// Define a function for running the simulation of a population system S with timestep
// dt. The number of timesteps and the data buffer are parameters of the defined function.
static Func <int, double[, ], int> DefineSimulate(double dt, PopulationSystem S)
{
CodeGen code = new CodeGen();
// Define a parameter for the current population x, and define mappings to the
// expressions defined above.
LinqExpr N = code.Decl <int>(Scope.Parameter, "N");
LinqExpr Data = code.Decl <double[, ]>(Scope.Parameter, "Data");
// Loop over the sample range requested. Note that this loop is a 'runtime' loop,
// while the rest of the loops nested in the body of this loop are 'compile time' loops.
LinqExpr n = code.DeclInit <int>("n", 1);
code.For(
() => { },
LinqExpr.LessThan(n, N),
() => code.Add(LinqExpr.PostIncrementAssign(n)),
() =>
{
// Define expressions representing the population of each species.
List <Expression> x = new List <Expression>();
for (int i = 0; i < S.N; ++i)
{
// Define a variable xi.
Expression xi = "x" + i.ToString();
x.Add(xi);
// xi = Data[n, i].
code.DeclInit(xi, LinqExpr.ArrayAccess(Data, LinqExpr.Subtract(n, LinqExpr.Constant(1)), LinqExpr.Constant(i)));
}
for (int i = 0; i < S.N; ++i)
{
// This list is the elements of the sum representing the i'th
// row of f, i.e. r_i + (A*x)_i.
Expression dx_dt = 1;
for (int j = 0; j < S.N; ++j)
{
dx_dt -= S.A[i, j] * x[j];
}
// Define dx_i/dt = x_i * f_i(x), as per the Lotka-Volterra equations.
dx_dt *= x[i] * S.r[i];
// Euler's method for x(t) is: x(t) = x(t - h) + h * x'(t - h).
Expression integral = x[i] + dt * dx_dt;
// Data[n, i] = Data[n - 1, i] + dt * dx_dt;
code.Add(LinqExpr.Assign(
LinqExpr.ArrayAccess(Data, n, LinqExpr.Constant(i)),
code.Compile(integral)));
}
});
code.Return(N);
// Compile the generated code.
LinqExprs.Expression <Func <int, double[, ], int> > expr = code.Build <Func <int, double[, ], int> >();
return(expr.Compile());
}
// Solve a system of linear equations
private static void Solve(CodeGen code, LinqExpr Ab, IEnumerable <LinearCombination> Equations, IEnumerable <Expression> Unknowns)
{
LinearCombination[] eqs = Equations.ToArray();
Expression[] deltas = Unknowns.ToArray();
int M = eqs.Length;
int N = deltas.Length;
// Initialize the matrix.
for (int i = 0; i < M; ++i)
{
LinqExpr Abi = code.ReDeclInit <double[]>("Abi", LinqExpr.ArrayAccess(Ab, LinqExpr.Constant(i)));
for (int x = 0; x < N; ++x)
{
code.Add(LinqExpr.Assign(
LinqExpr.ArrayAccess(Abi, LinqExpr.Constant(x)),
code.Compile(eqs[i][deltas[x]])));
}
code.Add(LinqExpr.Assign(
LinqExpr.ArrayAccess(Abi, LinqExpr.Constant(N)),
code.Compile(eqs[i][1])));
}
// Gaussian elimination on this turd.
//RowReduce(code, Ab, M, N);
code.Add(LinqExpr.Call(
GetMethod <Simulation>("RowReduce", Ab.Type, typeof(int), typeof(int)),
Ab,
LinqExpr.Constant(M),
LinqExpr.Constant(N)));
// Ab is now upper triangular, solve it.
for (int j = N - 1; j >= 0; --j)
{
LinqExpr _j = LinqExpr.Constant(j);
LinqExpr Abj = code.ReDeclInit <double[]>("Abj", LinqExpr.ArrayAccess(Ab, _j));
LinqExpr r = LinqExpr.ArrayAccess(Abj, LinqExpr.Constant(N));
for (int ji = j + 1; ji < N; ++ji)
{
r = LinqExpr.Add(r, LinqExpr.Multiply(LinqExpr.ArrayAccess(Abj, LinqExpr.Constant(ji)), code[deltas[ji]]));
}
code.DeclInit(deltas[j], LinqExpr.Divide(LinqExpr.Negate(r), LinqExpr.ArrayAccess(Abj, _j)));
}
}
// Use homotopy method with newton's method to find a solution for F(x) = 0.
private static List <Arrow> NSolve(List <Expression> F, List <Arrow> x0, double Epsilon, int MaxIterations)
{
int M = F.Count;
int N = x0.Count;
// Compute JxF, the Jacobian of F.
