R Programming matrix exercises-part2

 

Get element at the specific position from matrix in R

At any point in time, a matrix may be required to be traversed for an element at a specific position. we are going to access the elements from a matrix in R Programming Language using integer vector, logical vector as the index.

Method 1: Accessing elements using integer vector

Integer vector is a vector, that includes all elements of integer type.

Syntax:

matrix_name[row_vector_with_values,column_vector_with_values,]

Example:

select rows 1 & 3 and columns 1 & 3 of matrix a.

print(a )

Program:

# create a vector named data with 9 elements

data=c(1,2,3,4,5,6,7,8,9)

  

# pass this vector to matrix input

a=matrix(data, nrow = 3, ncol = 3)

print(a)

  

# select rows 1 & 3 and columns 1 & 3

print(a[c(1,3),c(1,3)] )   

  

# select rows 1 & 2 and columns 1 & 2

print(a[c(1,2),c(1,2)] )   

  

# select rows 2 & 1 and columns 2 & 2

print(a[c(2,1),c(2,2)] )   

Method 2: Accessing matrix elements using logic vector

Logical vector includes a vector comprising boolean values i.e. TRUE or FALSE.

Syntax :

matrix_name[logical_vector]

If TRUE at that position, matrix element is accessed 

If FALSE at that position, matrix element is not accessed.

Example:

data=c(TRUE,TRUE,FALSE)

Program 1:

# create a vector named data with 9 elements

data=c(1,2,3,4,5,6,7,8,9)

  

# pass this vector to matrix input

a=matrix(data, nrow = 3, ncol = 3)

print(a)

  

a[c(TRUE, FALSE,TRUE, FALSE,TRUE, FALSE,TRUE, FALSE,TRUE)]

# accessing elements 

Program 2:

# create a vector named data with 9 elements

data=c(1,2,3,4,5,6,7,8,9)

  

# pass this vector to matrix input

a=matrix(data, nrow = 3, ncol = 3)

print(a)

  

print(a[c(TRUE)])

# accessing elements by placing all TRUE

  

print(a[c(FALSE)])

# accessing elements by placing all FALSE

Find row and column index of maximum and minimum value in a matrix in R

Finding Maximum value:

·         In the code below, we have created a sample matrix, in which we have passed “nrow=3“(matrix will have only 3 rows) in example 1 and  “ncol=2“(matrix will have only 2 columns) in example 2. 

·         Then we have printed the sample matrix in the next line with the message “Sample Matrix”.

·         Then we have used the syntax below to find the row and column number of the maximum element and stored it in the variable “max”. We have made use of the max() function which is used to find the maximum element present in an object. This object can be a Vector, a list, a matrix, a data frame, etc. 

·         The “which()” function is used to get the index or position of the value which satisfies the given condition. Then we have printed the maximum value along with its row and column index. 

Syntax: which(m == max(m), arr.ind=TRUE)

Example 1:

# defining a sample matrix

m = matrix(c(11, 20, 13, -9, 1, 99, 36, 81, 77), 

           nrow = 3)  

  

print("Sample Matrix:")

print(m)

  

# stores indexes of max value 

max = which(m == max(m), arr.ind = TRUE)  

print(paste("Maximum value: ", m[max]))

print(max)

Example 2:

# defining a sample matrix

m = matrix(c(1:16), ncol = 2)  

print("Sample Matrix:")

print(m)

  

# stores indexes of max value

max = which(m == max(m), arr.ind=TRUE)   

print(paste("Maximum value: ",m[max]))

print(max)

 

Finding Minimum value:

·         In the code below, we have created a sample matrix, in which we have passed “nrow=3“(matrix will have only 3 rows) in example 1 and  “ncol=8“(matrix will have only 8 columns) in example 2 as a parameter while defining the matrix. 

·         Then we have printed the sample matrix in the next line with the message “Sample Matrix”. 

·         Then we have used the syntax below to find the row and column number of the minimum element and stored it in the variable “min”. We have made use of the min() function which is used to find the minimum element present in an object. This object can be a Vector, a list, a matrix, a data frame, etc. 

