The second uses indexing in the function body to access the components. The first uses the components and is arguably, much easier to read. These can be defined in terms of the vector's components or the vector as a whole, as below:į ( x, y, z ) = x ^ 2 + y ^ 2 + z ^ 2 f ( v ) = v ^ 2 + v ^ 2 + v ^ 2 f (generic function with 2 methods) Another use of splatting we will see is with functions of vectors. Whereas the quiver argument expects a tuple of vectors, so no splatting is used for that part of the definition. The unzip function returns these in a container, so splatting is used to turn the values in the container into distinct arguments of the function. The quiver function expects 2 (or 3) arguments describing the xs and ys (and sometimes zs). It was used above in the definition for the arrow! function: essentially quiver!(unzip()., quiver=unzip()). ", to "splat" the values from a container like a vector (or tuple) into arguments of a function can be very convenient. ", in a few ways to simplify usage when containers, such as vectors, are involved: (Though here it is redundant, as that package is loaded when the CalculusWithJulia package is loaded.) Aside: review of Julia's use of dots to work with containers The norm function is in the standard library, LinearAlgebra, which must be loaded first through the command using LinearAlgebra. To see that a unit vector has the same "direction" as the vector, we might draw them with different widths: using LinearAlgebra v = u = v / norm ( v ) p = plot ( legend = false ) arrow! ( p, v ) arrow! ( p, u, linewidth = 5 ) Mathematically, the notation for a point is $p=(x,y,z)$ while the notation for a vector is $\vec$) by imagining the point as a vector anchored at the origin. Vectors and points are related, but distinct. (The direction is undefined in the case the magnitude is $0$.) Vectors are typically visualized with an arrow, where the anchoring of the arrow is context dependent and is not particular to a given vector. A vector mathematically is a geometric object with two attributes a magnitude and a direction. For example, create a 2-by-3 matrix and add an additional row and column to it by inserting an element in the (3,4) position. MATLAB automatically pads the matrix with zeros to keep it rectangular. 0.5849248 1.97291039 0.52678525 0.78435948 0.0107882 You can add one or more elements to a matrix by placing them outside of the existing row and column index boundaries. To create a three-dimensional array of different size we would need to use the proper number of rows and columns within the array function. Also, all the elements in an array are of same data type. A three-dimensional array can have matrices of different size and they are not necessarily to be square or rectangular.
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