/*
* 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.
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package org.apache.commons.math4.analysis.differentiation;
import java.lang.reflect.Field;
import java.util.HashMap;
import java.util.Map;
import org.apache.commons.math4.analysis.differentiation.DSCompiler;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.util.CombinatoricsUtils;
import org.junit.Assert;
import org.junit.Test;
/**
* Test for class {@link DSCompiler}.
*/
public class DSCompilerTest {
@Test
public void testSize() {
for (int i = 0; i < 6; ++i) {
for (int j = 0; j < 6; ++j) {
long expected = CombinatoricsUtils.binomialCoefficient(i + j, i);
Assert.assertEquals(expected, DSCompiler.getCompiler(i, j).getSize());
Assert.assertEquals(expected, DSCompiler.getCompiler(j, i).getSize());
}
}
}
@Test
public void testIndices() {
DSCompiler c = DSCompiler.getCompiler(0, 0);
checkIndices(c.getPartialDerivativeOrders(0), new int[0]);
c = DSCompiler.getCompiler(0, 1);
checkIndices(c.getPartialDerivativeOrders(0), new int[0]);
c = DSCompiler.getCompiler(1, 0);
checkIndices(c.getPartialDerivativeOrders(0), 0);
c = DSCompiler.getCompiler(1, 1);
checkIndices(c.getPartialDerivativeOrders(0), 0);
checkIndices(c.getPartialDerivativeOrders(1), 1);
c = DSCompiler.getCompiler(1, 2);
checkIndices(c.getPartialDerivativeOrders(0), 0);
checkIndices(c.getPartialDerivativeOrders(1), 1);
checkIndices(c.getPartialDerivativeOrders(2), 2);
c = DSCompiler.getCompiler(2, 1);
checkIndices(c.getPartialDerivativeOrders(0), 0, 0);
checkIndices(c.getPartialDerivativeOrders(1), 1, 0);
checkIndices(c.getPartialDerivativeOrders(2), 0, 1);
c = DSCompiler.getCompiler(1, 3);
checkIndices(c.getPartialDerivativeOrders(0), 0);
checkIndices(c.getPartialDerivativeOrders(1), 1);
checkIndices(c.getPartialDerivativeOrders(2), 2);
checkIndices(c.getPartialDerivativeOrders(3), 3);
c = DSCompiler.getCompiler(2, 2);
checkIndices(c.getPartialDerivativeOrders(0), 0, 0);
checkIndices(c.getPartialDerivativeOrders(1), 1, 0);
checkIndices(c.getPartialDerivativeOrders(2), 2, 0);
checkIndices(c.getPartialDerivativeOrders(3), 0, 1);
checkIndices(c.getPartialDerivativeOrders(4), 1, 1);
checkIndices(c.getPartialDerivativeOrders(5), 0, 2);
c = DSCompiler.getCompiler(3, 1);
checkIndices(c.getPartialDerivativeOrders(0), 0, 0, 0);
checkIndices(c.getPartialDerivativeOrders(1), 1, 0, 0);
checkIndices(c.getPartialDerivativeOrders(2), 0, 1, 0);
checkIndices(c.getPartialDerivativeOrders(3), 0, 0, 1);
c = DSCompiler.getCompiler(1, 4);
checkIndices(c.getPartialDerivativeOrders(0), 0);
checkIndices(c.getPartialDerivativeOrders(1), 1);
checkIndices(c.getPartialDerivativeOrders(2), 2);
checkIndices(c.getPartialDerivativeOrders(3), 3);
