static public double RayleighQuotient(Digraph G, double[] xs)
{
Debug.Assert(xs.Length == G.n);
double denominator = Vector.L2Norm(xs);
double numerator = 0;
for (int u = 0; u < G.n; u++)
{
foreach (var v in G.OutNeighbors[u])
{
if (xs [u] > xs [v])
{
numerator += (xs [u] - xs [v]) * (xs [u] - xs [v]);
}
}
}
return(numerator / denominator);
}
static public double[] Gradient(Digraph G, double[] xs)
{
Debug.Assert(xs.Length == G.n);
var ys = Enumerable.Range(0, G.n).Select(
u => xs [u] / Math.Sqrt(G.Degree(u))
).ToArray();
var res = new double[G.n];
for (int u = 0; u < G.n; u++)
{
res [u] = xs [u];
foreach (var v in G.OutNeighbors[u])
{
if (ys [u] > ys [v])
{
res [u] -= xs [v] / Math.Sqrt(G.Degree(u) * G.Degree(v));
}
else
{
res [u] -= xs [u] / G.Degree(u);
}
}
foreach (var v in G.InNeighbors[u])
{
if (ys [u] < ys [v])
{
res [u] -= xs [v] / Math.Sqrt(G.Degree(u) * G.Degree(v));
}
else
{
res [u] -= xs [u] / G.Degree(u);
}
}
}
for (int u = 0; u < G.n; u++)
{
res [u] = -res [u];
}
return(res);
}
static public double[] Iterate(Digraph G, double[] xs, double dt, List <double[]> Pi = null)
{
var dx = Gradient(G, xs);
for (int u = 0; u < G.n; u++)
{
xs [u] = xs [u] + dx [u] * dt;
}
if (Pi != null)
{
foreach (var p in Pi)
{
var dot = Vector.Dot(xs, p);
xs = Vector.Subtract(xs, Vector.Multiply(dot, p));
}
}
xs = Vector.L2Normalize(xs);
return(xs);
}
static public double[] Gradient(Digraph G, double[] xs)
{
Debug.Assert(xs.Length == G.n);
var res = new double[G.n];
for (int u = 0; u < G.n; u++)
{
res [u] = xs [u] * G.Degree(u);
foreach (var v in G.OutNeighbors[u])
{
if (xs [u] > xs [v])
{
res [u] -= xs [v];
}
else
{
res [u] -= xs [u];
}
}
foreach (var v in G.InNeighbors[u])
{
if (xs [u] < xs [v])
{
res [u] -= xs [v];
}
else
{
res [u] -= xs [u];
}
}
}
for (int u = 0; u < G.n; u++)
{
res [u] = -res [u];
}
return(res);
}
static public double RayleighQuotient(Digraph G, double[] xs)
{
Debug.Assert(xs.Length == G.n);
double denominator = Vector.L2Norm(xs);
double numerator = 0;
var ys = Enumerable.Range(0, G.n).Select(
u => xs [u] / Math.Sqrt(G.Degree(u))
).ToArray();
for (int u = 0; u < G.n; u++)
{
foreach (var v in G.OutNeighbors[u])
{
if (ys [u] > ys [v])
{
numerator += (ys [u] - ys [v]) * (ys [u] - ys [v]);
}
}
}
return(numerator / denominator);
}
static public double[] FirstEigenvector(Digraph G)
{
var res = Enumerable.Range(0, G.n).Select(u => Math.Sqrt(G.Degree(u))).ToArray();
return(Vector.L2Normalize(res));
}
static public double[] FirstEigenvector(Digraph G)
{
var res = Enumerable.Repeat(1.0, G.n).ToArray();
return(Vector.L2Normalize(res));
}
