sgeqlf(l) [redhat man page]

SGEQLF(l)								 )								 SGEQLF(l)

NAME

       SGEQLF - compute a QL factorization of a real M-by-N matrix A

SYNOPSIS

       SUBROUTINE SGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

	   INTEGER	  INFO, LDA, LWORK, M, N

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

PURPOSE

       SGEQLF 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/output) REAL array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The dimension of the array WORK.  LWORK >= max(1,N).  For optimum performance LWORK >= N*NB, where NB is the optimal blocksize.

	       If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of  the  WORK  array,  returns  this
	       value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

       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 							 SGEQLF(l)

DGEQLF(l)								 )								 DGEQLF(l)

NAME

       DGEQLF - compute a QL factorization of a real M-by-N matrix A

SYNOPSIS

       SUBROUTINE DGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

	   INTEGER	  INFO, LDA, LWORK, M, N

	   DOUBLE	  PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       DGEQLF 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors (see Further Details).

       WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The dimension of the array WORK.  LWORK >= max(1,N).  For optimum performance LWORK >= N*NB, where NB is the optimal blocksize.

	       If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of  the  WORK  array,  returns  this
	       value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

       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 							 DGEQLF(l)