  The matrix V stores the elementary reflectors H(i) in the i-th row
  above the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (         1 v3 v3 )


  where the vi's represent the vectors which define H(i), which are returned
  in the matrix A.  The 1's along the diagonal of V are not stored in A.
  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/MB), where each
  block is of order MB except for the last block, which is of order
  IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
  for the last block) T's are stored in the MB-by-K matrix T as

               T = (T1 T2 ... TB).

Definition at line 123 of file sgelqt.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 ..
      INTEGER INFO, LDA, LDT, M, N, MB
*     ..
*     .. Array Arguments ..
      REAL     A( LDA, * ), T( LDT, * ), WORK( * )
*     ..
*
* =====================================================================
*
*     ..
*     .. Local Scalars ..
      INTEGER    I, IB, IINFO, K
*     ..
*     .. External Subroutines ..
      EXTERNAL   sgeqrt2, sgeqrt3, sgelqt3, slarfb, xerbla
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( mb.LT.1 .OR. ( mb.GT.min(m,n) .AND. min(m,n).GT.0 ) )THEN
         info = -3
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -5
      ELSE IF( ldt.LT.mb ) THEN
         info = -7
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SGELQT', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      k = min( m, n )
      IF( k.EQ.0 ) RETURN
*
*     Blocked loop of length K
*
      DO i = 1, k,  mb
         ib = min( k-i+1, mb )
*
*     Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
*
         CALL sgelqt3( ib, n-i+1, a(i,i), lda, t(1,i), ldt, iinfo )
         IF( i+ib.LE.m ) THEN
*
*     Update by applying H**T to A(I:M,I+IB:N) from the right
*
         CALL slarfb( 'R', 'N', 'F', 'R', m-i-ib+1, n-i+1, ib,
     $                   a( i, i ), lda, t( 1, i ), ldt,
     $                   a( i+ib, i ), lda, work , m-i-ib+1 )
         END IF
      END DO
      RETURN
*
*     End of SGELQT
*

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