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Diffstat (limited to 'src/main/java/org/apache/commons/math3/ode/nonstiff/LutherFieldIntegrator.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/ode/nonstiff/LutherFieldIntegrator.java | 146 |
1 files changed, 146 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherFieldIntegrator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherFieldIntegrator.java new file mode 100644 index 0000000..7b57b5a --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/LutherFieldIntegrator.java @@ -0,0 +1,146 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to You under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +package org.apache.commons.math3.ode.nonstiff; + +import org.apache.commons.math3.Field; +import org.apache.commons.math3.RealFieldElement; +import org.apache.commons.math3.ode.FieldEquationsMapper; +import org.apache.commons.math3.ode.FieldODEStateAndDerivative; +import org.apache.commons.math3.util.MathArrays; + + +/** + * This class implements the Luther sixth order Runge-Kutta + * integrator for Ordinary Differential Equations. + + * <p> + * This method is described in H. A. Luther 1968 paper <a + * href="http://www.ams.org/journals/mcom/1968-22-102/S0025-5718-68-99876-1/S0025-5718-68-99876-1.pdf"> + * An explicit Sixth-Order Runge-Kutta Formula</a>. + * </p> + + * <p>This method is an explicit Runge-Kutta method, its Butcher-array + * is the following one : + * <pre> + * 0 | 0 0 0 0 0 0 + * 1 | 1 0 0 0 0 0 + * 1/2 | 3/8 1/8 0 0 0 0 + * 2/3 | 8/27 2/27 8/27 0 0 0 + * (7-q)/14 | ( -21 + 9q)/392 ( -56 + 8q)/392 ( 336 - 48q)/392 ( -63 + 3q)/392 0 0 + * (7+q)/14 | (-1155 - 255q)/1960 ( -280 - 40q)/1960 ( 0 - 320q)/1960 ( 63 + 363q)/1960 ( 2352 + 392q)/1960 0 + * 1 | ( 330 + 105q)/180 ( 120 + 0q)/180 ( -200 + 280q)/180 ( 126 - 189q)/180 ( -686 - 126q)/180 ( 490 - 70q)/180 + * |-------------------------------------------------------------------------------------------------------------------------------------------------- + * | 1/20 0 16/45 0 49/180 49/180 1/20 + * </pre> + * where q = √21</p> + * + * @see EulerFieldIntegrator + * @see ClassicalRungeKuttaFieldIntegrator + * @see GillFieldIntegrator + * @see MidpointFieldIntegrator + * @see ThreeEighthesFieldIntegrator + * @param <T> the type of the field elements + * @since 3.6 + */ + +public class LutherFieldIntegrator<T extends RealFieldElement<T>> + extends RungeKuttaFieldIntegrator<T> { + + /** Simple constructor. + * Build a fourth-order Luther integrator with the given step. + * @param field field to which the time and state vector elements belong + * @param step integration step + */ + public LutherFieldIntegrator(final Field<T> field, final T step) { + super(field, "Luther", step); + } + + /** {@inheritDoc} */ + public T[] getC() { + final T q = getField().getZero().add(21).sqrt(); + final T[] c = MathArrays.buildArray(getField(), 6); + c[0] = getField().getOne(); + c[1] = fraction(1, 2); + c[2] = fraction(2, 3); + c[3] = q.subtract(7).divide(-14); + c[4] = q.add(7).divide(14); + c[5] = getField().getOne(); + return c; + } + + /** {@inheritDoc} */ + public T[][] getA() { + final T q = getField().getZero().add(21).sqrt(); + final T[][] a = MathArrays.buildArray(getField(), 6, -1); + for (int i = 0; i < a.length; ++i) { + a[i] = MathArrays.buildArray(getField(), i + 1); + } + a[0][0] = getField().getOne(); + a[1][0] = fraction(3, 8); + a[1][1] = fraction(1, 8); + a[2][0] = fraction(8, 27); + a[2][1] = fraction(2, 27); + a[2][2] = a[2][0]; + a[3][0] = q.multiply( 9).add( -21).divide( 392); + a[3][1] = q.multiply( 8).add( -56).divide( 392); + a[3][2] = q.multiply( -48).add( 336).divide( 392); + a[3][3] = q.multiply( 3).add( -63).divide( 392); + a[4][0] = q.multiply(-255).add(-1155).divide(1960); + a[4][1] = q.multiply( -40).add( -280).divide(1960); + a[4][2] = q.multiply(-320) .divide(1960); + a[4][3] = q.multiply( 363).add( 63).divide(1960); + a[4][4] = q.multiply( 392).add( 2352).divide(1960); + a[5][0] = q.multiply( 105).add( 330).divide( 180); + a[5][1] = fraction(2, 3); + a[5][2] = q.multiply( 280).add( -200).divide( 180); + a[5][3] = q.multiply(-189).add( 126).divide( 180); + a[5][4] = q.multiply(-126).add( -686).divide( 180); + a[5][5] = q.multiply( -70).add( 490).divide( 180); + return a; + } + + /** {@inheritDoc} */ + public T[] getB() { + + final T[] b = MathArrays.buildArray(getField(), 7); + b[0] = fraction( 1, 20); + b[1] = getField().getZero(); + b[2] = fraction(16, 45); + b[3] = getField().getZero(); + b[4] = fraction(49, 180); + b[5] = b[4]; + b[6] = b[0]; + + return b; + + } + + /** {@inheritDoc} */ + @Override + protected LutherFieldStepInterpolator<T> + createInterpolator(final boolean forward, T[][] yDotK, + final FieldODEStateAndDerivative<T> globalPreviousState, + final FieldODEStateAndDerivative<T> globalCurrentState, + final FieldEquationsMapper<T> mapper) { + return new LutherFieldStepInterpolator<T>(getField(), forward, yDotK, + globalPreviousState, globalCurrentState, + globalPreviousState, globalCurrentState, + mapper); + } + +} |