Source Code Cross Referenced for PolynomialSplineFunction.java in  » Science » Apache-commons-math-1.1 » org » apache » commons » math » analysis » Java Source Code / Java DocumentationJava Source Code and Java Documentation

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Java Source Code / Java Documentation » Science » Apache commons math 1.1 » org.apache.commons.math.analysis 
Source Cross Referenced  Class Diagram Java Document (Java Doc) 


001:        /*
002:         * Copyright 2003-2005 The Apache Software Foundation.
003:         *
004:         * Licensed under the Apache License, Version 2.0 (the "License");
005:         * you may not use this file except in compliance with the License.
006:         * You may obtain a copy of the License at
007:         *
008:         *      http://www.apache.org/licenses/LICENSE-2.0
009:         *
010:         * Unless required by applicable law or agreed to in writing, software
011:         * distributed under the License is distributed on an "AS IS" BASIS,
012:         * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
013:         * See the License for the specific language governing permissions and
014:         * limitations under the License.
015:         */
016:        package org.apache.commons.math.analysis;
017:
018:        import java.io.Serializable;
019:        import java.util.Arrays;
020:
021:        import org.apache.commons.math.FunctionEvaluationException;
022:
023:        /**
024:         * Represents a polynomial spline function.
025:         * <p>
026:         * A <strong>polynomial spline function</strong> consists of a set of 
027:         * <i>interpolating polynomials</i> and an ascending array of domain 
028:         * <i>knot points</i>, determining the intervals over which the spline function
029:         * is defined by the constituent polynomials.  The polynomials are assumed to
030:         * have been computed to match the values of another function at the knot
031:         * points.  The value consistency constraints are not currently enforced by 
032:         * <code>PolynomialSplineFunction</code> itself, but are assumed to hold among
033:         * the polynomials and knot points passed to the constructor.
034:         * <p>
035:         * N.B.:  The polynomials in the <code>polynomials</code> property must be
036:         * centered on the knot points to compute the spline function values.  See below.
037:         * <p>
038:         * The domain of the polynomial spline function is 
039:         * <code>[smallest knot, largest knot]</code>.  Attempts to evaluate the
040:         * function at values outside of this range generate IllegalArgumentExceptions.
041:         * <p>
042:         * The value of the polynomial spline function for an argument <code>x</code>
043:         * is computed as follows:
044:         * <ol>
045:         * <li>The knot array is searched to find the segment to which <code>x</code>
046:         * belongs.  If <code>x</code> is less than the smallest knot point or greater
047:         * than the largest one, an <code>IllegalArgumentException</code>
048:         * is thrown.</li>
049:         * <li> Let <code>j</code> be the index of the largest knot point that is less
050:         * than or equal to <code>x</code>.  The value returned is <br>
051:         * <code>polynomials[j](x - knot[j])</code></li></ol>
052:         *
053:         * @version $Revision: 348761 $ $Date: 2005-11-24 09:04:20 -0700 (Thu, 24 Nov 2005) $
054:         */
055:        public class PolynomialSplineFunction implements 
056:                DifferentiableUnivariateRealFunction, Serializable {
057:
058:            /** Serializable version identifier */
059:            private static final long serialVersionUID = 7011031166416885789L;
060:
061:            /** Spline segment interval delimiters (knots).   Size is n+1 for n segments. */
062:            private double knots[];
063:
064:            /**
065:             * The polynomial functions that make up the spline.  The first element
066:             * determines the value of the spline over the first subinterval, the
067:             * second over the second, etc.   Spline function values are determined by
068:             * evaluating these functions at <code>(x - knot[i])</code> where i is the
069:             * knot segment to which x belongs.
070:             */
071:            private PolynomialFunction polynomials[] = null;
072:
073:            /** 
074:             * Number of spline segments = number of polynomials
075:             *  = number of partition points - 1 
076:             */
077:            private int n = 0;
078:
079:            /**
080:             * Construct a polynomial spline function with the given segment delimiters
081:             * and interpolating polynomials.
082:             * <p>
083:             * The constructor copies both arrays and assigns the copies to the knots
084:             * and polynomials properties, respectively.
085:             * 
086:             * @param knots spline segment interval delimiters
087:             * @param polynomials polynomial functions that make up the spline
088:             * @throws NullPointerException if either of the input arrays is null
089:             * @throws IllegalArgumentException if knots has length less than 2,  
090:             * <code>polynomials.length != knots.length - 1 </code>, or the knots array
091:             * is not strictly increasing.
