Now the dot product only defines the angle between both vectors. In the graph below we can see that the vectors \(\color = 1 \cdot 1 \cdot \cos \theta = \cos \theta\] Since vectors represent directions, the origin of the vector does not change its value. Because it is more intuitive to display vectors in 2D (rather than 3D) you can think of the 2D vectors as 3D vectors with a z coordinate of 0. If a vector has 2 dimensions it represents a direction on a plane (think of 2D graphs) and when it has 3 dimensions it can represent any direction in a 3D world.īelow you'll see 3 vectors where each vector is represented with (x,y) as arrows in a 2D graph. Vectors can have any dimension, but we usually work with dimensions of 2 to 4. The directions for the treasure map thus contains 3 vectors. In this context, a scalar is any real number. You can think of vectors like directions on a treasure map: 'go left 10 steps, now go north 3 steps and go right 5 steps' here 'left' is the direction and '10 steps' is the magnitude of the vector. In addition to multiplying two vectors, you can also multiply a vector by a scalar. A vector has a direction and a magnitude (also known as its strength or length). So you would need to create a new Mat instance of the same size and type, initialised with the scalar value you want to multiply by. In its most basic definition, vectors are directions and nothing more. If the subjects are difficult, try to understand them as much as you can and come back to this chapter later to review the concepts whenever you need them. The focus of this chapter is to give you a basic mathematical background in topics we will require later on. However, to fully understand transformations we first have to delve a bit deeper into vectors before discussing matrices. When discussing matrices, we'll have to make a small dive into some mathematics and for the more mathematically inclined readers I'll post additional resources for further reading. Matrices are very powerful mathematical constructs that seem scary at first, but once you'll grow accustomed to them they'll prove extremely useful. This doesn't mean we're going to talk about Kung Fu and a large digital artificial world. There are much better ways to transform an object and that's by using (multiple) matrix objects. Stata has two matrix programming languages, one that might be called Statas older matrix. We could try and make them move by changing their vertices and re-configuring their buffers each frame, but that's cumbersome and costs quite some processing power. every element of a matrix by the same number (scalar multiplication). We now know how to create objects, color them and/or give them a detailed appearance using textures, but they're still not that interesting since they're all static objects. 1.1 Entering and addressing matrices and matrix. It's encouraging to know there is an optimized library to do it anyway (I was expecting MKL would directly provide this kind of common operations).Transformations Getting-started/Transformations Right now I guess I will just write the plain subroutine to do the job, hope it still has a good performance. So it is a separate package independent of ifort or MKL? It looks like the server I am working on doesn't have the package. In-place operations on floating point data.Ĭase 4. Not-in-place operations on integer data.Ĭase 3. Not-in-place operations on floating point data.Ĭase 2. One version performs the operation in-place, while the other stores the results of the operation in a different destination vector, that is, executes an out-of-place operation.Īdds a constant value to each element of a vectorĬase 1. Intel IPP software provides two versions of each function. The arithmetic functions include basic element-wise arithmetic operations between vectors, as well as more complex calculations such as computing absolute values, square and square root, natural logarithm and exponential of vector elements. This section describes the Intel IPP signal processing functions that perform vector arithmetic operations on vectors. But I d recommend you draw attention on IPP ( Intel Integrating Primitives, see the link on IPP: )
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