C++ Programming Assignment

Background This exercise is on programming of some statistical functions. No preliminary knowledge of statistics is required. All necessary concepts are explained in this section. Standard deviation Standard deviation is a popular measure of variability or diversity of data used in statistics. If we have some set of data, each data point being a real or rational number (e.g. hight of a person expressed in cm), then low standard deviation indicates that the data points tend to be very close to the mean value, while high standard deviation indicates that the data points are spread over a large range of values, far away from the mean value. The standard deviation1 is defined as follows. For a set of data points X = {x1, x2, . . . , xn} its mean value is mean(X) = x1+x2+...+xn n . Then the standard deviation of X is the value X = s (x1 − mean(X))2 + (x2 − mean(X))2 + . . . + (xn − mean(X))2 n . Pearson correlation coefficient Assume now that we have two data sets of equal size X = {x1, . . . , xn} and X = {y1, . . . yn} and we would like to find out if there is some correlation between the values xi and yi. For example, if xi and yi represent the height and the weight of a person, respectively, then, perhaps, there is some correlation. On the other hand, if xi and yi represent the height of a person and his/her performance in COMP528, then I doubt that there is a correlation. There are different ways to measure the correlation between two data sets. Perhaps, the most popular is a Pearson correlation coefficient, which is defined as follows. For two data sets X = {x1, . . . , xn} and Y = {y1, . . . , yn}, their Pearson coefficient X,Y = 1 ni=n i=1 (xi − mean(X)) · (yi − mean(Y )) X · Y where X and Y are standard deviations of X and Y , respectively, as defined above. The Pearson correlation coefficient always has the value in between −1 and 1. The closer it to 1 the more indication of the correlation between data values2. If you would like to learn more on the standard deviation and Pearson correlation, the Wikipedia entries are good starting points. 1we use here so called population standard deviation, there are other versions, which are not of our concern 2notice that Pearson correlation coefficient captures only one type of the correlation that is a linear dependence 2 Computing the Pearson correlation coefficient asks you to write a program computing Pearson correlation coefficient using parallel loop templates from Intel Threading Building Blocks library (TBB). The input data are given in two arrays a and b of values of type double. The length of each array is 100000. You need to write a C++ program which • implements a serial (not using parallelism) algorithm for computing Pearson correlation coefficient of data presented in arrays a and b; • implements a parallel algorithm using parallel loop templates from TBB library for computing the same; • for a given data computes the Pearson correlation by both serial and parallel algorithm; • prints out the results of both algorithms and the acceleration achieved by paralleliza- tion; The program speed will be evaluated using particular initialization of the arrays by the values of the trigonometric functions sine and cosine applied to the indexes, that is a[i] = sin(i) and b[i] = cosin(i).