public ILinAlgMat Mul(params ILinAlgMat[] mats)
{
Func <ILinAlgMat[], ILinAlgMat> func = _Mul;
if (HDebug.Selftest(func))
{
ILinAlgMat tA = ToILMat(new double[, ] {
{ 1, 2 }, { 3, 4 }, { 5, 6 }
});
ILinAlgMat tB = ToILMat(new double[, ] {
{ 7, 8 }, { 9, 1 }
});
ILinAlgMat tC = ToILMat(new double[, ] {
{ 2, 3, 4 }, { 5, 6, 7 }
});
ILinAlgMat tR = Mul(tA, tB, tC);
ILinAlgMat tRR = ToILMat(new double[, ] {
{ 100, 135, 170 }, { 254, 339, 424 }, { 408, 543, 678 }
});
double terr = (tR - tRR).ToArray().HAbs().HMax();
if (terr > 0.00000001)
{
Exit("Mul, (A * B * C) is wrong");
}
}
return(func(mats));
}
public ILinAlgMat Diag(ILinAlgMat mat)
{
Func <ILinAlgMat, ILinAlgMat> func = _Diag;
if (HDebug.Selftest(func))
{
ILinAlgMat tA = ToILMat(new double[, ] {
{ 1, 2, 3 }, { 2, 4, 5 }, { 3, 5, 6 }
});
ILinAlgMat tADiag0 = Diag(tA);
ILinAlgMat tADiag1 = ToILMat(new double[] { 1, 4, 6 });
double tAerr = (tADiag1 - tADiag0).ToArray().HAbs().HMax();
if (tAerr > 0.00000001)
{
Exit("Diag(A) is wrong");
}
ILinAlgMat tB = ToILMat(new double[] { 1, 2, 3 });
ILinAlgMat tBDiag0 = Diag(tB);
ILinAlgMat tBDiag1 = ToILMat(new double[, ] {
{ 1, 0, 0 }, { 0, 2, 0 }, { 0, 0, 3 }
});
double tBerr = (tADiag1 - tADiag0).ToArray().HAbs().HMax();
if (tBerr > 0.00000001)
{
Exit("Diag(B) is wrong");
}
}
return(func(mat));
}
public Tuple <ILinAlgMat, double[]> EigSymm(ILinAlgMat A)
{
Func <ILinAlgMat, Tuple <ILinAlgMat, double[]> > func = _EigSymm;
if (HDebug.Selftest(func))
{
ILinAlgMat tA = ToILMat(new double[, ] {
{ 1, 2, 3 }, { 2, 4, 5 }, { 3, 5, 6 }
});
var tVD = EigSymm(tA);
ILinAlgMat tV = tVD.Item1;
double[] tD = tVD.Item2;
ILinAlgMat tDD = Diag(ToILMat(tD));
ILinAlgMat tAA = Mul(tV, tDD, tV.Tr);
double err = (tAA - tA).ToArray().HAbs().HMax();
if (err > 0.00000001)
{
Exit("EigSymm, A != V D V'");
}
ILinAlgMat tV_Vt = Mul(tV, tV.Tr);
ILinAlgMat tI = Eye(3);
err = (tV_Vt - tI).ToArray().HAbs().HMax();
if (err > 0.00000001)
{
Exit("EigSymm, I != V V'");
}
}
return(func(A));
}
public ILinAlgMat PInv(ILinAlgMat A)
{
Func <ILinAlgMat, ILinAlgMat> func = _PInv;
if (HDebug.Selftest(func))
{
ILinAlgMat tA = ToILMat(new double[, ] {
{ 1, 2, 3 }, { 2, 3, 5 }, { 3, 4, 5 }
});
ILinAlgMat tiA = PInv(tA);
ILinAlgMat tiAA = ToILMat(new double[, ] {
{ -2.5, 1.0, 0.5 }, { 2.5, -2.0, 0.5 }, { -0.5, 1.0, -0.5 }
});
double err0 = (tiA - tiAA).ToArray().HAbs().HMax();
if (err0 > 0.00000001)
{
Exit("Pinv, is incorrect");
}
ILinAlgMat tI = Eye(3);
double err1 = (tA * tiA - tI).ToArray().HAbs().HMax();
if (err1 > 0.00000001)
{
Exit("Pinv, A * invA != I");
}
double err2 = (tiA * tA - tI).ToArray().HAbs().HMax();
if (err2 > 0.00000001)
{
Exit("Pinv, invA * A != I");
}
}
return(func(A));
}
public override ILinAlgMat _Inv(ILinAlgMat A)
{
using (new Matlab.NamedLock("LA"))
{
Matlab.PutMatrix("LA.A", A.ToArray());
CMatrix inv = Matlab.GetMatrix("inv(LA.A)");
Matlab.Clear();
return(inv);
}
}
public override double _Det(ILinAlgMat mat)
{
using (new Matlab.NamedLock("LA"))
{
Matlab.PutMatrix("LA.A", mat.ToArray());
double det = Matlab.GetValue("det(LA.A)");
