Guide to Programming and Algorithms Using R
Format: PDF / Kindle (mobi) / ePub
This easy-to-follow textbook provides a student-friendly introduction to programming and algorithms. Emphasis is placed on the threshold concepts that present barriers to learning, including the questions that students are often too embarrassed to ask. The book promotes an active learning style in which a deeper understanding is gained from evaluating, questioning, and discussing the material, and practised in hands-on exercises. Although R is used as the language of choice for all programs, strict assumptions are avoided in the explanations in order for these to remain applicable to other programming languages. Features: provides exercises at the end of each chapter; includes three mini projects in the final chapter; presents a list of titles for further reading at the end of the book; discusses the key aspects of loops, recursions, program and algorithm efficiency and accuracy, sorting, linear systems of equations, and file processing; requires no prior background knowledge in this area.
the following program can be used: In the above, the program polyevalhorner is used as a function at n points in the range [x min,x max], which are indicated by the inputs xmin, xmax, and n. The polynomial coefficients are again provided by an input vector a. Using the program above as polyevalhornermultiple(c(1,-3,3,-1),0.99999,1.00001,200) one may obtain the oscillatory curve depicted in Fig. 5.5. The correct values of the polynomial are also plotted using the factored form p(x)=(x−1)3,
the elements of the vector are sorted as [−3,1,3,4,5,6]. Figure 6.1 depicts the application of the bubble sort algorithm to this example vector and the elements of the vector at different steps. In this figure, the elements compared are shown as opaque, whereas other elements are transparent. The status of the vector at the end of each step is also shown. Fig. 6.1Application of the bubble sort algorithm to a vector [5,−3,4,6,3,1] and the steps that require swap operations The bubble sort
elimination steps. Now, let us consider the additional time cost due to the partial pivoting. Considering the worst case, i.e., where swapping is required and the pivot is located in the last row in each step, we have Evaluating the summations, we obtain Consequently, considering the time complexity of the Gaussian elimination without pivoting, the additional cost due to the partial pivoting is negligible when n is large. In other words, the Gaussian eliminations with and without partial
systems where x i and e i are the columns of X and I, respectively. When the vectors x i are solved using the Gaussian elimination or the LU factorization, one can obtain X=A −1 as the inverse matrix. Using the Gauss–Jordan elimination is particularly suitable for inverting matrices. Consider an n×2n augmented matrix [A|I]. Using the Gauss–Jordan elimination, we have where D is a diagonal matrix. The rows of the resulting augmented matrix can be further scaled as and the inverse of the
following program: In this program, the command nrow(A) gives the number of rows in the input matrix A. This value is stored in the variable m, similar to the number of columns that is stored in n. Note that different variables, i.e., i and j, are used for the outer and inner loops, respectively. In the program above, the variable sumvalue is reinitialized as zero before each inner loop. Having said this, the following program is incorrect: Using this program, where sumvalue is initialized