我正在研究比較各種矩陣求逆算法（Gauss-Jordan，Strassen和Coppersmith-Winograd）的項目。我找到了gauss-jordan的實現，但是我一直沒能找到任何Strassens矩陣求逆算法的實現。 Google的大量時間還沒有發現任何東西。我檢查了Jama庫，Colt庫和Apache Math庫，但是這些都使用Gauss Elimination或LU Decomp。有誰知道一個實現Strassen矩陣求逆算法的java庫嗎？是否有一個Java庫實現Strassen的矩陣求逆算法？
對於那些不熟悉該算法的人，請查看此page的底部。此外，Coppersmith-Winograd維基百科頁面還有關於Strassen算法的簡短介紹。
感謝
public class Strassen
{
public static double[][] multiply(double[][] A, double[][] B)
{
try
{
checkInputStrassen(A,B);
}
catch (RuntimeException e)
{
throw e;
}
return strassenRecursive(A,B);
}
private static double[][] reconstructAnswer(double[][] r, double[][] s,
double[][] t, double[][] u)
{
int n = r.length*2;
double[][] C = new double[n][n];
copyBack(C,r,0,0);
copyBack(C,s,0,n/2);
copyBack(C,t,n/2,0);
copyBack(C,u,n/2,n/2);
return C;
}
private static void copyBack(double[][] C, double[][] r, int x, int y)
{
for (int i=0; i<r.length; i++)
{
for (int j=0; j<r.length; j++)
{
C[x+i][y+j] = r[i][j];
}
}
}
private static void copy(double[][] a, double[][] A, int x, int y)
{
for (int i=0; i<a.length; i++)
{
for (int j=0; j<a.length; j++)
{
a[i][j] = A[x+i][y+j];
}
}
}
private static double[][] strassenRecursive(double[][] A, double[][] B)
{
int n = A.length;
if (n==1)
{
double[][] C = new double[1][1];
C[0][0]=A[0][0]*B[0][0];
return C;
}
double[][] r,s,t,u, a,b,c,d,e,f,g,h, P1,P2,P3,P4,P5,P6,P7;
r = new double[n/2][n/2]; s = new double[n/2][n/2]; t = new double[n/2][n/2];
u = new double[n/2][n/2]; a = new double[n/2][n/2]; b = new double[n/2][n/2];
c = new double[n/2][n/2]; d = new double[n/2][n/2]; e = new double[n/2][n/2];
f = new double[n/2][n/2]; g = new double[n/2][n/2]; h = new double[n/2][n/2];
P1 = new double[n/2][n/2]; P2 = new double[n/2][n/2]; P3 = new double[n/2][n/2];
P4 = new double[n/2][n/2]; P5 = new double[n/2][n/2]; P6 = new double[n/2][n/2];
P7 = new double[n/2][n/2];
copy(a,A,0,0);
copy(b,A,0,n/2);
copy(c,A,n/2,0);
copy(d,A,n/2,n/2);
copy(e,B,0,0);
copy(f,B,0,n/2);
copy(g,B,n/2,0);
copy(h,B,n/2,n/2);
P1= strassenRecursive(a, add(f,h,-1)); // P1 = a(f-h) = af-ah
P2= strassenRecursive(add(a,b,1), h); // P2 = (a+b)h = ah+bh
P3= strassenRecursive(add(c,d,1), e); // P3 = (c+d)e = ce+de
P4= strassenRecursive(d, add(g,e,-1)); // P4 = d(g-e) = dg-de
P5= strassenRecursive(add(a,d,1), add(e,h,1)); // P5 = (a+d)(e+h)=ae+de+ah+dh
P6= strassenRecursive(add(b,d,-1), add(g,h,1)); // P6 = (b-d)(g+h)=bg-dg+bh-dh
P7= strassenRecursive(add(a,c,-1), add(e,f,1)); // P7 = (a-c)(e+f)=ae-ce+af-cf
r = add(add(P5,P4,1),add(P2,P6,-1),-1); // r = P5+P4-P2+P6 = ae+bg
s = add(P1,P2,1); // s = P1+P2 = af+bh
t = add(P3,P4,1); // t = P3+P4 = ce+dg
u = add(add(P5,P1,1),add(P3,P7,1),-1); //u = P5+P1-P3-P7 = cf+dh
return reconstructAnswer(r,s,t,u);
}
private static double[][] add(double[][] A, double[][] B, int signofB)
{
int n = A.length;
double[][] C = new double[n][n];
for (int i=0; i<n; i++)
{
for (int j=0; j<n; j++)
{
C[i][j] = A[i][j] + signofB*B[i][j];
}
}
return C;
}
private static void checkInputStrassen(double[][] A, double[][] B)
{
int p = A.length;
if (p==0)
{
throw new IllegalArgumentException("Null matrix");
}
int n=p;
while (n>1)
{
if (n%2 != 0)
{
throw new IllegalArgumentException("Non power of 2 matrix");
}
n/=2;
}
int q = A[0].length;
if (q==0)
{
throw new IllegalArgumentException("Null matrix");
}
if (q!=p)
{
throw new IllegalArgumentException("Nonsquare Matrix");
}
for (int i=1; i<p; i++)
{
if (A[i].length != q)
{
throw new IllegalArgumentException("Inconsistent matrix");
}
}
if (B.length != q)
{
throw new IllegalArgumentException("Inconsistent dimensions");
}
int r = B[0].length;
if (r!=p)
{
throw new IllegalArgumentException("Nonsquare Matrix");
}
for (int i=1; i<q; i++)
{
if (B[i].length != r)
{
throw new IllegalArgumentException("Inconsistent matrix");
}
}
}
}