protected override bool InvEigImpl(Matrix mat, double?thresEigval, int?numZeroEigval, out Matrix inv, InfoPack extra)
{
NamedLock.FuncO <Matrix, bool> func = delegate(out Matrix linv)
{
Matlab.Clear("HTLib2_Matlab_InvEigImpl");
Matlab.PutMatrix("HTLib2_Matlab_InvEigImpl.A", mat.ToArray());
Matlab.PutValue("HTLib2_Matlab_InvEigImpl.ze", numZeroEigval.GetValueOrDefault(0));
Matlab.PutValue("HTLib2_Matlab_InvEigImpl.th", Math.Abs(thresEigval.GetValueOrDefault(0)));
Matlab.Execute("[HTLib2_Matlab_InvEigImpl.V, HTLib2_Matlab_InvEigImpl.D] = eig(HTLib2_Matlab_InvEigImpl.A);");
Matlab.Execute("HTLib2_Matlab_InvEigImpl.D = diag(HTLib2_Matlab_InvEigImpl.D);");
Matlab.Execute("HTLib2_Matlab_InvEigImpl.sortAbsD = sort(abs(HTLib2_Matlab_InvEigImpl.D));");
Matlab.Execute("HTLib2_Matlab_InvEigImpl.sortAbsD0 = [0; HTLib2_Matlab_InvEigImpl.sortAbsD];"); // add zero to the first list, for the case ze=0 (null)
Matlab.Execute("HTLib2_Matlab_InvEigImpl.ze = HTLib2_Matlab_InvEigImpl.sortAbsD0(HTLib2_Matlab_InvEigImpl.ze+1);");
Matlab.Execute("HTLib2_Matlab_InvEigImpl.th = max(HTLib2_Matlab_InvEigImpl.th, HTLib2_Matlab_InvEigImpl.ze);");
Matlab.Execute("HTLib2_Matlab_InvEigImpl.idx = abs(HTLib2_Matlab_InvEigImpl.D) <= HTLib2_Matlab_InvEigImpl.th;");
Matlab.Execute("HTLib2_Matlab_InvEigImpl.invD = ones(size(HTLib2_Matlab_InvEigImpl.D)) ./ HTLib2_Matlab_InvEigImpl.D;");
Matlab.Execute("HTLib2_Matlab_InvEigImpl.invD(HTLib2_Matlab_InvEigImpl.idx) = 0;");
Matlab.Execute("HTLib2_Matlab_InvEigImpl.invD = diag(HTLib2_Matlab_InvEigImpl.invD);");
Matlab.Execute("HTLib2_Matlab_InvEigImpl.invA = HTLib2_Matlab_InvEigImpl.V * HTLib2_Matlab_InvEigImpl.invD * inv(HTLib2_Matlab_InvEigImpl.V);");
linv = Matlab.GetMatrix("HTLib2_Matlab_InvEigImpl.invA");
if (extra != null)
{
int num_zero_eigvals = Matlab.GetValueInt("sum(HTLib2_Matlab_InvEigImpl.idx)");
HDebug.AssertIf(numZeroEigval != null, numZeroEigval.GetValueOrDefault() <= num_zero_eigvals);
extra["num_zero_eigvals"] = num_zero_eigvals;
extra["eigenvalues"] = Matlab.GetVector("HTLib2_Matlab_InvEigImpl.D");
}
Matlab.Clear("HTLib2_Matlab_InvEigImpl");
return(true);
};
//return NamedLock.LockedCall("bool HTLib2.Matlab.NumericSolver.InvEigImpl(Matrix, double?, int?, out Matrix, InfoPack)", func, out inv);
return(NamedLock.LockedCall(Matlab.NamedLock.GetName("HTLib2_Matlab_InvEigImpl"), func, out inv));
}
protected override bool QuadraticProgrammingConstrainedImpl(out Vector x
, Matrix H, Vector f
, Matrix A = null, Vector b = null
, Matrix Aeq = null, Vector beq = null
, Vector lb = null, Vector ub = null
, Vector x0 = null
, string options = null
)
{
