From 8ce2128585be00b451355dd616fc995ddb0be741 Mon Sep 17 00:00:00 2001 From: Luc Maisonobe Date: Sun, 1 Feb 2009 21:13:55 +0000 Subject: [PATCH] added a PolynomialsUtils class providing factory methods for Chebyshev, Hermite, Laguerre and Legendre polynomials the code was extracted from mantissa and modified git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@739840 13f79535-47bb-0310-9956-ffa450edef68 --- .../polynomials/PolynomialsUtils.java | 280 ++++++++++++++++++ .../commons/math/fraction/Fraction.java | 14 +- .../mantissa/algebra/Chebyshev.java | 70 ----- .../algebra/CoefficientsGenerator.java | 157 ---------- .../spaceroots/mantissa/algebra/Hermite.java | 69 ----- .../spaceroots/mantissa/algebra/Laguerre.java | 70 ----- .../spaceroots/mantissa/algebra/Legendre.java | 71 ----- .../algebra/OrthogonalPolynomial.java | 49 --- .../spaceroots/mantissa/algebra/AllTests.java | 4 - .../mantissa/algebra/ChebyshevTest.java | 85 ------ .../mantissa/algebra/HermiteTest.java | 76 ----- .../mantissa/algebra/LaguerreTest.java | 82 ----- .../mantissa/algebra/LegendreTest.java | 101 ------- src/site/xdoc/changes.xml | 3 + src/site/xdoc/userguide/analysis.xml | 12 +- .../polynomials/PolynomialsUtilsTest.java | 225 ++++++++++++++ 16 files changed, 529 insertions(+), 839 deletions(-) create mode 100644 src/java/org/apache/commons/math/analysis/polynomials/PolynomialsUtils.java delete mode 100644 src/mantissa/src/org/spaceroots/mantissa/algebra/Chebyshev.java delete mode 100644 src/mantissa/src/org/spaceroots/mantissa/algebra/CoefficientsGenerator.java delete mode 100644 src/mantissa/src/org/spaceroots/mantissa/algebra/Hermite.java delete mode 100644 src/mantissa/src/org/spaceroots/mantissa/algebra/Laguerre.java delete mode 100644 src/mantissa/src/org/spaceroots/mantissa/algebra/Legendre.java delete mode 100644 src/mantissa/src/org/spaceroots/mantissa/algebra/OrthogonalPolynomial.java delete mode 100644 src/mantissa/tests-src/org/spaceroots/mantissa/algebra/ChebyshevTest.java delete mode 100644 src/mantissa/tests-src/org/spaceroots/mantissa/algebra/HermiteTest.java delete mode 100644 src/mantissa/tests-src/org/spaceroots/mantissa/algebra/LaguerreTest.java delete mode 100644 src/mantissa/tests-src/org/spaceroots/mantissa/algebra/LegendreTest.java create mode 100644 src/test/org/apache/commons/math/analysis/polynomials/PolynomialsUtilsTest.java diff --git a/src/java/org/apache/commons/math/analysis/polynomials/PolynomialsUtils.java b/src/java/org/apache/commons/math/analysis/polynomials/PolynomialsUtils.java new file mode 100644 index 000000000..ef3559c1d --- /dev/null +++ b/src/java/org/apache/commons/math/analysis/polynomials/PolynomialsUtils.java @@ -0,0 +1,280 @@ +/* + * 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.polynomials; + +import java.util.ArrayList; + +import org.apache.commons.math.fraction.Fraction; + +/** + * A collection of static methods that operate on or return polynomials. + * + * @version $Revision$ $Date$ + * @since 2.0 + */ +public class PolynomialsUtils { + + /** Coefficients for Chebyshev polynomials. */ + private static final ArrayList CHEBYSHEV_COEFFICIENTS; + + /** Coefficients for Hermite polynomials. */ + private static final ArrayList HERMITE_COEFFICIENTS; + + /** Coefficients for Laguerre polynomials. */ + private static final ArrayList LAGUERRE_COEFFICIENTS; + + /** Coefficients for Legendre polynomials. */ + private static final ArrayList LEGENDRE_COEFFICIENTS; + + static { + + // initialize recurrence for Chebyshev polynomials + // T0(X) = 1, T1(X) = 0 + 1 * X + CHEBYSHEV_COEFFICIENTS = new ArrayList(); + CHEBYSHEV_COEFFICIENTS.add(Fraction.ONE); + CHEBYSHEV_COEFFICIENTS.add(Fraction.ZERO); + CHEBYSHEV_COEFFICIENTS.add(Fraction.ONE); + + // initialize recurrence for Hermite polynomials + // H0(X) = 1, H1(X) = 0 + 2 * X + HERMITE_COEFFICIENTS = new ArrayList(); + HERMITE_COEFFICIENTS.add(Fraction.ONE); + HERMITE_COEFFICIENTS.add(Fraction.ZERO); + HERMITE_COEFFICIENTS.add(Fraction.TWO); + + // initialize recurrence for Laguerre polynomials + // L0(X) = 1, L1(X) = 1 - 1 * X + LAGUERRE_COEFFICIENTS = new ArrayList(); + LAGUERRE_COEFFICIENTS.add(Fraction.ONE); + LAGUERRE_COEFFICIENTS.add(Fraction.ONE); + LAGUERRE_COEFFICIENTS.add(Fraction.MINUS_ONE); + + // initialize recurrence for Legendre polynomials + // P0(X) = 1, P1(X) = 0 + 1 * X + LEGENDRE_COEFFICIENTS = new ArrayList(); + LEGENDRE_COEFFICIENTS.add(Fraction.ONE); + LEGENDRE_COEFFICIENTS.add(Fraction.ZERO); + LEGENDRE_COEFFICIENTS.add(Fraction.ONE); + + } + + /** + * Private constructor, to prevent instantiation. + */ + private PolynomialsUtils() { + } + + /** + * Create a Chebyshev polynomial of the first kind. + *