092:             * 
093:             */
094:            public PolynomialSplineFunction(double knots[],
095:                    PolynomialFunction polynomials[]) {
096:                if (knots.length < 2) {
097:                    throw new IllegalArgumentException(
098:                            "Not enough knot values -- spline partition must have at least 2 points.");
099:                }
100:                if (knots.length - 1 != polynomials.length) {
101:                    throw new IllegalArgumentException(
102:                            "Number of polynomial interpolants must match the number of segments.");
103:                }
104:                if (!isStrictlyIncreasing(knots)) {
105:                    throw new IllegalArgumentException(
106:                            "Knot values must be strictly increasing.");
107:                }
108:
109:                this .n = knots.length - 1;
110:                this .knots = new double[n + 1];
111:                System.arraycopy(knots, 0, this .knots, 0, n + 1);
112:                this .polynomials = new PolynomialFunction[n];
113:                System.arraycopy(polynomials, 0, this .polynomials, 0, n);
114:            }
115:
116:            /**
117:             * Compute the value for the function.
118:             * <p>
119:             * Throws FunctionEvaluationException if v is outside of the domain of the
120:             * function.  The domain is [smallest knot, largest knot].
121:             * <p>
122:             * See {@link PolynomialSplineFunction} for details on the algorithm for
123:             * computing the value of the function.
124:             * 
125:             * @param v the point for which the function value should be computed
126:             * @return the value
127:             * @throws FunctionEvaluationException if v is outside of the domain of
128:             * of the spline function (less than the smallest knot point or greater
129:             * than the largest knot point)
130:             */
131:            public double value(double v) throws FunctionEvaluationException {
132:                if (v < knots[0] || v > knots[n]) {
133:                    throw new FunctionEvaluationException(v,
134:                            "Argument outside domain");
135:                }
136:                int i = Arrays.binarySearch(knots, v);
137:                if (i < 0) {
138:                    i = -i - 2;
139:                }
140:                //This will handle the case where v is the last knot value
141:                //There are only n-1 polynomials, so if v is the last knot
142:                //then we will use the last polynomial to calculate the value.
143:                if (i >= polynomials.length) {
144:                    i--;
145:                }
146:                return polynomials[i].value(v - knots[i]);
147:            }
148:
149:            /**
150:             * Returns the derivative of the polynomial spline function as a UnivariateRealFunction
151:             * @return  the derivative function
152:             */
153:            public UnivariateRealFunction derivative() {
154:                return polynomialSplineDerivative();
155:            }
156:
157:            /**
158:             * Returns the derivative of the polynomial spline function as a PolynomialSplineFunction
159:             * 
160:             * @return  the derivative function
161:             */
162:            public PolynomialSplineFunction polynomialSplineDerivative() {
163:                PolynomialFunction derivativePolynomials[] = new PolynomialFunction[n];
164:                for (int i = 0; i < n; i++) {
165:                    derivativePolynomials[i] = polynomials[i]
166:                            .polynomialDerivative();
167:                }
168:                return new PolynomialSplineFunction(knots,
169:                        derivativePolynomials);
170:            }
171:
172:            /**
173:             * Returns the number of spline segments = the number of polynomials 
174:             * = the number of knot points - 1.
175:             * 
176:             * @return the number of spline segments
177:             */
178:            public int getN() {
179:                return n;
180:            }
181:
182:            /**
183:             * Returns a copy of the interpolating polynomials array.
184:             * <p>
185:             * Returns a fresh copy of the array. Changes made to the copy will
186:             * not affect the polynomials property.
187:             * 
188:             * @return the interpolating polynomials
189:             */
190:            public PolynomialFunction[] getPolynomials() {
191:                PolynomialFunction p[] = new PolynomialFunction[n];
192:                System.arraycopy(polynomials, 0, p, 0, n);
193:                return p;
194:            }
195:
196:            /**
197:             * Returns an array copy of the knot points.
198:             * <p>
199:             * Returns a fresh copy of the array. Changes made to the copy
200:             * will not affect the knots property.
201:             * 
202:             * @return the knot points
203:             */
204:            public double[] getKnots() {
205:                double out[] = new double[n + 1];
206:                System.arraycopy(knots, 0, out, 0, n + 1);
207:                return out;
208:            }
209:
210:            /**
211:             * Determines if the given array is ordered in a strictly increasing
212:             * fashion.
213:             * 
214:             * @param x the array to examine.
215:             * @return <code>true</code> if the elements in <code>x</code> are ordered
216:             * in a stricly increasing manner.  <code>false</code>, otherwise.
217:             */
218:            private static boolean isStrictlyIncreasing(double[] x) {
219:                for (int i = 1; i < x.length; ++i) {
220:                    if (x[i - 1] >= x[i]) {
221:                        return false;
222:                    }
223:                }
224:                return true;
225:            }
226:        }
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