Matlab.Clear();
return(det);
}
}
public override ILinAlgMat _Diag(ILinAlgMat mat)
{
using (new Matlab.NamedLock("LA"))
{
Matlab.PutMatrix("LA.A", mat.ToArray());
CMatrix diag = Matlab.GetMatrix("diag(LA.A)");
Matlab.Clear();
return(diag);
}
}
public override ILinAlgMat _LinSolve(ILinAlgMat A, ILinAlgMat B)
{
using (new Matlab.NamedLock("LA"))
{
Matlab.PutMatrix("LA.A", A.ToArray());
Matlab.PutMatrix("LA.B", B.ToArray());
CMatrix X = Matlab.GetMatrix(@"LA.A \ LA.B"); /// A X = B => X = A\B
Matlab.Clear();
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 double Det(ILinAlgMat mat)
{
Func <ILinAlgMat, double> func = _Det;
if (HDebug.Selftest(func))
{
ILinAlgMat tA = ToILMat(new double[, ] {
{ 1, 2, 3 }, { 2, 4, 5 }, { 3, 5, 6 }
});
double tdet = Det(tA);
if (Math.Abs(tdet - (-1.0)) > 0.00000001)
{
Exit("Det(A) is wrong");
}
}
return(func(mat));
}
public override Tuple <ILinAlgMat, double[]> _EigSymm(ILinAlgMat A)
{
using (new Matlab.NamedLock("LA"))
{
Matlab.PutMatrix("LA.A", A.ToArray());
Matlab.Execute("LA.A = (LA.A + LA.A)/2;");
Matlab.Execute("[LA.V, LA.D] = eig(LA.A);");
Matlab.Execute("LA.D = diag(LA.D);");
CMatrix V = Matlab.GetMatrix("LA.V");
double[] D = Matlab.GetVector("LA.D");
if (HDebug.IsDebuggerAttached)
{
Matlab.Execute("LA.ERR = LA.A - (LA.V * diag(LA.D) * LA.V');");
Matlab.Execute("LA.ERR = max(max(abs(LA.ERR)));");
double err = Matlab.GetValue("LA.ERR");
HDebug.AssertTolerance(0.00000001, err);
}
Matlab.Clear();
return(new Tuple <ILinAlgMat, double[]>(V, D));
}
}
public ILinAlgMat InvSymm(ILinAlgMat A)
{
Func <ILinAlgMat, ILinAlgMat> func = _InvSymm;
if (HDebug.Selftest(func))
{
ILinAlgMat tA = ToILMat(new double[, ] {
{ 1, 2, 3 }, { 2, 4, 5 }, { 3, 5, 6 }
});
ILinAlgMat tI = ToILMat(new double[, ] {
{ 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 }
});
ILinAlgMat tInvA = func(tA);
double err = (tInvA * tA - tI).ToArray().HAbs().HMax();
if (err > 0.00000001)
{
Exit("LinSolve, is incorrect");
}
}
return(func(A));
}
public ILinAlgMat LinSolve(ILinAlgMat A, ILinAlgMat B)
{
Func <ILinAlgMat, ILinAlgMat, ILinAlgMat> func = _LinSolve;
if (HDebug.Selftest(func))
{
ILinAlgMat tA = ToILMat(new double[, ] {
{ 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 }
});
ILinAlgMat tB = ToILMat(new double[, ] {
{ 3, 4, 5 }, { 6, 7, 8 }, { 9, 10, 11 }
});
ILinAlgMat tX = _LinSolve(tA, tB);
double err = (tA * tX - tB).ToArray().HAbs().HMax();
if (err > 0.00000001)
{
Exit("LinSolve, is incorrect");
}
}
return(func(A, B));
}
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 abstract double _Det(ILinAlgMat mat);
public abstract ILinAlgMat _InvSymm(ILinAlgMat A);
public abstract ILinAlgMat _Inv(ILinAlgMat A);
public abstract ILinAlgMat _LinSolve(ILinAlgMat A, ILinAlgMat B);
public abstract ILinAlgMat _Diag(ILinAlgMat mat);
public abstract Tuple <ILinAlgMat, double[]> _EigSymm(ILinAlgMat A);
public override ILinAlgMat op_Mul(/*ILinAlgMat mat1, */ ILinAlgMat mat2)
{
return(new CMatrix(matrix * (mat2 as CMatrix).matrix));
}
public abstract ILinAlgMat op_Mul(/*ILinAlgMat mat1, */ ILinAlgMat mat2);