void sub(const Array2D<E> &aobj,const Array2D<E> &bobj,Array2D<E> &cobj)
{
int astarti=aobj.low1(),astartj=aobj.low2(),arow=aobj.size1(),acol=aobj.size2();
int bstarti=bobj.low1(),bstartj=bobj.low2(),brow=bobj.size1(),bcol=bobj.size2();
//Array2D<E> c(0,arow-1,0,acol-1);
cobj.init(0,arow-1,0,acol-1);
for(int i=0;i<arow;i++)
{
for(int j=0;j<acol;j++)
cobj(i,j)=aobj(i+astarti,j+astartj)-bobj(i+bstarti,j+bstartj);
}
}
void mul(const Array2D<E> &a,const Array2D<E> &b,Array2D<E> &obj)
{
int arow=a.size1();
int acol=a.size2();
int brow=b.size1();
int bcol=b.size2();
OGDF_ASSERT(arow==acol && acol==brow && brow==bcol); //checking matrix is square and equal or not
int ai=a.low1(),aj=a.low2(),bi=b.low1(),bj=b.low2();
obj.init(0,arow-1,0,arow-1,0);
for(int i=0;i<arow;i++)
for(int j=0;j<acol;j++)
for(int k=0;k<brow;k++)
obj(i,j)+=a(i+ai,k+aj)*b(k+bi,j+bj);
}
void show(Array2D<E> &aka)
{
// Inbulit functions used for reading index values and dimensions of matrix
int starti=aka.low1(),startj=aka.low2(),endi=aka.high1(),endj=aka.high2();
for(int i=starti;i<=endi;i++)
{
cout<<endl;
for(int j=startj;j<=endj;j++)
{
cout<<aka(i,j)<<" ";
}
}
cout<<endl;
}
void strassen(const Array2D<E> &a,const Array2D<E> &b,Array2D<E> &c)
{
int astarti=a.low1(),astartj=a.low2(),arow=a.size1(),acol=a.size2();
int bstarti=b.low1(),bstartj=b.low2(),brow=b.size1(),bcol=b.size2();
OGDF_ASSERT(arow==acol && acol==brow && brow==bcol); //checking matrix is square and equal or not
if(arow<=2)
{
mul(a,b,c); // naive method for calculating matrix multiplication of size less than or equal to 4
}
else
{
int val1=arow/2-1;
int val2=arow-1;
Array2D<E> a11,a12,a21,a22,b11,b12,b21,b22;
submatrix(a,astarti,astartj,astarti+val1,astartj+val1,a11);
submatrix(a,astarti,astartj+val1+1,astarti+val1,astartj+val2,a12);
submatrix(a,astarti+val1+1,astartj,astarti+val2,astartj+val1,a21);
submatrix(a,astarti+val1+1,astartj+val1+1,astarti+val2,astartj+val2,a22);
submatrix(b,bstarti,bstartj,bstarti+val1,bstartj+val1,b11);
submatrix(b,bstarti,bstartj+val1+1,bstarti+val1,bstartj+val2,b12);
submatrix(b,bstarti+val1+1,bstartj,bstarti+val2,bstartj+val1,b21);
submatrix(b,bstarti+val1+1,bstartj+val1+1,bstarti+val2,bstartj+val2,b22);
//calulating p(i) for applying strassen method
Array2D<E> obj1,obj2;
add(a11,a22,obj1);
add(b11,b22,obj2);
Array2D<E> p1,p2,p3,p4,p5,p6,p7;
strassen(obj1,obj2,p1);
add(a21,a22,obj1);
strassen(obj1,b11,p2);
sub(b12,b22,obj2);
strassen(a11,obj2,p3);
sub(b21,b11,obj2);
strassen(a22,obj2,p4);
add(a11,a12,obj1);
strassen(obj1,b22,p5);
sub(a21,a11,obj1);
add(b11,b12,obj2);
strassen(obj1,obj2,p6);
sub(a12,a22,obj1);
add(b21,b22,obj2);
strassen(obj1,obj2,p7);
//calculating submatrix of final result matrix
Array2D<E> c11,c22,c21,c12,cnn;
add(p1,p4,c11);
sub(c11,p5,cnn);
add(cnn,p7,c11);
add(p3,p5,c12);
add(p2,p4,c21);
add(p1,p3,c22);
add(c22,p6,cnn);
sub(cnn,p2,c22);
c.init(0,val2,0,val2);
//function call for info of submatrices
int c11i=c11.low1(),c11j=c11.low2();
int c12i=c12.low1(),c12j=c12.low2();
int c21i=c21.low1(),c21j=c21.low2();
int c22i=c22.low1(),c22j=c22.low2();
//Method for grouping of submatrix into 1
for(int i=0;i<=val1;i++)
{
for(int j=0;j<=val1;j++)
{
c(i,j)=c11(c11i+i,c11j+j);
c(i,j+val1+1)=c12(c12i+i,c12j+j);
c(i+val1+1,j)=c21(c21i+i,c21j+j);
c(i+val1+1,j+val1+1)=c22(c22i+i,c22j+j);
}
}
}
}
