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TilmanNeumannTilmanNeumann
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convert MpiPartitionGenerator tests into unit tests
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3 files changed

+199
-163
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‎src/main/java/de/tilman_neumann/jml/partitions/MpiPartitionGenerator.java

+46
Original file line numberDiff line numberDiff line change
@@ -188,4 +188,50 @@ public static long numberOfFactorizationsOf(BigInteger n) {
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PrimePowers mpiFromFactors = PrimePowers_DefaultImpl.valueOf(n);
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return numberOfPartitionsOf(mpiFromFactors);
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}
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/**
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* Computes the number of partitions of partitions.
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* A001970 = 1, 1, 3, 6, 14, 27, 58, 111, 223, 424, 817, 1527, 2870, 5279, 9710, 17622, 31877, 57100, 101887, 180406, 318106, 557453, 972796, 1688797, 2920123, ...
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*/
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public static long numberOfPartitionsOfPartitions(int n) {
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long totalNumberOfPartitions = 0;
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// run over all additive partition of n
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IntegerPartitionGenerator partgen = new IntegerPartitionGenerator(n);
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while (partgen.hasNext()) {
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int[] flatPartition = partgen.next();
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// partition is in flat form, i.e. a list of all parts. convert this into the multiset form:
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IntegerPartition expPartition = new IntegerPartition(flatPartition);
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if (DEBUG) LOG.debug("expPartition from n=" + n + ": " + expPartition);
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// now we have all the multiplicities
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Mpi mpiFromPartition = new Mpi_IntegerArrayImpl(expPartition.values());
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MpiPartitionGenerator mpiPartGen = new MpiPartitionGenerator(mpiFromPartition);
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while (mpiPartGen.hasNext()) {
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mpiPartGen.next();
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totalNumberOfPartitions++;
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}
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}
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return totalNumberOfPartitions;
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}
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/**
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* Computes the number of partitions of strong multisets.
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* This is A035310 = "Ways of partitioning an n-multiset with multiplicities some partition of n."
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* = 1, 4, 12, 47, 170, 750, 3255, 16010, 81199, 448156, 2579626, 15913058, 102488024, 698976419, 4976098729, 37195337408, 289517846210, 2352125666883, 19841666995265, 173888579505200, 1577888354510786, 14820132616197925, 143746389756336173, 1438846957477988926, ...
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*/
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public static long numberOfMultisetPartitions(int n) {
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int totalNumberOfPartitions = 0;
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// run over all additive partition of n:
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IntegerPartitionGenerator partgen = new IntegerPartitionGenerator(n);
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while (partgen.hasNext()) {
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int[] flatPartition = partgen.next();
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// partition is in flat form, i.e. a list of all parts.
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Mpi mpiFromPartition = new Mpi_IntegerArrayImpl(flatPartition);
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MpiPartitionGenerator mpiPartGen = new MpiPartitionGenerator(mpiFromPartition);
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while (mpiPartGen.hasNext()) {
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mpiPartGen.next();
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totalNumberOfPartitions++;
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}
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}
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return totalNumberOfPartitions;
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}
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}

‎src/main/java/de/tilman_neumann/jml/partitions/MpiPartitionGeneratorTest.java

-163
This file was deleted.

