[Numpy-discussion] dot function or dot notation, matrices, arrays?
Christopher Barker
Chris.Barker at noaa.gov
Sat Dec 19 13:18:09 EST 2009
Wayne Watson wrote:
> Yes, flat sounds useful here. However, numpy isn't bending over
> backwards to tie in conventional mathematical language into it.
exactly -- it isn't bending over at all! (well a little -- see below).
numpy was designed for general purpose computational needs, not any one
branch of math. nd-arrays are very useful for lots of things. In
contrast, Matlab, for instance, was originally designed to be an easy
front-end to linear algebra package. Personally, when I used Matlab, I
found that very awkward -- I was usually writing 100s of lines of code
that had nothing to do with linear algebra, for every few lines that
actually did matrix math. So I much prefer numpy's way -- the linear
algebra lines of code are longer an more awkward, but the rest is much
better.
The Matrix class is the exception to this: is was written to provide a
natural way to express linear algebra. However, things get a bit tricky
when you mix matrices and arrays, and even when sticking with matrices
there are confusions and limitations -- how do you express a row vs a
column vector? what do you get when you iterate over a matrix? etc.
There has been a bunch of discussion about these issues, a lot of good
ideas, a little bit of consensus about how to improve it, but no one
with the skill to do it has enough motivation to do it.
As for your problem, I think a 3-d euclidean vector is well expressed as
a (3,) shape array, and then you don't need flat, etc.
In [6]: v1 = np.array((1,2,3), dtype=np.float)
In [7]: v2 = np.array((3,1,2), dtype=np.float)
In [8]: np.dot(v1,v2)
Out[8]: 11.0
-Chris
> I don't recall flat in any calculus books. :-) Maybe I've been away so
> long from it, that it is a common math concept? Although I doubt that.
>
>
> Alan G Isaac wrote:
>> On 12/19/2009 11:45 AM, Wayne Watson wrote:
>>
>>> A 4x1, 1x7, and 1x5 would be examples of a 1D array or matrix, right?
>>>
>>> Are you saying that instead of using a rotational matrix ...
>>> 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?
>>>
>>> To get the scalar value (sum of squares) I had to use a transpose, T, on
>>> one argument.
>>>
>>
>> At this point, you have raised some long standing issues.
>> There are a couple standard replies people give to some of them.
>> E.g.,
>>
>> 1. don't use matrices, OR
>> 2. don't mix the use of matrices and arrays
>>
>> Matrices are *always* 2d (e.g., a "row vector" or a "column vector" is 2d).
>> So in fact you should find it quite natural that that transpose was needed.
>> Matrices change * to matrix multiplication and ** to matrix exponentiation.
>> I find this very convenient, especially in a teaching setting, so I use
>> NumPy matrices all the time. Many on this list avoid them completely.
>>
>> Again, if you want a *scalar* as the product of vectors for which you
>> created matrix objects (e.g., a and b), you can just use flat:
>> np.dot(a.flat,b.flat)
>>
>> hth,
>> Alan Isaac
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>>
>>
>
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