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Posted to dev@commons.apache.org by ps...@apache.org on 2004/04/02 23:08:49 UTC
cvs commit: jakarta-commons/math/src/java/org/apache/commons/math/analysis PolynomialFunction.java
psteitz 2004/04/02 13:08:48
Modified: math/src/java/org/apache/commons/math/analysis
PolynomialFunction.java
Log:
Modified constructor to copy input coefficients array.
Changed evaluation to use Horner's method.
Exposed coefficients as read-only property
Implemented DifferentiableUnivariateRealFunction interfaces
Dropped redundant firstDerivative, secondDerivative methods
Revision Changes Path
1.8 +98 -71 jakarta-commons/math/src/java/org/apache/commons/math/analysis/PolynomialFunction.java
Index: PolynomialFunction.java
===================================================================
RCS file: /home/cvs/jakarta-commons/math/src/java/org/apache/commons/math/analysis/PolynomialFunction.java,v
retrieving revision 1.7
retrieving revision 1.8
diff -u -r1.7 -r1.8
--- PolynomialFunction.java 22 Feb 2004 22:01:29 -0000 1.7
+++ PolynomialFunction.java 2 Apr 2004 21:08:48 -0000 1.8
@@ -20,112 +20,139 @@
import java.io.Serializable;
/**
- * Represents a polynomial function with real coefficients.
+ * Immutable representation of a real polynomial function with real coefficients.
+ * <p>
+ * <a href="http://mathworld.wolfram.com/HornersMethod.html">Horner's Method</a>
+ * is used to evaluate the function.
*
* @version $Revision$ $Date$
*/
-public class PolynomialFunction implements UnivariateRealFunction, Serializable {
+public class PolynomialFunction implements DifferentiableUnivariateRealFunction, Serializable {
/**
- * The coefficients of the polynomial, ordered by degree -- i.e., c[0] is the constant term
- * and c[n] is the coefficient of x^n where n is the degree of the polynomial.
+ * The coefficients of the polynomial, ordered by degree -- i.e., coefficients[0] is the constant term
+ * and coefficients[n] is the coefficient of x^n where n is the degree of the polynomial.
*/
- private double c[];
+ private double coefficients[];
/**
- * Construct a polynomial with the given coefficients
+ * Construct a polynomial with the given coefficients.
+ * <p>
+ * The constructor makes a copy of the input array and assigns the copy to
+ * the coefficients property.
*
* @param c polynominal coefficients
+ * @throws NullPointerException if c is null
+ * @throws IllegalArgumentException if c is empty
*/
public PolynomialFunction(double c[]) {
super();
- this.c = new double[c.length];
- System.arraycopy(c, 0, this.c, 0, c.length);
+ if (c.length < 1) {
+ throw new IllegalArgumentException("Polynomial coefficient array must have postive length.");
+ }
+ this.coefficients = new double[c.length];
+ System.arraycopy(c, 0, this.coefficients, 0, c.length);
}
/**
* Compute the value of the function for the given argument.
- *
- * <p>This can be explicitly determined by
- * <tt>c_n * x^n + ... + c_1 * x + c_0</tt>
- * </p>
+ * <p>
+ * The value returned is <br>
+ * <code>coefficients[n] * x^n + ... + coefficients[1] * x + coefficients[0]</code>
*
* @param x the argument for which the function value should be computed
- * @return the value
- * @throws MathException if the function couldn't be computed due to
- * missing additional data or other environmental problems.
+ * @return the value of the polynomial at the given point
* @see UnivariateRealFunction#value(double)
*/
- public double value(double x) {
-
- double value = c[0];
-
- for (int i=1; i < c.length; i++ ) {
- value += c[i] * Math.pow( x, (int)i);
- }
-
- return value;
+ public double value(double x) {
+ return evaluate(coefficients, x);
}
/**
- * Compute the value for the first derivative of the function.
