sgeqr2(l) [redhat man page]

SGEQR2(l)								 )								 SGEQR2(l)

NAME

       SGEQR2 - compute a QR factorization of a real m by n matrix A

SYNOPSIS

       SUBROUTINE SGEQR2( M, N, A, LDA, TAU, WORK, INFO )

	   INTEGER	  INFO, LDA, M, N

	   REAL 	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.

ARGUMENTS

       M       (input) INTEGER
	       The number of rows of the matrix A.  M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix A.  N >= 0.

       A       (input/output) 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 trape-
	       zoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU,	represent  the	orthogonal
	       matrix  Q  as a product of elementary reflectors (see Further Details).	LDA	(input) INTEGER The leading dimension of the array
	       A.  LDA >= max(1,M).

       TAU     (output) REAL array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors (see Further Details).

       WORK    (workspace) REAL array, dimension (N)

       INFO    (output) INTEGER
	       = 0: successful exit
	       < 0: if INFO = -i, the i-th argument had an illegal value

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'

       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).

LAPACK version 3.0						   15 June 2000 							 SGEQR2(l)

sgeqr2.f(3)							      LAPACK							       sgeqr2.f(3)

NAME

       sgeqr2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgeqr2 (M, N, A, LDA, TAU, WORK, INFO)
	   SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation
   subroutine sgeqr2 (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)
       SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

       Purpose:

	    SGEQR2 computes a QR factorization of a real m by n matrix A:
	    A = Q * R.

       Parameters:
	   M

		     M is INTEGER
		     The number of rows of the matrix A.  M >= 0.

	   N

		     N is INTEGER
		     The number of columns of the matrix A.  N >= 0.

	   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 elements below the diagonal,
		     with the array TAU, represent the orthogonal matrix Q as a
		     product of elementary reflectors (see Further Details).

	   LDA

		     LDA is INTEGER
		     The leading dimension of the array A.  LDA >= max(1,M).

	   TAU

		     TAU is REAL array, dimension (min(M,N))
		     The scalar factors of the elementary reflectors (see Further
		     Details).

	   WORK

		     WORK is REAL array, dimension (N)

	   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:
	   September 2012

       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).

       Definition at line 122 of file sgeqr2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sgeqr2.f(3)