Re: [Numpy-discussion] 3D array and the right hand rule
Hello, Sorry to disturb again, but the topic still bugs me somehow... I'll try to rephrase the question: - What's the influence of the type of N-array representation with respect to TENSOR-calculus? - Are multiple representations possible? - I assume that the order of the dimensions plays a major role in for example TENSOR product. Is this assumption correct? As I said before, my math skills are lacking in this area... I hope you consider this a valid question. kind regards, Dieter On Fri, Jan 30, 2015 at 2:32 AM, Alexander Belopolsky ndar...@mac.com wrote: On Mon, Jan 26, 2015 at 6:06 AM, Dieter Van Eessen dieter.van.ees...@gmail.com wrote: I've read that numpy.array isn't arranged according to the 'right-hand-rule' (right-hand-rule = thumb = +x; index finger = +y, bend middle finder = +z). This is also confirmed by an old message I dug up from the mailing list archives. (see message below) Dieter, It looks like you are confusing dimensionality of the array with the dimensionality of a vector that it might store. If you are interested in using numpy for 3D modeling, you will likely only encounter 1-dimensional arrays (vectors) of size 3 and 2-dimensional arrays (matrices) of size 9 or shape (3, 3). A 3-dimensional array is a stack of matrices and the 'right-hand-rule' does not really apply. The notion of C/F-contiguous deals with the order of axes (e.g. width first or depth first) while the right-hand-rule is about the direction of the axes (if you flip the middle finger right hand becomes left.) In the case of arrays this would probably correspond to little-endian vs. big-endian: is a[0] stored at a higher or lower address than a[1]. However, whatever the answer to this question is for a particular system, it is the same for all axes in the array, so right-hand - left-hand distinction does not apply. ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion -- gtz, Dieter VE ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] 3D array and the right hand rule
On 17 Mar 2015, at 09:11, Dieter Van Eessen dieter.van.ees...@gmail.com wrote: Hello, Sorry to disturb again, but the topic still bugs me somehow... I'll try to rephrase the question: - What's the influence of the type of N-array representation with respect to TENSOR-calculus? - Are multiple representations possible? - I assume that the order of the dimensions plays a major role in for example TENSOR product. Is this assumption correct? As I said before, my math skills are lacking in this area... I hope you consider this a valid question. kind regards, Dieter On Fri, Jan 30, 2015 at 2:32 AM, Alexander Belopolsky ndar...@mac.com wrote: On Mon, Jan 26, 2015 at 6:06 AM, Dieter Van Eessen dieter.van.ees...@gmail.com wrote: I've read that numpy.array isn't arranged according to the 'right-hand-rule' (right-hand-rule = thumb = +x; index finger = +y, bend middle finder = +z). This is also confirmed by an old message I dug up from the mailing list archives. (see message below) Dieter, It looks like you are confusing dimensionality of the array with the dimensionality of a vector that it might store. If you are interested in using numpy for 3D modeling, you will likely only encounter 1-dimensional arrays (vectors) of size 3 and 2-dimensional arrays (matrices) of size 9 or shape (3, 3). A 3-dimensional array is a stack of matrices and the 'right-hand-rule' does not really apply. The notion of C/F-contiguous deals with the order of axes (e.g. width first or depth first) while the right-hand-rule is about the direction of the axes (if you flip the middle finger right hand becomes left.) In the case of arrays this would probably correspond to little-endian vs. big-endian: is a[0] stored at a higher or lower address than a[1]. However, whatever the answer to this question is for a particular system, it is the same for all axes in the array, so right-hand - left-hand distinction does not apply. Hi, let us say you have an n-dimensional rank k tensor. Then you could represent that beast as a numpy array of dimension k*n. So, if n is 4 and k is 2 you have a 4D tensor of rank 2. This tensor would be an array of shape (4,4). If you want to have higher order tensors you have higher dimensional arrays, a tensor of rank 3 would be an array of shape (4,4,4) in this example. Of course you have to be careful over which axes you do tensor operations. Something like V_ik = C_ijk v_j would then mean that you want to sum over the first axis of the 3-dimensional array C (of shape (4,4,4) and along the zero-axis of the 1-dimensional array v_j (of shape (4,)). By the way, of you think about doing those things, np.einsum might help. Of course, knowing which axis in the numpy array corresponds to which axis (or index) in your tensor is quite important. Hanno ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] 3D array and the right hand rule
Ok, thanks for the reply! Indeed, I know about the use of transformation matrices to manipulate points in space. That's all matrix manipulation anyway But, (and perhaps this is not the right place to ask the following question): But are there no known mathmatical algorithms which involve the use of 3n arrays (or higher dimensions) to transform an object between one state and the other? This is an open question, as my knowledge of math is lacking on this area. I'm currently limited to 3D object manipulation and some statistics which all rely on matrix calculus... kind regards, Dieter On Fri, Jan 30, 2015 at 2:32 AM, Alexander Belopolsky ndar...@mac.com wrote: On Mon, Jan 26, 2015 at 6:06 AM, Dieter Van Eessen dieter.van.ees...@gmail.com wrote: I've read that numpy.array isn't arranged according to the 'right-hand-rule' (right-hand-rule = thumb = +x; index finger = +y, bend middle finder = +z). This is also confirmed by an old message I dug up from the mailing list archives. (see message below) Dieter, It looks like you are confusing dimensionality of the array with the dimensionality of a vector that it might store. If you are interested in using numpy for 3D modeling, you will likely only encounter 1-dimensional arrays (vectors) of size 3 and 2-dimensional arrays (matrices) of size 9 or shape (3, 3). A 3-dimensional array is a stack of matrices and the 'right-hand-rule' does not really apply. The notion of C/F-contiguous deals with the order of axes (e.g. width first or depth first) while the right-hand-rule is about the direction of the axes (if you flip the middle finger right hand becomes left.) In the case of arrays this would probably correspond to little-endian vs. big-endian: is a[0] stored at a higher or lower address than a[1]. However, whatever the answer to this question is for a particular system, it is the same for all axes in the array, so right-hand - left-hand distinction does not apply. ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion -- gtz, Dieter VE ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] 3D array and the right hand rule
On Mon, Jan 26, 2015 at 6:06 AM, Dieter Van Eessen dieter.van.ees...@gmail.com wrote: I've read that numpy.array isn't arranged according to the 'right-hand-rule' (right-hand-rule = thumb = +x; index finger = +y, bend middle finder = +z). This is also confirmed by an old message I dug up from the mailing list archives. (see message below) Dieter, It looks like you are confusing dimensionality of the array with the dimensionality of a vector that it might store. If you are interested in using numpy for 3D modeling, you will likely only encounter 1-dimensional arrays (vectors) of size 3 and 2-dimensional arrays (matrices) of size 9 or shape (3, 3). A 3-dimensional array is a stack of matrices and the 'right-hand-rule' does not really apply. The notion of C/F-contiguous deals with the order of axes (e.g. width first or depth first) while the right-hand-rule is about the direction of the axes (if you flip the middle finger right hand becomes left.) In the case of arrays this would probably correspond to little-endian vs. big-endian: is a[0] stored at a higher or lower address than a[1]. However, whatever the answer to this question is for a particular system, it is the same for all axes in the array, so right-hand - left-hand distinction does not apply. ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
