public ArgumentsValue Function(MatrixValue X, MatrixValue Y)
{
if (X.Length != Y.Length)
throw new YAMPDifferentLengthsException(X.Length, Y.Length);
var x1 = new ScalarValue();
var y1 = new ScalarValue();
var xy = new ScalarValue();
var x2 = new ScalarValue();
var slope = new ScalarValue();
var offset = new ScalarValue();
for (var i = 1; i <= X.Length; i++)
{
x1 = x1 + X[i];
y1 = y1 + Y[i];
xy = xy + X[i] * Y[i];
x2 = x2 + X[i] * X[i];
}
var J = ((Double)X.Length * x2) - (x1 * x1);
if (J.Re != 0.0)
{
slope = (((Double)X.Length * xy) - (x1 * y1)) / J.Re;
offset = ((y1 * x2) - (x1 * xy)) / J.Re;
}
return new ArgumentsValue(slope, offset);
}
public MatrixValue Function(MatrixValue M)
{
if (M.DimensionX != 3 && M.DimensionY != 3)
throw new YAMPMatrixDimensionException(3, M.DimensionX, M.DimensionY, M.DimensionX);
var isTransposed = M.DimensionY != 3;
if (isTransposed)
{
M = M.Transpose();
}
var m = new MatrixValue(3, M.DimensionX);
for (var i = 1; i <= M.DimensionX; i++)
{
var r = M[1, i].Re;
var theta = M[2, i].Re;
var phi = M[3, i].Re;
var rt = r * Math.Sin(theta);
m[1, i] = new ScalarValue(rt * Math.Cos(phi));
m[2, i] = new ScalarValue(rt * Math.Sin(phi));
m[3, i] = new ScalarValue(r * Math.Cos(theta));
}
return isTransposed ? m.Transpose() : m;
}
public MatrixValue Function(MatrixValue M)
{
if (M.DimensionX != 3 && M.DimensionY != 3)
throw new YAMPMatrixDimensionException(3, M.DimensionX, M.DimensionY, M.DimensionX);
var isTransposed = M.DimensionY != 3;
if (isTransposed)
{
M = M.Transpose();
}
var m = new MatrixValue(3, M.DimensionX);
for (var i = 1; i <= M.DimensionX; i++)
{
var x = M[1, i].Re;
var y = M[2, i].Re;
var z = M[3, i].Re;
var r = Math.Sqrt(x * x + y * y + z * z);
var phi = Math.Atan2(y, x);
var theta = Math.Acos(z / r);
m[1, i] = new ScalarValue(r);
m[2, i] = new ScalarValue(theta);
m[3, i] = new ScalarValue(phi);
}
return isTransposed ? m.Transpose() : m;
}
// R is the radix, N the total length, and u contains the Nth complex roots of unity
public Transformlet(int R, int N, ScalarValue[] u)
{
this.R = R;
this.N = N;
this.u = u;
this.dx = N / R;
}
public MatrixValue Function(ScalarValue x, ScalarValue y, ScalarValue z)
{
var r = Math.Sqrt(x.Re * x.Re + y.Re * y.Re + z.Re * z.Re);
var phi = Math.Atan2(y.Re, x.Re);
var theta = Math.Acos(z.Re / r);
return new MatrixValue(new[] { new ScalarValue(r), new ScalarValue(theta), new ScalarValue(phi) }, 3, 1);
}
public MatrixValue Function(ScalarValue j1, ScalarValue j2)
{
if (isNotHalf(j1))
throw new ArgumentException("0, +-0.5, +-1, +-1.5, ...", j1.Re.ToString());
if (isNotHalf(j2))
throw new ArgumentException("0, +-0.5, +-1, +-1.5, ...", j2.Re.ToString());
var l = 1;
var M = new MatrixValue();
for (var m1 = -j1.Re; m1 <= j1.Re; m1 += 1.0)
{
for (var m2 = -j2.Re; m2 <= j2.Re; m2 += 1.0)
{
var m = m1 + m2;
var ja = j1.Re + j2.Re;
for (var j = Math.Abs(m); j <= ja; j += 1.0)
{
var v = CGCoefficients(j1.Re, j2.Re, j, m1, m2);
