sgeql2(l) [redhat man page]

SGEQL2(l)								 )								 SGEQL2(l)

NAME

       SGEQL2 - compute a QL factorization of a real m by n matrix A

SYNOPSIS

       SUBROUTINE SGEQL2( M, N, A, LDA, TAU, WORK, INFO )

	   INTEGER	  INFO, LDA, M, N

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

PURPOSE

       SGEQL2 computes a QL factorization of a real m by n matrix A: A = Q * L.

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, if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the n by n lower
	       triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix L;
	       the  remaining  elements,  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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).

LAPACK version 3.0						   15 June 2000 							 SGEQL2(l)

SGERQ2(l)								 )								 SGERQ2(l)

NAME

       SGERQ2 - compute an RQ factorization of a real m by n matrix A

SYNOPSIS

       SUBROUTINE SGERQ2( M, N, A, LDA, TAU, WORK, INFO )

	   INTEGER	  INFO, LDA, M, N

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

PURPOSE

       SGERQ2 computes an RQ factorization of a real m by n matrix A: A = R * Q.

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, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper
	       triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal	matrix	R;
	       the  remaining  elements,  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 (M)

       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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

LAPACK version 3.0						   15 June 2000 							 SGERQ2(l)