private (Matrix <double>, Matrix <double>) Filter(Matrix <double> A, Matrix <double> B)
{
var Ap = A.SubMatrix(0, 1, 0, A.ColumnCount);
var Bp = B.SubMatrix(0, 1, 0, B.ColumnCount);
for (int i = 1; i < A.RowCount; i++)
{
var At = SignalUtils.Stack(Ap, A.SubMatrix(i, 1, 0, A.ColumnCount));
var Bt = SignalUtils.Stack(Bp, B.SubMatrix(i, 1, 0, B.ColumnCount));
if (At.Rank() == At.RowCount)
{
Ap = At;
Bp = Bt;
}
else if (SignalUtils.Append(At, Bt).Rank() != At.RowCount)
{
logger.Debug($"Same constrains detected at NO.{i}, which will be ignored.");
}
else
{
logger.Debug(SignalUtils.SPrint(At, "At"));
logger.Debug(SignalUtils.SPrint(Bt, "Bt"));
throw logger.Error(new LigralException($"Conflict constrains detected at NO.{i}."));
}
}
return(Ap, Bp);
}
private (Matrix <double>, Matrix <double>) Filter(Matrix <double> A, Matrix <double> B, Matrix <double> A0, Matrix <double> B0)
{
if (A == null || B == null)
{
return(A0, B0);
}
if (A0 == null || B0 == null)
{
return(Filter(A, B));
}
var Ap = A0;
var Bp = B0;
if (Ap.ColumnCount != A.ColumnCount)
{
throw logger.Error(new LigralException($"Constrain dimensions do not agree in SQP(A) {Ap.ColumnCount}: {A.ColumnCount}"));
}
if (Bp.ColumnCount != B.ColumnCount)
{
throw logger.Error(new LigralException($"Constrain dimensions do not agree in SQP(B) {Bp.ColumnCount}: {B.ColumnCount}"));
}
for (int i = 0; i < A.RowCount; i++)
{
var At = SignalUtils.Stack(Ap, A.SubMatrix(i, 1, 0, A.ColumnCount));
var Bt = SignalUtils.Stack(Bp, B.SubMatrix(i, 1, 0, B.ColumnCount));
if (At.Rank() == At.RowCount)
{
Ap = At;
Bp = Bt;
}
else if (SignalUtils.Append(At, Bt).Rank() == At.RowCount)
{
logger.Debug($"Same constrains detected at NO.{i}, which will be ignored.");
}
else
{
logger.Debug($"Conflict constrains detected at NO.{i}, which are resulted from bound constrains and will be ignore.");
}
}
return(Ap, Bp);
}
public override Matrix <double> Optimize(MFunc cost, Matrix <double> x0, MFunc equal, MFunc bound)
{
int n = x0.RowCount;
if (x0.ColumnCount != 1)
{
throw logger.Error(new LigralException($"Only x with shape nx1 is supported, but we got {n}x{x0.ColumnCount}"));
}
var x = x0;
var c = cost(x);
for (int i = 0; i < MaximumIteration; i++)
{
var H = Algorithm.RoughHessian(cost, x);
var C = Algorithm.RoughPartial(cost, x);
var Ae = Algorithm.RoughPartial(equal, x);
var Be = equal(x);
if (Ae != null)
{
Ae = Ae.Transpose();
(Ae, Be) = Filter(Ae, Be);
if (Be.ColumnCount != 1)
{
throw logger.Error(new LigralException($"Only h(x) with shape mx1 is supported, but we got {Be.RowCount}x{Be.ColumnCount}"));
}
}
logger.Debug(SignalUtils.SPrint(Ae, "Ae"));
logger.Debug(SignalUtils.SPrint(Be, "Be"));
var Ab = Algorithm.RoughPartial(bound, x);
var Bb = bound(x);
if (Ab != null)
{
Ab = Ab.Transpose();
int bRowCount = Bb.RowCount;
for (int j = 0, k = 0; j < bRowCount; j++)
{
if (Bb[j - k, 0] < BoundaryConstrainTolerant)
{
Ab = Ab.RemoveRow(j - k);
Bb = Bb.RemoveRow(j - k);
k++;
}
}
}
logger.Debug(SignalUtils.SPrint(Ab, "Ab"));
logger.Debug(SignalUtils.SPrint(Bb, "Bb"));
(var A, var B) = Filter(Ab, Bb, Ae, Be);
logger.Debug(SignalUtils.SPrint(A, "A"));
logger.Debug(SignalUtils.SPrint(B, "B"));
if (B != null && B.ColumnCount != 1)
{
throw logger.Error(new LigralException($"Only g(x) with shape px1 is supported, but we got {B.RowCount-Be.RowCount}x{B.ColumnCount}"));
}
var build = Matrix <double> .Build;
int mp = B == null?0:B.RowCount;
var K = SignalUtils.Stack(
SignalUtils.Append(H, A == null?A:A.Transpose()),
SignalUtils.Append(A, mp == 0?null:build.Dense(mp, mp, 0))
);
if (K == null)
{
logger.Warn("No constrain is given, optimizer quit");
return(x);
}
logger.Debug(SignalUtils.SPrint(K, "K"));
var p = SignalUtils.Stack(-C, -B);
logger.Debug(SignalUtils.SPrint(p, "p"));
var r = K.Solve(p);
var s = r.SubMatrix(0, n, 0, 1);
logger.Debug(SignalUtils.SPrint(s, "s"));
var lambda = r.SubMatrix(n, mp, 0, 1);
logger.Debug(SignalUtils.SPrint(lambda, "lambda"));
x += s;
var cp = cost(x);
if (lambda.RowAbsoluteSums().ForAll(sum => sum < OptimizationStopLambdaTolerant))
{
logger.Info("SQP Optimizer stops as lambda is close to zero");
break;
}
else if ((cp - c).RowAbsoluteSums().ForAll(sum => sum < OptimizationStopCostTolerant))
{
logger.Info("SQP Optimizer stops as costs did not change.");
break;
}
else
{
c = cp;
}
}
return(x);
}