◆ sgeqr2p()

subroutine sgeqr2p	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( * )	WORK,
		integer	INFO
	)

SGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

Download SGEQR2P + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 SGEQR2P computes a QR factorization of a real m-by-n matrix A:

    A = Q * ( R ),
            ( 0 )

 where:

    Q is a m-by-m orthogonal matrix;
    R is an upper-triangular n-by-n matrix with nonnegative diagonal
    entries;
    0 is a (m-n)-by-n zero matrix, if m > n.

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,out]	A	A is REAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are nonnegative; the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]	TAU	TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	WORK	WORK is REAL array, dimension (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.

Date: November 2019

Further Details:

  The matrix Q is represented as a product of elementary reflectors

     Q = H(1) H(2) . . . H(k), where k = min(m,n).

  Each H(i) has the form

     H(i) = I - tau * v * v**T

  where tau is a real scalar, and v is a real vector with
  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
  and tau in TAU(i).

 See Lapack Working Note 203 for details

Definition at line 136 of file sgeqr2p.f.

 *
 *  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N
 *     ..
 *     .. Array Arguments ..
       REAL               A( LDA, * ), TAU( * ), WORK( * )
 *     ..
 *
 *  =====================================================================
 *
 *     .. Parameters ..
       REAL               ONE
       parameter( one = 1.0e+0 )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, K
       REAL               AII
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           slarf, slarfgp, xerbla
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          max, min
 *     ..
 *     .. 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( lda.LT.max( 1, m ) ) THEN
          info = -4
       END IF
       IF( info.NE.0 ) THEN
          CALL xerbla( 'SGEQR2P', -info )
          RETURN
       END IF
 *
       k = min( m, n )
 *
       DO 10 i = 1, k
 *
 *        Generate elementary reflector H(i) to annihilate A(i+1:m,i)
 *
          CALL slarfgp( m-i+1, a( i, i ), a( min( i+1, m ), i ), 1,
      $                tau( i ) )
          IF( i.LT.n ) THEN
 *
 *           Apply H(i) to A(i:m,i+1:n) from the left
 *
             aii = a( i, i )
             a( i, i ) = one
             CALL slarf( 'Left', m-i+1, n-i, a( i, i ), 1, tau( i ),
      $                  a( i, i+1 ), lda, work )
             a( i, i ) = aii
          END IF
    10 CONTINUE
       RETURN
 *
 *     End of SGEQR2P
 *

Here is the call graph for this function:

Here is the caller graph for this function: