public static Matrix SubMatrixOfInv(this Matrix mat, IList <int> idxs, ILinAlg ila, string invopt)
{
Matrix InvInvA = mat.InvOfSubMatrixOfInv(idxs, ila, invopt);
/// (inv(M))_00 = inv(A - B inv(D) C)
var InvInvAA = ila.ToILMat(InvInvA);
var InvAA = ila.PInv(InvInvAA);
Matrix InvA = InvAA.ToArray();
return(InvA);
}
public static Matrix InvSymm(this ILinAlg ila, Matrix A)
{
var AA = ila.ToILMat(A);
var invAA = ila.InvSymm(AA);
Matrix invA = ToMatrix(invAA);
AA.Dispose();
invAA.Dispose();
GC.Collect();
return(invA);
}
public static Tuple <Matrix, Vector> EigSymm(this ILinAlg ila, Matrix A)
{
var AA = ila.ToILMat(A);
var VVDD = ila.EigSymm(AA);
Matrix V = VVDD.Item1.ToMatrix();
Vector D = VVDD.Item2;
AA.Dispose();
VVDD.Item1.Dispose();
GC.Collect();
return(new Tuple <Matrix, Vector>(V, D));
}
public static Matrix LinSolve(this ILinAlg ila, Matrix A, Matrix B)
{
var AA = ila.ToILMat(A);
var BB = ila.ToILMat(B);
var XX = ila.LinSolve(AA, BB);
Matrix X = XX.ToMatrix();
AA.Dispose();
BB.Dispose();
XX.Dispose();
GC.Collect();
return(X);
}
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 Mul(this ILinAlg ila, params Matrix[] mats)
{
ILinAlgMat[] MATS = new ILinAlgMat[mats.Length];
for (int i = 0; i < mats.Length; i++)
{
MATS[i] = ila.ToILMat(mats[i]);
}
ILinAlgMat MUL = ila.Mul(MATS);
Matrix mul = ToMatrix(MUL);
MUL.Dispose();
foreach (var MAT in MATS)
{
MAT.Dispose();
}
return(mul);
}
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);
}
public static ILinAlgMat HInv(this ILinAlg ila, ILinAlgMat AA, string invtype, params object[] invopt)
{
if (invtype == null)
{
invtype = "inv";
}
object optparam = null;
switch (invtype)
{
case "inv":
return(ila.Inv(AA));
case "pinv":
return(ila.PInv(AA));
case "eig-zerothres":
{
var VVDD = ila.EigSymm(AA);
double threshold = (double)invopt[0];
for (int i = 0; i < VVDD.Item2.Length; i++)
{
if (Math.Abs(VVDD.Item2[i]) < threshold)
{
VVDD.Item2[i] = 0;
}
}
optparam = VVDD;
}
goto case "eig-VVDD";
case "eig-zerocount":
{
var VVDD = ila.EigSymm(AA);
int zerocount = (int)invopt[0];
for (int i = 0; i < zerocount; i++)
{
VVDD.Item2[i] = 0;
}
optparam = VVDD;
}
goto case "eig-VVDD";
case "eig-VVDD":
{
Tuple <ILinAlgMat, double[]> VVDD = optparam as Tuple <ILinAlgMat, double[]>;
for (int i = 0; i < VVDD.Item2.Length; i++)
{
if (VVDD.Item2[i] != 0)
{
VVDD.Item2[i] = 1 / VVDD.Item2[i];
}
}
var invAA = ila.Mul(VVDD.Item1, ila.ToILMat(VVDD.Item2).Diag(), VVDD.Item1.Tr);
if (HDebug.IsDebuggerAttached)
{
var check = AA * invAA;
check.Dispose();
}
VVDD.Item1.Dispose();
return(invAA);
}
default:
throw new NotImplementedException();
}
}
public static ILinAlg.ILinAlgMat AddDisposable(this ILinAlg.ILinAlgMat mat)
{
ILinAlg.AddDisposable(mat);
return(mat);
}
