givens
======

Givens transformation



Calling Sequence
~~~~~~~~~~~~~~~~


::

    U=givens(xy)
    U=givens(x,y)
    [U,c]=givens(xy)
    [U,c]=givens(x,y)




Arguments
~~~~~~~~~

:x,y two real or complex numbers
: :xy real or complex size 2 column vector
: :U 2x2 unitary matrix
: :c real or complex size 2 column vector
:



Description
~~~~~~~~~~~

`U= givens(x, y)` or `U = givens(xy)` with `xy = [x;y]` returns a `2`x
`2` unitary matrix `U` such that:

`U*xy=[r;0]=c`.

Note that `givens(x,y)` and `givens([x;y])` are equivalent.



Examples
~~~~~~~~


::

    A=[3,4;5,6];
    U=givens(A(:,1));
    U*A




See Also
~~~~~~~~


+ `qr`_ QR decomposition


.. _qr: qr.html