Читать книгу Algorithms For Dummies - John Paul Mueller, John Mueller Paul, Luca Massaron - Страница 84

Adding, subtracting, or dividing vectors occurs on an element-by-element basis, as described in the previous section. However, when it comes to multiplication, things get a little odd. In fact, depending on what you really want to do, things can become quite odd indeed. Consider the sort of multiplication discussed in the previous section. Both myVect * myVect and np.multiply(myVect, myVect) produce an element-by-element output of [ 1, 4, 9, 16] when starting with an array of [1, 2, 3, 4].

Unfortunately, an element-by-element multiplication can produce incorrect results when working with algorithms. In many cases, what you really need is a dot product, which is the sum of the products of two number sequences. When working with vectors, the dot product is always the sum of the individual element-by-element multiplications and results in a single number. For example, myVect.dot(myVect) results in an output of 30. If you sum the values from the element-by-element multiplication, you find that they do indeed add up to 30. The discussion at https://www.mathsisfun.com/algebra/vectors-dot-product.html tells you about dot products and helps you understand where they might fit in with algorithms. You can learn more about the linear algebra manipulation functions for numpy at https://numpy.org/doc/stable/reference/routines.linalg.html.