Updated April 17, 2023

## Introduction to Sparse Matrix in C

The following article provides an outline for Sparse Matrix in C. Sparse matrix is a type of matrix which is used in almost every programming language, numerical analysis and computational problems. The sparse matrix consists of a sparse array which has all the elements in the format of zero. There is no strict rule that elements present within the matrix will be zero; rather, the sparse can be roughly designed in rows and columns comprising elements that can have zeros as value. A sparse matrix having most of the zeros in rows and columns instead of other digit is called a dense Matrix.

**Syntax of Sparse Matrix in C**

There is no specific syntax to be followed, but certain steps and data structures will be used for manipulation and working, which includes the following algorithm in it and is represented as follows.

```
main()
{
Define a sparse matrix
int sp_mtrx [] [] = {
{} {} {} {}
};
Calculate the size of the matrix defined;
for {
if {
}
else {
}
}
Define and estimate the size of final matrix;
Int mt_[4] [size]
Compute the final matrix that is being sparsed;
for
{
If
{
}
else
{
}
}
Display the final matrix.
```

### How Sparse Matrix Works in C?

- A sparse matrix not only in the C programming language but also to any computational and analysis process is quite useful. In a sense, it helps in making a matrix divided and represented in a two-dimensional array with a and b two columns representing a*b matrix.
- Since most of the elements involved within the matrix are zero thus, it is called a density matrix alternatively. Most of the elements as zero give a clear indication towards a sparse matrix.
- Sometimes a question arises that when a simple matrix already exists, why it is required to have a sparse matrix?
- The answer lies in the fact that any simple matrix is just used to store the elements in memory, whereas the sparse matrix has a lot more significance like it contains more number of zeros and less of non-zeros; therefore, the storage space required to store such non-zeros element is eliminated since the main focus is on handling zero elements of a matrix.
- The computational time for the elements, especially non-zero elements present in a sparse matrix, saves a lot of computation time as it has many non-zero elements, which logically design some kind of data structure for traversal of traversal of non-zero elements.
- 2 Dimensional representation of sparse matrix by a 2D array leads to wastage of memory. Also, a number of zeros present in any of the sparse matrix with a blend of a number of non-zeros are somehow consumed time which gets reduced on the usage of a sparse matrix with respect to both computations, storage space and traversal time as well.
- Representation of sparse matrix is basically performed in two ways with stored triples or attributes in rows, columns using array representation and linked list representation.
- Array representation involves a sparse matrix with row, column and values with their respective locations and usage.
- Certain specifications and important points to be kept in mind while using sparse matrix in c, like using sparse matrix in C and its implementation, are quite beneficial to use specialized algorithms and data structure.
- Many machine learning algorithms and systems are designed using this sparse matrix as it saves computation time, making usage proper.
- Operations using these sparse matrixes have a lot of advantage in terms of memory, space and processing all the kind of storage elements within it.
- All the partial differential algorithms and combinatory are applied to this sparse C and thus make it overall dense and useful.
- There are lots of iterative and direct methods that exist between the sparse matrixes solving problem having some of the preconditioners that can iterate much more methods for usage.
- A sparse matrix in one or the other form is quite beneficial than using a simple matrix that does not satisfy most of the conditions and doesn’t check most of the parameters related to analysis, computation, processing, and storage. However, it can be used for many other related fields like machine learning and regression activities.

### Example of Sparse Matrix in C

Different example is mentioned below:

This program demonstrates the implementation of a sparse matrix which shows if the condition and the number of input and output given to the sparse matrix satisfy or not and is shown in the output below.

**Code:**

```
#include <stdio.h>
int main()
{
int k_0, p_1, row_0, col_0, x[5][6], Total_vl = 0;
printf("\n Enter required rows_and_columns for_user: ");
scanf("%d %d", &k_0, &p_1);
printf("\n Enter all the matrix_elements in proper_frmt. \n");
for(row_0 = 0; row_0 < k_0; row_0++)
{
for(col_0 = 0;col_0 < p_1;col_0++)
{
scanf("%d", &x[row_0][col_0]);
}
}
for(row_0 = 0; row_0 < k_0; row_0++)
{
for(col_0 = 0; col_0 < p_1; col_0++)
{
if(x[row_0][col_0] == 0)
{
Total_vl++;
}
}
}
if(Total_vl > (row_0 * col_0)/2)
{
printf("\n Matrix satisfies_the proper_condition then sparse_matrix ");
}
else
{
printf("\n Matrix didn't satisfied the condition thus not a sparse_matrix. ");
}
return 0;
}
```

**Output:**

**Explanation:**

- In the above program, the user can input the desired number of rows and column, which indeed needs to be manipulated and computed in a way where the sparse matrix condition needs to be satisfied.
- If in case the sparse matrix input given and the other form of a matrix, i.e. normal matrix, have some mismatch, then it will be a problem for computation, and the else part giving a pop up will be given as acknowledgement.
- All the elements entered must be in proper format; otherwise, it will throw an error, as shown in the above screenshot.

### Conclusion

A sparse matrix is useful and plays a pivotal role in the C programming language because of its feature and the abilities it provides to the programmers for implementation. It makes the legacy system with storage and slow processing a bit fast when it comes to usage of a sparse matrix in C. Sparse matrix in one or the other form saves a lot of time.

### Recommended Articles

This is a guide to Sparse Matrix in C. Here we discuss the introduction, how sparse matrix works in C? and example, respectively. You may also have a look at the following articles to learn more –