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Excessive Interconversion between Multidimensional and Linear Indexing

I am looking for a quick way to translate between linear and multidimensional indexing in Numpy.

To make my use specific, I have a large collection of N particles, each of which has 5 float values ​​(sizes) giving an Nx5 array. Then I take each dimension using numpy.digitize with the appropriate bin selection to assign each particle a cell in 5-dimensional space.

N = 10
ndims = 5
p = numpy.random.normal(size=(N,ndims))
for idim in xrange(ndims):
    bbnds[idim] = numpy.array([-float('inf')]+[-2.,-1.,0.,1.,2.]+[float('inf')])

binassign = ndims*[None]
for idim in xrange(ndims):
    binassign[idim] = numpy.digitize(p[:,idim],bbnds[idim]) - 1

binassign then contains the rows corresponding to the multidimensional index. If then I want to convert a multidimensional index to a linear index, I think I would like to do something like:

linind = numpy.arange(6**5).reshape(6,6,6,6,6)

This will enable each multidimensional index to map it to a linear index. Then you can return with:

mindx = numpy.unravel_index(x,linind.shape)

, , , ( Nx5), , 1d, linind.

- ( ) - , N , .

+5
2

EOL-, , C F . :

ndims = 5
N = 10

# Define bin boundaries 
binbnds = ndims*[None]
nbins = []
for idim in xrange(ndims):
    binbnds[idim] = numpy.linspace(-10.0,10.0,numpy.random.randint(2,15))
    binbnds[idim][0] = -float('inf')
    binbnds[idim][-1] = float('inf')
    nbins.append(binbnds[idim].shape[0]-1)

nstates = numpy.cumprod(nbins)[-1]

# Define variable values for N particles in ndims dimensions
p = numpy.random.normal(size=(N,ndims))

# Assign to bins along each dimension
binassign = ndims*[None]
for idim in xrange(ndims):
    binassign[idim] = numpy.digitize(p[:,idim],binbnds[idim]) - 1

binassign = numpy.array(binassign)

# multidimensional array with elements mapping from multidim to linear index
# Two different arrays for C vs F ordering
linind_C = numpy.arange(nstates).reshape(nbins,order='C')
linind_F = numpy.arange(nstates).reshape(nbins,order='F')


# Fast conversion to linear index
b_F = numpy.cumprod([1] + nbins)[:-1]
b_C = numpy.cumprod([1] + nbins[::-1])[:-1][::-1]

box_index_F = numpy.dot(b_F,binassign)
box_index_C = numpy.dot(b_C,binassign)

:

# Check
print 'Checking correct mapping for each particle F order'
for k in xrange(N):
    ii = box_index_F[k]
    jj = linind_F[tuple(binassign[:,k])]
    print 'particle %d %s (%d %d)' % (k,ii == jj,ii,jj)

print 'Checking correct mapping for each particle C order'
for k in xrange(N):
    ii = box_index_C[k]
    jj = linind_C[tuple(binassign[:,k])]
    print 'particle %d %s (%d %d)' % (k,ii == jj,ii,jj)

, 1d , :

print 'Convert C-style from linear to multi'
x = box_index_C.reshape(-1,1)
bassign_rev_C = x / b_C % nbins 

print 'Convert F-style from linear to multi'
x = box_index_F.reshape(-1,1)
bassign_rev_F = x / b_F % nbins

:

print 'Check C-order'
for k in xrange(N):
    ii = tuple(binassign[:,k])
    jj = tuple(bassign_rev_C[k,:])
    print ii==jj,ii,jj

print 'Check F-order'
for k in xrange(N):
    ii = tuple(binassign[:,k])
    jj = tuple(bassign_rev_F[k,:])
    print ii==jj,ii,jj
+3

:

box_indices = numpy.dot(ndims**numpy.arange(ndims), binassign)

1 * x0 + 5 * x1 + 5 * 5 * x2 +... NumPy dot().

+4

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