M[l, 1] = new ScalarValue(m);
M[l, 2] = new ScalarValue(m1);
M[l, 3] = new ScalarValue(m2);
M[l, 4] = new ScalarValue(j);
M[l, 5] = new ScalarValue(v);
l++;
}
}
}
return M;
}
static MatrixValue Generate(Int32 n, Int32 m)
{
var distribution = new DiscreteUniformDistribution(Rng);
var l = n * m;
var M = new MatrixValue(n, m);
var numbers = new List<Int32>();
distribution.Alpha = 0;
for (var i = 1; i <= l; i++)
{
numbers.Add(i);
}
for (var j = 1; j <= n; j++)
{
for (var i = 1; i <= m; i++)
{
distribution.Beta = numbers.Count - 1;
var index = distribution.Next();
index = Math.Max(Math.Min(0, index), numbers.Count - 1);
M[j, i] = new ScalarValue(numbers[index]);
numbers.RemoveAt(index);
}
}
return M;
}
Plot2DValue Plot(IFunction f, Double minx, Double maxx, Double precision)
{
var cp = new Plot2DValue();
var N = (Int32)((maxx - minx) / precision) + 1;
var M = new MatrixValue(N, 2);
var x = new ScalarValue(minx);
for (var i = 0; i < N; i++)
{
var row = i + 1;
var y = f.Perform(Context, x);
M[row, 1] = x.Clone();
if (y is ScalarValue)
{
M[row, 2] = (ScalarValue)y;
}
else if (y is MatrixValue)
{
var Y = (MatrixValue)y;
for (var j = 1; j <= Y.Length; j++)
{
M[row, j + 1] = Y[j];
}
}
x.Re += precision;
}
cp.AddPoints(M);
return cp;
}
public MatrixValue Function(MatrixValue M)
{
if (M.DimensionX != 2 && M.DimensionY != 2)
throw new YAMPMatrixDimensionException(2, M.DimensionX, M.DimensionY, M.DimensionX);
var isTransposed = M.DimensionY != 2;
if (isTransposed)
{
M = M.Transpose();
}
var m = new MatrixValue(2, M.DimensionX);
for (var i = 1; i <= M.DimensionX; i++)
{
var x = M[1, i].Re;
var y = M[2, i].Re;
var phi = Math.Atan2(y, x);
var r = x == 0.0 ? y : (y == 0.0 ? x : x / Math.Cos(phi));
m[1, i] = new ScalarValue(r * Math.Cos(phi));
m[2, i] = new ScalarValue(r * Math.Sin(phi));
}
return isTransposed ? m.Transpose() : m;
}
/// <summary>
/// Returns the complex dot product (a, b).
/// </summary>
/// <param name="aStore">The first vector a.</param>
/// <param name="aOffset">Offset in the vector a.</param>
/// <param name="aStride">The offset between two elements of the vector a.</param>
/// <param name="bStore">The second vector b.</param>
/// <param name="bOffset">Offset in the vector a.</param>
/// <param name="bStride">The offset between two elements of the vector a.</param>
/// <param name="count">The number of elements to consider.</param>
/// <returns>The result of the complex dot product.</returns>
public static ScalarValue cDot(ScalarValue[] aStore, int aOffset, int aStride, ScalarValue[] bStore, int bOffset, int bStride, int count)
{
double re = 0.0;
double im = 0.0;
int n = 0;
int a = aOffset;
int b = bOffset;
while (n < count)
{
var re1 = aStore[a].Re;
var im1 = aStore[a].Im;
var re2 = bStore[b].Re;
var im2 = bStore[b].Im;
re += (re1 * re2 - im1 * im2);
im += (re1 * im2 + im1 * re2);
n++;
a += aStride;
b += bStride;
}
return new ScalarValue(re, im);
}
