Re: [Numpy-discussion] Interleaved Arrays and
Most excellent solutions, thanks! ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Interleaved Arrays and
Ian Mallett wrote: n = #blah testlist = [] for x in xrange(n): for y in xrange(n): testlist.append([x,y]) testlist.append([x+1,y]) If testlist is an array (i.e., I could go: array(testlist)), it works nicely. However, my Python method is certainly improveable with numpy. I suspect the best way is interleaving the arrays [x,y-yn] and [x+1,y-yn] n times, but I couldn't figure out how to do that... e.g with column_stack n = 10 xx = np.ones(n) yy = np.arange(n) aa = np.column_stack((xx,yy)) bb = np.column_stack((xx+1,yy)) aa array([[ 1., 0.], [ 1., 1.], [ 1., 2.], [ 1., 3.], [ 1., 4.], [ 1., 5.], [ 1., 6.], [ 1., 7.], [ 1., 8.], [ 1., 9.]]) bb array([[ 2., 0.], [ 2., 1.], [ 2., 2.], [ 2., 3.], [ 2., 4.], [ 2., 5.], [ 2., 6.], [ 2., 7.], [ 2., 8.], [ 2., 9.]]) np.column_stack((aa,bb)) array([[ 1., 0., 2., 0.], [ 1., 1., 2., 1.], [ 1., 2., 2., 2.], [ 1., 3., 2., 3.], [ 1., 4., 2., 4.], [ 1., 5., 2., 5.], [ 1., 6., 2., 6.], [ 1., 7., 2., 7.], [ 1., 8., 2., 8.], [ 1., 9., 2., 9.]]) cc = _ cc.reshape((n*2,2)) array([[ 1., 0.], [ 2., 0.], [ 1., 1.], [ 2., 1.], [ 1., 2.], [ 2., 2.], [ 1., 3.], [ 2., 3.], [ 1., 4.], [ 2., 4.], [ 1., 5.], [ 2., 5.], [ 1., 6.], [ 2., 6.], [ 1., 7.], [ 2., 7.], [ 1., 8.], [ 2., 8.], [ 1., 9.], [ 2., 9.]]) However I feel too, there is a intuitive abbrev function like 'interleave' or so missing in numpy shape_base or so. Robert ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Interleaved Arrays and
On 06/16/2009 02:18 PM, Robert wrote: n = 10 xx = np.ones(n) yy = np.arange(n) aa = np.column_stack((xx,yy)) bb = np.column_stack((xx+1,yy)) aa array([[ 1., 0.], [ 1., 1.], [ 1., 2.], [ 1., 3.], [ 1., 4.], [ 1., 5.], [ 1., 6.], [ 1., 7.], [ 1., 8.], [ 1., 9.]]) bb array([[ 2., 0.], [ 2., 1.], [ 2., 2.], [ 2., 3.], [ 2., 4.], [ 2., 5.], [ 2., 6.], [ 2., 7.], [ 2., 8.], [ 2., 9.]]) np.column_stack((aa,bb)) array([[ 1., 0., 2., 0.], [ 1., 1., 2., 1.], [ 1., 2., 2., 2.], [ 1., 3., 2., 3.], [ 1., 4., 2., 4.], [ 1., 5., 2., 5.], [ 1., 6., 2., 6.], [ 1., 7., 2., 7.], [ 1., 8., 2., 8.], [ 1., 9., 2., 9.]]) cc = _ cc.reshape((n*2,2)) array([[ 1., 0.], [ 2., 0.], [ 1., 1.], [ 2., 1.], [ 1., 2.], [ 2., 2.], [ 1., 3.], [ 2., 3.], [ 1., 4.], [ 2., 4.], [ 1., 5.], [ 2., 5.], [ 1., 6.], [ 2., 6.], [ 1., 7.], [ 2., 7.], [ 1., 8.], [ 2., 8.], [ 1., 9.], [ 2., 9.]]) However I feel too, there is a intuitive abbrev function like 'interleave' or so missing in numpy shape_base or so. Using fancy indexing, you can set strided portions of an array equal to another array. So:: In [2]: aa = np.empty((10,2)) In [3]: aa[:, 0] = 1 In [4]: aa[:,1] = np.arange(10) In [5]: bb = np.empty((10,2)) In [6]: bb[:,0] = 2 In [7]: bb[:,1] = aa[:,1] # this works In [8]: cc = np.empty((20,2)) In [9]: cc[::2,:] = aa In [10]: cc[1::2,:] = bb In [11]: cc Out[11]: array([[ 1., 0.], [ 2., 0.], [ 1., 1.], [ 2., 1.], [ 1., 2.], [ 2., 2.], [ 1., 3.], [ 2., 3.], [ 1., 4.], [ 2., 4.], [ 1., 5.], [ 2., 5.], [ 1., 6.], [ 2., 6.], [ 1., 7.], [ 2., 7.], [ 1., 8.], [ 2., 8.], [ 1., 9.], [ 2., 9.]]) Using this syntax, interleave could be a one-liner. -Neil ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Interleaved Arrays and