checkIndices(c.getPartialDerivativeOrders(4), 4);
c = DSCompiler.getCompiler(2, 3);
checkIndices(c.getPartialDerivativeOrders(0), 0, 0);
checkIndices(c.getPartialDerivativeOrders(1), 1, 0);
checkIndices(c.getPartialDerivativeOrders(2), 2, 0);
checkIndices(c.getPartialDerivativeOrders(3), 3, 0);
checkIndices(c.getPartialDerivativeOrders(4), 0, 1);
checkIndices(c.getPartialDerivativeOrders(5), 1, 1);
checkIndices(c.getPartialDerivativeOrders(6), 2, 1);
checkIndices(c.getPartialDerivativeOrders(7), 0, 2);
checkIndices(c.getPartialDerivativeOrders(8), 1, 2);
checkIndices(c.getPartialDerivativeOrders(9), 0, 3);
c = DSCompiler.getCompiler(3, 2);
checkIndices(c.getPartialDerivativeOrders(0), 0, 0, 0);
checkIndices(c.getPartialDerivativeOrders(1), 1, 0, 0);
checkIndices(c.getPartialDerivativeOrders(2), 2, 0, 0);
checkIndices(c.getPartialDerivativeOrders(3), 0, 1, 0);
checkIndices(c.getPartialDerivativeOrders(4), 1, 1, 0);
checkIndices(c.getPartialDerivativeOrders(5), 0, 2, 0);
checkIndices(c.getPartialDerivativeOrders(6), 0, 0, 1);
checkIndices(c.getPartialDerivativeOrders(7), 1, 0, 1);
checkIndices(c.getPartialDerivativeOrders(8), 0, 1, 1);
checkIndices(c.getPartialDerivativeOrders(9), 0, 0, 2);
c = DSCompiler.getCompiler(4, 1);
checkIndices(c.getPartialDerivativeOrders(0), 0, 0, 0, 0);
checkIndices(c.getPartialDerivativeOrders(1), 1, 0, 0, 0);
checkIndices(c.getPartialDerivativeOrders(2), 0, 1, 0, 0);
checkIndices(c.getPartialDerivativeOrders(3), 0, 0, 1, 0);
checkIndices(c.getPartialDerivativeOrders(4), 0, 0, 0, 1);
}
@Test(expected=DimensionMismatchException.class)
public void testIncompatibleParams() {
DSCompiler.getCompiler(3, 2).checkCompatibility(DSCompiler.getCompiler(4, 2));
}
@Test(expected=DimensionMismatchException.class)
public void testIncompatibleOrder() {
DSCompiler.getCompiler(3, 3).checkCompatibility(DSCompiler.getCompiler(3, 2));
}
@Test
public void testSymmetry() {
for (int i = 0; i < 6; ++i) {
for (int j = 0; j < 6; ++j) {
DSCompiler c = DSCompiler.getCompiler(i, j);
for (int k = 0; k < c.getSize(); ++k) {
Assert.assertEquals(k, c.getPartialDerivativeIndex(c.getPartialDerivativeOrders(k)));
}
}
}
}
@Test public void testMultiplicationRules()
throws SecurityException, NoSuchFieldException, IllegalArgumentException, IllegalAccessException {
Map<String,String> referenceRules = new HashMap<>();
referenceRules.put("(f*g)", "f * g");
referenceRules.put("d(f*g)/dx", "f * dg/dx + df/dx * g");
referenceRules.put("d(f*g)/dy", referenceRules.get("d(f*g)/dx").replaceAll("x", "y"));
referenceRules.put("d(f*g)/dz", referenceRules.get("d(f*g)/dx").replaceAll("x", "z"));
referenceRules.put("d(f*g)/dt", referenceRules.get("d(f*g)/dx").replaceAll("x", "t"));
