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Class org.netlib.lapack.DTZRQF

java.lang.Object
   |
   +----org.netlib.lapack.DTZRQF

public class DTZRQF

extends Object

DTZRQF is a simplified interface to the JLAPACK routine dtzrqf.
This interface converts Java-style 2D row-major arrays into
the 1D column-major linearized arrays expected by the lower
level JLAPACK routines.  Using this interface also allows you
to omit offset and leading dimension arguments.  However, because
of these conversions, these routines will be slower than the low
level ones.  Following is the description from the original Fortran
source.  Contact seymour@cs.utk.edu with any questions.

 *     ..
 *
 *  Purpose
 *  =======
 *
 *  DTZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
 *  to upper triangular form by means of orthogonal transformations.
 *
 *  The upper trapezoidal matrix A is factored as
 *
 *     A = ( R  0 ) * Z,
 *
 *  where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
 *  triangular matrix.
 *
 *  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 >= M.
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 *          On entry, the leading M-by-N upper trapezoidal part of the
 *          array A must contain the matrix to be factorized.
 *          On exit, the leading M-by-M upper triangular part of A
 *          contains the upper triangular matrix R, and elements M+1 to
 *          N of the first M rows of A, with the array TAU, represent the
 *          orthogonal matrix Z as a product of M elementary reflectors.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,M).
 *
 *  TAU     (output) DOUBLE PRECISION array, dimension (M)
 *          The scalar factors of the elementary reflectors.
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
 *          < 0:  if INFO = -i, the i-th argument had an illegal value
 *
 *  Further Details
 *  ===============
 *
 *  The factorization is obtained by Householder's method.  The kth
 *  transformation matrix, Z( k ), which is used to introduce zeros into
 *  the ( m - k + 1 )th row of A, is given in the form
 *
 *     Z( k ) = ( I     0   ),
 *              ( 0  T( k ) )
 *
 *  where
 *
 *     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
 *                                                 (   0    )
 *                                                 ( z( k ) )
 *
 *  tau is a scalar and z( k ) is an ( n - m ) element vector.
 *  tau and z( k ) are chosen to annihilate the elements of the kth row
 *  of X.
 *
 *  The scalar tau is returned in the kth element of TAU and the vector
 *  u( k ) in the kth row of A, such that the elements of z( k ) are
 *  in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
 *  the upper triangular part of A.
 *
 *  Z is given by
 *
 *     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
 *
 *  =====================================================================
 *
 *     .. Parameters ..

DTZRQF()

DTZRQF(int, int, double[][], double[], intW)

 public DTZRQF()

 public static void DTZRQF(int m,
                           int n,
                           double a[][],
                           double tau[],
                           intW info)

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