Neil Martinsen-Burrell wrote: On 06/16/2009 02:18 PM, Robert wrote: n = 10 xx = np.ones(n) yy = np.arange(n) aa = np.column_stack((xx,yy)) bb = np.column_stack((xx+1,yy)) aa array([[ 1., 0.], [ 1., 1.], [ 1., 2.], [ 1., 3.], [ 1., 4.], [ 1., 5.], [ 1., 6.], [ 1., 7.], [ 1., 8.], [ 1., 9.]]) bb array([[ 2., 0.], [ 2., 1.], [ 2., 2.], [ 2., 3.], [ 2., 4.], [ 2., 5.], [ 2., 6.], [ 2., 7.], [ 2., 8.], [ 2., 9.]]) np.column_stack((aa,bb)) array([[ 1., 0., 2., 0.], [ 1., 1., 2., 1.], [ 1., 2., 2., 2.], [ 1., 3., 2., 3.], [ 1., 4., 2., 4.], [ 1., 5., 2., 5.], [ 1., 6., 2., 6.], [ 1., 7., 2., 7.], [ 1., 8., 2., 8.], [ 1., 9., 2., 9.]]) cc = _ cc.reshape((n*2,2)) array([[ 1., 0.], [ 2., 0.], [ 1., 1.], [ 2., 1.], [ 1., 2.], [ 2., 2.], [ 1., 3.], [ 2., 3.], [ 1., 4.], [ 2., 4.], [ 1., 5.], [ 2., 5.], [ 1., 6.], [ 2., 6.], [ 1., 7.], [ 2., 7.], [ 1., 8.], [ 2., 8.], [ 1., 9.], [ 2., 9.]]) However I feel too, there is a intuitive abbrev function like 'interleave' or so missing in numpy shape_base or so. Using fancy indexing, you can set strided portions of an array equal to another array. So:: In [2]: aa = np.empty((10,2)) In [3]: aa[:, 0] = 1 In [4]: aa[:,1] = np.arange(10) In [5]: bb = np.empty((10,2)) In [6]: bb[:,0] = 2 In [7]: bb[:,1] = aa[:,1] # this works In [8]: cc = np.empty((20,2)) In [9]: cc[::2,:] = aa In [10]: cc[1::2,:] = bb In [11]: cc Out[11]: array([[ 1., 0.], [ 2., 0.], [ 1., 1.], [ 2., 1.], [ 1., 2.], [ 2., 2.], [ 1., 3.], [ 2., 3.], [ 1., 4.], [ 2., 4.], [ 1., 5.], [ 2., 5.], [ 1., 6.], [ 2., 6.], [ 1., 7.], [ 2., 7.], [ 1., 8.], [ 2., 8.], [ 1., 9.], [ 2., 9.]]) Using this syntax, interleave could be a one-liner. -Neil that method of 'filling an empty with a pattern' was mentioned in the other (general) interleaving question. It requires however a lot of particular numbers and :'s in the code, and requires even more statements which can hardly be written in functional style - in one line?. The other approach is more jount, free of fancy indexing assignments. The general interleaving should work efficiently in one like this: np.column_stack/concatenate((r,g,b,), axis=...).reshape(..) But as all this is not intuitive, something like this should be in numpy perhaps? : def interleave( tup_arrays, axis = None ) Robert ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Interleaved Arrays and
On 2009-06-16 16:05 , Robert wrote: Neil Martinsen-Burrell wrote: On 06/16/2009 02:18 PM, Robert wrote: n = 10 xx = np.ones(n) yy = np.arange(n) aa = np.column_stack((xx,yy)) bb = np.column_stack((xx+1,yy)) aa array([[ 1., 0.], [ 1., 1.], [ 1., 2.], [ 1., 3.], [ 1., 4.], [ 1., 5.], [ 1., 6.], [ 1., 7.], [ 1., 8.], [ 1., 9.]]) bb array([[ 2., 0.], [ 2., 1.], [ 2., 2.], [ 2., 3.], [ 2., 4.], [ 2., 5.], [ 2., 6.], [ 2., 7.], [ 2., 8.], [ 2., 9.]]) np.column_stack((aa,bb)) array([[ 1., 0., 2., 0.], [ 1., 1., 2., 1.], [ 1., 2., 2., 2.], [ 1., 3., 2., 3.], [ 1., 4., 2., 4.], [ 1., 5., 2., 5.], [ 1., 6., 2., 6.], [ 1., 7., 2., 7.], [ 1., 8., 2., 8.], [ 1., 9., 2., 9.]]) cc = _ cc.reshape((n*2,2)) array([[ 1., 0.], [ 2., 0.], [ 1., 1.], [ 2., 1.], [ 1., 2.], [ 2., 2.], [ 1., 3.], [ 2., 3.], [ 1., 4.], [ 2., 4.], [ 1., 5.], [ 2., 5.], [ 1., 6.], [ 2., 6.], [ 1., 7.], [ 2., 7.], [ 1., 8.], [ 2., 8.], [ 1., 9.], [ 2., 9.]]) However I feel too, there is a intuitive abbrev function like 'interleave' or so missing in numpy shape_base or so. Using fancy indexing, you can set strided portions of an array equal to another array. So:: In [2]: aa = np.empty((10,2)) In [3]: aa[:, 0] = 1 In [4]: aa[:,1] = np.arange(10) In [5]: bb = np.empty((10,2)) In [6]: bb[:,0] = 2 In [7]: bb[:,1] = aa[:,1] # this works In [8]: cc = np.empty((20,2)) In [9]: cc[::2,:] = aa In [10]: cc[1::2,:] = bb In [11]: cc Out[11]: array([[ 1., 0.], [ 2., 0.], [ 1., 1.], [ 2., 1.], [ 1., 2.], [ 2., 2.], [ 1., 3.], [ 2., 3.], [ 1., 4.], [ 2., 4.], [ 1., 5.], [ 2., 5.], [ 1., 6.], [ 2., 6.], [ 1., 7.], [ 2., 7.], [ 