referenceRules.put("d2(f*g)/dx2", "f * d2g/dx2 + 2 * df/dx * dg/dx + d2f/dx2 * g");
referenceRules.put("d2(f*g)/dy2", referenceRules.get("d2(f*g)/dx2").replaceAll("x", "y"));
referenceRules.put("d2(f*g)/dz2", referenceRules.get("d2(f*g)/dx2").replaceAll("x", "z"));
referenceRules.put("d2(f*g)/dt2", referenceRules.get("d2(f*g)/dx2").replaceAll("x", "t"));
referenceRules.put("d2(f*g)/dxdy", "f * d2g/dxdy + df/dy * dg/dx + df/dx * dg/dy + d2f/dxdy * g");
referenceRules.put("d2(f*g)/dxdz", referenceRules.get("d2(f*g)/dxdy").replaceAll("y", "z"));
referenceRules.put("d2(f*g)/dxdt", referenceRules.get("d2(f*g)/dxdy").replaceAll("y", "t"));
referenceRules.put("d2(f*g)/dydz", referenceRules.get("d2(f*g)/dxdz").replaceAll("x", "y"));
referenceRules.put("d2(f*g)/dydt", referenceRules.get("d2(f*g)/dxdt").replaceAll("x", "y"));
referenceRules.put("d2(f*g)/dzdt", referenceRules.get("d2(f*g)/dxdt").replaceAll("x", "z"));
referenceRules.put("d3(f*g)/dx3", "f * d3g/dx3 +" +
" 3 * df/dx * d2g/dx2 +" +
" 3 * d2f/dx2 * dg/dx +" +
" d3f/dx3 * g");
referenceRules.put("d3(f*g)/dy3", referenceRules.get("d3(f*g)/dx3").replaceAll("x", "y"));
referenceRules.put("d3(f*g)/dz3", referenceRules.get("d3(f*g)/dx3").replaceAll("x", "z"));
referenceRules.put("d3(f*g)/dt3", referenceRules.get("d3(f*g)/dx3").replaceAll("x", "t"));
referenceRules.put("d3(f*g)/dx2dy", "f * d3g/dx2dy +" +
" df/dy * d2g/dx2 +" +
" 2 * df/dx * d2g/dxdy +" +
" 2 * d2f/dxdy * dg/dx +" +
" d2f/dx2 * dg/dy +" +
" d3f/dx2dy * g");
referenceRules.put("d3(f*g)/dxdy2", "f * d3g/dxdy2 +" +
" 2 * df/dy * d2g/dxdy +" +
" d2f/dy2 * dg/dx +" +
" df/dx * d2g/dy2 +" +
" 2 * d2f/dxdy * dg/dy +" +
" d3f/dxdy2 * g");
referenceRules.put("d3(f*g)/dx2dz", referenceRules.get("d3(f*g)/dx2dy").replaceAll("y", "z"));
referenceRules.put("d3(f*g)/dy2dz", referenceRules.get("d3(f*g)/dx2dz").replaceAll("x", "y"));
referenceRules.put("d3(f*g)/dxdz2", referenceRules.get("d3(f*g)/dxdy2").replaceAll("y", "z"));
referenceRules.put("d3(f*g)/dydz2", referenceRules.get("d3(f*g)/dxdz2").replaceAll("x", "y"));
referenceRules.put("d3(f*g)/dx2dt", referenceRules.get("d3(f*g)/dx2dz").replaceAll("z", "t"));
referenceRules.put("d3(f*g)/dy2dt", referenceRules.get("d3(f*g)/dx2dt").replaceAll("x", "y"));
referenceRules.put("d3(f*g)/dz2dt", referenceRules.get("d3(f*g)/dx2dt").replaceAll("x", "z"));
referenceRules.put("d3(f*g)/dxdt2", referenceRules.get("d3(f*g)/dxdy2").replaceAll("y", "t"));
referenceRules.put("d3(f*g)/dydt2", referenceRules.get("d3(f*g)/dxdt2").replaceAll("x", "y"));
referenceRules.put("d3(f*g)/dzdt2", referenceRules.get("d3(f*g)/dxdt2").replaceAll("x", "z"));
referenceRules.put("d3(f*g)/dxdydz", "f * d3g/dxdydz +" +
" df/dz * d2g/dxdy +" +
" df/dy * d2g/dxdz +" +
