/// <summary>
/// Performs reverse-mode (adjoint) automatic differentiation
/// </summary>
/// <param name="builder"></param>
/// <param name="dependentVariable"></param>
/// <param name="independentVariables"></param>
public static void Differentiate(BlockExpressionBuilder builder,
out IList <Expression> derivativeExpressions,
VectorParameterExpression dependentVariable,
params VectorParameterExpression[] independentVariables)
{
if (independentVariables.Length == 0)
{
derivativeExpressions = null;
return;
}
var block = builder.ToBlock();
// change the numbering of variables; arguments first, then locals
List <int>[] jLookup;
Function[] f;
// we want a list of functions which can be unary or binary (in principle high order if it makes sense) and a look-up
// each function is associated with a parameter, which is either an argument or a local
// for each function index we return a list of the indices of the functions that reference the parameter
GetFunctions(block, out f, out jLookup);
int N = dependentVariable.Index;
bool[] derivativeRequired; int[] derivativeExpressionIndex;
IdentifyNeccesaryDerivatives(N, jLookup, independentVariables, out derivativeRequired, out derivativeExpressionIndex);
// the list of operations needed to calculate the derivatives (*all* derivatives)
derivativeExpressions = new Expression[independentVariables.Length];
var dxNdx = new Expression[N + 1];
dxNdx[N] = new ConstantExpression <double>(1.0);
for (int i = N - 1; i >= 0; i--)
{
if (!derivativeRequired[i])
{
continue;
}
// dxN / dxi
// need to find all operation indices j such that p(j) contains i
// that is, all functions that have xi as an argument (these must therefore have a higher index than i)
VectorParameterExpression total = new ConstantExpression <double>(0);
var xi = f[i].Parameter;
//need sum of dfj/dxi dXN/dxj
foreach (var j in jLookup[i])
{
var fj = f[j];
var dfjdxi = Differentiate(fj, xi, builder); // dfj/dxi
var dXNdxj = dxNdx[j]; // dXN/dxj
var product = builder.AddProductExpression(dfjdxi, dXNdxj);
total = builder.AddAdditionExpression(total, product);
}
dxNdx[i] = total;
int targetIndex = derivativeExpressionIndex[i];
if (targetIndex != -1)
{
derivativeExpressions[targetIndex] = total;
}
}
}
/// <summary>
/// Performs reverse-mode (adjoint) automatic differentiation
/// </summary>
/// <param name="builder"></param>
/// <param name="dependentVariable"></param>
/// <param name="independentVariables"></param>
public static void Differentiate(BlockExpressionBuilder builder,
out IList<Expression> derivativeExpressions,
VectorParameterExpression dependentVariable,
params VectorParameterExpression[] independentVariables)
{
if (independentVariables.Length == 0)
{
derivativeExpressions = null;
return;
}
var block = builder.ToBlock();
// change the numbering of variables; arguments first, then locals
List<int>[] jLookup;
Function[] f;
// we want a list of functions which can be unary or binary (in principle high order if it makes sense) and a look-up
// each function is associated with a parameter, which is either an argument or a local
// for each function index we return a list of the indices of the functions that reference the parameter
GetFunctions(block, out f, out jLookup);
int N = dependentVariable.Index;
bool[] derivativeRequired; int[] derivativeExpressionIndex;
IdentifyNeccesaryDerivatives(N, jLookup, independentVariables, out derivativeRequired, out derivativeExpressionIndex);
// the list of operations needed to calculate the derivatives (*all* derivatives)
derivativeExpressions = new Expression[independentVariables.Length];
var dxNdx = new Expression[N + 1];
dxNdx[N] = new ConstantExpression<double>(1.0);
for (int i = N - 1; i >= 0; i--)
{
if (!derivativeRequired[i]) continue;
// dxN / dxi
// need to find all operation indices j such that p(j) contains i
// that is, all functions that have xi as an argument (these must therefore have a higher index than i)
VectorParameterExpression total = new ConstantExpression<double>(0);
var xi = f[i].Parameter;
//need sum of dfj/dxi dXN/dxj
foreach (var j in jLookup[i])
{
var fj = f[j];
var dfjdxi = Differentiate(fj, xi, builder); // dfj/dxi
var dXNdxj = dxNdx[j]; // dXN/dxj
var product = builder.AddProductExpression(dfjdxi, dXNdxj);
total = builder.AddAdditionExpression(total, product);
}
dxNdx[i] = total;
int targetIndex = derivativeExpressionIndex[i];
if (targetIndex != -1) derivativeExpressions[targetIndex] = total;
}
}