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(ScalarValue x0, ScalarValue xn, ScalarValue y0, ScalarValue yn)
{
var m = new Newton();
var xsteps = (int)Math.Abs(Math.Ceiling((xn.Re - x0.Re) / 0.1));
var ysteps = (int)Math.Abs(Math.Ceiling((yn.Re - y0.Re) / 0.1));
return m.CalculateMatrix(x0.Re, xn.Re, y0.Re, yn.Re, xsteps, ysteps);
}
public virtual void FftKernel(ScalarValue[] x, ScalarValue[] y, int y0, int dy, int sign)
{
int yi = y0;
y[yi] = ScalarValue.Zero;
for (int j = 0; j < R; j++)
y[yi] += x[j];
// now do the higher index entries
for (int i = 1; i < R; i++)
{
yi += dy;
y[yi] = x[0];
int ui = 0; if (sign < 0) ui = N;
int du = dx * i; if (sign < 0) du = -du;
for (int j = 1; j < R; j++)
{
ui += du;
if (ui >= N)
ui -= N;
if (ui < 0)
ui += N;
y[yi] += x[j] * u[ui];
}
}
}
public MatrixValue Function(ScalarValue x0, ScalarValue xn, ScalarValue y0, ScalarValue yn, ScalarValue xsteps, ScalarValue ysteps)
{
var xs = xsteps.GetIntegerOrThrowException("xsteps", Name);
var ys = ysteps.GetIntegerOrThrowException("ysteps", Name);
var m = new Mandelbrot();
return m.CalculateMatrix(x0.Re, xn.Re, y0.Re, yn.Re, xs, ys);
}
public virtual void FftPass(ScalarValue[] x, ScalarValue[] y, int Ns, int sign)
{
var v = new ScalarValue[R];
int dx = N / R;
for (int j = 0; j < dx; j++)
{
int xi = j;
int ui = 0;
if (sign < 0)
ui = N;
int du = (dx / Ns) * (j % Ns);
if (sign < 0)
du = -du;
v[0] = x[xi];
for (int r = 1; r < R; r++)
{
xi += dx;
ui += du;
v[r] = x[xi] * u[ui];
}
int y0 = Expand(j, Ns, R);
FftKernel(v, y, y0, Ns, sign);
}
}
public static ScalarValue Ylm(int l, int m, double theta, double phi)
{
var expphi = new ScalarValue(0.0, m * phi).Exp();
var factor = m < 0 ? Math.Pow(-1, -m) : 1.0;
var legend = Plm(l, Math.Abs(m), Math.Cos(theta));
return factor * expphi * legend;
}
public ArgumentsValue Function(ScalarValue n)
{
var nn = n.GetIntegerOrThrowException("n", Name);
int dim = nn + 1;
if (dim < 2)
throw new YAMPArgumentRangeException("n", 1.0);
var X = new MatrixValue(dim, dim); // x = sin(phi) * cos(theta)
var Y = new MatrixValue(dim, dim); // y = sin(phi) * sin(theta)
var Z = new MatrixValue(dim, dim); // z = cos(phi)
var stheta = Table(0.0, 2.0 * Math.PI, dim, Math.Sin);
var ctheta = Table(0.0, 2.0 * Math.PI, dim, Math.Cos);
var sphi = Table(0.0, Math.PI, dim, Math.Sin);
var cphi = Table(0.0, Math.PI, dim, Math.Cos);
for (var j = 0; j < dim; j++)
{
var col = j + 1;
for (var i = 0; i < dim; i++)
{
var row = i + 1;
X[row, col] = new ScalarValue(sphi[j] * ctheta[i]);
Y[row, col] = new ScalarValue(sphi[j] * stheta[i]);
Z[row, col] = new ScalarValue(cphi[j]);
}
}
return new ArgumentsValue(X, Y, Z);
}
public MatrixValue Function(MatrixValue x, MatrixValue y, ScalarValue n)
{
if (x.Length != y.Length)
throw new YAMPDifferentLengthsException(x.Length, y.Length);
var nn = n.GetIntegerOrThrowException("n", Name);
var m = nn + 1;
if (m < 2)
throw new YAMPArgumentRangeException("n", 0.0);
var M = new MatrixValue(x.Length, m);