" d2f/dydz * dg/dx +" +
" df/dx * d2g/dydz +" +
" d2f/dxdz * dg/dy +" +
" d2f/dxdy * dg/dz +" +
" d3f/dxdydz * g");
referenceRules.put("d3(f*g)/dxdydt", referenceRules.get("d3(f*g)/dxdydz").replaceAll("z", "t"));
referenceRules.put("d3(f*g)/dxdzdt", referenceRules.get("d3(f*g)/dxdydt").replaceAll("y", "z"));
referenceRules.put("d3(f*g)/dydzdt", referenceRules.get("d3(f*g)/dxdzdt").replaceAll("x", "y"));
Field multFieldArrayField = DSCompiler.class.getDeclaredField("multIndirection");
multFieldArrayField.setAccessible(true);
for (int i = 0; i < 5; ++i) {
for (int j = 0; j < 4; ++j) {
DSCompiler compiler = DSCompiler.getCompiler(i, j);
int[][][] multIndirection = (int[][][]) multFieldArrayField.get(compiler);
for (int k = 0; k < multIndirection.length; ++k) {
String product = ordersToString(compiler.getPartialDerivativeOrders(k),
"(f*g)", "x", "y", "z", "t");
StringBuilder rule = new StringBuilder();
for (int[] term : multIndirection[k]) {
if (rule.length() > 0) {
rule.append(" + ");
}
if (term[0] > 1) {
rule.append(term[0]).append(" * ");
}
rule.append(ordersToString(compiler.getPartialDerivativeOrders(term[1]),
"f", "x", "y", "z", "t"));
rule.append(" * ");
rule.append(ordersToString(compiler.getPartialDerivativeOrders(term[2]),
"g", "x", "y", "z", "t"));
}
Assert.assertEquals(product, referenceRules.get(product), rule.toString());
}
}
}
}
@Test public void testCompositionRules()
throws SecurityException, NoSuchFieldException, IllegalArgumentException, IllegalAccessException {
// the following reference rules have all been computed independently from the library,
// using only pencil and paper and some search and replace to handle symmetries
Map<String,String> referenceRules = new HashMap<>();
referenceRules.put("(f(g))", "(f(g))");
referenceRules.put("d(f(g))/dx", "d(f(g))/dg * dg/dx");
referenceRules.put("d(f(g))/dy", referenceRules.get("d(f(g))/dx").replaceAll("x", "y"));
referenceRules.put("d(f(g))/dz", referenceRules.get("d(f(g))/dx").replaceAll("x", "z"));
referenceRules.put("d(f(g))/dt", referenceRules.get("d(f(g))/dx").replaceAll("x", "t"));
referenceRules.put("d2(f(g))/dx2", "d2(f(g))/dg2 * dg/dx * dg/dx + d(f(g))/dg * d2g/dx2");
referenceRules.put("d2(f(g))/dy2", referenceRules.get("d2(f(g))/dx2").replaceAll("x", "y"));
referenceRules.put("d2(f(g))/dz2", referenceRules.get("d2(f(g))/dx2").replaceAll("x", "z"));
referenceRules.put("d2(f(g))/dt2", referenceRules.get("d2(f(g))/dx2").replaceAll("x", "t"));
referenceRules.put("d2(f(g))/dxdy", "d2(f(g))/dg2 * dg/dx * dg/dy + d(f(g))/dg * d2g/dxdy");
referenceRules.put("d2(f(g))/dxdz", referenceRules.get("d2(f(g))/dxdy").replaceAll("y", "z"));
referenceRules.put("d2(f(g))/dxdt", referenceRules.get("d2(f(g))/dxdy").replaceAll("y", "t"));
