8/27/2023 0 Comments Armor python script dim destiny 2You just think about the "middle" axes being dotted, and disappearing from the resultant shape. However, I don't really recommend trying to visualize NumPy arrays this way - at least I never do. If you want to visualize this: np.dot(V, M) looks as though V has 1 row and 2 columns: ] * ,Īnd so, when V is multiplied by M, np.dot(V, M) equals, [2, The last (and only) axis of V and the second-to-last axis of M (aka the first axis of M) are multiplied and summed over, leaving only the last axis of M. So np.dot(V,M) is like matrix multiplication of a (2,)-shaped matrix with a (2,2)-shaped matrix, which should result in a (2,)-shaped matrix. Look at the shape of V and M: In : V.shape There is no surprise here this is just matrix-vector multiplication. In : M = np.arange(4).reshape(2,2) Mįirst, the easy part: In : np.dot(M, V) Let's see how this rule looks when applied to In : V = np.arange(2) V An array of shape (u,v,M) dotted with an array of shape (w,x,y,M,z) would result in an array of shape (u,v,w,x,y,z). "For N dimensions it is a sum product over the last axis of a and the This is the property that np.dot preserves while generalizing to arrays of higher dimension. The resultant shape can be thought of as being formed by squashing the two shapes together ( (N,M,M,P)) and then removing the middle numbers, M (to produce (N,P)). In regular matrix multiplication, an (N,M)-shape matrix multiplied with a (M,P)-shaped matrix results in a (N,P)-shaped matrix. Np.dot is a generalization of matrix multiplication. (*) Arrays of dtype=object are a bit of an exception, since they treat any Python object as a scalar. The rule "sum product over the last axis of a and the second-to-last of b" matches and generalizes the common definition of matrix multiplication. as a (1, n, 1)-shaped array, but these are quite rare.) np.dot performs vector multiplication when both arguments are 1-d, matrix-vector multiplication when one argument is 1-d and the other is 2-d, and otherwise it performs a (generalized) matrix multiplication: > A = np.random.randn(2, 3)Īrray()Īrray(]) Now regarding np.dot, what you have to understand is that there are three ways to represent a vector in NumPy: 1-d array, a column vector of shape (n, 1) or a row vector of shape (1, n). To be honest, I find this definition of "rank" confusing since it matches neither the name of the attribute ndim nor the linear algebra definition of rank. The rank of X is its number of dimensions: > X.ndimĪxis is roughly synonymous with dimension it's used in broadcasting operations: > X.sum(axis=0) Indexing twice gives a 1-d array (vector), and indexing three times gives a scalar. Indexing once gives a 2-d array (matrix): > X it's the number of scalar indices you need to obtain a scalar value.(*)Į.g., this is a 3-d array: > X = np.arange(24).reshape(2, 3, 4) I don't understand like if V is a N:1 vector and M is N:N matrix, how dot(V,M) or dot(M,V) work and the difference between them.Ĭan anyone then please explain to me what is a N dimensional array, what's a shape, what's an axis and how does it relate to the documentation of the dot() function? It would be great if the explanation visualizes the ideas.ĭimensionality of NumPy arrays must be understood in the data structures sense, not the mathematical sense, i.e. I'm so confused and unable to understand this. I don't understand for example the dot() documentation when it says "For N dimensions it is a sum product over the last axis of a and the second-to-last of b". But I really I am unable to go out side the thinking of a 2D matrices. Then all I can think of is a 2x3 matrix (two rows and three columns). So if you say that A is a matrix that looks like this: A = My mind seems to be stuck at the matrix representation. I read several tutorials and still so confused between the differences in dim, ranks, shape, aixes and dimensions.
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