Chebyshev + * polynomials of the first kind are orthogonal polynomials. + * They can be defined by the following recurrence relations: + * 

+     *  T0(X)   = 1
+     *  T1(X)   = X
+     *  Tk+1(X) = 2X Tk(X) - Tk-1(X)
+     *

+ * @param degree degree of the polynomial + * @return Chebyshev polynomial of specified degree + */ + public static PolynomialFunction createChebyshevPolynomial(final int degree) { + return buildPolynomial(degree, CHEBYSHEV_COEFFICIENTS, + new RecurrenceCoefficientsGenerator() { + private final Fraction[] coeffs = { Fraction.ZERO, Fraction.TWO, Fraction.ONE}; + /** {@inheritDoc} */ + public Fraction[] generate(int k) { + return coeffs; + } + }); + } + + /** + * Create a Hermite polynomial. + *

Hermite + * polynomials are orthogonal polynomials. + * They can be defined by the following recurrence relations: + * 

+     *  H0(X)   = 1
+     *  H1(X)   = 2X
+     *  Hk+1(X) = 2X Hk(X) - 2k Hk-1(X)
+     *

+ + * @param degree degree of the polynomial + * @return Hermite polynomial of specified degree + */ + public static PolynomialFunction createHermitePolynomial(final int degree) { + return buildPolynomial(degree, HERMITE_COEFFICIENTS, + new RecurrenceCoefficientsGenerator() { + /** {@inheritDoc} */ + public Fraction[] generate(int k) { + return new Fraction[] { + Fraction.ZERO, + Fraction.TWO, + new Fraction(2 * k, 1)}; + } + }); + } + + /** + * Create a Laguerre polynomial. + *

Laguerre + * polynomials are orthogonal polynomials. + * They can be defined by the following recurrence relations: + * 

+     *        L0(X)   = 1
+     *        L1(X)   = 1 - X
+     *  (k+1) Lk+1(X) = (2k + 1 - X) Lk(X) - k Lk-1(X)
+     *

+ * @param degree degree of the polynomial + * @return Laguerre polynomial of specified degree + */ + public static PolynomialFunction createLaguerrePolynomial(final int degree) { + return buildPolynomial(degree, LAGUERRE_COEFFICIENTS, + new RecurrenceCoefficientsGenerator() { + /** {@inheritDoc} */ + public Fraction[] generate(int k) { + final int kP1 = k + 1; + return new Fraction[] { + new Fraction(2 * k + 1, kP1), + new Fraction(-1, kP1), + new Fraction(k, kP1)}; + } + }); + } + + /** + * Create a Legendre polynomial. + *