referenceRules.put("d2(f(g))/dydz", referenceRules.get("d2(f(g))/dxdz").replaceAll("x", "y"));
referenceRules.put("d2(f(g))/dydt", referenceRules.get("d2(f(g))/dxdt").replaceAll("x", "y"));
referenceRules.put("d2(f(g))/dzdt", referenceRules.get("d2(f(g))/dxdt").replaceAll("x", "z"));
referenceRules.put("d3(f(g))/dx3", "d3(f(g))/dg3 * dg/dx * dg/dx * dg/dx +" +
" 3 * d2(f(g))/dg2 * dg/dx * d2g/dx2 +" +
" d(f(g))/dg * d3g/dx3");
referenceRules.put("d3(f(g))/dy3", referenceRules.get("d3(f(g))/dx3").replaceAll("x", "y"));
referenceRules.put("d3(f(g))/dz3", referenceRules.get("d3(f(g))/dx3").replaceAll("x", "z"));
referenceRules.put("d3(f(g))/dt3", referenceRules.get("d3(f(g))/dx3").replaceAll("x", "t"));
referenceRules.put("d3(f(g))/dxdy2", "d3(f(g))/dg3 * dg/dx * dg/dy * dg/dy +" +
" 2 * d2(f(g))/dg2 * dg/dy * d2g/dxdy +" +
" d2(f(g))/dg2 * dg/dx * d2g/dy2 +" +
" d(f(g))/dg * d3g/dxdy2");
referenceRules.put("d3(f(g))/dxdz2", referenceRules.get("d3(f(g))/dxdy2").replaceAll("y", "z"));
referenceRules.put("d3(f(g))/dxdt2", referenceRules.get("d3(f(g))/dxdy2").replaceAll("y", "t"));
referenceRules.put("d3(f(g))/dydz2", referenceRules.get("d3(f(g))/dxdz2").replaceAll("x", "y"));
referenceRules.put("d3(f(g))/dydt2", referenceRules.get("d3(f(g))/dxdt2").replaceAll("x", "y"));
referenceRules.put("d3(f(g))/dzdt2", referenceRules.get("d3(f(g))/dxdt2").replaceAll("x", "z"));
referenceRules.put("d3(f(g))/dx2dy", "d3(f(g))/dg3 * dg/dx * dg/dx * dg/dy +" +
" 2 * d2(f(g))/dg2 * dg/dx * d2g/dxdy +" +
" d2(f(g))/dg2 * d2g/dx2 * dg/dy +" +
" d(f(g))/dg * d3g/dx2dy");
referenceRules.put("d3(f(g))/dx2dz", referenceRules.get("d3(f(g))/dx2dy").replaceAll("y", "z"));
referenceRules.put("d3(f(g))/dx2dt", referenceRules.get("d3(f(g))/dx2dy").replaceAll("y", "t"));
referenceRules.put("d3(f(g))/dy2dz", referenceRules.get("d3(f(g))/dx2dz").replaceAll("x", "y"));
referenceRules.put("d3(f(g))/dy2dt", referenceRules.get("d3(f(g))/dx2dt").replaceAll("x", "y"));
referenceRules.put("d3(f(g))/dz2dt", referenceRules.get("d3(f(g))/dx2dt").replaceAll("x", "z"));
referenceRules.put("d3(f(g))/dxdydz", "d3(f(g))/dg3 * dg/dx * dg/dy * dg/dz +" +
" d2(f(g))/dg2 * dg/dy * d2g/dxdz +" +
" d2(f(g))/dg2 * dg/dx * d2g/dydz +" +
" d2(f(g))/dg2 * d2g/dxdy * dg/dz +" +
" d(f(g))/dg * d3g/dxdydz");
referenceRules.put("d3(f(g))/dxdydt", referenceRules.get("d3(f(g))/dxdydz").replaceAll("z", "t"));
referenceRules.put("d3(f(g))/dxdzdt", referenceRules.get("d3(f(g))/dxdydt").replaceAll("y", "z"));
referenceRules.put("d3(f(g))/dydzdt", referenceRules.get("d3(f(g))/dxdzdt").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dx4", "d4(f(g))/dg4 * dg/dx * dg/dx * dg/dx * dg/dx +" +
" 6 * d3(f(g))/dg3 * dg/dx * dg/dx * d2g/dx2 +" +