1., 8.], [ 2., 8.], [ 1., 9.], [ 2., 9.]]) Using this syntax, interleave could be a one-liner. -Neil that method of 'filling an empty with a pattern' was mentioned in the other (general) interleaving question. It requires however a lot of particular numbers and :'s in the code, and requires even more statements which can hardly be written in functional style - in one line?. The other approach is more jount, free of fancy indexing assignments. jount? I think that assigning to a strided index is very clear, but that is a difference of opinion. All of the calls to np.empty are the equivalent of the column_stack's in your example. I think that operations on segments of arrays are fundamental to an array-processing language such as NumPy. Using ; you can put as many of those statements as you would like one line. :) The general interleaving should work efficiently in one like this: np.column_stack/concatenate((r,g,b,), axis=...).reshape(..) But as all this is not intuitive, something like this should be in numpy perhaps? : def interleave( tup_arrays, axis = None ) Here is a minimally tested implementation. If anyone really wants this for numpy, I'll gladly add comments and tests. I couldn't figure out how to automatically find the greatest dtype, so I added an argument to specify, otherwise it uses the type of the first array. def interleave(arrays, axis=0, dtype=None): assert len(arrays) 0 first = arrays[0] assert all([arr.shape == first.shape for arr in arrays]) new_shape = list(first.shape) new_shape[axis] *= len(arrays) if dtype is None: new_dtype = first.dtype else: new_dtype = dtype interleaved = np.empty(new_shape, new_dtype) axis_slice = [slice(None, None, None)]*axis + \ [slice(0,None,len(arrays))] + [Ellipsis] for i, arr in enumerate(arrays): axis_slice[axis] = slice(i, None, len(arrays)) interleaved[tuple(axis_slice)] = arr return interleaved ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Interleaved Arrays and
I'm not sure it's worth having a function to replace a one-liner (column_stack followed by reshape). But if you're going to implement this with slice assignment, you should take advantage of the flexibility this method allows and offer the possibility of interleaving raggedly, that is, where the size of the arrays drops at some point, so that you could interleave arrays of size 4, 4, and 3 to get one array of size 11. This allows split and join operations, for example for multiprocessing. On the other hand you should also include a documentation warning that this can be slow when interleaving large numbers of small arrays. Anne 2009/6/16 Neil Martinsen-Burrell n...@wartburg.edu: On 2009-06-16 16:05 , Robert wrote: Neil Martinsen-Burrell wrote: On 06/16/2009 02:18 PM, Robert wrote: n = 10 xx = np.ones(n) yy = np.arange(n) aa = np.column_stack((xx,yy)) bb = np.column_stack((xx+1,yy)) aa array([[ 1., 0.], [ 1., 1.], [ 1., 2.], [ 1., 3.], [ 1., 4.], [ 1., 5.], [ 1., 6.], [ 1., 7.], [ 1., 8.], [ 1., 9.]]) bb array([[ 2., 0.], [ 2., 1.], [ 2., 2.], [ 2., 3.], [ 2., 4.], [ 2., 5.], [ 2., 6.], [ 2., 7.], [ 2., 8.], [ 2., 9.]]) np.column_stack((aa,bb)) array([[ 1., 0., 2., 0.], [ 1., 1., 2., 1.], [ 1., 2., 2., 2.], [ 1., 3., 2., 3.], [ 1., 4., 2., 4.], [ 1., 5., 2., 5.], [ 1., 6., 2., 6.], [ 1., 7., 2., 7.], [ 1., 8., 2., 8.], [ 1., 9., 2., 9.]]) cc = _ cc.reshape((n*2,2)) array([[ 1., 0.], [ 2., 0.], [ 1., 1.], [ 2., 1.], [ 1., 2.], [ 2., 2.], [ 1., 3.], [ 2., 3.], [ 1., 4.], [ 2., 4.], [ 1., 5.], [ 2., 5.], [ 1., 6.], [ 2., 6.], [ 1., 7.], [ 2., 7.], [ 1., 8.], [ 2., 8.], [ 1., 9.], [ 2., 9.]]) However I feel too, there is a intuitive