- *
- * <p>This can be explicitly determined by
- * <tt>n * c_n * x^(n-1) + ... + 2 * c_2 * x + c_1</tt>
- * </p>
- *
- * @param x the point for which the first derivative should be computed
- * @return the value
+ * Returns the degree of the polynomial
+ *
+ * @return the degree of the polynomial
*/
- public double firstDerivative(double x) {
-
- if (this.degree() == 0) {
- return 0;
+ public int degree() {
+ return coefficients.length - 1;
+ }
+
+ /**
+ * Returns a copy of the coefficients array.
+ * <p>
+ * Changes made to the returned copy will not affect the coefficients of
+ * the polynomial.
+ *
+ * @return a fresh copy of the coefficients array
+ */
+ public double[] getCoefficients() {
+ double[] out = new double[coefficients.length];
+ System.arraycopy(coefficients,0, out, 0, coefficients.length);
+ return out;
+ }
+
+ /**
+ * Uses Horner's Method to evaluate the polynomial with the given coefficients at
+ * the argument.
+ *
+ * @param coefficients the coefficients of the polynomial to evaluate
+ * @param argument the input value
+ * @return the value of the polynomial
+ * @throws IllegalArgumentException if coefficients is empty
+ * @throws NullPointerException if coefficients is null
+ */
+ protected static double evaluate(double[] coefficients, double argument) {
+ int n = coefficients.length;
+ if (n < 1) {
+ throw new IllegalArgumentException("Coefficient array must have positive length for evaluation");
}
- double value = c[1];
-
- if ( c.length > 1 ) {
- for (int i=2; i < c.length; i++ ) {
- value += i * c[i] * Math.pow( x, (int)i-1);
- }
+ double result = coefficients[n - 1];
+ for (int j = n -2; j >=0; j--) {
+ result = argument * result + coefficients[j];
}
-
- return value;
+ return result;
}
-
+
/**
- * Compute the value for the second derivative of the function.
- *
- * <p>This can be explicitly determined by
- * <tt>n * (n-1) * c_n * x^(n-2) + ... + 3 * 2 * c_3 * x + 2 * c_2</tt>
- * </p>
+ * Returns the coefficients of the derivative of the polynomial with the given coefficients.
*
- * @param x the point for which the first derivative should be computed
- * @return the value
- */
- public double secondDerivative(double x) {
-
- if (this.degree() < 2) {
- return 0;
+ * @param coefficients the coefficients of the polynomial to differentiate
+ * @return the coefficients of the derivative or null if coefficients has length 1.
+ * @throws IllegalArgumentException if coefficients is empty
+ * @throws NullPointerException if coefficients is null
+ */
+ protected static double[] differentiate(double[] coefficients) {
+ int n = coefficients.length;
+ if (n < 1) {
+ throw new IllegalArgumentException("Coefficient array must have positive length for differentiation");
}
- double value = 2.0 * c[2];
-
- if ( c.length > 2 ) {
- for (int i=3; i < c.length; i++ ) {
- value += i * (i-1) * c[i] * Math.pow( x, (int)i-2);
- }
+ if (n == 1) {
+ return new double[]{0};
}
-
- return value;
+ double[] result = new double[n - 1];
+ for (int i = n - 1; i > 0; i--) {
+ result[i - 1] = (double) i * coefficients[i];
+ }
+ return result;
}
-
+
/**
- * Returns the degree of the polynomial
+ * Returns the derivative as a PolynomialRealFunction
*
- * @return the degree of the polynomial
+ * @return the derivative polynomial
*/
- public int degree() {
- return c.length - 1;
+ public PolynomialFunction polynomialDerivative() {
+ return new PolynomialFunction(differentiate(coefficients));
+ }
+
+ /**
+ * Returns the derivative as a UnivariateRealFunction
+ *
+ * @return the derivative function
+ */
+ public UnivariateRealFunction derivative() {
+ return polynomialDerivative();
}
+
}
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