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new 82070d092 MATH-1650.
82070d092 is described below
commit 82070d092e617ab5e5d58ef5f93b3df0df50d61b
Author: Gilles Sadowski <[email protected]>
AuthorDate: Sat Apr 5 17:59:16 2025 +0200
MATH-1650.
---
.../interpolation/ClampedSplineInterpolator.java | 160 +++++++++++++++++++++
src/changes/changes.xml | 3 +
2 files changed, 163 insertions(+)
diff --git
a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/ClampedSplineInterpolator.java
b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/ClampedSplineInterpolator.java
new file mode 100644
index 000000000..074ce87d9
--- /dev/null
+++
b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/ClampedSplineInterpolator.java
@@ -0,0 +1,160 @@
+/*
+ * 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.math4.legacy.analysis.interpolation;
+
+import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialFunction;
+import
org.apache.commons.math4.legacy.analysis.polynomials.PolynomialSplineFunction;
+import org.apache.commons.math4.legacy.core.MathArrays;
+import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
+import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException;
+import org.apache.commons.math4.legacy.exception.util.LocalizedFormats;
+
+/**
+ * Clamped cubic spline interpolator.
+ * The interpolating function consists in cubic polynomial functions defined
over the
+ * subintervals determined by the "knot points".
+ *
+ * The interpolating polynomials satisfy:
+ * <ol>
+ * <li>The value of the interpolating function at each of the input {@code x}
values
+ * equals the corresponding input {@code y} value.</li>
+ * <li>Adjacent polynomials are equal through two derivatives at the knot
points
+ * (i.e., adjacent polynomials "match up" at the knot points, as do their
first and
+ * second derivatives).</li>
+ * <li>The clamped boundary condition, i.e. the interpolating function takes
"a
+ * specific direction" at both its start point and its end point by
providing the
+ * desired first derivative values (slopes) as function parameters to
+ * {@link #interpolate(double[], double[], double, double)}.</li>
+ * </ol>
+ *
+ * The algorithm is implemented as described in
+ * <blockquote>
+ * R.L. Burden, J.D. Faires,
+ * <em>Numerical Analysis</em>, 9th Ed., 2010, Cengage Learning, ISBN
0-538-73351-9, pp 153-156.
+ * </blockquote>
+ *
+ */
+public class ClampedSplineInterpolator implements UnivariateInterpolator {
+ /**
+ *
+ * The first derivatives evaluated at the first and last knot points are
+ * approximated from a natural/unclamped spline that passes through the
same
+ * set of points.
+ *
+ * @param x Arguments for the interpolation points.
+ * @param y Values for the interpolation points.
+ * @return the interpolating function.
+ * @throws DimensionMismatchException if {@code x} and {@code y} have
different sizes.
+ * @throws NumberIsTooSmallException if the size of {@code x < 3}.
+ * @throws
org.apache.commons.math4.legacy.exception.NonMonotonicSequenceException if
{@code x} is not sorted in strict increasing order.
+ */
+ @Override
+ public PolynomialSplineFunction interpolate(final double[] x,
+ final double[] y) {
+ final SplineInterpolator spliner = new SplineInterpolator();
+ final PolynomialSplineFunction spline = spliner.interpolate(x, y);
+ final PolynomialSplineFunction derivativeSpline =
spline.polynomialSplineDerivative();
+ final double fpStart = derivativeSpline.value(x[0]);
+ final double fpEnd = derivativeSpline.value(x[x.length - 1]);
+
+ return this.interpolate(x, y, fpStart, fpEnd);
+ }
+
+ /**
+ * Computes an interpolating function for the data set with defined
+ * boundary conditions.
+ *
+ * @param x Arguments for the interpolation points.
+ * @param y Values for the interpolation points.
+ * @param fpStart First derivative at the starting point of the returned
+ * spline function (starting slope).
