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Fixed field-based Dormand-Prince 8(5,3) step interpolator.

This commit is contained in:
Luc Maisonobe 2016-01-06 12:41:39 +01:00
parent 73b76598e7
commit 7a1c10a162
4 changed files with 70 additions and 15 deletions
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57
src/main/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldStepInterpolator.java
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@ -55,7 +55,7 @@ class DormandPrince853FieldStepInterpolator<T extends RealFieldElement<T>>
d = MathArrays.buildArray(getField(), 7, 16);
// this row is the same as the b array
d[0][ 0] = fraction(104257, 1929240);
d[0][ 0] = fraction(104257, 1920240);
d[0][ 1] = getField().getZero();
d[0][ 2] = getField().getZero();
d[0][ 3] = getField().getZero();
@ -101,7 +101,7 @@ class DormandPrince853FieldStepInterpolator<T extends RealFieldElement<T>>
d[2][ 9] = d[0][ 9].multiply(2);
d[2][10] = d[0][10].multiply(2);
d[2][11] = d[0][11].multiply(2);
d[2][12] = d[0][12].multiply(2); // really 0
d[2][12] = d[0][12].multiply(2).subtract(1); // really -1
d[2][13] = d[0][13].multiply(2); // really 0
d[2][14] = d[0][14].multiply(2); // really 0
d[2][15] = d[0][15].multiply(2); // really 0
@ -215,7 +215,7 @@ class DormandPrince853FieldStepInterpolator<T extends RealFieldElement<T>>
final T oneMinusThetaH)
throws MaxCountExceededException {
final T one = theta.getField().getOne();
final T one = getField().getOne();
final T eta = one.subtract(theta);
final T twoTheta = theta.multiply(2);
final T theta2 = theta.multiply(theta);
@ -228,6 +228,7 @@ class DormandPrince853FieldStepInterpolator<T extends RealFieldElement<T>>
final T[] interpolatedState;
final T[] interpolatedDerivatives;
if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
final T f0 = theta.multiply(h);
final T f1 = f0.multiply(eta);
@ -236,18 +237,58 @@ class DormandPrince853FieldStepInterpolator<T extends RealFieldElement<T>>
final T f4 = f3.multiply(theta);
final T f5 = f4.multiply(eta);
final T f6 = f5.multiply(theta);
interpolatedState = previousStateLinearCombination(f0, f1, f2, f3, f4, f5, f6);
interpolatedDerivatives = derivativeLinearCombination(one, dot1, dot2, dot3, dot4, dot5, dot6);
final T[] p = MathArrays.buildArray(getField(), 16);
final T[] q = MathArrays.buildArray(getField(), 16);
for (int i = 0; i < p.length; ++i) {
p[i] = f0.multiply(d[0][i]).
add(f1.multiply(d[1][i])).
add(f2.multiply(d[2][i])).
add(f3.multiply(d[3][i])).
add(f4.multiply(d[4][i])).
add(f5.multiply(d[5][i])).
add(f6.multiply(d[6][i]));
q[i] = d[0][i].
add(dot1.multiply(d[1][i])).
add(dot2.multiply(d[2][i])).
add(dot3.multiply(d[3][i])).
add(dot4.multiply(d[4][i])).
add(dot5.multiply(d[5][i])).
add(dot6.multiply(d[6][i]));
}
interpolatedState = previousStateLinearCombination(p[0], p[1], p[ 2], p[ 3], p[ 4], p[ 5], p[ 6], p[ 7],
p[8], p[9], p[10], p[11], p[12], p[13], p[14], p[15]);
interpolatedDerivatives = derivativeLinearCombination(q[0], q[1], q[ 2], q[ 3], q[ 4], q[ 5], q[ 6], q[ 7],
q[8], q[9], q[10], q[11], q[12], q[13], q[14], q[15]);
} else {
final T f0 = oneMinusThetaH;
final T f0 = oneMinusThetaH.negate();
final T f1 = f0.multiply(theta).negate();
final T f2 = f1.multiply(theta);
final T f3 = f2.multiply(eta);
final T f4 = f3.multiply(theta);
final T f5 = f4.multiply(eta);
final T f6 = f5.multiply(theta);
interpolatedState = currentStateLinearCombination(f0, f1, f2, f3, f4, f5, f6);
interpolatedDerivatives = derivativeLinearCombination(one, dot1, dot2, dot3, dot4, dot5, dot6);
final T[] p = MathArrays.buildArray(getField(), 16);
final T[] q = MathArrays.buildArray(getField(), 16);
for (int i = 0; i < p.length; ++i) {
p[i] = f0.multiply(d[0][i]).
add(f1.multiply(d[1][i])).
add(f2.multiply(d[2][i])).
add(f3.multiply(d[3][i])).
add(f4.multiply(d[4][i])).
add(f5.multiply(d[5][i])).
add(f6.multiply(d[6][i]));
q[i] = d[0][i].
add(dot1.multiply(d[1][i])).
add(dot2.multiply(d[2][i])).
add(dot3.multiply(d[3][i])).
add(dot4.multiply(d[4][i])).
add(dot5.multiply(d[5][i])).
add(dot6.multiply(d[6][i]));
}
interpolatedState = currentStateLinearCombination(p[0], p[1], p[ 2], p[ 3], p[ 4], p[ 5], p[ 6], p[ 7],
p[8], p[9], p[10], p[11], p[12], p[13], p[14], p[15]);
interpolatedDerivatives = derivativeLinearCombination(q[0], q[1], q[ 2], q[ 3], q[ 4], q[ 5], q[ 6], q[ 7],
q[8], q[9], q[10], q[11], q[12], q[13], q[14], q[15]);
}
return new FieldODEStateAndDerivative<T>(time, interpolatedState, interpolatedDerivatives);