var b = new MatrixValue(x.Length, 1);
for (var j = 1; j <= M.Rows; j++)
{
var el = ScalarValue.One;
var z = x[j];
for (var i = 1; i <= M.Columns; i++)
{
M[j, i] = el;
el *= z;
}
b[j, 1] = y[j];
}
var qr = QRDecomposition.Create(M);
return qr.Solve(b);
}
public MatrixValue Function(MatrixValue original, ScalarValue x)
{
var spline = new SplineInterpolation(original);
var M = new MatrixValue(1, 2);
M[1, 1].Re = x.Re;
M[1, 2].Re = spline.ComputeValue(x.Re);
return M;
}
protected override ScalarValue GetValue(ScalarValue value)
{
if (value.Re == 0.0 && value.Im == 0.0)
return ScalarValue.One;
var arg = value * Math.PI;
return arg.Sin() / arg;
}
public MatrixValue Function(ScalarValue r, ScalarValue phi, ScalarValue theta)
{
var rt = r.Re * Math.Sin(theta.Re);
var x = new ScalarValue(rt * Math.Cos(phi.Re));
var y = new ScalarValue(rt * Math.Sin(phi.Re));
var z = new ScalarValue(r.Re * Math.Cos(theta.Re));
return new MatrixValue(new[] { x, y, z }, 3, 1);
}
public ScalarValue Function(ScalarValue n, ScalarValue z)
{
var nn = n.GetIntegerOrThrowException("n", Name);
if (nn < 0)
throw new Exception("Hermite polynomial of order n < 0 does not make sense.");
return HermitePolynomial(nn, z);
}
public ScalarValue Function(ScalarValue n, ScalarValue alpha, ScalarValue beta, ScalarValue z)
{
var nn = n.GetIntegerOrThrowException("n", Name);
if (nn < 0)
throw new Exception("Jacobi polynomial of order n < 0 does not make sense.");
return JacobiPolynomial(nn, alpha, beta, z);
}
public ScalarValue Function(ScalarValue n, ScalarValue x)
{
var nn = n.GetIntegerOrThrowException("n", Name);
if (nn < 0)
throw new Exception("Chebyshev polynomial of order n < 0 does not make sense.");
var f = GetPolynom(nn);
return new ScalarValue(f(x.Re));
}
static void FftKernel(ScalarValue x0, ScalarValue x1, out ScalarValue y0, out ScalarValue y1)
{
double a0 = x0.Re;
double b0 = x0.Im;
double a1 = x1.Re;
double b1 = x1.Im;
y0 = new ScalarValue(a0 + a1, b0 + b1);
y1 = new ScalarValue(a0 - a1, b0 - b1);
}
public ScalarValue Function(ScalarValue l, ScalarValue m, ScalarValue theta, ScalarValue phi)
{
var nn = l.GetIntegerOrThrowException("l", Name);
if (nn < 0)
throw new Exception("Spherical harmonics of order l < 0 does not make sense.");
var nm = m.GetIntegerOrThrowException("m", Name);
return Ylm(nn, nm, theta.Re, phi.Re);
}
ScalarValue GetValue(int n, ScalarValue z)
{
if (n == 1)
return z.Arctan();
else if (n == 0)
return z / (1.0 + z * z);
var iz = z * ScalarValue.I;
return IMAGONEHALF * (PolyLogFunction.Polylog(n, iz) - PolyLogFunction.Polylog(n, -iz));
}
public MatrixValue Function(ScalarValue s, MatrixValue Z)
{
var n = s.GetIntegerOrThrowException("s", Name);
var M = new MatrixValue(Z.DimensionY, Z.DimensionX);
for (var j = 1; j <= Z.DimensionY; j++)
for (var i = 1; i <= Z.DimensionX; i++)
M[j, i] = GetValue(n, Z[j, i]);
return M;
}
/// <summary>
/// Returns the result of the product x = a * x, with a complex a and a complex vector x.
