[Tutor] location of points in a covariance matrix

[Bob Gailer]

Beanan O Loughlin wrote:
> Hi all, I'm a meteorology postgrad working with python for the first time.
>
> I have found the location minimum in a large covariance matrix. this 
> value corresponds to the covariance of two points on a latitude, 
> longitude grid.
>
> I need to find a method to locate these two points on the lat,lon grid.
Usually multi-dimensional arrays are stored in "row-major" order. So the 
subscripts of an array of shape 2,3,4 (planes, rows. columns) would look 
like:
1,1,1  1,1,2  1,1,3 1,1 4  1,2,1  1,2,2  1,2,3  1,2,4  1,3,1  1,3,2  
1,3,3  1,3,4  2,1,1  2,1,2  2,1,3 2,1 4  2,2,1  2,2,2  2,2,3  2,2,4  
2,3,1  2,3,2  2,3,3  2,3,4

When you reshape it to 2,12 the elements remain "in place", and the 
subscripts now are:
1,1  1,2  1,3  1,4  1,5  1,6  1,7  1,8  1,9  1,10  1,11  1,12  2,1  2,2  
2,3  2,4  2,5  2,6  2,7  2,8  2,9  2,10  2,11  2,12

Is that enough of a hint?
>
> this is the code i have used, where 'se' is a 3-D array of data
>
>
> >>> nt,nlat,nlon = shape(se)       
> >>>nt,nlat,nlon                            # 3-D array of data taken 
> 1464 times, over 41 latitudes and 58 longitudes
> (1464, 41, 58)
> >>>
> >>>
> >>>m=reshape(se,(nt,nlat*nlon))    # reshape to (time,latitude 
> longitude data point) where 2378 = 41*58
> >>>
> >>>shape(m)
> (1464,2378)
> >>>
> >>>
> >>>covmat=cov(m)                           # calculate covariance matrix
> >>>
> >>>shape(covmat)
> (2378,2378)
>
> >>>def min(R):
>        U = triu(R)                              #just use one half of 
> the diagonal matrix
>        n = U.shape[0]    
>        U.flat[::n+1] = 1000000000.0    #give the diagonal elements a 
> large value so they wont be selected
>        k = argmin(U.flat)                    #find the min value of 
> the flattened array
>        i, j = divmod(k,n)                     #calculate the index of 
> the minimum data
>        return i, j, R[i,j]    
>
> >>>
> >>> min(covmat)
> (7, 1914, -2.3016361721151051)
>
> so the minimum is found at (7,1914) in the covariance matrix and has a 
> value of - 2.3
>
> This min point corresponds to the covariance between two 'lat,lon' 
> data points in my (41,58) sample grid.
>
> Is there a way i can move back from my (2378,2378) covariance matrix 
> to see where these two points are located on the (41, 58) grid?
>
> Thank you very much in advance
>
> B.
>
> ------------------------------------------------------------------------
>
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-- 
Bob Gailer
510-978-4454 Oakland, CA
919-636-4239 Chapel Hill, NC