14
src/test/java/org/apache/commons/math4/ode/nonstiff/AbstractEmbeddedRungeKuttaFieldIntegratorTest.java
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@ -64,6 +64,20 @@ public abstract class AbstractEmbeddedRungeKuttaFieldIntegratorTest {
T[][] fieldA = fieldIntegrator.getA();
T[] fieldB = fieldIntegrator.getB();
T[] fieldC = fieldIntegrator.getC();
if (fieldIntegrator instanceof DormandPrince853FieldIntegrator) {
// special case for Dormand-Prince 8(5,3), the array in the regular
// integrator is smaller because as of 3.X, the interpolation steps
// are not performed by the integrator itself
T[][] reducedFieldA = MathArrays.buildArray(field, 12, -1);
T[] reducedFieldB = MathArrays.buildArray(field, 13);
T[] reducedFieldC = MathArrays.buildArray(field, 12);
System.arraycopy(fieldA, 0, reducedFieldA, 0, reducedFieldA.length);
System.arraycopy(fieldB, 0, reducedFieldB, 0, reducedFieldB.length);
System.arraycopy(fieldC, 0, reducedFieldC, 0, reducedFieldC.length);
fieldA = reducedFieldA;
fieldB = reducedFieldB;
fieldC = reducedFieldC;
}
String fieldName = fieldIntegrator.getClass().getName();
String regularName = fieldName.replaceAll("Field", "");

4
src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldIntegratorTest.java
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@ -49,12 +49,12 @@ public class DormandPrince853FieldIntegratorTest extends AbstractEmbeddedRungeKu
@Test
public void testBackward() {
doTestBackward(Decimal64Field.getInstance(), 1.1e-7, 1.1e-7, 1.0e-12, "Dormand-Prince 8 (5, 3)");
doTestBackward(Decimal64Field.getInstance(), 8.1e-8, 1.1e-7, 1.0e-12, "Dormand-Prince 8 (5, 3)");
}
@Test
public void testKepler() {
doTestKepler(Decimal64Field.getInstance(), 2.4e-10);
doTestKepler(Decimal64Field.getInstance(), 4.4e-11);
}
@Override

4
src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldStepInterpolatorTest.java
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@ -38,12 +38,12 @@ public class DormandPrince853FieldStepInterpolatorTest extends AbstractRungeKutt
@Test
public void interpolationInside() {
doInterpolationInside(Decimal64Field.getInstance(), 1.0e-50, 1.0e-50);
doInterpolationInside(Decimal64Field.getInstance(), 3.1e-17, 3.4e-16);
}
@Test
public void nonFieldInterpolatorConsistency() {
doNonFieldInterpolatorConsistency(Decimal64Field.getInstance(), 1.0e-50, 1.0e-50, 1.0e-50, 1.0e-50);
doNonFieldInterpolatorConsistency(Decimal64Field.getInstance(), 3.4e-12, 5.7e-11, 1.9e-10, 3.1e-9);
}
}