/// <summary>
/// Sobol sequence.
/// </summary>
public static IEnumerable <Rational> SobolR(PolyGF2 primitivePolynomial, params int[] initialValues)
{
var v = SobolDirectionVectors(64, primitivePolynomial, initialValues);
ulong s = 0;
var d = ((System.Numerics.BigInteger) 1) << 64;
foreach (var r in Sequences.Ruler())
{
s ^= v[r];
yield return(new Rational(s, d));
}
}
/// <summary>
/// Sobol sequence.
/// </summary>
public static IEnumerable <Decimal> SobolM(PolyGF2 primitivePolynomial, params int[] initialValues)
{
var v = SobolDirectionVectors(64, primitivePolynomial, initialValues);
ulong s = 0;
var d = ((System.Numerics.BigInteger) 1) << 64;
foreach (var r in Sequences.Ruler())
{
s ^= v[r];
yield return(s / 18446744073709551616M);
}
}
public void SobolInitialValues(int max)
{
int d = 2;
var g = new Generator("SobolInitialValue");
var v = new bool[max + 1][];
v[0] = new bool[max];
v[0][0] = true;
foreach (var p in PolyGF2.GetAllPrimitive().Take(max - 1))
{
v[d - 1] = new bool[max];
int s = p.Degree;
var m = new int[s];
var V = new SquareMatrixGF2(d);
while (true)
{
for (int i = 0; i < s; i++)
{
m[i] = g.Int32(2 << i) | 1;
}
var dv = Subrandom.SobolDirectionVectors(max, p, m);
for (int i = 0; i < max; i++)
{
v[d - 1][i] = dv[i] > (ulong)long.MaxValue;
}
for (int row = 0; row < d; row++)
{
for (int col = 0; col < d; col++)
{
V[row, col] = v[row][col];
}
}
bool det = V.GetDeterminant();
if (det)
{
break;
}
}
Trace.Write($"{d}\t{s}\t{p.GetCode() / 2 ^ (1UL << (s-1))}\t");
for (int i = 0; i < s; i++)
{
Trace.Write($"{m[i]} ");
}
Trace.WriteLine("");
d++;
}
}
public void SobolRationalTest()
{
var p = new PolyGF2(3, 1, 0);
var m = new[] { 1, 3, 7 };
foreach (var item in Subrandom.SobolR(p, m).Take(1000))
{
System.Diagnostics.Trace.WriteLine(item);
}
var g = new Generator("SobolRationalTest");
Test(g, () => Subrandom.SobolR(p, m));
}
internal static ulong[] SobolDirectionVectors(int d, PolyGF2 primitivePolynomial, int[] initialValues)
{
if (initialValues == null)
{
throw new ArgumentNullException(nameof(initialValues));
}
int n = initialValues.Length;
if (n != primitivePolynomial.Degree)
{
throw new ArgumentException("The number of initial values must be the same as the degree of the primitive polynomial.");
}
PolyGF2 factor;
long order;
if (!primitivePolynomial.IsPrimitive(out factor, out order))
{
ulong q = (1UL << primitivePolynomial.Degree) - 1UL;
var o = new PolyGF2((int)order, 0);
if (factor != PolyGF2.Zero)
{
throw new ArgumentException($"Polynomial is not primitive because it is divisible by {factor} = ({primitivePolynomial}) / ({primitivePolynomial / factor}).");
}
else
{
throw new ArgumentException($"Polynomial is not primitive because it only has order {order} and not {q}. ({o}) / ({primitivePolynomial}) = ({o / primitivePolynomial})");
}
}
// Validate initial values.
var v = new ulong[d];
long max = 1;
var m = initialValues;
for (int i = 0; i < n; i++)
{
max <<= 1;
if (m[i] < 0)
{
throw new ArgumentException($"Initial values cannot be negative. {m[i]} is definitely negative.");
}
if (m[i] >= max)
{
throw new ArgumentException($"The i-th initial value (starting with i=0) must be less than 2^i. ${m[i]} should be less than {max}.");
}
if ((m[i] & 1) == 0)
{
throw new ArgumentException($"Initial values must be odd. {m[i]} is even.");
}
v[i] = (ulong)m[i] << (63 - i);
}
// Compute remaining direction vectors.
var exponents = new HashSet <int>(primitivePolynomial.Exponents);
for (int i = n; i < d; i++)
{
ulong sum = v[i - n] >> n;
for (int j = 1; j <= n; j++)
{
if (exponents.Contains(n - j))
{
sum ^= v[i - j];
}
}
v[i] = sum;
}
return(v);
}
/// <summary>
/// Sobol sequence.
/// </summary>
public static IEnumerable <Rational> SobolR(int polynomialCode, params int[] initialValues)
{
var primitivePolynomial = PolyGF2.FromCode(2UL * (ulong)polynomialCode ^ 1UL ^ (1UL << initialValues.Length));
return(SobolR(primitivePolynomial, initialValues));
}
/// <summary>
/// Creates a <see cref="Sobol"/> with specified initial
/// values and primitive polynomial coefficients packed into
/// bits, with leading and trailing coefficient omitted.
/// </summary>
/// <param name="polynomialCode">Bit 0 corresponds to x^1.</param>
/// <param name="initialValues">Initial values.</param>
public Sobol(int polynomialCode, params int[] initialValues)
: this(PolyGF2.FromCode(2UL * (ulong)polynomialCode ^ 1UL ^ (1UL << initialValues.Length))
.Exponents.ToArray(), initialValues)
{
}