Legendre + * polynomials are orthogonal polynomials. + * They can be defined by the following recurrence relations: + * 

+     *        P0(X)   = 1
+     *        P1(X)   = X
+     *  (k+1) Pk+1(X) = (2k+1) X Pk(X) - k Pk-1(X)
+     *

+ * @param degree degree of the polynomial + * @return Legendre polynomial of specified degree + */ + public static PolynomialFunction createLegendrePolynomial(final int degree) { + return buildPolynomial(degree, LEGENDRE_COEFFICIENTS, + new RecurrenceCoefficientsGenerator() { + /** {@inheritDoc} */ + public Fraction[] generate(int k) { + final int kP1 = k + 1; + return new Fraction[] { + Fraction.ZERO, + new Fraction(k + kP1, kP1), + new Fraction(k, kP1)}; + } + }); + } + + /** Get the coefficients array for a given degree. + * @param degree degree of the polynomial + * @param coefficients list where the computed coefficients are stored + * @param generator recurrence coefficients generator + * @return coefficients array + */ + private static PolynomialFunction buildPolynomial(final int degree, + final ArrayList coefficients, + final RecurrenceCoefficientsGenerator generator) { + + final int maxDegree = (int) Math.floor(Math.sqrt(2 * coefficients.size())) - 1; + synchronized (PolynomialsUtils.class) { + if (degree > maxDegree) { + computeUpToDegree(degree, maxDegree, generator, coefficients); + } + } + + // coefficient for polynomial 0 is l [0] + // coefficients for polynomial 1 are l [1] ... l [2] (degrees 0 ... 1) + // coefficients for polynomial 2 are l [3] ... l [5] (degrees 0 ... 2) + // coefficients for polynomial 3 are l [6] ... l [9] (degrees 0 ... 3) + // coefficients for polynomial 4 are l[10] ... l[14] (degrees 0 ... 4) + // coefficients for polynomial 5 are l[15] ... l[20] (degrees 0 ... 5) + // coefficients for polynomial 6 are l[21] ... l[27] (degrees 0 ... 6) + // ... + final int start = degree * (degree + 1) / 2; + + final double[] a = new double[degree + 1]; + for (int i = 0; i <= degree; ++i) { + a[i] = coefficients.get(start + i).doubleValue(); + } + + // build the polynomial + return new PolynomialFunction(a); + + } + + /** Compute polynomial coefficients up to a given degree. + * @param degree maximal degree + * @param maxDegree current maximal degree + * @param generator recurrence coefficients generator + * @param coefficients list where the computed coefficients should be appended + */ + private static void computeUpToDegree(final int degree, final int maxDegree, + final RecurrenceCoefficientsGenerator generator, + final ArrayList coefficients) { + + int startK = (maxDegree - 1) * maxDegree / 2; + for (int k = maxDegree; k < degree; ++k) { + + // start indices of two previous polynomials Pk(X) and Pk-1(X) + int startKm1 = startK; + startK += k; + + // Pk+1(X) = (a[0] + a[1] X) Pk(X) - a[2] Pk-1(X) + Fraction[] ai = generator.generate(k); + + Fraction ck = coefficients.get(startK); + Fraction ckm1 = coefficients.get(startKm1); + + // degree 0 coefficient + coefficients.add(ck.multiply(ai[0]).subtract(ckm1.multiply(ai[2]))); + + // degree 1 to degree k-1 coefficients + for (int i = 1; i < k; ++i) { + final Fraction ckPrev = ck; + ck = coefficients.get(startK + i); + ckm1 = coefficients.get(startKm1 + i); + coefficients.add(ck.multiply(ai[0]).add(ckPrev.multiply(ai[1])).subtract(ckm1.multiply(ai[2]))); + } + + // degree k coefficient + final Fraction ckPrev = ck; + ck = coefficients.get(startK + k); + coefficients.add(ck.multiply(ai[0]).add(ckPrev.multiply(ai[1]))); + + // degree k+1 coefficient + coefficients.add(ck.multiply(ai[1])); + + } + + } + + /** Interface for recurrence coefficients generation. */ + private static interface RecurrenceCoefficientsGenerator { + /** + * Generate recurrence coefficients. + * @param k highest degree of the polynomials used in the recurrence + * @return an array of three coefficients such that + * Pk+1(X) = (a[0] + a[1] X) Pk(X) - a[2] Pk-1(X) + */ + Fraction[] generate(int k); + } + +} diff --git a/src/java/org/apache/commons/math/fraction/Fraction.java b/src/java/org/apache/commons/math/fraction/Fraction.java index b11b01dfc..7597f71de 100644 --- a/src/java/org/apache/commons/math/fraction/Fraction.java +++ b/src/java/org/apache/commons/math/fraction/Fraction.java @@ -29,15 +29,21 @@ import org.apache.commons.math.util.MathUtils; */ public class Fraction extends Number implements Comparable { + /** A fraction representing "2 / 1". */ + public static final Fraction TWO = new Fraction(2, 1); + /** A fraction representing "1 / 1". */ public static final Fraction ONE = new Fraction(1, 1); /** A fraction representing "0 / 1". */ public static final Fraction ZERO = new Fraction(0, 1); + /** A fraction representing "-1 / 1". */ + public static final Fraction MINUS_ONE = new Fraction(-1, 1); + /** Serializable version identifier */ - private static final long serialVersionUID = -5731055832688548463L; - + private static final long serialVersionUID = 3071409609509774764L; + /** The denominator. */ private final int denominator; @@ -145,7 +151,7 @@ public class Fraction extends Number implements Comparable { return; } - long p0 = 1; + long p0 = 1; long q0 = 0; long p1 = a0; long q1 = 1; @@ -197,7 +203,7 @@ public class Fraction extends Number implements Comparable { * reduced to lowest terms. * @param num the numerator. * @param den the denominator. - * @throws ArithmeticException if the denomiator is zero + * @throws ArithmeticException if the denominator is zero */ public Fraction(int num, int den) { super(); diff --git a/src/mantissa/src/org/spaceroots/mantissa/algebra/Chebyshev.java b/src/mantissa/src/org/spaceroots/mantissa/algebra/Chebyshev.java deleted file mode 100644 index 089b89925..000000000 --- a/src/mantissa/src/org/spaceroots/mantissa/algebra/Chebyshev.java +++ /dev/null @@ -1,70 +0,0 @@ -// 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.spaceroots.mantissa.algebra; - -/** - * This class implements Chebyshev polynomials. - - *

