MATH-503

Step function.


git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1066018 13f79535-47bb-0310-9956-ffa450edef68

src/main/java/org/apache/commons/math/analysis/function/StepFunction.java

@@ -0,0 +1,89 @@
+/*
+ * 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.math.analysis.function;
+
+import java.util.Arrays;
+import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.exception.DimensionMismatchException;
+import org.apache.commons.math.exception.NullArgumentException;
+import org.apache.commons.math.exception.NoDataException;
+import org.apache.commons.math.util.MathUtils;
+
+/**
+ * <a href="http://en.wikipedia.org/wiki/Step_function">
+ *  Step function</a>.
+ *
+ * @version $Revision$ $Date$
+ * @since 3.0
+ */
+public class StepFunction implements UnivariateRealFunction {
+    /** Abscissae. */
+    private final double[] abscissa;
+    /** Ordinates. */
+    private final double[] ordinate;
+
+    /**
+     * Builds a step function from a list of abscissae and the corresponding
+     * ordinates.
+     *
+     * @param x Abscissae.
+     * @param y Ordinates.
+     * @throws org.apache.commons.math.exception.NonMonotonousSequenceException
+     * if the {@code x} array is not sorted in strictly increasing order.
+     * @throws NullArgumentException if {@code x} or {@code y} are {@code null}.
+     * @throws NoDataException if {@code x} or {@code y} are zero-length.
+     */
+    public StepFunction(double[] x,
+                        double[] y) {
+        if (x == null ||
+            y == null) {
+            throw new NullArgumentException();
+        }
+        if (x.length == 0 ||
+            y.length == 0) {
+            throw new NoDataException();
+        }
+        if (y.length != x.length) {
+            throw new DimensionMismatchException(y.length, x.length);
+        }
+        MathUtils.checkOrder(x);
+
+        abscissa = MathUtils.copyOf(x);
+        ordinate = MathUtils.copyOf(y);
+    }
+
+    /** {@inheritDoc} */
+    public double value(double x) {
+        int index = Arrays.binarySearch(abscissa, x);
+        double fx = 0;
+
+        if (index < -1) {
+            // "x" is between "abscissa[-index-2]" and "abscissa[-index-1]".
+            fx = ordinate[-index-2];
+        } else if (index >= 0) {
+            // "x" is exactly "abscissa[index]".
+            fx = ordinate[index];
+        } else {
+            // Otherwise, "x" is smaller than the first value in "abscissa"
+            // (hence the returned value should be "ordinate[0]").
+            fx = ordinate[0];
+        }
+
+        return fx;
+    }
+}

src/test/java/org/apache/commons/math/analysis/function/StepFunctionTest.java

@@ -0,0 +1,95 @@
+/*
+ * 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.math.analysis.function;
+
+import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.exception.DimensionMismatchException;
+import org.apache.commons.math.exception.NonMonotonousSequenceException;
+import org.apache.commons.math.exception.NullArgumentException;
+import org.apache.commons.math.exception.NoDataException;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Test for class {@link StepFunction}.
+ */
+public class StepFunctionTest {
+    private final double EPS = Math.ulp(1d);
+
+    @Test
+    public void testPreconditions() {
+        try {
+            final UnivariateRealFunction f = new StepFunction(null,
+                                                              new double[] {0, -1, -2});
+        } catch (NullArgumentException e) {
+            // Expected.
+        }
+        try {
+            final UnivariateRealFunction f = new StepFunction(new double[] {0, 1},
+                                                              null);
+        } catch (NullArgumentException e) {
+            // Expected.
+        }
+
+        try {
+            final UnivariateRealFunction f = new StepFunction(new double[] {0},
+                                                              new double[] {});
+        } catch (NoDataException e) {
+            // Expected.
+        }
+
+        try {
+            final UnivariateRealFunction f = new StepFunction(new double[] {},
+                                                              new double[] {0});
+        } catch (NoDataException e) {
+            // Expected.
+        }
+
+        try {
+            final UnivariateRealFunction f = new StepFunction(new double[] {0, 1},
+                                                              new double[] {0, -1, -2});
+        } catch (DimensionMismatchException e) {
+            // Expected.
+        }
+
+        try {
+            final UnivariateRealFunction f = new StepFunction(new double[] {1, 0, 1},
+                                                              new double[] {0, -1, -2});
+        } catch (NonMonotonousSequenceException e) {
+            // Expected.
+        }
+    }
+
+    @Test
+    public void testSomeValues() {
+        final double[] x = { -2, -0.5, 0, 1.9, 7.4, 21.3 };
+        final double[] y = { 4, -1, -5.5, 0.4, 5.8, 51.2 };
+
+        final UnivariateRealFunction f = new StepFunction(x, y);
+
+        Assert.assertEquals(4, f.value(Double.NEGATIVE_INFINITY), EPS);
+        Assert.assertEquals(4, f.value(-10), EPS);
+        Assert.assertEquals(-1, f.value(-0.4), EPS);
+        Assert.assertEquals(-5.5, f.value(0), EPS);
+        Assert.assertEquals(0.4, f.value(2), EPS);
+        Assert.assertEquals(5.8, f.value(10), EPS);
+        Assert.assertEquals(51.2, f.value(30), EPS);
+        Assert.assertEquals(51.2, f.value(Double.POSITIVE_INFINITY), EPS);
+    }
+}