+ * @param fpEnd First derivative at the ending point of the returned
+ * spline function (ending slope).
+ * @return the interpolating function.
+ * @throws DimensionMismatchException if {@code x} and {@code y} have
different sizes.
+ * @throws NumberIsTooSmallException if the size of {@code x < 3}.
+ * @throws
org.apache.commons.math4.legacy.exception.NonMonotonicSequenceException if
{@code x} is not sorted in strict increasing order.
+ */
+ public PolynomialSplineFunction interpolate(final double[] x,
+ final double[] y,
+ final double fpStart,
+ final double fpEnd) {
+ if (x.length != y.length) {
+ throw new DimensionMismatchException(x.length, y.length);
+ }
+
+ if (x.length < 3) {
+ throw new
NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
+ x.length, 3, true);
+ }
+
+ // Number of intervals. The number of data points is n + 1.
+ final int n = x.length - 1;
+
+ MathArrays.checkOrder(x);
+
+ // Differences between knot points.
+ final double[] h = new double[n];
+ for (int i = 0; i < n; i++) {
+ h[i] = x[i + 1] - x[i];
+ }
+
+ final double[] mu = new double[n];
+ final double[] z = new double[n + 1];
+
+ final double alpha0 = 3 * ((y[1] - y[0]) / h[0] - fpStart);
+ final double alphaN = 3 * (fpEnd - (y[n] - y[n - 1]) / h[n - 1]);
+
+ mu[0] = 0.5;
+ final double ell0 = 2 * h[0];
+ z[0] = alpha0 / ell0;
+
+ for (int i = 1; i < n; i++) {
+ final double alpha = 3 * ((y[i + 1] - y[i]) / h[i] - (y[i] - y[i -
1]) / h[i - 1]);
+ final double ell = 2 * (x[i + 1] - x[i - 1]) - h[i - 1] * mu[i -
1];
+ mu[i] = h[i] / ell;
+ z[i] = (alpha - h[i - 1] * z[i - 1]) / ell;
+ }
+
+ // Cubic spline coefficients.
+ final double[] b = new double[n]; // Linear.
+ final double[] c = new double[n + 1]; // Quadratic.
+ final double[] d = new double[n]; // Cubic.
+
+ final double ellN = h[n - 1] * (2 - mu[n - 1]);
+ z[n] = (alphaN - h[n - 1] * z[n - 1]) / ellN;
+ c[n] = z[n];
+
+ for (int j = n - 1; j >= 0; j--) {
+ c[j] = z[j] - mu[j] * c[j + 1];
+ b[j] = ((y[j + 1] - y[j]) / h[j]) - h[j] * (c[j + 1] + 2 * c[j]) /
3;
+ d[j] = (c[j + 1] - c[j]) / (3 * h[j]);
+ }
+
+ final PolynomialFunction[] polynomials = new PolynomialFunction[n];
+ final double[] coefficients = new double[4];
+ for (int i = 0; i < n; i++) {
+ coefficients[0] = y[i];
+ coefficients[1] = b[i];
+ coefficients[2] = c[i];
+ coefficients[3] = d[i];
+ polynomials[i] = new PolynomialFunction(coefficients);
+ }
+
+ return new PolynomialSplineFunction(x, polynomials);
+ }
+}
diff --git a/src/changes/changes.xml b/src/changes/changes.xml
index 4ebf51410..05841a497 100644
--- a/src/changes/changes.xml
+++ b/src/changes/changes.xml
@@ -96,6 +96,9 @@ Caveat:
to support the whole codebase (it was one of the main reasons for
creating more focused components).
">
+ <action dev="erans" type="add" issue="MATH-1650" due-to="Michael Scholz">
+ New class: "ClampedSplineInterpolator".
+ </action>
<action dev="aherbert" type="update" issue="MATH-1671">
Update o.a.c.m.legacy.stat.descriptive package. Functionality has been
partially transferred to Commons Statistics descriptive.