List <Dictionary <Expression, Expression> > JxF = Jacobian(F, x0.Select(i => i.Left)).ToList();
// Define a function to evaluate JxH(x), where H = F(x) - s*F(x0).
CodeGen code = new CodeGen();
ParamExpr _JxH = code.Decl <double[, ]>(Scope.Parameter, "JxH");
ParamExpr _x0 = code.Decl <double[]>(Scope.Parameter, "x0");
ParamExpr _s = code.Decl <double>(Scope.Parameter, "s");
// Load x_j from the input array and add them to the map.
for (int j = 0; j < N; ++j)
{
code.DeclInit(x0[j].Left, LinqExpr.ArrayAccess(_x0, LinqExpr.Constant(j)));
}
LinqExpr error = code.Decl <double>("error");
// Compile the expressions to assign JxH
for (int i = 0; i < M; ++i)
{
LinqExpr _i = LinqExpr.Constant(i);
for (int j = 0; j < N; ++j)
{
code.Add(LinqExpr.Assign(
LinqExpr.ArrayAccess(_JxH, _i, LinqExpr.Constant(j)),
code.Compile(JxF[i][x0[j].Left])));
}
// e = F(x) - s*F(x0)
LinqExpr e = code.DeclInit <double>("e", LinqExpr.Subtract(code.Compile(F[i]), LinqExpr.Multiply(LinqExpr.Constant((double)F[i].Evaluate(x0)), _s)));
code.Add(LinqExpr.Assign(LinqExpr.ArrayAccess(_JxH, _i, LinqExpr.Constant(N)), e));
// error += e * e
code.Add(LinqExpr.AddAssign(error, LinqExpr.Multiply(e, e)));
}
// return error
code.Return(error);
Func <double[, ], double[], double, double> JxH = code.Build <Func <double[, ], double[], double, double> >().Compile();
double[] x = new double[N];
// Remember where we last succeeded/failed.
double s0 = 0.0;
double s1 = 1.0;
do
{
try
{
// H(F, s) = F - s*F0
NewtonsMethod(M, N, JxH, s0, x, Epsilon, MaxIterations);
// Success at this s!
s1 = s0;
for (int i = 0; i < N; ++i)
{
x0[i] = Arrow.New(x0[i].Left, x[i]);
}
// Go near the goal.
s0 = Lerp(s0, 0.0, 0.9);
}
catch (FailedToConvergeException)
{
// Go near the last success.
s0 = Lerp(s0, s1, 0.9);
for (int i = 0; i < N; ++i)
{
x[i] = (double)x0[i].Right;
}
}
} while (s0 > 0.0 && s1 >= s0 + 1e-6);
// Make sure the last solution is at F itself.
if (s0 != 0.0)
{
NewtonsMethod(M, N, JxH, 0.0, x, Epsilon, MaxIterations);
for (int i = 0; i < N; ++i)
{
x0[i] = Arrow.New(x0[i].Left, x[i]);
}
}
return(x0);
}
// Generate code to perform row reduction.
private static void RowReduce(CodeGen code, LinqExpr Ab, int M, int N)
{
// For each variable in the system...
for (int j = 0; j + 1 < N; ++j)
{
LinqExpr _j = LinqExpr.Constant(j);
LinqExpr Abj = code.ReDeclInit <double[]>("Abj", LinqExpr.ArrayAccess(Ab, _j));
// int pi = j
LinqExpr pi = code.ReDeclInit <int>("pi", _j);
// double max = |Ab[j][j]|
LinqExpr max = code.ReDeclInit <double>("max", Abs(LinqExpr.ArrayAccess(Abj, _j)));
// Find a pivot row for this variable.
//code.For(j + 1, M, _i =>
//{
for (int i = j + 1; i < M; ++i)
{
LinqExpr _i = LinqExpr.Constant(i);
// if(|Ab[i][j]| > max) { pi = i, max = |Ab[i][j]| }
LinqExpr maxj = code.ReDeclInit <double>("maxj", Abs(LinqExpr.ArrayAccess(LinqExpr.ArrayAccess(Ab, _i), _j)));
code.Add(LinqExpr.IfThen(
LinqExpr.GreaterThan(maxj, max),
LinqExpr.Block(
LinqExpr.Assign(pi, _i),
LinqExpr.Assign(max, maxj))));
}
// (Maybe) swap the pivot row with the current row.
