How to download & install RStudio?

RStudio is an integrated development environment (IDE) for R, a programming language for statistical computing and graphics.

RStudio can be downloaded in two formats.

RStudio Desktop: a regular desktop application.

RStudio Server: runs on a remote server to get access through a web browser.

The latest version of RStudio can be downloaded from

https://rstudio.com/products/rstudio/download/

Once the appropriate 'Download' is clicked, the page will be redirected to Download page.

Once it is downloaded and installed, it can be opened through its shortcut icon.

RStudio will have four section.

Script Section
Console Section
Environment Section
Plot Section

Script Section: To write the code of R programming.

Console Section: To execute the code.

Environment Section: To display Data and values of parameters.

Plot Section: To display the different type of plots.

Exercise 2 - Amdahl's Law

A programmer has parallelized 99% of a program, but there is no value in increasing the problem size, i.e., the program will always be run with the same problem size regardless of the number of processors or cores used. What is the expected speedup on 20 processors? Solution As per Amdahl's law, the speedup, N - No of processors = 20 f - % of parallel operation = 99% = 1 / (1 - 0.99) + (0.99 / 20) = 1 / 0.01 + (0.99 / 20) = 16.807 The expected speedup on 20 processors is 16.807

Exercise 1 - Amdahl's Law

A programmer is given the job to write a program on a computer with processor having speedup factor 3.8 on 4 processors. He makes it 95% parallel and goes home dreaming of a big pay raise. Using Amdahl’s law, and assuming the problem size is the same as the serial version, and ignoring communication costs, what is the speedup factor that the programmer will get? Solution Speedup formula as per Amdahl's Law, N - no of processor = 4 f - % of parallel operation = 95% Speedup = 1 / (1 - 0.95) + (0.95/4) = 1 / 0.5 + (0.95/4) Speedup = 3.478 The programmer gets 3.478 as t he speedup factor.

Minor, Cofactor, Determinant, Adjoint & Inverse of a Matrix

Consider a matrix Minor of a Matrix I n the above matrix A, the minor of first element a 11 shall be Cofactor The Cofactor C ij of an element a ij shall be When the sum of row number and column number is even, then Cofactor shall be positive, and for odd, Cofactor shall be negative. The determinant of an n x n matrix can be defined as the sum of multiplication of the first row element and their respective cofactors. Example, For a 2 x 2 matrix Cofactor C 11 = m 11 = | a 22 | = a 22 = 2 Determinant The determinant of A is |A| = (3 x 2) - (1 x 1) = 5 Adjoint or Adjucate The Adjoint matrix of A , adjA is the transpose of its cofactor matrix. Inverse Matrix A matrix should be square matrix to have an inverse matrix and also its determinant should not be zero. The multiplication of matrix and its inverse shall be Identity matrix. The square matrix has no inverse is called Singular. Inv A = adjA / |A| [ adjoint A / determ...

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