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Numpy: how to find a unique local minimum of submatrices in matrix A?

Given a matrix A of dimension MxN (4x4), how to find the nearest minimum minimum of each submatrix 2x2?

A = array([[ 32673.    ,  15108.2   ,  26767.2   ,   9420.   ],
           [ 32944.2   ,  14604.01  ,  26757.01  ,   9127.2  ],
           [ 26551.2   ,  9257.01   ,  26595.01  ,   9309.2  ],
           [ 26624.    ,   8935.2   ,  26673.2   ,   8982.   ]])

The next best minimum of the set of submatrices is the minimum of this submatrix, which does not contradict the local position of the other minima:

Algorithm Example:

1. Find the minimum in A: 8935.2 global coords[3,1], local coords [1,1]
2. No other matrix has been evaluated so no conflict yet.
3. Find the next submatrix min: 8982. gc [3,3], lc [1,1]
4. Conflict exists, find next min in same submatrix: 9309.2 gc [2,3], lc [0,1]
5. Find next submatrix min: 9420 gc [0,3] lc[0,1]
6. Conflict exists, find next min: 26757.01 gc [1,2] lc [1,0]
7. Find next submatrix min: 14604 -- conflict with lc[1,1]
8. Find next submatrix min: 15108.2 -- conflict with lc [0,1]
9. Find next submatrix min: 32673. gc [0,0], lc [0,0]

one of the approaches that I thought about trying to follow the above algorithm, but instead of exhaustively searching for each submatrix, again globally updates each local position of the submatrix with a “high” value (→ max (A)), which increases by each successful finding of the minima.

The expected result will be a list:

[((0, 0), (0, 0), 32673), ((0, 1), (1, 0), 26757.01), ((1, 0), (1, 1), 8935.2), ((1, 1), (0, 1), 9309.2)]

forms [((t1), (t2), value) ...], where t1 are the coordinates of the submatrix in A, and t2 are the coordinates of the selected minimum in the submatrix.

: ZxZ, MxN ZxZ == 0, , (0,0), MxN.

: , . , , , , .

    def get_mins(self, result):
    # result is the 2d array
    dim = 2  # 2x2 submatrix
    mins = []
    count = 0
    while count < dim**2:
        a, b = result.shape
        M4D = result.reshape(a//dim, dim, b//dim, dim)
        lidx = M4D.transpose(0, 2, 1, 3).reshape(-1, b//dim, dim**2).argmin(-1)
        r, c = numpy.unravel_index(lidx, [dim, dim])

        yy = M4D.min(axis=(1, 3))
        ww = numpy.dstack((r, c))

        super_min = numpy.unravel_index(numpy.argmin(yy), (dim, dim))

        rows = super_min[0]
        cols = super_min[1]

        # ww[rows,cols] g_ves us 2x2 position
        offset_r, offset_c = ww[rows, cols]
        # super_min gives us submatrix position

        mins.append((tuple(super_min), (offset_r, offset_c), yy.min()))

        if dim > 1:
            # update all other positions with inf >> max(result)
            result[numpy.ix_([offset_r + (d * dim) for d in range(dim)], [offset_c + (d * dim) for d in range(dim)])] = numpy.inf
            # update the submatrix to all == numpy.inf
            result[rows*dim:((rows*dim)+dim), cols*dim:((cols*dim)+dim)] = numpy.inf
        count += 1
    return mins
+4
3

, -

def unq_localmin(A, dim):
    m, n = A.shape
    M4D = A.reshape(m//dim, dim, n//dim, dim)
    M2Dr = M4D.swapaxes(1,2).reshape(-1,dim**2)
    a = M2Dr.copy()

    N = M2Dr.shape[0]
    R = np.empty(N,dtype=int)
    C = np.empty(N,dtype=int)
    shp = M2Dr.shape
    for i in range(N):
        r,c = np.unravel_index(np.argmin(a),shp)
        a[r] = np.inf
        a[:,c] = np.inf
        R[i], C[i] = r, c
    out = M2Dr[R,C]
    idr = np.column_stack(np.unravel_index(R,(dim,dim)))
    idc = np.column_stack(np.unravel_index(C,(dim,dim)))
    return zip(map(tuple,idr),map(tuple,idc),out)

