LECTURE 4 Matrices and Arrays

Page 1: Lecture Introduction

• Lecture 4 Outline: Matrices, Arrays, Lists

Page 2: Review of Data Structures

• Data Structures Covered:

  • Scalars

  • Vectors

  • Matrices

  • Arrays

  • Lists

  • Data Frames

Page 3: Understanding Matrices

• Definition:

  • Matrices are R objects with elements arranged in a two-dimensional rectangular layout.

  • All elements must be of the same type.

• Creation:

  • Use matrix() function to create a matrix.

Page 4: Matrix Syntax

• Function Syntax: matrix(data, nrow, ncol, byrow, dimnames)

  • data: Input vector for matrix elements.

  • nrow: Number of rows for the matrix.

  • ncol: Number of columns for the matrix.

  • byrow: Logical value; if TRUE, fills by row, defaults to FALSE (fills by column).

  • dimnames: Names assigned to rows and columns (optional).

Page 5: Matrix Operations

• Practical Demonstration: a) Create a 5 x 4 numeric matrix with elements 1 to 20. b) Select the 3rd column of the matrix. c) Select rows 2, 3, 4 of columns 1, 2, 3. d) Determine the dimensions of the matrix.

Page 6: R Matrices for Statistical Analysis

• Steps:

  1. Construct a matrix using provided data in RStudio, filling by row.

  2. Add appropriate row and column names.

  3. Analyze data: Count people with blond hair and blue eyes.

  4. Perform sum operations on row and column values.

Page 7: Matrix Modification Techniques

• Column Binding: Use cbind() to create a matrix with vector values as columns.

• Row Binding: Use rbind() to create a matrix with vector values as rows.

• Removing Elements: Use subset() function.

• Overwriting Elements: Use [ ] notation for specific elements.

Page 8: Creating and Modifying Matrices

• Practical Tasks:

  • Create vectors a, b, d.

  • Combine a, b, d into matrix CC as columns and matrix CR as rows.

  • Remove column 'a' from matrix CC.

  • Replace the first row of matrix CC with sequence 1:2.

  • Replace the second column of matrix CR with sequence 4:6.

Page 9: Understanding Arrays

• Definition:

  • Arrays are matrices in higher dimensions.

  • Comprised of 2 or more matrices.

  • Accept vectors as input.

Page 10: Array Creation

• Creation Function: array()

  • Syntax: array(data=NA, dim=length(data), dimnames=NULL)

    • data: Values used to fill the array.

    • dim: Dimensions of the array defined by the length of the data.

    • dimnames: Optional list of names for the dimensions.

Page 11: Practical Array Tasks

• Tasks:

  1. Create an array of two 3x3 matrices.

  2. Modify the matrix to include:

     • a) Column names

     • b) Row names

     • c) Matrix names.

Page 12: Calculations Across Arrays

• Syntax for Function Application:

  • apply(x, margin, fun)

    • x: The array.

    • margin: Indicates rows/columns for function application (1 for rows, 2 for columns, c(1, 2) for both).

    • fun: The function to apply across the array.

Page 13: Array Calculations Demonstration

• Vectors:

  • aaa <- c(2,3,4,6)

  • bbb <- c(5,6,10,12,45)

  • Instructions:

    1. Create an array with two 3x4 matrices from aaa and bbb.

    2. Sum the rows.

    3. Sum the columns.

    4. Sum the individual cells.

Page 14: Additional Matrix Insights

• Points of Interest:

  • Code examples shown in lecture.

  • Methods to create integer/numeric vectors.

  • Converting vectors to matrices.

  • Changing column and row names.

  • byrow option/argument explanations.

Page 15: Introduction to Lists

• Definition:

  • A list in R can contain objects of any type, including other lists.

  • Useful for statistical tests that return lists.

  • Created using the list() function.

  • Lists help organize and manipulate data efficiently.

Page 16: Working with Lists

• Key Topics:

  • Creating a list.

  • Accessing elements within a list.

  • Adding new elements to a list.

Page 17: Summary

• Covered data structures:

  • Matrices

  • Arrays

  • Lists.

Page 18: Next Lecture Preview

• Topics: Logical Values and Factors.

• Focus: Applied Statistical Computing and Graphics.