" 3 * d2(f(g))/dg2 * d2g/dx2 * d2g/dx2 +" +
" 4 * d2(f(g))/dg2 * dg/dx * d3g/dx3 +" +
" d(f(g))/dg * d4g/dx4");
referenceRules.put("d4(f(g))/dy4", referenceRules.get("d4(f(g))/dx4").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dz4", referenceRules.get("d4(f(g))/dx4").replaceAll("x", "z"));
referenceRules.put("d4(f(g))/dt4", referenceRules.get("d4(f(g))/dx4").replaceAll("x", "t"));
referenceRules.put("d4(f(g))/dx3dy", "d4(f(g))/dg4 * dg/dx * dg/dx * dg/dx * dg/dy +" +
" 3 * d3(f(g))/dg3 * dg/dx * dg/dx * d2g/dxdy +" +
" 3 * d3(f(g))/dg3 * dg/dx * d2g/dx2 * dg/dy +" +
" 3 * d2(f(g))/dg2 * d2g/dx2 * d2g/dxdy +" +
" 3 * d2(f(g))/dg2 * dg/dx * d3g/dx2dy +" +
" d2(f(g))/dg2 * d3g/dx3 * dg/dy +" +
" d(f(g))/dg * d4g/dx3dy");
referenceRules.put("d4(f(g))/dx3dz", referenceRules.get("d4(f(g))/dx3dy").replaceAll("y", "z"));
referenceRules.put("d4(f(g))/dx3dt", referenceRules.get("d4(f(g))/dx3dy").replaceAll("y", "t"));
referenceRules.put("d4(f(g))/dxdy3", "d4(f(g))/dg4 * dg/dx * dg/dy * dg/dy * dg/dy +" +
" 3 * d3(f(g))/dg3 * dg/dy * dg/dy * d2g/dxdy +" +
" 3 * d3(f(g))/dg3 * dg/dx * dg/dy * d2g/dy2 +" +
" 3 * d2(f(g))/dg2 * d2g/dxdy * d2g/dy2 +" +
" 3 * d2(f(g))/dg2 * dg/dy * d3g/dxdy2 +" +
" d2(f(g))/dg2 * dg/dx * d3g/dy3 +" +
" d(f(g))/dg * d4g/dxdy3");
referenceRules.put("d4(f(g))/dxdz3", referenceRules.get("d4(f(g))/dxdy3").replaceAll("y", "z"));
referenceRules.put("d4(f(g))/dxdt3", referenceRules.get("d4(f(g))/dxdy3").replaceAll("y", "t"));
referenceRules.put("d4(f(g))/dy3dz", referenceRules.get("d4(f(g))/dx3dz").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dy3dt", referenceRules.get("d4(f(g))/dx3dt").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dydz3", referenceRules.get("d4(f(g))/dxdz3").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dydt3", referenceRules.get("d4(f(g))/dxdt3").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dz3dt", referenceRules.get("d4(f(g))/dx3dt").replaceAll("x", "z"));
referenceRules.put("d4(f(g))/dzdt3", referenceRules.get("d4(f(g))/dxdt3").replaceAll("x", "z"));
referenceRules.put("d4(f(g))/dx2dy2", "d4(f(g))/dg4 * dg/dx * dg/dx * dg/dy * dg/dy +" +
" 4 * d3(f(g))/dg3 * dg/dx * dg/dy * d2g/dxdy +" +
" d3(f(g))/dg3 * dg/dx * dg/dx * d2g/dy2 +" +
" 2 * d2(f(g))/dg2 * d2g/dxdy * d2g/dxdy +" +
" 2 * d2(f(g))/dg2 * dg/dx * d3g/dxdy2 +" +
" d3(f(g))/dg3 * d2g/dx2 * dg/dy * dg/dy +" +
" 2 * d2(f(g))/dg2 * dg/dy * d3g/dx2dy +" +
" d2(f(g))/dg2 * d2g/dx2 * d2g/dy2 +" +
" d(f(g))/dg * d4g/dx2dy2");
referenceRules.put("d4(f(g))/dx2dz2", referenceRules.get("d4(f(g))/dx2dy2").replaceAll("y", "z"));
referenceRules.put("d4(f(g))/dx2dt2", referenceRules.get("d4(f(g))/dx2dy2").replaceAll("y", "t"));
