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

[Wayne Watson]

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?

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?

To get the scalar value (sum of squares) I had to use a transpose, T, on 
one argument.

> NumPy is all about arrays, not matrices and vectors.
>
> Dag Sverre
>
>   
>> *Maybe it's about something else related to it.
>>
>>
>> David Goldsmith wrote:
>>     
>>> np.dot(x.flat, x.flat) _is exactly_ "sum of squares"(x.flat).  Your
>>> math education appears to have drawn a distinction between "dot
>>> product" and "scalar product," that, when one is talking about
>>> Euclidean vectors, just isn't there: in that context, they are one and
>>> the same thing.
>>>
>>> DG
>>>
>>> On Fri, Dec 18, 2009 at 9:29 PM, Wayne Watson
>>> <sierra_mtnview@sbcglobal.net> wrote:
>>>   
>>>       
>>>> I'll amend that. I should have said, "Dot's all folks." -- Bugs Bunny
>>>>
>>>> --
>>>>           Wayne Watson (Watson Adventures, Prop., Nevada City, CA)
>>>>
>>>>             (121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time)
>>>>              Obz Site:  39° 15' 7" N, 121° 2' 32" W, 2700 feet
>>>>
>>>>             "... humans'innate skills with numbers isn't much
>>>>              better than that of rats and dolphins."
>>>>                       -- Stanislas Dehaene, neurosurgeon
>>>>
>>>>                    Web Page: <www.speckledwithstars.net/>
>>>>
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>>>>     
>>>>         
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>>>   
>>>       
>
>
>   

-- 
           Wayne Watson (Watson Adventures, Prop., Nevada City, CA)

             (121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time)
              Obz Site:  39° 15' 7" N, 121° 2' 32" W, 2700 feet  
                
             "... humans'innate skills with numbers isn't much
              better than that of rats and dolphins." 
                       -- Stanislas Dehaene, neurosurgeon 
 
                    Web Page: <www.speckledwithstars.net/>