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The default matrix multiplication is computed as
c[i,j] = sum(a[i,k] * b[k,j])
I am trying to use a custom formula instead of the dot product to get
c[i,j] = sum(a[i,k] == b[k,j])
Is there an efficient way to do this in numpy?
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Multiplication of two matrices involves dot products between rows of first matrix and columns of the second matrix. The first step is the dot product between the first row of A and the first column of B. The result of this dot product is the element of resulting matrix at position [0,0] (i.e. first row, first column).
If both inputs are 1-dimensional arrays, np. dot() will compute the dot product of the inputs. If both inputs are 2-dimensional arrays, then np. dot() will perform matrix multiplication.
Dot product of two arrays. Specifically, If both a and b are 1-D arrays, it is inner product of vectors (without complex conjugation). If both a and b are 2-D arrays, it is matrix multiplication, but using matmul or a @ b is preferred.
You could use broadcasting:
c = sum(a[...,np.newaxis]*b[np.newaxis,...],axis=1) # == np.dot(a,b)
c = sum(a[...,np.newaxis]==b[np.newaxis,...],axis=1)
I included the newaxis in b just make it clear how that array is expanded. There are other ways of adding dimensions to arrays (reshape, repeat, etc), but the effect is the same. Expand a and b to the same shape to do element by element multiplying (or ==), and then sum on the correct axis.
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