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authorTavian Barnes <tavianator@gmail.com>2010-10-13 15:45:40 -0400
committerTavian Barnes <tavianator@gmail.com>2010-10-13 17:51:10 -0400
commit2829763fc5f9d222a966402bf073083dbc1da51c (patch)
treeffd1a0df6f6db26aa98c273faf4fef509d3e024a /src/vZ
parentdbd081ad1808d4e8550dd23971b60b862c7904e0 (diff)
downloadvz-2829763fc5f9d222a966402bf073083dbc1da51c.tar.xz
Implement FSAL.
Diffstat (limited to 'src/vZ')
-rw-r--r--src/vZ/Adaptive.hpp47
-rw-r--r--src/vZ/RK.hpp21
2 files changed, 59 insertions, 9 deletions
diff --git a/src/vZ/Adaptive.hpp b/src/vZ/Adaptive.hpp
index f0cfed1..a422bb4 100644
--- a/src/vZ/Adaptive.hpp
+++ b/src/vZ/Adaptive.hpp
@@ -50,10 +50,7 @@ namespace vZ
GenericAdaptiveIntegrator(Function f, unsigned int order,
ACoefficients a, BCoefficients b,
- BCoefficients bStar)
- : GenericRKIntegrator<Y>(f), m_order(order), m_rejections(0),
- m_a(a), m_b(b), m_bStar(bStar)
- { }
+ BCoefficients bStar);
virtual ~GenericAdaptiveIntegrator() { }
void step();
@@ -64,6 +61,9 @@ namespace vZ
unsigned int m_rejections;
ACoefficients m_a;
BCoefficients m_b, m_bStar;
+
+ bool m_fsal, m_k1Set;
+ Y m_k1;
};
// Type alias
@@ -72,18 +72,45 @@ namespace vZ
// Implementations
template <typename Y>
+ GenericAdaptiveIntegrator<Y>::GenericAdaptiveIntegrator(
+ Function f, unsigned int order,
+ ACoefficients a, BCoefficients b, BCoefficients bStar
+ )
+ : GenericRKIntegrator<Y>(f), m_order(order), m_rejections(0),
+ m_a(a), m_b(b), m_bStar(bStar), m_fsal(true), m_k1Set(false)
+ {
+ std::size_t i;
+ for (i = 0; i < m_a.back().size(); ++i) {
+ if (m_a.back()[i] != m_b.at(i)) {
+ m_fsal = false;
+ return;
+ }
+ }
+
+ if (m_b.at(i) != Scalar(0))
+ m_fsal = false;
+ }
+
+ template <typename Y>
void
GenericAdaptiveIntegrator<Y>::step()
{
static const Scalar S = Scalar(19)/Scalar(20); // Arbitrary saftey factor
Scalar newH = this->h();
Y y;
+ KVector k;
// Attempt the integration step in a loop
while (true) {
- KVector k = calculateK(m_a);
- y = calculateY(k, m_b);
- Y yStar = calculateY(k, m_bStar);
+ if (m_k1Set) {
+ k = calculateK(m_k1, y, m_a);
+ } else if (m_fsal) {
+ k = calculateK(y, m_a);
+ } else {
+ k = calculateK(m_a);
+ y = calculateY(k, m_b);
+ }
+ Y yStar = calculateY(k, m_bStar);
// Get an error estimate
@@ -111,6 +138,12 @@ namespace vZ
this->y(y);
this->x(this->x() + this->h());
+ // Handle FSAL optimization
+ if (m_fsal) {
+ m_k1Set = true;
+ m_k1 = k.back();
+ }
+
// Adjust the stepsize for the next iteration
this->h(newH);
}
diff --git a/src/vZ/RK.hpp b/src/vZ/RK.hpp
index 97ab487..8964741 100644
--- a/src/vZ/RK.hpp
+++ b/src/vZ/RK.hpp
@@ -46,6 +46,8 @@ namespace vZ
// Perform the stages of an RK integration
KVector calculateK(const ACoefficients& a) const;
+ KVector calculateK(Y& y, const ACoefficients& a) const;
+ KVector calculateK(Y k1, Y& y, const ACoefficients& a) const;
Y calculateY(const KVector& k, const BCoefficients& b) const;
};
@@ -58,11 +60,26 @@ namespace vZ
typename GenericRKIntegrator<Y>::KVector
GenericRKIntegrator<Y>::calculateK(const ACoefficients& a) const
{
+ Y ytemp; // Ignored
+ return calculateK(ytemp, a);
+ }
+
+ template <typename Y>
+ typename GenericRKIntegrator<Y>::KVector
+ GenericRKIntegrator<Y>::calculateK(Y& y, const ACoefficients& a) const
+ {
+ return calculateK(this->f()(this->x(), this->y()), y, a);
+ }
+
+ template <typename Y>
+ typename GenericRKIntegrator<Y>::KVector
+ GenericRKIntegrator<Y>::calculateK(Y k1, Y& y, const ACoefficients& a) const
+ {
KVector k;
k.reserve(a.size() + 1);
// k1
- k.push_back(this->f()(this->x(), this->y()));
+ k.push_back(k1);
// k2..n
for (typename ACoefficients::const_iterator i = a.begin();
@@ -70,7 +87,7 @@ namespace vZ
++i)
{
Scalar c(0);
- Y y = this->y();
+ y = this->y();
for (typename std::vector<Scalar>::size_type j = 0; j < i->size(); ++j) {
Scalar aij = i->at(j);
c += aij;