using (new Matlab.NamedLock("NUMSLV"))
{
Matlab.Clear("NUMSLV");
Matlab.PutMatrix("NUMSLV.H", H.ToArray());
Matlab.PutVector("NUMSLV.f", f.ToArray());
Matlab.Execute("NUMSLV.A = [];"); if (A != null)
{
Matlab.PutMatrix("NUMSLV.A", A.ToArray());
}
Matlab.Execute("NUMSLV.b = [];"); if (b != null)
{
Matlab.PutVector("NUMSLV.b", b.ToArray());
}
Matlab.Execute("NUMSLV.Aeq = [];"); if (Aeq != null)
{
Matlab.PutMatrix("NUMSLV.Aeq", Aeq.ToArray());
}
Matlab.Execute("NUMSLV.beq = [];"); if (beq != null)
{
Matlab.PutVector("NUMSLV.beq", beq.ToArray());
}
Matlab.Execute("NUMSLV.lb = [];"); if (lb != null)
{
Matlab.PutVector("NUMSLV.lb", lb.ToArray());
}
Matlab.Execute("NUMSLV.ub = [];"); if (ub != null)
{
Matlab.PutVector("NUMSLV.ub", ub.ToArray());
}
Matlab.Execute("NUMSLV.x0 = [];"); if (x0 != null)
{
Matlab.PutVector("NUMSLV.x0", x0.ToArray());
}
if (options == null)
{
options = "[]";
}
Matlab.Execute("NUMSLV.x = quadprog(NUMSLV.H, NUMSLV.f, NUMSLV.A, NUMSLV.b, NUMSLV.Aeq, NUMSLV.beq, NUMSLV.lb, NUMSLV.ub, NUMSLV.x0, " + options + ");", true);
x = Matlab.GetVector("NUMSLV.x");
Matlab.Clear("NUMSLV");
}
return(true);
}
protected override bool LeastSquareConstrainedImpl(out Vector x
, Matrix C, Vector d
, Matrix A = null, Vector b = null
, Matrix Aeq = null, Vector beq = null
, Vector lb = null, Vector ub = null
, Vector x0 = null
, string options = null
)
{
using (new Matlab.NamedLock("NUMSLV"))
{
Matlab.Clear("NUMSLV");
Matlab.PutMatrix("NUMSLV.C", C.ToArray());
Matlab.PutVector("NUMSLV.d", d.ToArray());
Matlab.Execute("NUMSLV.A = [];"); if (A != null)
{
Matlab.PutMatrix("NUMSLV.A", A.ToArray());
}
Matlab.Execute("NUMSLV.b = [];"); if (b != null)
{
Matlab.PutVector("NUMSLV.b", b.ToArray());
}
Matlab.Execute("NUMSLV.Aeq = [];"); if (Aeq != null)
{
Matlab.PutMatrix("NUMSLV.Aeq", Aeq.ToArray());
}
Matlab.Execute("NUMSLV.beq = [];"); if (beq != null)
{
Matlab.PutVector("NUMSLV.beq", beq.ToArray());
}
Matlab.Execute("NUMSLV.lb = [];"); if (lb != null)
{
Matlab.PutVector("NUMSLV.lb", lb.ToArray());
}
Matlab.Execute("NUMSLV.ub = [];"); if (ub != null)
{
Matlab.PutVector("NUMSLV.ub", ub.ToArray());
}
Matlab.Execute("NUMSLV.x0 = [];"); if (x0 != null)
{
Matlab.PutVector("NUMSLV.x0", x0.ToArray());
}
if (options == null)
{
options = "[]";
}
Matlab.Execute("NUMSLV.x = lsqlin(NUMSLV.C, NUMSLV.d, NUMSLV.A, NUMSLV.b, NUMSLV.Aeq, NUMSLV.beq, NUMSLV.lb, NUMSLV.ub, NUMSLV.x0, " + options + ");", true);
x = Matlab.GetVector("NUMSLV.x");
Matlab.Clear("NUMSLV");
}
return(true);
}
protected override bool SvdImpl(Matrix X, out Matrix U, out Vector S, out Matrix V)
{
using (new Matlab.NamedLock("NUMSLV"))