9x9 / 3x3 OP get_mins -

In [66]: A   # Input data array
Out[66]: 
array([[ 927.,  852.,   18.,  949.,  933.,  558.,  519.,  118.,   82.],
       [ 939.,  782.,  178.,  987.,  534.,  981.,  879.,  895.,  407.],
       [ 968.,  187.,  539.,  986.,  506.,  499.,  529.,  978.,  567.],
       [ 767.,  272.,  881.,  858.,  621.,  301.,  675.,  151.,  670.],
       [ 874.,  221.,   72.,  210.,  273.,  823.,  784.,  289.,  425.],
       [ 621.,  510.,  303.,  935.,   88.,  970.,  278.,  125.,  669.],
       [ 702.,  722.,  620.,   51.,  845.,  414.,  154.,  154.,  635.],
       [ 600.,  928.,  540.,  462.,  772.,  487.,  196.,  499.,  208.],
       [ 654.,  335.,  258.,  297.,  649.,  712.,  292.,  767.,  819.]])

In [67]: unq_localmin(A, dim = 3) # Using proposed approach
Out[67]: 
[((0, 0), (0, 2), 18.0),
 ((2, 1), (0, 0), 51.0),
 ((1, 0), (1, 2), 72.0),
 ((1, 1), (2, 1), 88.0),
 ((0, 2), (0, 1), 118.0),
 ((2, 2), (1, 0), 196.0),
 ((2, 0), (2, 2), 258.0),
 ((1, 2), (2, 0), 278.0),
 ((0, 1), (1, 1), 534.0)]

In [68]: out = np.empty((9,9))

In [69]: get_mins(out,A) # Using OP soln with dim = 3 edited
Out[69]: 
[((0, 0), (0, 2), 18.0),
 ((2, 1), (0, 0), 51.0),
 ((1, 0), (1, 2), 72.0),
 ((1, 1), (2, 1), 88.0),
 ((0, 2), (0, 1), 118.0),
 ((2, 2), (1, 0), 196.0),
 ((2, 0), (2, 2), 258.0),
 ((1, 2), (2, 0), 278.0),
 ((0, 1), (1, 1), 534.0)]

, , get_mins. , , :

def unq_localmin_v2(A, dim):
    m, n = A.shape
    M4D = A.reshape(m//dim, dim, n//dim, dim)
    M2Dr = M4D.swapaxes(1,2).reshape(-1,dim**2)    
    N = M2Dr.shape[0]
    out = np.empty(N)
    shp = M2Dr.shape
    for i in range(N):
        r,c = np.unravel_index(np.argmin(M2Dr),shp)
        out[i] = M2Dr[r,c]
        M2Dr[r] = np.inf
        M2Dr[:,c] = np.inf        
    return out

-

In [52]: A = np.random.randint(11,999,(9,9)).astype(float)

In [53]: %timeit unq_localmin_v2(A, dim=3)
10000 loops, best of 3: 93.1 µs per loop

In [54]: out = np.empty((9,9))

In [55]: %timeit get_mins(out,A)
1000 loops, best of 3: 907 µs per loop
+2

, , 4 - :

In [113]: A1=A.reshape(4,2,2).transpose(0,2,1)
In [114]: A1
Out[114]: 
array([[[ 32673.  ,  26767.2 ],
        [ 15108.2 ,   9420.  ]],

       [[ 32944.2 ,  26757.01],
        [ 14604.01,   9127.2 ]],

       [[ 26551.2 ,  26595.01],
        [  9257.01,   9309.2 ]],

       [[ 26624.  ,  26673.2 ],
        [  8935.2 ,   8982.  ]]])

argmin ( )

In [115]: np.argmin(A1[1])
Out[115]: 3
In [116]: [np.argmin(a) for a in A1]
Out[116]: [3, 3, 2, 2]

, 2x2 - 1- - argmin

In [117]: A2=A1.reshape(4,4)
In [118]: A2
Out[118]: 
array([[ 32673.  ,  26767.2 ,  15108.2 ,   9420.  ],
       [ 32944.2 ,  26757.01,  14604.01,   9127.2 ],
       [ 26551.2 ,  26595.01,   9257.01,   9309.2 ],
       [ 26624.  ,  26673.2 ,   8935.2 ,   8982.  ]])
In [119]: [np.argmin(a) for a in A2]
Out[119]: [3, 3, 2, 2]

2d:

In [123]: [np.unravel_index(np.argmin(a),(2,2)) for a in A2]
Out[123]: [(1, 1), (1, 1), (1, 0), (1, 0)]

, - A2.