/// </summary>
/// <param name="alpha">Some arbitrary complex scalar.</param>
/// <param name="store">The complex vector x.</param>
/// <param name="offset">The offset in the vector x.</param>
/// <param name="stride">The offset between two elements in x.</param>
/// <param name="count">The number of elements to consider (from x).</param>
public static void cScal(ScalarValue alpha, ScalarValue[] store, int offset, int stride, int count)
{
int n = 0;
int i = offset;
while (n < count)
{
store[i] *= alpha;
n++;
i += stride;
}
}
public MatrixValue Function(ScalarValue from, ScalarValue to, ScalarValue count)
{
var c = count.GetIntegerOrThrowException("count", Name);
if (c < 2)
{
throw new ArgumentException("linspace");
}
var step = (to.Re - from.Re) / (c - 1);
return new RangeValue(from.Re, to.Re, step);
}
public ScalarValue Function(ScalarValue z)
{
var m = new Mandelbrot();
return(new ScalarValue(m.Run(z.Re, z.Im)));
}
public ContourPlotValue Function(MatrixValue X, MatrixValue Y, MatrixValue Z, ScalarValue n)
{
var nn = n.GetIntegerOrThrowException("n", Name);
var plot = new ContourPlotValue();
plot.AddPoints(X, Y, Z);
plot.SetLevels(nn);
return(plot);
}
protected override ScalarValue GetValue(ScalarValue value)
{
return(Zeta.RiemannZeta(value));
}
/// <summary>
/// Creates a new scalar value from the given one.
/// </summary>
/// <param name="value">Copies the contents of the given value.</param>
public ScalarValue(ScalarValue value)
: this(value._real, value._imag)
{
}
protected override ScalarValue GetValue(ScalarValue z)
{
var zi = 1.0 / z;
return((zi + (zi + 1.0).Sqrt() * (zi - 1.0).Sqrt()).Ln());
}
public ComplexPlotValue Function(FunctionValue f, ScalarValue min, ScalarValue max)
{
return(Plot(f, min.Re, max.Re, min.Im, max.Im));
}
public MatrixValue Function(ScalarValue start, ScalarValue end, ScalarValue count)
{
return(Function(start, end, count, new ScalarValue(10)));
}
public FunctionValue Function(MatrixValue Y, ScalarValue nbins, ScalarValue nParameters)
{
var nn = nbins.GetIntegerOrThrowException("nbins", Name);
var nP = nParameters.GetIntegerOrThrowException("nParameters", Name);
var N = Y.Length;
var min_idx = Y.Min();
var min = Y[min_idx.Row, min_idx.Column];
var max_idx = Y.Max();
var max = Y[max_idx.Row, max_idx.Column];
var median = YMath.Median(Y);
var variance = ScalarValue.Zero;
var mean = Y.Sum() / Y.Length;
for (var i = 1; i <= Y.Length; i++)
{
variance += (Y[i] - mean).Square();
}
variance /= Y.Length;
var delta = (max - min) / nn;
var x = new MatrixValue(nn, 1);
for (var i = 0; i < nn; i++)
{
x[i + 1] = min + delta * i;
}
var histogram = new HistogramFunction();
var fx = histogram.Function(Y, x);
var linearfit = new LinfitFunction(Context);
var dist = linearfit.Function(x, fx, new FunctionValue((context, argument) =>
{
var _x = (argument as ScalarValue - median / 2) / (variance / 4);
var _exp_x_2 = (-_x * _x).Exp();
var result = new MatrixValue(1, nP - 1);
for (var i = 0; i < nP - 1; i++)
{
result[i + 1] = _exp_x_2 * _x.Pow(new ScalarValue(i));
}
return(result);
}, true));
var norm = Y.Length * (max - min) / nbins;
var normed_dist = new FunctionValue((context, argument) =>
{
var temp = dist.Perform(context, argument);
if (temp is ScalarValue)
{
return(((ScalarValue)temp) / norm);
}
else if (temp is MatrixValue)
{
return(((MatrixValue)temp) / norm);
}
throw new YAMPOperationInvalidException();
}, true);
return(normed_dist);
}
public ScalarValue Function(ScalarValue order, ScalarValue argument)
{
var n = order.GetIntegerOrThrowException("order", Name);