abbrev function like 'interleave' or so missing in numpy shape_base or so. Using fancy indexing, you can set strided portions of an array equal to another array. So:: In [2]: aa = np.empty((10,2)) In [3]: aa[:, 0] = 1 In [4]: aa[:,1] = np.arange(10) In [5]: bb = np.empty((10,2)) In [6]: bb[:,0] = 2 In [7]: bb[:,1] = aa[:,1] # this works In [8]: cc = np.empty((20,2)) In [9]: cc[::2,:] = aa In [10]: cc[1::2,:] = bb In [11]: cc Out[11]: array([[ 1., 0.], [ 2., 0.], [ 1., 1.], [ 2., 1.], [ 1., 2.], [ 2., 2.], [ 1., 3.], [ 2., 3.], [ 1., 4.], [ 2., 4.], [ 1., 5.], [ 2., 5.], [ 1., 6.], [ 2., 6.], [ 1., 7.], [ 2., 7.], [ 1., 8.], [ 2., 8.], [ 1., 9.], [ 2., 9.]]) Using this syntax, interleave could be a one-liner. -Neil that method of 'filling an empty with a pattern' was mentioned in the other (general) interleaving question. It requires however a lot of particular numbers and :'s in the code, and requires even more statements which can hardly be written in functional style - in one line?. The other approach is more jount, free of fancy indexing assignments. jount? I think that assigning to a strided index is very clear, but that is a difference of opinion. All of the calls to np.empty are the equivalent of the column_stack's in your example. I think that operations on segments of arrays are fundamental to an array-processing language such as NumPy. Using ; you can put as many of those statements as you would like one line. :) The general interleaving should work efficiently in one like this: np.column_stack/concatenate((r,g,b,), axis=...).reshape(..) But as all this is not intuitive, something like this should be in numpy perhaps? : def interleave( tup_arrays, axis = None ) Here is a minimally tested implementation. If anyone really wants this for numpy, I'll gladly add comments and tests. I couldn't figure out how to automatically find the greatest dtype, so I added an argument to specify, otherwise it uses the type of the first array. def interleave(arrays, axis=0, dtype=None): assert len(arrays) 0 first = arrays[0] assert all([arr.shape == first.shape for arr in arrays]) new_shape = list(first.shape) new_shape[axis] *= len(arrays) if dtype is None: new_dtype = first.dtype else: new_dtype = dtype interleaved = np.empty(new_shape, new_dtype) axis_slice = [slice(None, None, None)]*axis + \
[Numpy-discussion] Interleaved Arrays and
Hi, So I'm trying to get a certain sort of 3D terrain working in PyOpenGL. The idea is to get vertex buffer objects to draw a simple 2D plane comprised of many flat polygons, and use a vertex shader to deform that with a heightmap and map that on a sphere. I've managed to do this with a grid (simple points), making the vertex buffer object: threedimensionalgrid = dstack(mgrid[0:size,0:size,0:1])/float(size-1) twodimensionalgrid = threedimensionalgrid.reshape(self.size_squared,3) floattwodimensionalgrid = array(twodimensionalgrid,f) self.vertex_vbo = vbo.VBO(floattwodimensionalgrid) However, landscapes tend to be, um, solid :D So, the landscape needs to be drawn as quads or triangles. Strips of triangles will be most effective, and the data must be specified to vbo.VBO() in a certain way: n = #blah testlist = [] for x in xrange(n): for y in xrange(n): testlist.append([x,y]) testlist.append([x+1,y]) If testlist is an array (i.e., I could go: array(testlist)), it works nicely. However, my Python method is certainly improveable with numpy. I suspect the best way is interleaving the arrays [x,y-yn] and [x+1,y-yn] ntimes, but I couldn't figure out how to do that... Help? Thanks, Ian ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