·         The “which()” function is used to get the index or position of the value which satisfies the given condition. Then we have printed the minimum value along with its row and column index. 

 

 

Syntax: which(m == min(m), arr.ind=TRUE)

Example 1:

# defining a sample matrix

m = matrix(c(11, 20, 13, -9, 1, 99, 36, 81, 77), nrow = 3)  

print("Sample Matrix:")

print(m)

  

# stores indexes of min value

min = which(m == min(m), arr.ind = TRUE)  

print(paste("Minimum value: ", m[min]))

print(min)

Example 2:

# defining a sample matrix

m = matrix(c(1:16), ncol = 8)  

print("Sample Matrix:")

print(m)

  

# stores indexes of min value 

min = which(m == min(m), arr.ind = TRUE) 

print(paste("Minimum value: ", m[min]))

print(min)

 

Select rows of a matrix in R that meet a condition

A large dataset is often required to be filtered according to our requirements. we will be discussing how we can select a row from a matrix in R that meets the condition. For better understanding let’s understand the problem statement with the help of an example.

Example:

Now, as the problem statement is that we want to select the rows of the matrix that meets the given condition. Suppose we want to select the rows from the matrix whose car_color = Red.

pproach:

·         Create dataset

·         Specify the condition

·         Pass it to the matrix

·         Select rows which specify this condition

Syntax:

dataset[condition]

Example:

mat[mat[,”car_color”]==”Red”,]

Here, Comma(‘,’) is used to return all the matrix rows.

·         Copy the resultant dataset to auxiliary dataset

·         Display dataset

# Creating Dataset

 

car_models <- c('Maruti','Hyundai','Tata',

                'Ford','Nissan','Toyota')

 

car_type <- c('Diesel','Petrol','Petrol',

              'Diesel','Petrol','Diesel')

 

car_color <- c('Red','Blue','Red',

               'Red','Blue','Red')

 

year <- c(2001,2011,2013,2012,2021,2021)

 

# Storing matrix in mat (variable)

mat <- cbind(car_models,car_type,car_color,year)

 

# condition to select only rows with

# color = Red

mat <- mat[mat[,"car_color"]=="Red",]

 

# displaying the resultant matrix

mat

How to multiply a matrix by its transpose while ignoring missing values in R ?

The replacement of values, can be performed in O(n*m), where n is the number of rows and m is the number of columns. Replacing by 0s doesn’t affect the multiplicative product, and therefore, this is an effective solution. The transpose can then be calculated by using t(matrix). The product can be calculated by the following syntax in R : 

m1 %*% m2 , where m1 and m2 are the matrices involved. 

If m1 is the matrix of n*m dimensions and m2 of m*n (since it’s the transpose), the product matrix obtained is a square matrix is n * n .

Example 1:

# declaring matrix 

mat = matrix(c(1, NA, 2, 3, NA, 4), ncol = 2)

  

# replacing matrix NA with 0s

mat[is.na(mat)] = 0

  

# printing original matrix

print ("Original Matrix")

print (mat)

  

# calculating transpose of the

# matrix

transmat = t(mat)

print ("Transpose Matrix")

print (transmat)

  

# calculating product of matrices

prod = mat%*%transmat

print ("Product Matrix")

print (prod)

The original matrix is of the dimensions 3 x 2 and the transpose is of the dimension 2×3. On replacing the missing values with 0 and multiplying these two together, we obtain the product matrix equivalent to 3×3 square matrix. 

Example 2: The original matrix is of the dimensions 1 x 3 and the transpose is of the dimension 3×1. On replacing the missing values with 0 and multiplying these two together, we obtain the product matrix equivalent to 1×1 square matrix, which is basically a singular cell matrix. 

# declaring matrix 

mat = matrix(c(10, NA, 7), ncol = 3)

  

# replacing matrix NA with 0s

mat[is.na(mat)] = 0

  

# printing original matrix

print ("Original Matrix")

print (mat)

  

# calculating transpose of the

# matrix

transmat = t(mat)

print ("Transpose Matrix")

print (transmat)

  

# calculating product of matrices

prod = mat%*%transmat

print ("Product Matrix")

print (prod)