return(GetValue(n, argument.Re));
}
protected override ScalarValue GetValue(ScalarValue value)
{
return(new ScalarValue(Bessel.j1(value.Re)));
}
protected override ScalarValue GetValue(ScalarValue value)
{
return(1.0 / value.Sin());
}
public MatrixValue Function(ScalarValue x0, ScalarValue xn, ScalarValue y0, ScalarValue yn, ScalarValue xsteps, ScalarValue ysteps)
{
var xs = xsteps.GetIntegerOrThrowException("xsteps", Name);
var ys = ysteps.GetIntegerOrThrowException("ysteps", Name);
var m = new Mandelbrot();
return(m.CalculateMatrix(x0.Re, xn.Re, y0.Re, yn.Re, xs, ys));
}
public MatrixValue Function(ScalarValue start, ScalarValue end, ScalarValue count, ScalarValue basis)
{
var c = count.GetIntegerOrThrowException("count", Name);
if (c < 2)
{
throw new ArgumentException("logspace");
}
var s = (end.Re - start.Re) / (c - 1);
var r = new RangeValue(start.Re, end.Re, s);
return(MatrixValue.PowSM(basis, r));
}
protected override ScalarValue GetValue(ScalarValue value)
{
return(2.0 / (value.Exp() - (-value).Exp()));
}
public ComplexPlotValue Function(FunctionValue f, ScalarValue minX, ScalarValue maxX, ScalarValue minY, ScalarValue maxY)
{
return(Plot(f, minX.Re, maxX.Re, minY.Re, maxY.Re));
}
protected override ScalarValue GetValue(ScalarValue value)
{
return(new ScalarValue(value.Arg()));
}
public MatrixValue Function(ScalarValue rows, ScalarValue cols, ScalarValue theta, ScalarValue k)
{
var n = rows.GetIntegerOrThrowException("rows", Name);
var l = cols.GetIntegerOrThrowException("cols", Name);
var m = new MatrixValue(n, l);
for (var i = 1; i <= l; i++)
{
for (var j = 1; j <= n; j++)
{
m[j, i] = new ScalarValue(Gamma(theta.Re, k.Re));
}
}
return(m);
}
protected override ScalarValue GetValue(ScalarValue value)
{
return(value.Conjugate());
}
public override ScalarValue Compare(ScalarValue left, ScalarValue right)
{
return(new ScalarValue(left == right));
}
public MatrixValue Function(ScalarValue rows, ScalarValue cols, ScalarValue mu, ScalarValue b)
{
var n = rows.GetIntegerOrThrowException("rows", Name);
var l = cols.GetIntegerOrThrowException("cols", Name);
var m = new MatrixValue(n, l);
for (var i = 1; i <= l; i++)
{
for (var j = 1; j <= n; j++)
{
m[j, i] = new ScalarValue(Laplace(mu.Re, b.Re));
}
}
return(m);
}
/// <summary> /// Implementation of the operation. /// </summary> /// <param name="left">The left scalar.</param> /// <param name="right">The right scalar.</param> /// <returns>The result of the operation.</returns> public abstract ScalarValue Operation(ScalarValue left, ScalarValue right);
public MatrixValue Function(ScalarValue dim)
{
var k = (int)dim.Re;
return(MatrixValue.Ones(k, k));
}
public MatrixValue Function(ScalarValue n)
{
var d = n.GetIntegerOrThrowException("n", Name);
return(Generate(d, d));
}
static ScalarValue GetValue(ScalarValue value, Double newBase)
{
return(value.Log(newBase));
}
public MatrixValue Function(ScalarValue rows, ScalarValue cols)
{
return(Function(rows, cols, new ScalarValue(1.0)));
}
protected override ScalarValue GetValue(ScalarValue value)
{
return(new ScalarValue(double.IsInfinity(value.Re) || double.IsInfinity(value.Im)));
}
public ScalarValue Function(ScalarValue a, ScalarValue b)
{
return(a / b);
}
protected override ScalarValue GetValue(ScalarValue value)
{
return(value.Log10());
}
public ScalarValue Function(ScalarValue x, ScalarValue y)
{
var m = new Mandelbrot();
return(new ScalarValue(m.Run(x.Re, y.Re)));
}
public MatrixValue Function(ScalarValue dim)
{
return(Function(dim, dim));
}
