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 CorrImpl(Vector vec1, Vector vec2, out double corr)
{
NamedLock.FuncO <double, bool> func = delegate(out double lcorr)
{
Matlab.Clear("HTLib2_Matlab_CorrImpl");
Matlab.PutVector("HTLib2_Matlab_CorrImpl.vec1", vec1.ToArray());
Matlab.PutVector("HTLib2_Matlab_CorrImpl.vec2", vec2.ToArray());
Matlab.Execute("HTLib2_Matlab_CorrImpl.corr = corr(HTLib2_Matlab_CorrImpl.vec1, HTLib2_Matlab_CorrImpl.vec2);");
lcorr = Matlab.GetValue("HTLib2_Matlab_CorrImpl.corr");
Matlab.Clear("HTLib2_Matlab_CorrImpl");
return(true);
};
//return NamedLock.LockedCall("bool HTLib2.Matlab.NumericSolver.CorrImpl(Vector, Vector, out double)", func, out corr);
return(NamedLock.LockedCall(Matlab.NamedLock.GetName("HTLib2_Matlab_CorrImpl"), func, out corr));
}
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,
});
}
public static void PlotScatter
(IEnumerable <double> x
, IEnumerable <double> y
, IEnumerable <double> size = null
, double?sizeall = null
, IEnumerable <ValueTuple <double, double, double> > RGB = null
, ValueTuple <double, double, double>?RGBall = null
, string xlabel = null
, string ylabel = null
, string title = null
, bool filled = false
, bool init_figure = true
, bool init_holdon = true
, bool last_holdoff = true
)
{
Matlab.PutVector("htlib2_matlab_PlotScatter.x", x.ToArray());
Matlab.PutVector("htlib2_matlab_PlotScatter.y", y.ToArray());
if (size != null)
{
Matlab.PutVector("htlib2_matlab_PlotScatter.sz", size.ToArray());
}
if (RGB != null)
{
Matlab.PutVector("htlib2_matlab_PlotScatter.R", RGB.HListItem1().ToArray());
}
if (RGB != null)
{
Matlab.PutVector("htlib2_matlab_PlotScatter.G", RGB.HListItem2().ToArray());
}
if (RGB != null)
{
Matlab.PutVector("htlib2_matlab_PlotScatter.B", RGB.HListItem3().ToArray());
}
if (RGB != null)
{
Matlab.Execute("htlib2_matlab_PlotScatter.RGB = [htlib2_matlab_PlotScatter.R; htlib2_matlab_PlotScatter.G; htlib2_matlab_PlotScatter.B];");
}
if (init_figure)
{
Matlab.Execute("figure;");
}
if (init_holdon)
{
Matlab.Execute("hold on;");
}
string script;
{
script = "scatter" +
"( htlib2_matlab_PlotScatter.x" +
", htlib2_matlab_PlotScatter.y";
// size
if (sizeall != null)
{
script += ", " + sizeall.Value;
}
else if (size != null)
{
script += ", htlib2_matlab_PlotScatter.sz";
}
else
{
script += ", []";
}
// color
if (RGBall != null)
{
script += string.Format(", [{0},{1},{2}]", RGBall.Value.Item1, RGBall.Value.Item2, RGBall.Value.Item3);
}
else if (RGB != null)
{
script += ", htlib2_matlab_PlotScatter.RGB";
}
// filled
if (filled)
{
script += ", 'filled'";
}
// close
script += ");";
}
Matlab.Execute(script);
if (xlabel != null)
{
Matlab.Execute("xlabel('" + xlabel + "');");
}
if (ylabel != null)
{
Matlab.Execute("ylabel('" + ylabel + "');");
}
if (title != null)
{
Matlab.Execute("title('" + title + "');");
}
if (last_holdoff)
{
Matlab.Execute("hold off;");
}
Matlab.Execute("clear htlib2_matlab_PlotScatter;");
}