LinqExpr Abpi = code.ReDecl <double[]>("Abpi");
code.Add(LinqExpr.IfThen(
LinqExpr.NotEqual(_j, pi), LinqExpr.Block(
new[] { LinqExpr.Assign(Abpi, LinqExpr.ArrayAccess(Ab, pi)) }.Concat(
Enumerable.Range(j, N + 1 - j).Select(x => Swap(
LinqExpr.ArrayAccess(Abj, LinqExpr.Constant(x)),
LinqExpr.ArrayAccess(Abpi, LinqExpr.Constant(x)),
code.ReDecl <double>("swap")))))));
//// It's hard to believe this swap isn't faster than the above...
//code.Add(LinqExpr.IfThen(LinqExpr.NotEqual(_j, pi), LinqExpr.Block(
// Swap(LinqExpr.ArrayAccess(Ab, _j), LinqExpr.ArrayAccess(Ab, pi), Redeclare<double[]>(code, "temp")),
// LinqExpr.Assign(Abj, LinqExpr.ArrayAccess(Ab, _j)))));
// Eliminate the rows after the pivot.
LinqExpr p = code.ReDeclInit <double>("p", LinqExpr.ArrayAccess(Abj, _j));
//code.For(j + 1, M, _i =>
//{
for (int i = j + 1; i < M; ++i)
{
LinqExpr _i = LinqExpr.Constant(i);
LinqExpr Abi = code.ReDeclInit <double[]>("Abi", LinqExpr.ArrayAccess(Ab, _i));
// s = Ab[i][j] / p
LinqExpr s = code.ReDeclInit <double>("scale", LinqExpr.Divide(LinqExpr.ArrayAccess(Abi, _j), p));
// Ab[i] -= Ab[j] * s
for (int ji = j + 1; ji < N + 1; ++ji)
{
code.Add(LinqExpr.SubtractAssign(
LinqExpr.ArrayAccess(Abi, LinqExpr.Constant(ji)),
LinqExpr.Multiply(LinqExpr.ArrayAccess(Abj, LinqExpr.Constant(ji)), s)));
}
}
}
}
// The resulting lambda processes N samples, using buffers provided for Input and Output:
// void Process(int N, double t0, double T, double[] Input0 ..., double[] Output0 ...)
// { ... }
private Delegate DefineProcess()
{
// Map expressions to identifiers in the syntax tree.
List <KeyValuePair <Expression, LinqExpr> > inputs = new List <KeyValuePair <Expression, LinqExpr> >();
List <KeyValuePair <Expression, LinqExpr> > outputs = new List <KeyValuePair <Expression, LinqExpr> >();
// Lambda code generator.
CodeGen code = new CodeGen();
// Create parameters for the basic simulation info (N, t, Iterations).
ParamExpr SampleCount = code.Decl <int>(Scope.Parameter, "SampleCount");
ParamExpr t = code.Decl(Scope.Parameter, Simulation.t);
// Create buffer parameters for each input...
foreach (Expression i in Input)
{
inputs.Add(new KeyValuePair <Expression, LinqExpr>(i, code.Decl <double[]>(Scope.Parameter, i.ToString())));
}
// ... and output.
foreach (Expression i in Output)
{
outputs.Add(new KeyValuePair <Expression, LinqExpr>(i, code.Decl <double[]>(Scope.Parameter, i.ToString())));
}
// Create globals to store previous values of inputs.
foreach (Expression i in Input.Distinct())
{
AddGlobal(i.Evaluate(t_t0));
}
// Define lambda body.
