#include <stdio.h>
#define MAX1 3
#define MAX2 3
struct sparse
{
int *sp ;
int row ;
} ;
void initsparse ( struct sparse * ) ;
void create_array ( struct sparse * ) ;
void display ( struct sparse ) ;
int count ( struct sparse ) ;
void create_tuple ( struct sparse *, struct sparse ) ;
void display_tuple ( struct sparse ) ;
void transpose ( struct sparse *, struct sparse ) ;
void display_transpose ( struct sparse ) ;
void delsparse ( struct sparse * ) ;
void main( )
{
struct sparse s[3] ;
int c, i ;
for ( i = 0 ; i <= 2 ; i++ )
initsparse ( &s[i] );
create_array ( &s[0] ) ;
printf ( "\nElements in Sparse Matrix: " ) ;
display ( s[0] ) ;
c = count ( s[0] ) ;
printf ( "\n\nNumber of non-zero elements: %d", c ) ;
create_tuple ( &s[1], s[0] ) ;
printf ( "\n\nArray of non-zero elements: " ) ;
display_tuple ( s[1] ) ;
transpose ( &s[2], s[1] ) ;
printf ( "\n\nTranspose of array: " ) ;
display_transpose ( s[2] ) ;
for ( i = 0 ; i <= 2 ; i++ )
delsparse ( &s[i] );
}
/* initialises data members */
void initsparse ( struct sparse *p )
{
p -> sp = NULL ;
}
/* dynamically creates the matrix of size MAX1 x MAX2 */
void create_array ( struct sparse *p )
{
int n, i ;
p -> sp = ( int * ) malloc ( MAX1 * MAX2 * sizeof ( int ) ) ;
for ( i = 0 ; i < MAX1 * MAX2 ; i++ )
{
printf ( "Enter element no. %d:", i ) ;
scanf ( "%d", &n ) ;
* ( p -> sp + i ) = n ;
}
}
/* displays the contents of the matrix */
void display ( struct sparse s )
{
int i ;
/* traverses the entire matrix */
for ( i = 0 ; i < MAX1 * MAX2 ; i++ )
{
/* positions the cursor to the new line for every new row */
if ( i % MAX2 0 )
printf ( "\n" ) ;
printf ( "%d\t", * ( p.sp + i ) ) ;
}
}
/* deallocates memory */
void delsparse ( struct sparse *p )
{
free ( p -> sp ) ;
}
Another sparse matrix.
A fast-transpose is a computer algorithm that quickly transposes a sparse matrix using a relatively small amount of memory. Using arrays normally to record a sparse matrix uses up a lot of memory since many of the matrix's values are zero. In addition, using the normal transpose algorithm to transpose this matrix will take O(cols*elements) amount of time. The fast-transpose algorithm only uses a little memory to record the matrix and takes only O(cols+elements) amount of time, which is efficient considering the number of elements equals cols*rows.
yes, it is true that the transpose of the transpose of a matrix is the original matrix
This is a directive, not a question.
The transpose of a sparse matrix is widely used in various applications, including optimization problems, graph algorithms, and machine learning. In graph theory, it helps in analyzing the properties of directed graphs, such as finding strongly connected components. In machine learning, the transpose is often used to facilitate operations on feature matrices, enabling efficient computation in algorithms like gradient descent. Additionally, in scientific computing, transposing sparse matrices can enhance performance in iterative methods, such as solving linear systems.
A sparse matrix is a matrix in which most of the elements are zero.
DataStructure-Program to transpose a sparse matrix.#include #include #include #define MAX1 3#define MAX2 3struct sparse{int *sp ;int row ;} ;void initsparse ( struct sparse * ) ;void create_array ( struct sparse * ) ;void display ( struct sparse ) ;int count ( struct sparse ) ;void create_tuple ( struct sparse *, struct sparse ) ;void display_tuple ( struct sparse ) ;void transpose ( struct sparse *, struct sparse ) ;void display_transpose ( struct sparse ) ;void delsparse ( struct sparse * ) ;void main( ){struct sparse s[3] ;int c, i ;for ( i = 0 ; i sp = ( int * ) malloc ( MAX1 * MAX2 * sizeof ( int ) ) ;for ( i = 0 ; i < MAX1 * MAX2 ; i++ ){printf ( "Enter element no. %d:", i ) ;scanf ( "%d", &n ) ;* ( p -> sp + i ) = n ;}}/* displays the contents of the matrix */void display ( struct sparse s ){int i ;/* traverses the entire matrix */for ( i = 0 ; i < MAX1 * MAX2 ; i++ ){/* positions the cursor to the new line for every new row */if ( i % MAX2 0 )printf ( "\n" ) ;printf ( "%d\t", * ( p.sp + i ) ) ;}}/* deallocates memory */void delsparse ( struct sparse *p ){free ( p -> sp ) ;}
The Transpose of a MatrixThe matrix of order n x m obtained by interchanging the rows and columns of the m X n matrix, A, is called the transpose of A and is denoted by A' or AT.
a square matrix that is equal to its transpose
You basically write a nested for loop (one for within another one), to copy the elements of the matrix to a new matrix.
A sparse matrix is one which normally contains a large proportion of elements whose value is 0. There is no exact proportion at which a matrix becomes sparse.
C Examples on Matrix OperationsA matrix is a rectangular array of numbers or symbols arranged in rows and columns. The following section contains a list of C programs which perform the operations of Addition, Subtraction and Multiplication on the 2 matrices. The section also deals with evaluating the transpose of a given matrix. The transpose of a matrix is the interchange of rows and columns.The section also has programs on finding the trace of 2 matrices, calculating the sum and difference of two matrices. It also has a C program which is used to perform multiplication of a matrix using recursion.C Program to Calculate the Addition or Subtraction & Trace of 2 MatricesC Program to Find the Transpose of a given MatrixC Program to Compute the Product of Two MatricesC Program to Calculate the Sum & Difference of the MatricesC Program to Perform Matrix Multiplication using Recursion