![]() ![]() ![]() The vector parallel to a given vector and unit in magnitude is denoted by a. ![]() That is why the vector is called a unit parallel vector. The unit vector parallel to the given vector gives the vector in the same direction as the previous vector, but the magnitude of that unit vector is 1. Easy formulas to determine if a set of vectors is a parallel vector Therefore, the cross-product of two parallel vectors is nothing but the zero vector. Using the definition of the cross product of vectors, we have, Let us assume two vectors, v and w, which are parallel. The Cross product of the vector is always a zero vector when the vectors are parallel Therefore, the dot product of two parallel vectors can be determined by just taking the product of the magnitudes. Using the definition of the dot product of vectors, we have, The dot product of the vector is calculated by taking the product of the magnitudes of both vectors. In the above one where v = bw, (‘b’ is a scalar) v and w are in the same direction if b > 0, i.e., the scalar is positive, and both the vectors v and w are in opposite directions if b < 0, that is the scalar is negative. Two vectors v and w are parallel to each other if v = bw, where ‘b’ is a scalar. That means we can have more than two vectors.Īny vector a is always parallel to itself, i.e., a is always parallel to a. Collinear vector means that the two parallel vectors are always parallel to the same line, but they may or may not be in the same direction. Parallel vectors are sometimes known as a set of collinear vectors. Now, these two vectors are always parallel to each other. ![]() The parallel vectors are vectors that are in the same direction or exactly the opposite direction, which means if we have any vector v, which is one vector, its opposite vector will be -v. Another way to say it is: Two vectors a and b are called parallel if and only if the angle they form between them is zero degrees or 0°.Ī pictorial representation of the parallel vector, which is in the same direction, is given in Figure I:Ī pictorial representation of the parallel vector, which is in opposite directions, is given in Figure II:Ī pictorial representation of non-parallel vectors, i.e., vectors that are not parallel, is given below in Figure III: The two following methods are almost the same and allow a simple syntax.Two vectors a and b are called parallel if the angle they form from the vertical axis or the horizontal axis (not necessarily together) is the same or equal. cout << "Hello World! Thread ID, " << tid << endl Ĭout << "main() : creating thread, " << i << endl Ĭout << "Error:unable to create thread," << rc << endl Īlso remember while compiling you have to use the -lpthread flag.Īs this thread has been my answer almost every time I've looked for a method to parallelize something, I've decided to add a bit to it, based on the method by arkan (see his answer). Single thread execution (for easy debugging)įor(unsigned i = 0 i < nb_threads ++i) My_threads = std::thread(functor, start, start+batch_size) Unsigned batch_remainder = nb_elements % nb_threads Unsigned batch_size = nb_elements / nb_threads Unsigned nb_threads = nb_threads_hint = 0 ? 8 : (nb_threads_hint) Unsigned nb_threads_hint = std::thread::hardware_concurrency() / "start" is the first index to process (included) until the index "end" / your function processing a sub chunk of the for loop. Here is the usage: /// Say you want to parallelize this:įinally here is the implementation of parallel_for(), just paste in a header file and use it at will: #include My function parallel_for() (define later in the post) splits a for loop into smaller chunks (sub loops), and each chunk assigned to a thread. With C++11 you can parallelize a for loop with only a few lines of code. ![]()
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