{
Matlab.Clear("NUMSLV");
Matlab.PutMatrix("NUMSLV.X", X.ToArray());
Matlab.Execute("[NUMSLV.U, NUMSLV.S, NUMSLV.V] = svd(NUMSLV.X);");
Matlab.Execute("NUMSLV.S = diag(NUMSLV.S);");
U = Matlab.GetMatrix("NUMSLV.U");
S = Matlab.GetVector("NUMSLV.S");
V = Matlab.GetMatrix("NUMSLV.V");
Matlab.Clear("NUMSLV");
}
return(true);
}
protected override bool EigImpl(Matrix A, Matrix B, out Matrix eigvec, out Vector eigval)
{
NamedLock.FuncOO <Matrix, Vector, bool> func = delegate(out Matrix leigvec, out Vector leigval)
{
Matlab.Clear("HTLib2_Matlab_EigImpl");
Matlab.PutMatrix("HTLib2_Matlab_EigImpl.A", A.ToArray());
Matlab.PutMatrix("HTLib2_Matlab_EigImpl.B", B.ToArray());
Matlab.Execute("[HTLib2_Matlab_EigImpl.V, HTLib2_Matlab_EigImpl.D] = eig(HTLib2_Matlab_EigImpl.A, HTLib2_Matlab_EigImpl.B);");
Matlab.Execute("HTLib2_Matlab_EigImpl.D = diag(HTLib2_Matlab_EigImpl.D);");
leigvec = Matlab.GetMatrix("HTLib2_Matlab_EigImpl.V");
leigval = Matlab.GetVector("HTLib2_Matlab_EigImpl.D");
Matlab.Clear("HTLib2_Matlab_EigImpl");
return(true);
};
//return NamedLock.LockedCall("bool HTLib2.Matlab.NumericSolver.EigImpl(Matrix, Matrix, out Matrix, out Vector)", func, out eigvec, out eigval);
return(NamedLock.LockedCall(Matlab.NamedLock.GetName("HTLib2_Matlab_EigImpl"), func, out eigvec, out eigval));
}
protected override bool EigImpl(Matrix mat, out Matrix eigvec, out Vector eigval)
{
NamedLock.FuncOO <Matrix, Vector, bool> func = delegate(out Matrix leigvec, out Vector leigval)
{
bool bUseFile = (mat.ColSize * mat.ColSize > 1000 * 1000);
Matlab.Clear("HTLib2_Matlab_EigImpl");
Matlab.PutMatrix("HTLib2_Matlab_EigImpl.A", mat.ToArray(), bUseFile);
Matlab.Execute("[HTLib2_Matlab_EigImpl.V, HTLib2_Matlab_EigImpl.D] = eig(HTLib2_Matlab_EigImpl.A);");
Matlab.Execute("HTLib2_Matlab_EigImpl.D = diag(HTLib2_Matlab_EigImpl.D);");
leigvec = Matlab.GetMatrix("HTLib2_Matlab_EigImpl.V", bUseFile);
leigval = Matlab.GetVector("HTLib2_Matlab_EigImpl.D");
Matlab.Clear("HTLib2_Matlab_EigImpl");
return(true);
};
//return NamedLock.LockedCall("bool HTLib2.Matlab.NumericSolver.EigImpl(Matrix, out Matrix, out Vector)", func, out eigvec, out eigval);
return(NamedLock.LockedCall(Matlab.NamedLock.GetName("HTLib2_Matlab_EigImpl"), func, out eigvec, out eigval));
}
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 static object LeastSquare
(double[,] As, double[] bs
, bool opt_get_stat = false
)
{
if (HDebug.Selftest())
{
/// >> A = [ 1,3,2, 1 ; 4,5,6, 1 ; 7,9,9, 1 ; 11,11,12, 1 ; 13,16,15, 1 ]
/// >> b = [1, 4, 6, 9, 12]'
/// >> x = inv(A' * A) * (A' * b)
/// 0.2171
/// 0.2125
/// 0.4205
/// -0.7339
