public BarPlotValue Function(MatrixValue Y, MatrixValue x)
{
var bp = new BarPlotValue();
var X = new double[x.Length];
for (var i = 0; i < x.Length; i++)
{
X[i] = x[i + 1].Re;
}
if (Y.IsVector)
{
bp.AddPoints(YMath.Histogram(Y, X));
}
else
{
var M = new MatrixValue();
for (var i = 1; i <= Y.DimensionX; i++)
{
var N = YMath.Histogram(Y.GetColumnVector(i), X);
for (var j = 1; j <= N.Length; j++)
{
M[j, i] = N[j];
}
}
bp.AddPoints(M);
}
return(bp);
}
public BarPlotValue Function(MatrixValue Y, ScalarValue nbins)
{
var nn = nbins.GetIntegerOrThrowException("nbins", Name);
var bp = new BarPlotValue();
if (Y.IsVector)
{
bp.AddPoints(YMath.Histogram(Y, nn));
}
else
{
var M = new MatrixValue();
for (var i = 1; i <= Y.DimensionX; i++)
{
var N = YMath.Histogram(Y.GetColumnVector(i), nn);
for (var j = 1; j <= N.Length; j++)
{
M[j, i] = N[j];
}
}
bp.AddPoints(M);
}
return(bp);
}
public MatrixValue Function(MatrixValue Y, MatrixValue x)
{
var X = new Double[x.Length];
for (var i = 0; i < x.Length; i++)
{
X[i] = x[i + 1].Re;
}
if (!Y.IsVector)
{
var M = new MatrixValue();
for (var i = 1; i <= Y.DimensionX; i++)
{
var N = YMath.Histogram(Y.GetColumnVector(i), X);
for (var j = 1; j <= N.Length; j++)
{
M[j, i] = N[j];
}
}
return(M);
}
return(YMath.Histogram(Y, X));
}
public override MatrixValue Function(MatrixValue m)
{
var M = new MatrixValue(1, m.DimensionX);
for (var i = 1; i <= m.DimensionX; i++)
{
M[1, i] = GetVectorMax(m.GetColumnVector(i));
}
return(M);
}
public MatrixValue Function(MatrixValue m)
{
if (m.DimensionX == 1)
{
return GetVectorProd(m.GetColumnVector(1));
}
else if (m.DimensionY == 1)
{
return GetVectorProd(m.GetRowVector(1));
}
else
{
var M = new MatrixValue(m.DimensionY, m.DimensionX);
for (var i = 1; i <= m.DimensionX; i++)
{
M.SetColumnVector(i, GetVectorProd(m.GetColumnVector(i)));
}
return M;
}
}
public Value Function(MatrixValue m)
{
if (m.DimensionX == 1)
{
return GetVectorSum(m.GetColumnVector(1));
}
else if (m.DimensionY == 1)
{
return GetVectorSum(m.GetRowVector(1));
}
else
{
var M = new MatrixValue(1, m.DimensionX);
for (var i = 1; i <= m.DimensionX; i++)
{
M[1, i] = GetVectorSum(m.GetColumnVector(i));
}
return M;
}
}
public Value Function(MatrixValue m)
{
if (m.DimensionX == 1)
{
return(GetVectorProduct(m.GetColumnVector(1)));
}
else if (m.DimensionY == 1)
{
return(GetVectorProduct(m.GetRowVector(1)));
}
else
{
var M = new MatrixValue(1, m.DimensionX);
for (var i = 1; i <= m.DimensionX; i++)
{
M[1, i] = GetVectorProduct(m.GetColumnVector(i));
}
return(M);
}
}
public MatrixValue Function(MatrixValue m)
{
if (m.DimensionX == 1)
{
return(GetVectorSum(m.GetColumnVector(1)));
}
else if (m.DimensionY == 1)
{
return(GetVectorSum(m.GetRowVector(1)));
}
else
{
var M = new MatrixValue(m.DimensionY, m.DimensionX);
for (var i = 1; i <= m.DimensionX; i++)
{
M.SetColumnVector(i, GetVectorSum(m.GetColumnVector(i)));
}
return(M);
}
}
/// <summary>
/// Solves the system of linear equations.