Chebyshev polynomials can be defined by the following recurrence - * relations: - * 

- *  T0(X)   = 1
- *  T1(X)   = X
- *  Tk+1(X) = 2X Tk(X) - Tk-1(X)
- *

- - * @version $Id$ - * @author L. Maisonobe - - */ - -public class Chebyshev - extends OrthogonalPolynomial { - - /** Generator for the Chebyshev polynomials. */ - private static final CoefficientsGenerator generator = - new CoefficientsGenerator(new RationalNumber(1l), - new RationalNumber(0l), - new RationalNumber(1l)) { - public void setRecurrenceCoefficients(int k) { - // the recurrence relation is - // Tk+1(X) = 2X Tk(X) - Tk-1(X) - setRecurrenceCoefficients(new RationalNumber(0l), - new RationalNumber(2l), - new RationalNumber(1l)); - } - }; - - /** Simple constructor. - * Build a degree 0 Chebyshev polynomial - */ - public Chebyshev() { - super(0, generator); - } - - /** Simple constructor. - * Build a degree d Chebyshev polynomial - * @param degree degree of the polynomial - */ - public Chebyshev(int degree) { - super(degree, generator); - } - - private static final long serialVersionUID = -893367988717182601L; - -} diff --git a/src/mantissa/src/org/spaceroots/mantissa/algebra/CoefficientsGenerator.java b/src/mantissa/src/org/spaceroots/mantissa/algebra/CoefficientsGenerator.java deleted file mode 100644 index f14b45ba2..000000000 --- a/src/mantissa/src/org/spaceroots/mantissa/algebra/CoefficientsGenerator.java +++ /dev/null @@ -1,157 +0,0 @@ -// 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.spaceroots.mantissa.algebra; - -import java.util.ArrayList; - -public abstract class CoefficientsGenerator { - - /** Build a generator with coefficients for two polynomials. - *

