# Example Sparse Matrices

Support for sparse matrices has recently been added to EJML. It supports many but not all of the standard operations that are supported for dense matrics. The code below shows the basics of working with a sparse matrix. In some situations the speed improvement of using a sparse matrix can be substantial. Do note that if your system isn't sparse enough or if its structure isn't advantageous it could run even slower using sparse operations!

Type Execution Time (ms)
Dense 12660
Sparse 1642

External Resources:

## Sparse Matrix Example

```/**
* Example showing how to construct and solve a linear system using sparse matrices
*
* @author Peter Abeles
*/
public class ExampleSparseMatrix {
public static int ROWS = 100000;
public static int COLS = 1000;
public static int XCOLS = 1;

public static void main( String[] args ) {
Random rand = new Random(234);

// easy to work with sparse format, but hard to do computations with
// NOTE: It is very important to you set 'initLength' to the actual number of elements in the final array
//       If you don't it will be forced to thrash memory as it grows its internal data structures.
//       Failure to heed this advice will make construction of large matrices 4x slower and use 2x more memory
var work = new DMatrixSparseTriplet(5, 4, 5);

// convert into a format that's easier to perform math with
DMatrixSparseCSC Z = DConvertMatrixStruct.convert(work, (DMatrixSparseCSC)null);

// print the matrix to standard out in two different formats
Z.print();
System.out.println();
Z.printNonZero();
System.out.println();

// Create a large matrix that is 5% filled
DMatrixSparseCSC A = RandomMatrices_DSCC.rectangle(ROWS, COLS, (int)(ROWS*COLS*0.05), rand);
//          large vector that is 70% filled
DMatrixSparseCSC x = RandomMatrices_DSCC.rectangle(COLS, XCOLS, (int)(XCOLS*COLS*0.7), rand);

System.out.println("Done generating random matrices");
// storage for the initial solution
var y = new DMatrixSparseCSC(ROWS, XCOLS, 0);
var z = new DMatrixSparseCSC(ROWS, XCOLS, 0);

// To demonstration how to perform sparse math let's multiply:
//                  y=A*x
// Optional storage is set to null so that it will declare it internally
long before = System.currentTimeMillis();
var workA = new IGrowArray(A.numRows);
var workB = new DGrowArray(A.numRows);
for (int i = 0; i < 100; i++) {
CommonOps_DSCC.mult(A, x, y, workA, workB);
CommonOps_DSCC.add(1.5, y, 0.75, y, z, workA, workB);
}
long after = System.currentTimeMillis();

System.out.println("norm = " + NormOps_DSCC.fastNormF(y) + "  sparse time = " + (after - before) + " ms");

DMatrixRMaj xd = DConvertMatrixStruct.convert(x, (DMatrixRMaj)null);
var yd = new DMatrixRMaj(y.numRows, y.numCols);
var zd = new DMatrixRMaj(y.numRows, y.numCols);

before = System.currentTimeMillis();
for (int i = 0; i < 100; i++) {