/// </summary>
/// <param name="b">The vector b in A * x = b.</param>
/// <returns>The solution vector x.</returns>
public override MatrixValue Solve(MatrixValue b)
{
var k = Restart;
MatrixValue x;
if (X0 == null)
{
X0 = new MatrixValue(b.DimensionY, b.DimensionX);
}
else if (X0.DimensionX != b.DimensionX || X0.DimensionY != b.DimensionY)
{
throw new YAMPDifferentDimensionsException(X0, b);
}
H = new MatrixValue(k + 1, k);
V = new MatrixValue(X0.DimensionY, k);
c = new MatrixValue(k - 1, 1);
s = new MatrixValue(k - 1, 1);
gamma = new MatrixValue(k + 1, 1);
var converged = false;
do
{
var j = 0;
x = X0.Clone();
var r0 = b - A * x;
var beta = r0.Abs().Re;
H.Clear();
V.Clear();
gamma.Clear();
gamma[1] = new ScalarValue(beta);
c.Clear();
s.Clear();
V.SetColumnVector(1, r0 / gamma[1]);
if (beta < Tolerance)
{
break;
}
do
{
j++;
i++;
var Avj = A * V.GetColumnVector(j);
var sum = new MatrixValue(Avj.DimensionY, Avj.DimensionX);
for (var m = 1; m <= j; m++)
{
var w = V.GetColumnVector(m);
H[m, j] = w.ComplexDot(Avj);
sum += H[m, j] * w;
}
var wj = Avj - sum;
H[j + 1, j] = wj.Abs();
Rotate(j);
if (H[j + 1, j].AbsSquare() == 0.0)
{
converged = true;
break;
}
V.SetColumnVector(j + 1, wj / H[j + 1, j]);
beta = gamma[j + 1].Abs();
if (beta < Tolerance)
{
converged = true;
break;
}
}while (j < k);
var y = new MatrixValue(j, 1);
for (int l = j; l >= 1; l--)
{
var sum = ScalarValue.Zero;
for (var m = l + 1; m <= j; m++)
{
sum += H[l, m] * y[m];
}
y[l] = (gamma[l] - sum) / H[l, l];
}
for (var l = 1; l <= j; l++)
{
x += y[l] * V.GetColumnVector(l);
}
if (converged)
{
break;
}
X0 = x;
}while (i < MaxIterations);
return(x);
}
/// <summary>
/// Solves the system of linear equations.
/// </summary>
/// <param name="b">The vector b in A * x = b.</param>
/// <returns>The solution vector x.</returns>
public override MatrixValue Solve(MatrixValue b)
{
var k = Restart;
MatrixValue x;
if (X0 == null)
{
X0 = new MatrixValue(b.DimensionY, b.DimensionX);
}
else if (X0.DimensionX != b.DimensionX || X0.DimensionY != b.DimensionY)
{
throw new YAMPDifferentDimensionsException(X0, b);
}
H = new MatrixValue(k + 1, k);
V = new MatrixValue(X0.DimensionY, k);
c = new MatrixValue(k - 1, 1);
s = new MatrixValue(k - 1, 1);
gamma = new MatrixValue(k + 1, 1);
var converged = false;
do
{
var j = 0;
x = X0.Clone();
var r0 = b - A * x;
var beta = r0.Abs().Re;
H.Clear();
V.Clear();
gamma.Clear();
gamma[1] = new ScalarValue(beta);
c.Clear();
s.Clear();
V.SetColumnVector(1, r0 / gamma[1]);
if (beta < Tolerance)
{
break;
}
do
{
j++;
i++;
var Avj = A * V.GetColumnVector(j);
var sum = new MatrixValue(Avj.DimensionY, Avj.DimensionX);
for (var m = 1; m <= j; m++)
{
var w = V.GetColumnVector(m);
H[m, j] = w.ComplexDot(Avj);
sum += H[m, j] * w;
}
var wj = Avj - sum;
H[j + 1, j] = wj.Abs();
Rotate(j);
if (H[j + 1, j].AbsSquare() == 0.0)
{
converged = true;
break;
}
V.SetColumnVector(j + 1, wj / H[j + 1, j]);
beta = gamma[j + 1].Abs();
if (beta < Tolerance)
{
converged = true;
break;
}
}
while (j < k);
var y = new MatrixValue(j, 1);
for (int l = j; l >= 1; l--)
{
var sum = ScalarValue.Zero;
for (var m = l + 1; m <= j; m++)
{
sum += H[l, m] * y[m];
}
y[l] = (gamma[l] - sum) / H[l, l];
}
for (var l = 1; l <= j; l++)
{
x += y[l] * V.GetColumnVector(l);
}
if (converged)
{
break;
}
X0 = x;
}
while (i < MaxIterations);
return x;
}