# Example Fixed Sized Matrices

Array access adds a significant amount of overhead to matrix operations. A fixed sized matrix gets around that issue by having each element in the matrix be a variable in the class. EJML provides support for fixed sized matrices and vectors up to 6x6, at which point it loses its advantage. The example below demonstrates how to use a fixed sized matrix and convert to other matrix types in EJML.

Code on GitHub:

## Example

```/**
* In some applications a small fixed sized matrix can speed things up a lot, e.g. 8 times faster.  One application
* which uses small matrices is graphics and rigid body motion, which extensively uses 3x3 and 4x4 matrices.  This
* example is to show some examples of how you can use a fixed sized matrix.
*
* @author Peter Abeles
*/
public class ExampleFixedSizedMatrix {

public static void main( String args[] ) {
// declare the matrix
FixedMatrix3x3_64F a = new FixedMatrix3x3_64F();
FixedMatrix3x3_64F b = new FixedMatrix3x3_64F();

// Can assign values the usual way
for( int i = 0; i < 3; i++ ) {
for( int j = 0; j < 3; j++ ) {
a.set(i,j,i+j+1);
}
}

// Direct manipulation of each value is the fastest way to assign/read values
a.a11 = 12;
a.a23 = 64;

// can print the usual way too
a.print();

// most of the standard operations are support
FixedOps3.transpose(a,b);
b.print();

System.out.println("Determinant = "+FixedOps3.det(a));

// matrix-vector operations are also supported
// Constructors for vectors and matrices can be used to initialize its value
FixedMatrix3_64F v = new FixedMatrix3_64F(1,2,3);
FixedMatrix3_64F result = new FixedMatrix3_64F();

FixedOps3.mult(a,v,result);

// Conversion into DenseMatrix64F can also be done
DenseMatrix64F dm = ConvertMatrixType.convert(a,null);

dm.print();

// This can be useful if you need do more advanced operations
SimpleMatrix sv = SimpleMatrix.wrap(dm).svd().getV();

// can then convert it back into a fixed matrix
FixedMatrix3x3_64F fv = ConvertMatrixType.convert(sv.getMatrix(),(FixedMatrix3x3_64F)null);

System.out.println("Original simple matrix and converted fixed matrix");
sv.print();
fv.print();
}
}
```