public static Matrix HInv(this ILinAlg ila, Matrix A, string invtype, params object[] invopt)
{
Matrix invA;
{
ILinAlgMat AA = ila.ToILMat(A);
ILinAlgMat invAA = ila.HInv(AA, invtype, invopt);
invA = invAA.ToMatrix();
AA.Dispose();
invAA.Dispose();
}
GC.Collect();
return(invA);
}
public static Matrix InvOfSubMatrixOfInv(this Matrix mat, IList <int> idxs, ILinAlg ila, string invtype, params object[] invopt)
{
if (HDebug.Selftest())
{
MatrixByArr tH = new double[, ] {
{ 1, 2, 3, 4 }
, { 2, 5, 6, 7 }
, { 3, 6, 8, 9 }
, { 4, 7, 9, 10 }
};
MatrixByArr tInvH = new double[, ] {
{ 0.5, -0.5, -1.5, 1.5 } // = inv(tH)
, { -0.5, 1.5, -1.5, 0.5 }
, { -1.5, -1.5, 3.5, -1.5 }
, { 1.5, 0.5, -1.5, 0.5 }
};
MatrixByArr tInvH12 = new double[, ] {
{ 0.5, -0.5 } // = block matrix of tInvH
, { -0.5, 1.5 }
};
MatrixByArr tInvtInvH12 = new double[, ] {
{ 3, 1 } // = inv([ 0.5, -0.5])
, { 1, 1 }
}; // [-0.5, 1.5]
MatrixByArr ttInvtInvH12 = tH.InvOfSubMatrixOfInv(new int[] { 0, 1 }, ila, null).ToArray();
HDebug.AssertTolerance(0.00000001, tInvtInvH12 - ttInvtInvH12);
}
int ColSize = mat.ColSize;
int RowSize = mat.RowSize;
if (ColSize != RowSize)
{
HDebug.Assert(false); return(null);
}
if (idxs.Count != idxs.HToHashSet().Count)
{
HDebug.Assert(false); return(null);
}
List <int> idxs0 = idxs.ToList();
List <int> idxs1 = new List <int>();
for (int i = 0; i < ColSize; i++)
{
if (idxs.Contains(i) == false)
{
idxs1.Add(i);
}
}
Matrix InvInvA;
{
Matrix A = mat.SubMatrix(idxs0, idxs0); Matrix B = mat.SubMatrix(idxs0, idxs1); // [A B]
Matrix C = mat.SubMatrix(idxs1, idxs0); Matrix D = mat.SubMatrix(idxs1, idxs1); // [C D]
/// http://en.wikipedia.org/wiki/Invertable_matrix#Blockwise_inversion
///
/// M^-1 = [M_00 M_01] = [A B]-1 = [ (A - B D^-1 C)^-1 ... ]
/// = [M_10 M_11] = [C D] [ ... ... ]
///
/// (inv(M))_00 = inv(A - B inv(D) C)
/// inv((inv(M))_00) = (A - B inv(D) C)
var AA = ila.ToILMat(A);
var BB = ila.ToILMat(B);
var CC = ila.ToILMat(C);
var DD = ila.ToILMat(D);
var InvDD = ila.HInv(DD, invtype, invopt);
var InvInvAA = AA - BB * InvDD * CC;
//var xx = BB * InvDD * CC;
InvInvA = InvInvAA.ToArray();
AA.Dispose();
BB.Dispose();
CC.Dispose();
DD.Dispose();
InvDD.Dispose();
InvInvAA.Dispose();
}
GC.Collect();
return(InvInvA);
}