In [124]: A2[1:,3]=np.inf
In [125]: [np.argmin(a) for a in A2]
Out[125]: [3, 2, 2, 2]
In [126]: A2[2:,2]=np.inf
In [127]: [np.argmin(a) for a in A2]
Out[127]: [3, 2, 0, 0]
In [128]: A2[3:,0]=np.inf
In [129]: [np.argmin(a) for a in A2]
Out[129]: [3, 2, 0, 1]

In [139]: A2
Out[139]: 
array([[ 32673.  ,  26767.2 ,  15108.2 ,   9420.  ],
       [ 32944.2 ,  26757.01,  14604.01,       inf],
       [ 26551.2 ,  26595.01,       inf,       inf],
       [      inf,  26673.2 ,       inf,       inf]])

, , , , . . .

+2

, , ^^. :

  • a 1d aSrt
  • aSrt 2x2
  • lstSubMat, (0,0)
  • lstSubMat, ,
  • , (.. msk). ( )

:

  • ndarrays
  • How to order adarray animation first by the index of the second column, then by the index of the first column
  • how to convert lists to tupel and vice versa.

the code:

#lc: local coordinates
#gc: global coordinates
#sc: submatrix coordinates


import numpy as np
a = np.array(
    [[ 32673.    ,  15108.2   ,  26767.2   ,   9420.   ],
    [ 32944.2   ,  14604.01  ,  26757.01  ,   9127.2  ],
    [ 26551.2   ,  9257.01   ,  26595.01  ,   9309.2  ],
    [ 26624.    ,   8935.2   ,  26673.2   ,   8982.   ]]
    )
#print(a)



#sort values of a in 1d array
aSrt=np.sort(a.flatten())
#print(aSrt)

#list of submatrix coordinates ordered by their minimum
lstSubMat=[]
for ii in range(0,len(aSrt)):
    #print('just to make things clear:',np.where(a==aSrt[ii]))
    gc=[elem[0] for elem in list(np.where(a==aSrt[ii]))]
    lc = [elem%2 for elem in gc]
    sc = [gc[jj]-lc[jj] for jj in range(0,2)]
    #print('gc:',gc,'sc',sc,'lc:',lc, 'value:',aSrt[0])
    if not sc in lstSubMat:
        lstSubMat.append(sc)
        #lstSubMat[1].append(lc)
        #lstSubMat[2].append(value)

# result is list of gc
result=np.empty((4,2),dtype=int)
#result=np.empty([4,2])
nmbFound=0

#check list with lc
msk=[]

while nmbFound<4:
    sc=lstSubMat[0]
    subMat=a[sc[0]:sc[0]+2,sc[1]:sc[1]+2]
    #print('subMat:',subMat)
    valSubMatSrt=np.sort(subMat.flatten())
    for ii in range(0,4):
        lc=[elem[0] for elem in list(np.where(subMat==valSubMatSrt[ii]))]
        if not lc in msk:
            msk.append(lc)
            #result.append([sc[jj]+lc[jj] for jj in range(0,2)])
            #result[nmbFound]=[sc[jj]+lc[jj] for jj in range(0,2)]
            result[nmbFound,0]=sc[0]+lc[0]
            result[nmbFound,1]=sc[1]+lc[1]
            nmbFound+=1
            #print('gc:',result[-1],'sc',sc,'lc:',lc, 'value:',aSrt[0])
            lstSubMat=lstSubMat[1:]
            break

#print(result)

#sort first by row then by col index of submatrix -> //2
result=result[(result[:,1]//2).argsort()] 
result=result[(result[:,0]//2).argsort()] 
#print(result)

print('\n\nresult:')
for ii in range(0,len(result)):
    sc=tuple([elem//2 for elem in result[ii,:]])
    lc=tuple([result[ii,jj]%2 for jj in range(0,2)])
    print(sc,lc,a[tuple(result[ii,:])])

Output:

result:
(0, 0) (0, 0) 32673.0
(0, 1) (1, 0) 26757.01
(1, 0) (1, 1) 8935.2
(1, 1) (0, 1) 9309.2
+2
source

Source: https://habr.com/ru/post/1661049/

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