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Diffstat (limited to 'src/main/java/org/apache/commons/math3/analysis/interpolation/SplineInterpolator.java')
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diff --git a/src/main/java/org/apache/commons/math3/analysis/interpolation/SplineInterpolator.java b/src/main/java/org/apache/commons/math3/analysis/interpolation/SplineInterpolator.java new file mode 100644 index 0000000..f37e1b1 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/analysis/interpolation/SplineInterpolator.java @@ -0,0 +1,127 @@ +/* + * 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.analysis.interpolation; + +import org.apache.commons.math3.analysis.polynomials.PolynomialFunction; +import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction; +import org.apache.commons.math3.exception.DimensionMismatchException; +import org.apache.commons.math3.exception.NonMonotonicSequenceException; +import org.apache.commons.math3.exception.NumberIsTooSmallException; +import org.apache.commons.math3.exception.util.LocalizedFormats; +import org.apache.commons.math3.util.MathArrays; + +/** + * Computes a natural (also known as "free", "unclamped") cubic spline interpolation for the data set. + * <p> + * The {@link #interpolate(double[], double[])} method returns a {@link PolynomialSplineFunction} + * consisting of n cubic polynomials, defined over the subintervals determined by the x values, + * {@code x[0] < x[i] ... < x[n].} The x values are referred to as "knot points." + * <p> + * The value of the PolynomialSplineFunction at a point x that is greater than or equal to the smallest + * knot point and strictly less than the largest knot point is computed by finding the subinterval to which + * x belongs and computing the value of the corresponding polynomial at <code>x - x[i] </code> where + * <code>i</code> is the index of the subinterval. See {@link PolynomialSplineFunction} for more details. + * </p> + * <p> + * The interpolating polynomials satisfy: <ol> + * <li>The value of the PolynomialSplineFunction at each of the input x values equals the + * corresponding 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> + * </ol> + * <p> + * The cubic spline interpolation algorithm implemented is as described in R.L. Burden, J.D. Faires, + * <u>Numerical Analysis</u>, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131. + * </p> + * + */ +public class SplineInterpolator implements UnivariateInterpolator { + /** + * Computes an interpolating function for the data set. + * @param x the arguments for the interpolation points + * @param y the values for the interpolation points + * @return a function which interpolates the data set + * @throws DimensionMismatchException if {@code x} and {@code y} + * have different sizes. + * @throws NonMonotonicSequenceException if {@code x} is not sorted in + * strict increasing order. + * @throws NumberIsTooSmallException if the size of {@code x} is smaller + * than 3. + */ + public PolynomialSplineFunction interpolate(double x[], double y[]) + throws DimensionMismatchException, + NumberIsTooSmallException, + NonMonotonicSequenceException { + 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]; + mu[0] = 0d; + z[0] = 0d; + double g = 0; + for (int i = 1; i < n; i++) { + g = 2d * (x[i+1] - x[i - 1]) - h[i - 1] * mu[i -1]; + mu[i] = h[i] / g; + z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) / + (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g; + } + + // cubic spline coefficients -- b is linear, c quadratic, d is cubic (original y's are constants) + final double b[] = new double[n]; + final double c[] = new double[n + 1]; + final double d[] = new double[n]; + + z[n] = 0d; + c[n] = 0d; + + 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] + 2d * c[j]) / 3d; + d[j] = (c[j + 1] - c[j]) / (3d * 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); + } +} |