// int Zero = 0
LinqExpr Zero = LinqExpr.Constant(0);
// double h = T / Oversample
LinqExpr h = LinqExpr.Constant(TimeStep / (double)Oversample);
// Load the globals to local variables and add them to the map.
foreach (KeyValuePair <Expression, GlobalExpr <double> > i in globals)
{
code.Add(LinqExpr.Assign(code.Decl(i.Key), i.Value));
}
foreach (KeyValuePair <Expression, LinqExpr> i in inputs)
{
code.Add(LinqExpr.Assign(code.Decl(i.Key), code[i.Key.Evaluate(t_t0)]));
}
// Create arrays for linear systems.
int M = Solution.Solutions.OfType <NewtonIteration>().Max(i => i.Equations.Count(), 0);
int N = Solution.Solutions.OfType <NewtonIteration>().Max(i => i.UnknownDeltas.Count(), 0) + 1;
LinqExpr JxF = code.DeclInit <double[][]>("JxF", LinqExpr.NewArrayBounds(typeof(double[]), LinqExpr.Constant(M)));
for (int j = 0; j < M; ++j)
{
code.Add(LinqExpr.Assign(LinqExpr.ArrayAccess(JxF, LinqExpr.Constant(j)), LinqExpr.NewArrayBounds(typeof(double), LinqExpr.Constant(N))));
}
// for (int n = 0; n < SampleCount; ++n)
ParamExpr n = code.Decl <int>("n");
code.For(
() => code.Add(LinqExpr.Assign(n, Zero)),
LinqExpr.LessThan(n, SampleCount),
() => code.Add(LinqExpr.PreIncrementAssign(n)),
() =>
{
// Prepare input samples for oversampling interpolation.
Dictionary <Expression, LinqExpr> dVi = new Dictionary <Expression, LinqExpr>();
foreach (Expression i in Input.Distinct())
{
LinqExpr Va = code[i];
// Sum all inputs with this key.
IEnumerable <LinqExpr> Vbs = inputs.Where(j => j.Key.Equals(i)).Select(j => j.Value);
LinqExpr Vb = LinqExpr.ArrayAccess(Vbs.First(), n);
foreach (LinqExpr j in Vbs.Skip(1))
{
Vb = LinqExpr.Add(Vb, LinqExpr.ArrayAccess(j, n));
}
// dVi = (Vb - Va) / Oversample
code.Add(LinqExpr.Assign(
Decl <double>(code, dVi, i, "d" + i.ToString().Replace("[t]", "")),
LinqExpr.Multiply(LinqExpr.Subtract(Vb, Va), LinqExpr.Constant(1.0 / (double)Oversample))));
}
// Prepare output sample accumulators for low pass filtering.
Dictionary <Expression, LinqExpr> Vo = new Dictionary <Expression, LinqExpr>();
foreach (Expression i in Output.Distinct())
{
code.Add(LinqExpr.Assign(
Decl <double>(code, Vo, i, i.ToString().Replace("[t]", "")),
LinqExpr.Constant(0.0)));
}
// int ov = Oversample;
// do { -- ov; } while(ov > 0)
ParamExpr ov = code.Decl <int>("ov");
code.Add(LinqExpr.Assign(ov, LinqExpr.Constant(Oversample)));
code.DoWhile(() =>
{
// t += h
code.Add(LinqExpr.AddAssign(t, h));
// Interpolate the input samples.
foreach (Expression i in Input.Distinct())
{
code.Add(LinqExpr.AddAssign(code[i], dVi[i]));
}
// Compile all of the SolutionSets in the solution.
foreach (SolutionSet ss in Solution.Solutions)
{
if (ss is LinearSolutions)
{
// Linear solutions are easy.
LinearSolutions S = (LinearSolutions)ss;
foreach (Arrow i in S.Solutions)
{
code.DeclInit(i.Left, i.Right);
}
}
else if (ss is NewtonIteration)
{
NewtonIteration S = (NewtonIteration)ss;
// Start with the initial guesses from the solution.
foreach (Arrow i in S.Guesses)
{
code.DeclInit(i.Left, i.Right);
}
// int it = iterations
LinqExpr it = code.ReDeclInit <int>("it", Iterations);
// do { ... --it } while(it > 0)
code.DoWhile((Break) =>
{
// Solve the un-solved system.
