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-rw-r--r--stokes.hpp42
1 files changed, 28 insertions, 14 deletions
diff --git a/stokes.hpp b/stokes.hpp
index 0756dc3..3814cf4 100644
--- a/stokes.hpp
+++ b/stokes.hpp
@@ -22,9 +22,9 @@ Vector<Scalar> variation(const Vector<Scalar>& z, const Vector<Scalar>& z´, con
Matrix<Scalar>::Identity(ddH.rows(), ddH.cols()) - z.conjugate() * z.transpose() / z²
);
- Vector<Scalar> dLdz = - Reż·z´ * (
+ Vector<Scalar> dLdz = - (
dżc * z´ + dż * z´.conjugate() - (dż * ż.conjugate() + dżc * ż) * Reż·z´ / ż²
- ) / (ż² * z´²);
+ ) / sqrt(ż² * z´²) / 2;
Vector<Scalar> ż´ = -(ddH * z´).conjugate() + ((ddH * z´).dot(z) / z²) * z.conjugate() + (
dH.dot(z) * z´.conjugate() + dH.dot(z´) * z.conjugate() - (
@@ -35,17 +35,16 @@ Vector<Scalar> variation(const Vector<Scalar>& z, const Vector<Scalar>& z´, con
double dReż·z´ = real(ż.dot(z´´) + ż´.dot(z´));
Vector<Scalar> ddtdLdz´ = - (
- Reż·z´ * (
+ (
ż´.conjugate() - (
Reż·z´ * z´´.conjugate() + dReż·z´ * z´.conjugate()
- (Reż·z´ / z´²) * (z´´.dot(z´) + z´.dot(z´´)) * z´.conjugate()
) / z´²
)
- + dReż·z´ * (ż.conjugate() - Reż·z´ / z´² * z´.conjugate())
- - Reż·z´ * (
+ - 0.5 * (
(ż.dot(ż´) + ż´.dot(ż)) / ż² + (z´´.dot(z´) + z´.dot(z´´)) / z´²
) * (ż.conjugate() - Reż·z´ / z´² * z´.conjugate())
- ) / (ż² * z´²);
+ ) / sqrt(ż² * z´²) / 2;
return dLdz - ddtdLdz´;
}
@@ -55,6 +54,27 @@ class Rope {
public:
std::vector<Vector<Scalar>> z;
+ Rope(unsigned N) : z(N + 2) {}
+
+ template <int p>
+ Rope(unsigned N, const Vector<Scalar>& z1, const Vector<Scalar>& z2, const Tensor<Scalar, p>& J) : z(N + 2) {
+ Scalar H1, H2;
+ std::tie(H1, std::ignore, std::ignore) = hamGradHess(J, z1);
+ std::tie(H2, std::ignore, std::ignore) = hamGradHess(J, z2);
+
+ if (real(H1) > real(H2)) {
+ z.front() = z1;
+ z.back() = z2;
+ } else {
+ z.front() = z2;
+ z.back() = z1;
+ }
+
+ for (unsigned i = 0; i < N + 2; i++) {
+ z[i] = normalize(z.front() + (z.back() - z.front()) * ((double)i / (N + 1.0)));
+ }
+ }
+
unsigned n() const {
return z.size() - 2;
}
@@ -89,12 +109,6 @@ class Rope {
return sqrt(err);
}
- Rope(unsigned N, const Vector<Scalar>& z1, const Vector<Scalar>& z2) : z(N + 2) {
- for (unsigned i = 0; i < N + 2; i++) {
- z[i] = normalize(z1 + (z2 - z1) * ((double)i / (N + 1.0)));
- }
- }
-
Vector<Scalar> dz(unsigned i) const {
return z[i + 1] - z[i - 1];
}
@@ -208,14 +222,14 @@ class Rope {
Vector<Scalar> zD = zDot(z[i], dH);
- c += 1.0 - pow(real(zD.dot(dz(i))), 2) / zD.squaredNorm() / dz(i).squaredNorm();
+ c += 1.0 - real(zD.dot(dz(i))) / zD.norm() / dz(i).norm();
}
return c;
}
Rope<Scalar> interpolate() const {
- Rope<Scalar> r(2 * n() + 1, z[0], z[z.size() - 1]);
+ Rope<Scalar> r(2 * n() + 1);
for (unsigned i = 0; i < z.size(); i++) {
r.z[2 * i] = z[i];