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多维索引与线性索引的相互转换

numpy indexing python

JoshAdel · 技术社区 · 15 年前

我正在寻找一种快速的方法来在Numpy的线性和多维索引之间进行转换。

为了使我的用法具体化,我有一个N个粒子的大集合,每个粒子分配5个浮点值(维度),给出一个Nx5数组。然后我使用numpy.digitalize对每个维度进行分类,并选择适当的分类边界,在5维空间中为每个粒子指定一个分类。

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

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

这将为每个多维索引提供一个查找,以便将其映射到一个线性索引。然后您可以使用:

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

我遇到的困难是如何获取每行中包含多维索引的二进制(Nx5数组),并将其转换为一维线性索引,方法是使用它对线性索引数组linind进行切片。

如果有人有一个(或几个)线索引技巧来来回之间的多维指数和线性指数的方式,矢量化所有N粒子的操作,我会感谢你的洞察力。

2 回复 | 直到 15 年前

Eric O. Lebigot 15 年前

您可以简单地计算每个箱子的索引:

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

标量积只做1*x0+5*x1+5*5*x2+这是通过NumPy的 dot() .

JoshAdel 15 年前

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')

现在进行转换

# 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)

并检查其正确性:

# 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)

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