[Numpy-discussion] design issues - octave 'incompatibilities'

[Soeren Sonnenburg]

On Mon, 2005-07-25 at 08:59 -0700, Chris Barker wrote:
> Soeren Sonnenburg wrote:
> > -- why do vectors have no 'orientation', i.e. there are only row but no
> > column vectors (or why do you treat matrices/vectors differently, i.e.
> > have vectors at all as a separate type)
> 
> I think the key to understanding this is that NumPy uses a 
> fundamentally different data type that MATLAB and it's derivatives. 
> MATLAB was originally just what it is called: a "Matrix" laboratory. The 
> basic data type of Matlab is a 2-d matrix. Even a scalar is really a 1X! 
> matrix. Matlab has a few tricks that can make these look like row and 
> column vectors, etc, but they are really always matrices.

Ok, I am realizing that R also distinguishes between vectors and
matrices.

> On the other hand, NumPy arrays are N-dimensional, where N is 
> theoretically unlimited. In practice, I think the max N is defined and 
> compiled in, but you could change it and re-compile if you wanted. In 
> any case, many of us frequently use 3-d and higher arrays, and they can 
> be very useful. When thought  of this way, you can see why there is no 

Well at least this is the same for octave/matlab.

> such thing as a column vs. a row vector. A vector is a one-dimensional 
> array: it has no orientation.

This makes life more difficult if one wants to convert 
from octave/matlab -> numarray and automated systems close to
impossible. If vectors had the same properties/functions as matrices one
would not have such problems, i.e. v^{transpose} * u == dot(v,u) and v*u
-> error

> However, NumPy does support NX1 and 1XN 2-d arrays which can be very handy:
>  >>> import numarray as N
>  >>> a = N.arange(5)
>  >>> a.shape = (1,-1)
>  >>> a
> array([[0, 1, 2, 3, 4]])
>  >>> b = N.arange(5)
>  >>> b.shape = (-1,1)
>  >>> a
> array([0, 1, 2, 3, 4])
>  >>> b
> array([[0],
>         [1],
>         [2],
>         [3],
>         [4]])
> 
> So a is a row vector and b is a column vector. If you multiply them, you 
> get "array broadcasting":
>  >>> a * b
> array([[ 0,  0,  0,  0,  0],
>         [ 0,  1,  2,  3,  4],
>         [ 0,  2,  4,  6,  8],
>         [ 0,  3,  6,  9, 12],
>         [ 0,  4,  8, 12, 16]])
> 
> This eliminates a LOT of extra duplicate arrays that you have to make in 
> Matlab with meshgrid.

In my eyes 'array broadcasting' is confusing and should rather be in a
function like meshgrid and instead a*b should return
matrixmultiply(a,b) ...

> When you index into an array, you reduce its rank (number of dimensions) 
> by 1:
>  >>> a = N.arange(27)
>  >>> a.shape = (3,3,3)
>  >>> a
> array([[[ 0,  1,  2],
>          [ 3,  4,  5],
>          [ 6,  7,  8]],
> 
>         [[ 9, 10, 11],
>          [12, 13, 14],
>          [15, 16, 17]],
> 
>         [[18, 19, 20],
>          [21, 22, 23],
>          [24, 25, 26]]])
>  >>> a.shape
> (3, 3, 3)
>  >>> a[1].shape
> (3, 3)
>  >>> a[1][1].shape
> (3,)
> 
> When you slice, you keep the rank the same:
> 
>  >>> a[1:2].shape
> (1, 3, 3)
> 
> This creates a way to make row and column "vectors" from your 2-d array 
> (matrix)
>  >>> a = N.arange(25)
>  >>> a.shape = (5,5)
>  >>> a
> array([[ 0,  1,  2,  3,  4],
>         [ 5,  6,  7,  8,  9],
>         [10, 11, 12, 13, 14],
>         [15, 16, 17, 18, 19],
>         [20, 21, 22, 23, 24]])
> 
> To make a "row vector" (really a 1XN matrix)
>  >>> a[0:1,:]
> array([[0, 1, 2, 3, 4]])
> 
> 
> To make a "column vector" (really a NX1 matrix)
>  >>> a[:,0:1]
> array([[ 0],
>         [ 5],
>         [10],
>         [15],
>         [20]])
> 
> 
> I hope that helps:

Indeed it does - Thanks!! Unfortunately I am not at all happy now that
'*' != matrixmultiply (but outerproduct) for vectors/matrices...

I realize that with lists it is ok to grow them via slicing.

x=[]
x[0]=1
IndexError: list assignment index out of range
x[0:0]=[1]
x
[1]

that seems not to work with numarray ... or ?

y=array()
y[0]=1
TypeError: object does not support item assignment
y[0:0]=array([1])
TypeError: object does not support item assignment

Soeren.