/// >> esti = A * x
/// 0.9619
/// 3.7203
/// 6.4832
/// 9.0381
/// 11.7965
/// >> corr(esti,b)
/// 0.9976
/// >> mean( (b-esti).^2 )
/// 0.0712
double[,] _A = new double[5, 3] {
{ 1, 3, 2 }, { 4, 5, 6 }, { 7, 9, 9 }, { 11, 11, 12 }, { 13, 16, 15 }
};
double[] _b = new double[5] {
1, 4, 6, 9, 12
};
dynamic _out = LeastSquare(_A, _b, true);
double _matlab_corr = 0.9976;
double _matlab_mse = 0.0712;
double[] _matlab_x = new double[] { 0.2171, 0.2125, 0.4205, -0.7339 };
double[] _matlab_esti = new double[] { 0.9619, 3.7203, 6.4832, 9.0381, 11.7965 };
double err1 = Math.Abs(_matlab_corr - _out.opt_estimation_corr);
double err2 = Math.Abs(_matlab_mse - _out.opt_mean_square_err);
double err3 = (_matlab_x - (Vector)_out.x).ToArray().MaxAbs();
double err4 = (_matlab_esti - (Vector)_out.opt_estimation).ToArray().MaxAbs();
HDebug.Assert(err1 < 0.0001);
HDebug.Assert(err2 < 0.0001);
HDebug.Assert(err3 < 0.0001);
HDebug.Assert(err4 < 0.0001);
}
/// => A x = b
///
/// => At A x = At b
///
/// => AA * x = Ab
/// => x = inv(AA) * Ab
HDebug.Assert(As.GetLength(0) == bs.Length);
int n = As.GetLength(0);
int k = As.GetLength(1);
Matrix A = Matrix.Zeros(n, k + 1);
for (int c = 0; c < n; c++)
{
for (int r = 0; r < k; r++)
{
A[c, r] = As[c, r];
}
A[c, k] = 1;
}
Matrix AA = LinAlg.MtM(A, A);
Vector Ab = LinAlg.MtV(A, bs);
Vector x;
switch (k + 1)
{
case 2: { Matrix invAA = LinAlg.Inv2x2(AA.ToArray()); x = LinAlg.MV(invAA, Ab); } break;
case 3: { Matrix invAA = LinAlg.Inv3x3(AA.ToArray()); x = LinAlg.MV(invAA, Ab); } break;
case 4: { Matrix invAA = LinAlg.Inv4x4(AA.ToArray()); x = LinAlg.MV(invAA, Ab); } break;
default:
Matlab.PutMatrix("LinAlg_LeastSquare.AA", AA);
Matlab.PutVector("LinAlg_LeastSquare.Ab", Ab);
Matlab.Execute("LinAlg_LeastSquare.AA = inv(LinAlg_LeastSquare.AA);");
Matlab.Execute("LinAlg_LeastSquare.x = LinAlg_LeastSquare.AA * LinAlg_LeastSquare.Ab;");
x = Matlab.GetVector("LinAlg_LeastSquare.x");
Matlab.Execute("clear LinAlg_LeastSquare;");
break;
}
double?opt_mean_square_err = null;
double?opt_estimation_corr = null;
Vector opt_estimation = null;
if (opt_get_stat)
{
opt_estimation = new double[n];
double avg_err2 = 0;
for (int i = 0; i < n; i++)
{
double esti = 0;
for (int j = 0; j < k; j++)
{
esti += As[i, j] * x[j];
}
esti += x[k];
opt_estimation[i] = esti;
avg_err2 += (esti - bs[i]) * (esti - bs[i]);
}
avg_err2 /= n;
opt_mean_square_err = avg_err2;
opt_estimation_corr = HMath.HCorr(opt_estimation, bs);
}
return(new
{
x = x,
/// optional outputs
opt_mean_square_err = opt_mean_square_err,
opt_estimation_corr = opt_estimation_corr,
opt_estimation = opt_estimation,
});
}