referenceRules.put("d4(f(g))/dy2dz2", referenceRules.get("d4(f(g))/dx2dz2").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dy2dt2", referenceRules.get("d4(f(g))/dx2dt2").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dz2dt2", referenceRules.get("d4(f(g))/dx2dt2").replaceAll("x", "z"));
referenceRules.put("d4(f(g))/dx2dydz", "d4(f(g))/dg4 * dg/dx * dg/dx * dg/dy * dg/dz +" +
" 2 * d3(f(g))/dg3 * dg/dx * dg/dy * d2g/dxdz +" +
" d3(f(g))/dg3 * dg/dx * dg/dx * d2g/dydz +" +
" 2 * d3(f(g))/dg3 * dg/dx * d2g/dxdy * dg/dz +" +
" 2 * d2(f(g))/dg2 * d2g/dxdy * d2g/dxdz +" +
" 2 * d2(f(g))/dg2 * dg/dx * d3g/dxdydz +" +
" d3(f(g))/dg3 * d2g/dx2 * dg/dy * dg/dz +" +
" d2(f(g))/dg2 * dg/dy * d3g/dx2dz +" +
" d2(f(g))/dg2 * d2g/dx2 * d2g/dydz +" +
" d2(f(g))/dg2 * d3g/dx2dy * dg/dz +" +
" d(f(g))/dg * d4g/dx2dydz");
referenceRules.put("d4(f(g))/dx2dydt", referenceRules.get("d4(f(g))/dx2dydz").replaceAll("z", "t"));
referenceRules.put("d4(f(g))/dx2dzdt", referenceRules.get("d4(f(g))/dx2dydt").replaceAll("y", "z"));
referenceRules.put("d4(f(g))/dxdy2dz", "d4(f(g))/dg4 * dg/dx * dg/dy * dg/dy * dg/dz +" +
" d3(f(g))/dg3 * dg/dy * dg/dy * d2g/dxdz +" +
" 2 * d3(f(g))/dg3 * dg/dx * dg/dy * d2g/dydz +" +
" 2 * d3(f(g))/dg3 * dg/dy * d2g/dxdy * dg/dz +" +
" 2 * d2(f(g))/dg2 * d2g/dxdy * d2g/dydz +" +
" 2 * d2(f(g))/dg2 * dg/dy * d3g/dxdydz +" +
" d3(f(g))/dg3 * dg/dx * d2g/dy2 * dg/dz +" +
" d2(f(g))/dg2 * d2g/dy2 * d2g/dxdz +" +
" d2(f(g))/dg2 * dg/dx * d3g/dy2dz +" +
" d2(f(g))/dg2 * d3g/dxdy2 * dg/dz +" +
" d(f(g))/dg * d4g/dxdy2dz");
referenceRules.put("d4(f(g))/dxdy2dt", referenceRules.get("d4(f(g))/dxdy2dz").replaceAll("z", "t"));
referenceRules.put("d4(f(g))/dy2dzdt", referenceRules.get("d4(f(g))/dx2dzdt").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dxdydz2", "d4(f(g))/dg4 * dg/dx * dg/dy * dg/dz * dg/dz +" +
" 2 * d3(f(g))/dg3 * dg/dy * dg/dz * d2g/dxdz +" +
" 2 * d3(f(g))/dg3 * dg/dx * dg/dz * d2g/dydz +" +
" d3(f(g))/dg3 * dg/dx * dg/dy * d2g/dz2 +" +
" 2 * d2(f(g))/dg2 * d2g/dxdz * d2g/dydz +" +
" d2(f(g))/dg2 * dg/dy * d3g/dxdz2 +" +
" d2(f(g))/dg2 * dg/dx * d3g/dydz2 +" +
" d3(f(g))/dg3 * d2g/dxdy * dg/dz * dg/dz +" +
" 2 * d2(f(g))/dg2 * dg/dz * d3g/dxdydz +" +
" d2(f(g))/dg2 * d2g/dxdy * d2g/dz2 +" +
" d(f(g))/dg * d4g/dxdydz2");
referenceRules.put("d4(f(g))/dxdz2dt", referenceRules.get("d4(f(g))/dxdy2dt").replaceAll("y", "z"));
referenceRules.put("d4(f(g))/dydz2dt", referenceRules.get("d4(f(g))/dxdz2dt").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dxdydt2", referenceRules.get("d4(f(g))/dxdydz2").replaceAll("z", "t"));
referenceRules.put("d4(f(g))/dxdzdt2", referenceRules.get("d4(f(g))/dxdydt2").replaceAll("y", "z"));
referenceRules.put("d4(f(g))/dydzdt2", referenceRules.get("d4(f(g))/dxdzdt2").replaceAll("x", "y"));