Solve(code, JxF, S.Equations, S.UnknownDeltas);
// Compile the pre-solved solutions.
if (S.KnownDeltas != null)
{
foreach (Arrow i in S.KnownDeltas)
{
code.DeclInit(i.Left, i.Right);
}
}
// bool done = true
LinqExpr done = code.ReDeclInit("done", true);
foreach (Expression i in S.Unknowns)
{
LinqExpr v = code[i];
LinqExpr dv = code[NewtonIteration.Delta(i)];
// done &= (|dv| < |v|*epsilon)
code.Add(LinqExpr.AndAssign(done, LinqExpr.LessThan(LinqExpr.Multiply(Abs(dv), LinqExpr.Constant(1e4)), LinqExpr.Add(Abs(v), LinqExpr.Constant(1e-6)))));
// v += dv
code.Add(LinqExpr.AddAssign(v, dv));
}
// if (done) break
code.Add(LinqExpr.IfThen(done, Break));
// --it;
code.Add(LinqExpr.PreDecrementAssign(it));
}, LinqExpr.GreaterThan(it, Zero));
//// bool failed = false
//LinqExpr failed = Decl(code, code, "failed", LinqExpr.Constant(false));
//for (int i = 0; i < eqs.Length; ++i)
// // failed |= |JxFi| > epsilon
// code.Add(LinqExpr.OrAssign(failed, LinqExpr.GreaterThan(Abs(eqs[i].ToExpression().Compile(map)), LinqExpr.Constant(1e-3))));
//code.Add(LinqExpr.IfThen(failed, ThrowSimulationDiverged(n)));
}
}
// Update the previous timestep variables.
foreach (SolutionSet S in Solution.Solutions)
{
foreach (Expression i in S.Unknowns.Where(i => globals.Keys.Contains(i.Evaluate(t_t0))))
{
code.Add(LinqExpr.Assign(code[i.Evaluate(t_t0)], code[i]));
}
}
// Vo += i
foreach (Expression i in Output.Distinct())
{
LinqExpr Voi = LinqExpr.Constant(0.0);
try
{
Voi = code.Compile(i);
}
catch (Exception Ex)
{
Log.WriteLine(MessageType.Warning, Ex.Message);
}
code.Add(LinqExpr.AddAssign(Vo[i], Voi));
}
// Vi_t0 = Vi
foreach (Expression i in Input.Distinct())
{
code.Add(LinqExpr.Assign(code[i.Evaluate(t_t0)], code[i]));
}
// --ov;
code.Add(LinqExpr.PreDecrementAssign(ov));
}, LinqExpr.GreaterThan(ov, Zero));
// Output[i][n] = Vo / Oversample
foreach (KeyValuePair <Expression, LinqExpr> i in outputs)
{
code.Add(LinqExpr.Assign(LinqExpr.ArrayAccess(i.Value, n), LinqExpr.Multiply(Vo[i.Key], LinqExpr.Constant(1.0 / (double)Oversample))));
}
// Every 256 samples, check for divergence.
if (Vo.Any())
{
code.Add(LinqExpr.IfThen(LinqExpr.Equal(LinqExpr.And(n, LinqExpr.Constant(0xFF)), Zero),
LinqExpr.Block(Vo.Select(i => LinqExpr.IfThenElse(IsNotReal(i.Value),
ThrowSimulationDiverged(n),
LinqExpr.Assign(i.Value, RoundDenormToZero(i.Value)))))));
}
});
// Copy the global state variables back to the globals.
foreach (KeyValuePair <Expression, GlobalExpr <double> > i in globals)
{
code.Add(LinqExpr.Assign(i.Value, code[i.Key]));
}
LinqExprs.LambdaExpression lambda = code.Build();
Delegate ret = lambda.Compile();
return(ret);
}
// Use homotopy method with newton's method to find a solution for F(x) = 0.
private static List<Arrow> NSolve(List<Expression> F, List<Arrow> x0, double Epsilon, int MaxIterations)
{
int M = F.Count;
int N = x0.Count;
// Compute JxF, the Jacobian of F.
List<Dictionary<Expression, Expression>> JxF = Jacobian(F, x0.Select(i => i.Left)).ToList();
// Define a function to evaluate JxH(x), where H = F(x) - s*F(x0).
