[Numpy-discussion] dot function or dot notation, matrices, arrays?

[Charles R Harris]

On Sat, Dec 19, 2009 at 9:45 AM, Wayne Watson
<sierra_mtnview at sbcglobal.net>wrote:

>
>
> Dag Sverre Seljebotn wrote:
> > Wayne Watson wrote:
> >
> >> I'm trying to compute the angle between two vectors in three dimensional
> >> space. For that, I need to use the "scalar (dot) product" , according to
> >> a calculus book (quoting the book) I'm holding in my hands right now.
> >> I've used dot() successfully to produce the necessary angle. My program
> >> works just fine.
> >>
> >> In the case of the dot(function), one must use np.dev(x.T,x), where x is
> >> 1x3.
> >>
> >> I'm not quite sure what your point is about dot()* unless you are
> >> thinking in some non-Euclidean fashion. One can form np.dot(a,b) with a
> >> and b arrays of 3x4 and 4x2 shape to arrive at a 3x2 array. That's
> >> definitely not a scalar. Is there a need for this sort of calculation in
> >> non-Euclidean geometry, which I have never dealt with?
> >>
> >
> > There's a difference between 1D and 2D arrays that's important here. For
> > a 1D array, np.dot(x.T, x) == np.dot(x, x), since there's only one
> > dimension.
> >
> A 4x1, 1x7, and 1x5 would be examples of a 1D array or matrix, right?
>

No, they are all 2D. All matrices are 2D. An array is 1D if it doesn't have
a second dimension, which might be confusing if you have only seen vectors
represented as arrays. To see the number of dimensions in a numpy array, use
shape:

In [1]: array([[1,2],[3,4]])
Out[1]:
array([[1, 2],
       [3, 4]])

In [2]: array([[1,2],[3,4]]).shape
Out[2]: (2, 2)

In [3]: array([1,2, 3,4])
Out[3]: array([1, 2, 3, 4])

In [4]: array([1,2, 3,4]).shape
Out[4]: (4,)


> Are you saying that instead of using a rotational matrix like
>    theta = 5.0 # degrees
>    m1 = matrix([[2] ,[5]])
>    rotCW = matrix([ [cosD(theta), sinD(theta)], [-sinD(theta),
> cosD(theta)] ])
>     m2= rotCW*m1
>    m1=np.array(m1)
>    m2=np.array(m2)
> that I should use a 2-D array for rotCW? So why does numpy have a matrix
> class?  Is the class only used when working with matplotlib?
>
>
Numpy has a matrix class because python lacks operators, so where * normally
means element-wise multiplication the matrix class uses it for matrix
multiplication, which is different. Having a short form for matrix
multiplication is sometimes a convenience and also more familiar for folks
coming to numpy from matlab.


> To get the scalar value (sum of squares) I had to use a transpose, T, on
> one argument.
>
>
That is if the argument is 2D. It's not strictly speaking a scalar product,
but we won't go into that here ;)

<snip>

Chuck
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