referenceRules.put("d4(f(g))/dxdydzdt", "d4(f(g))/dg4 * dg/dx * dg/dy * dg/dz * dg/dt +" +
" d3(f(g))/dg3 * dg/dy * dg/dz * d2g/dxdt +" +
" d3(f(g))/dg3 * dg/dx * dg/dz * d2g/dydt +" +
" d3(f(g))/dg3 * dg/dx * dg/dy * d2g/dzdt +" +
" d3(f(g))/dg3 * dg/dy * d2g/dxdz * dg/dt +" +
" d2(f(g))/dg2 * d2g/dxdz * d2g/dydt +" +
" d2(f(g))/dg2 * dg/dy * d3g/dxdzdt +" +
" d3(f(g))/dg3 * dg/dx * d2g/dydz * dg/dt +" +
" d2(f(g))/dg2 * d2g/dydz * d2g/dxdt +" +
" d2(f(g))/dg2 * dg/dx * d3g/dydzdt +" +
" d3(f(g))/dg3 * d2g/dxdy * dg/dz * dg/dt +" +
" d2(f(g))/dg2 * dg/dz * d3g/dxdydt +" +
" d2(f(g))/dg2 * d2g/dxdy * d2g/dzdt +" +
" d2(f(g))/dg2 * d3g/dxdydz * dg/dt +" +
" d(f(g))/dg * d4g/dxdydzdt");
Field compFieldArrayField = DSCompiler.class.getDeclaredField("compIndirection");
compFieldArrayField.setAccessible(true);
for (int i = 0; i < 5; ++i) {
for (int j = 0; j < 5; ++j) {
DSCompiler compiler = DSCompiler.getCompiler(i, j);
int[][][] compIndirection = (int[][][]) compFieldArrayField.get(compiler);
for (int k = 0; k < compIndirection.length; ++k) {
String product = ordersToString(compiler.getPartialDerivativeOrders(k),
"(f(g))", "x", "y", "z", "t");
StringBuilder rule = new StringBuilder();
for (int[] term : compIndirection[k]) {
if (rule.length() > 0) {
rule.append(" + ");
}
if (term[0] > 1) {
rule.append(term[0]).append(" * ");
}
rule.append(orderToString(term[1], "(f(g))", "g"));
for (int l = 2; l < term.length; ++l) {
rule.append(" * ");
rule.append(ordersToString(compiler.getPartialDerivativeOrders(term[l]),
"g", "x", "y", "z", "t"));
}
}
Assert.assertEquals(product, referenceRules.get(product), rule.toString());
}
}
}
}
private void checkIndices(int[] indices, int ... expected) {
Assert.assertEquals(expected.length, indices.length);
for (int i = 0; i < expected.length; ++i) {
Assert.assertEquals(expected[i], indices[i]);
}
}
private String orderToString(int order, String functionName, String parameterName) {
if (order == 0) {
return functionName;
} else if (order == 1) {
return "d" + functionName + "/d" + parameterName;
} else {
return "d" + order + functionName + "/d" + parameterName + order;
}
}
private String ordersToString(int[] orders, String functionName, String ... parametersNames) {
int sumOrders = 0;
for (int order : orders) {
sumOrders += order;
}
if (sumOrders == 0) {
return functionName;
}
StringBuilder builder = new StringBuilder();
builder.append('d');
if (sumOrders > 1) {
builder.append(sumOrders);
}
builder.append(functionName).append('/');
for (int i = 0; i < orders.length; ++i) {
if (orders[i] > 0) {
builder.append('d').append(parametersNames[i]);
if (orders[i] > 1) {
builder.append(orders[i]);
}
}
}
return builder.toString();
}
}