CodeGen code = new CodeGen();
ParamExpr _JxH = code.Decl<double[,]>(Scope.Parameter, "JxH");
ParamExpr _x0 = code.Decl<double[]>(Scope.Parameter, "x0");
ParamExpr _s = code.Decl<double>(Scope.Parameter, "s");
// Load x_j from the input array and add them to the map.
for (int j = 0; j < N; ++j)
code.DeclInit(x0[j].Left, LinqExpr.ArrayAccess(_x0, LinqExpr.Constant(j)));
LinqExpr error = code.Decl<double>("error");
// Compile the expressions to assign JxH
for (int i = 0; i < M; ++i)
{
LinqExpr _i = LinqExpr.Constant(i);
for (int j = 0; j < N; ++j)
code.Add(LinqExpr.Assign(
LinqExpr.ArrayAccess(_JxH, _i, LinqExpr.Constant(j)),
code.Compile(JxF[i][x0[j].Left])));
// e = F(x) - s*F(x0)
LinqExpr e = code.DeclInit<double>("e", LinqExpr.Subtract(code.Compile(F[i]), LinqExpr.Multiply(LinqExpr.Constant((double)F[i].Evaluate(x0)), _s)));
code.Add(LinqExpr.Assign(LinqExpr.ArrayAccess(_JxH, _i, LinqExpr.Constant(N)), e));
// error += e * e
code.Add(LinqExpr.AddAssign(error, LinqExpr.Multiply(e, e)));
}
// return error
code.Return(error);
Func<double[,], double[], double, double> JxH = code.Build<Func<double[,], double[], double, double>>().Compile();
double[] x = new double[N];
// Remember where we last succeeded/failed.
double s0 = 0.0;
double s1 = 1.0;
do
{
try
{
// H(F, s) = F - s*F0
NewtonsMethod(M, N, JxH, s0, x, Epsilon, MaxIterations);
// Success at this s!
s1 = s0;
for (int i = 0; i < N; ++i)
x0[i] = Arrow.New(x0[i].Left, x[i]);
// Go near the goal.
s0 = Lerp(s0, 0.0, 0.9);
}
catch (FailedToConvergeException)
{
// Go near the last success.
s0 = Lerp(s0, s1, 0.9);
for (int i = 0; i < N; ++i)
x[i] = (double)x0[i].Right;
}
} while (s0 > 0.0 && s1 >= s0 + 1e-6);
// Make sure the last solution is at F itself.
if (s0 != 0.0)
{
NewtonsMethod(M, N, JxH, 0.0, x, Epsilon, MaxIterations);
for (int i = 0; i < N; ++i)
x0[i] = Arrow.New(x0[i].Left, x[i]);
}
return x0;
}
// Define a function for running the simulation of a population system S with timestep
// dt. The number of timesteps and the data buffer are parameters of the defined function.
static Func<int, double[, ], int> DefineSimulate(double dt, PopulationSystem S)
{
CodeGen code = new CodeGen();
// Define a parameter for the current population x, and define mappings to the
// expressions defined above.
LinqExpr N = code.Decl<int>(Scope.Parameter, "N");
LinqExpr Data = code.Decl<double[,]>(Scope.Parameter, "Data");
// Loop over the sample range requested. Note that this loop is a 'runtime' loop,
// while the rest of the loops nested in the body of this loop are 'compile time' loops.
LinqExpr n = code.DeclInit<int>("n", 1);
code.For(
() => { },
LinqExpr.LessThan(n, N),
() => code.Add(LinqExpr.PostIncrementAssign(n)),
() =>
{
// Define expressions representing the population of each species.
List<Expression> x = new List<Expression>();
for (int i = 0; i < S.N; ++i)
{
// Define a variable xi.
Expression xi = "x" + i.ToString();
x.Add(xi);
// xi = Data[n, i].
code.DeclInit(xi, LinqExpr.ArrayAccess(Data, LinqExpr.Subtract(n, LinqExpr.Constant(1)), LinqExpr.Constant(i)));
}
for (int i = 0; i < S.N; ++i)
{
// This list is the elements of the sum representing the i'th
// row of f, i.e. r_i + (A*x)_i.
Expression dx_dt = 1;
for (int j = 0; j < S.N; ++j)
dx_dt -= S.A[i, j] * x[j];
// Define dx_i/dt = x_i * f_i(x), as per the Lotka-Volterra equations.
dx_dt *= x[i] * S.r[i];
// Euler's method for x(t) is: x(t) = x(t - h) + h * x'(t - h).
Expression integral = x[i] + dt * dx_dt;
// Data[n, i] = Data[n - 1, i] + dt * dx_dt;
code.Add(LinqExpr.Assign(
LinqExpr.ArrayAccess(Data, n, LinqExpr.Constant(i)),
code.Compile(integral)));
}
});
code.Return(N);
// Compile the generated code.
LinqExprs.Expression<Func<int, double[,], int>> expr = code.Build<Func<int, double[,], int>>();
return expr.Compile();
}