‎src/test/java/de/tilman_neumann/jml/partitions/MpiPartitionGeneratorTest.java

+153
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@@ -0,0 +1,153 @@
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/*
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* java-math-library is a Java library focused on number theory, but not necessarily limited to it. It is based on the PSIQS 4.0 factoring project.
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* Copyright (C) 2018-2024 Tilman Neumann - [email protected]
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*
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* This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied
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* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along with this program;
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* if not, see <http://www.gnu.org/licenses/>.
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*/
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package de.tilman_neumann.jml.partitions;
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import static org.junit.Assert.assertEquals;
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import java.math.BigInteger;
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import java.util.ArrayList;
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import org.apache.logging.log4j.Logger;
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import org.junit.BeforeClass;
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import org.junit.Test;
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import org.apache.logging.log4j.LogManager;
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import de.tilman_neumann.jml.combinatorics.Factorial;
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import de.tilman_neumann.util.ConfigUtil;
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public class MpiPartitionGeneratorTest {
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private static final Logger LOG = LogManager.getLogger(MpiPartitionGeneratorTest.class);
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private static final boolean DEBUG = false;
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@BeforeClass
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public static void setup() {
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ConfigUtil.initProject();
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}
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/**
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* Test the number of essentially different factorizations of n= 1, 2, 3, ...
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* A001055 (n=1...) = 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 5, 1, 4, 1, 4, 2, 2, 1, 7, 2, 2, 3, 4, 1, ...
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*/
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@Test
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public void testNumberOfFactorizations() {
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int maxListSize = 30;
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ArrayList<Long> list = new ArrayList<>();
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for (int n=1; n<=10000; n++) {
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long numberOfFactorizations = MpiPartitionGenerator.numberOfFactorizationsOf(BigInteger.valueOf(n));
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if (DEBUG) LOG.debug(n + " can be factored in " + numberOfFactorizations + " different ways");
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if (list.size() < maxListSize) list.add(numberOfFactorizations);
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}
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if (DEBUG) LOG.debug("First 30 sequence elements = " + list);
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assertEquals("[1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 5, 1, 4, 1, 4, 2, 2, 1, 7, 2, 2, 3, 4, 1, 5]", list.toString());
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}
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/**
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* Test record numbers of essentially different factorizations of n = 1, 2, 3, ...
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* A033833 = 1, 4, 8, 12, 16, 24, 36, 48, 72, 96, 120, 144, 192, 216, 240, 288, 360, 432, 480, 576, 720, 960, 1080, 1152, 1440, 2160, 2880, 4320, 5040, 5760, 7200, 8640, 10080, 11520, ...
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*/
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@Test
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public void testNumberOfFactorizationsRecords() {
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int maxListSize = 30;
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ArrayList<Integer> list = new ArrayList<>();
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long record = 0;
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for (int n=1; n<=10000; n++) {
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long numberOfFactorizations = MpiPartitionGenerator.numberOfFactorizationsOf(BigInteger.valueOf(n));
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if (numberOfFactorizations > record) { // same value does not count as new record
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LOG.info(n + " can be factored in " + numberOfFactorizations + " different ways");
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record = numberOfFactorizations;
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if (list.size() < maxListSize) list.add(n);
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}
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}
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if (DEBUG) LOG.debug("First 30 sequence elements = " + list);
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assertEquals("[1, 4, 8, 12, 16, 24, 36, 48, 72, 96, 120, 144, 192, 216, 240, 288, 360, 432, 480, 576, 720, 960, 1080, 1152, 1440, 2160, 2880, 4320, 5040, 5760]", list.toString());
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}
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/**
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* Test record numbers of essentially different factorizations of n per bit.
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* This sequence S(n) = 1, 12, 16, 24, 36, 48, 72, 96, 120, 144, 240, 288, 360, 432, 480, 576, 720, 960, 1080, 1152, ... is not in OEIS.
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*/
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@Test
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public void testNumberOfFactorizationsRecordsPerBit() {
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int maxListSize = 30;
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ArrayList<Integer> list = new ArrayList<>();
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double recordRatio = 0;
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for (int n=1; n<=10000; n++) {
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long numberOfFactorizations = MpiPartitionGenerator.numberOfFactorizationsOf(BigInteger.valueOf(n));
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double bits = n==1 ? 1.0 : Math.log(n)/Math.log(2.0); // ld(n)
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double ratio = numberOfFactorizations/bits;
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if (ratio > recordRatio) { // same value does not count as new record
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LOG.info(n + " (" + bits + " bit) can be factored in " + numberOfFactorizations + " different ways -> ratio = " + ratio);
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recordRatio = ratio;
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if (list.size() < maxListSize) list.add(n);
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}
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}
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if (DEBUG) LOG.debug("First 30 sequence elements = " + list);
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assertEquals("[1, 12, 16, 24, 36, 48, 72, 96, 120, 144, 240, 288, 360, 432, 480, 576, 720, 960, 1080, 1152, 1440, 2160, 2880, 4320, 5040, 5760, 7200, 8640]", list.toString());
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}
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/**
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* Test the number of essentially different factorizations of n!.
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* This is A076716(n=2, 3, ...) = 1, 2, 7, 21, 98, 392, 2116, 11830, 70520, 425240, ...
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*/
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@Test
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public void testNumberOfFactorialFactorizations() {
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ArrayList<Long> list = new ArrayList<>();
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for (int n=2; n<=11; n++) {
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long start = System.currentTimeMillis();
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BigInteger factorial = Factorial.factorial(n);
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long numberOfFactorizations = MpiPartitionGenerator.numberOfFactorizationsOf(factorial);
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LOG.info(n + "! = " + factorial + " can be factored in " + numberOfFactorizations + " different ways (computed in " + (System.currentTimeMillis()-start) + " ms)");
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list.add(numberOfFactorizations);
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}
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if (DEBUG) LOG.debug("list = " + list);
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assertEquals("[1, 2, 7, 21, 98, 392, 2116, 11830, 70520, 425240]", list.toString());
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}
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/**
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* Test the number of partitions of partitions.
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* A001970 = 1, 1, 3, 6, 14, 27, 58, 111, 223, 424, 817, 1527, 2870, 5279, 9710, 17622, 31877, 57100, 101887, 180406, 318106, 557453, 972796, 1688797, 2920123, ...
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*/
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@Test
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public void testPartitionsOfPartitions() {
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ArrayList<Long> list = new ArrayList<>();
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for (int n=0; n<=20; n++) {
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long start = System.currentTimeMillis();
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long totalNumberOfPartitions = MpiPartitionGenerator.numberOfPartitionsOfPartitions(n);
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LOG.info(n + " has " + totalNumberOfPartitions + " partitions of partitions (computed in " + (System.currentTimeMillis()-start) + " ms)");
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list.add(totalNumberOfPartitions);
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}
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if (DEBUG) LOG.debug("list = " + list);
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assertEquals("[1, 1, 3, 6, 14, 27, 58, 111, 223, 424, 817, 1527, 2870, 5279, 9710, 17622, 31877, 57100, 101887, 180406, 318106]", list.toString());
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}
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/**
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* Test the number of partitions of strong multisets.
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* This is A035310 = "Ways of partitioning an n-multiset with multiplicities some partition of n."
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* = 1, 4, 12, 47, 170, 750, 3255, 16010, 81199, 448156, 2579626, 15913058, 102488024, 698976419, 4976098729, 37195337408, 289517846210, 2352125666883, 19841666995265, 173888579505200, 1577888354510786, 14820132616197925, 143746389756336173, 1438846957477988926, ...
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*/
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@Test
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public void testMultisetPartitions() {
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ArrayList<Long> list = new ArrayList<>();
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for (int n=1; n<=10; n++) {
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long start = System.currentTimeMillis();
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long totalNumberOfPartitions = MpiPartitionGenerator.numberOfMultisetPartitions(n);
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LOG.info(n + " has " + totalNumberOfPartitions + " multiset partitions (computed in " + (System.currentTimeMillis()-start) + " ms)");
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list.add(totalNumberOfPartitions);
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}
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if (DEBUG) LOG.debug("list = " + list);
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assertEquals("[1, 4, 12, 47, 170, 750, 3255, 16010, 81199, 448156]", list.toString());
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}
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}

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