The first polynomial must be a degree 0 polynomial - * P0(X)=a0,0 and the second polynomial - * must be a degree 1 polynomial P1(X)=a0,1 - * +a1,1X

- * @param a00 constant term for the degree 0 polynomial - * @param a01 constant term for the degree 1 polynomial - * @param a11 X term for the degree 1 polynomial - */ - protected CoefficientsGenerator(RationalNumber a00, - RationalNumber a01, RationalNumber a11) { - l = new ArrayList(); - l.add(a00); - l.add(a01); - l.add(a11); - maxDegree = 1; - } - - /** Set the recurrence coefficients. - * @param b2k b2,k coefficient (b2,k = a2,k / a1,k) - * @param b3k b3,k coefficient (b3,k = a3,k / a1,k) - * @param b4k b4,k coefficient (b4,k = a4,k / a1,k) - */ - protected void setRecurrenceCoefficients(RationalNumber b2k, - RationalNumber b3k, - RationalNumber b4k) { - this.b2k = b2k; - this.b3k = b3k; - this.b4k = b4k; - } - - /** Set the recurrence coefficients. - * The recurrence relation is - * 
a1,k Ok+1(X) =(a2,k + a3,k X) Ok(X) - a4,k Ok-1(X)
- * the method must call {@link #setRecurrenceCoefficients(RationalNumber, - * RationalNumber, RationalNumber)} to provide the coefficients - * @param k index of the current step - */ - protected abstract void setRecurrenceCoefficients(int k); - - /** Compute all the polynomial coefficients up to a given degree. - * @param degree maximal degree - */ - private void computeUpToDegree(int degree) { - - int startK = (maxDegree - 1) * maxDegree / 2; - for (int k = maxDegree; k < degree; ++k) { - - // start indices of two previous polynomials Ok(X) and Ok-1(X) - int startKm1 = startK; - startK += k; - - // a1k Ok+1(X) = (a2k + a3k X) Ok(X) - a4k Ok-1(X) - // we use bik = aik/a1k - setRecurrenceCoefficients(k); - - RationalNumber ckPrev = null; - RationalNumber ck = (RationalNumber) l.get(startK); - RationalNumber ckm1 = (RationalNumber) l.get(startKm1); - - // degree 0 coefficient - l.add(ck.multiply(b2k).subtract(ckm1.multiply(b4k))); - - // degree 1 to degree k-1 coefficients - for (int i = 1; i < k; ++i) { - ckPrev = ck; - ck = (RationalNumber) l.get(startK + i); - ckm1 = (RationalNumber) l.get(startKm1 + i); - l.add(ck.multiply(b2k).add(ckPrev.multiply(b3k)).subtract(ckm1.multiply(b4k))); - } - - // degree k coefficient - ckPrev = ck; - ck = (RationalNumber) l.get(startK + k); - l.add(ck.multiply(b2k).add(ckPrev.multiply(b3k))); - - // degree k+1 coefficient - l.add(ck.multiply(b3k)); - - } - - maxDegree = degree; - - } - - /** Get the coefficients array for a given degree. - * @param degree degree of the polynomial - * @return coefficients array - */ - public RationalNumber[] getCoefficients(int degree) { - - synchronized (this) { - if (degree > maxDegree) { - computeUpToDegree(degree); - } - } - - // coefficient for polynomial 0 is l [0] - // coefficients for polynomial 1 are l [1] ... l [2] (degrees 0 ... 1) - // coefficients for polynomial 2 are l [3] ... l [5] (degrees 0 ... 2) - // coefficients for polynomial 3 are l [6] ... l [9] (degrees 0 ... 3) - // coefficients for polynomial 4 are l[10] ... l[14] (degrees 0 ... 4) - // coefficients for polynomial 5 are l[15] ... l[20] (degrees 0 ... 5) - // coefficients for polynomial 6 are l[21] ... l[27] (degrees 0 ... 6) - // ... - int start = degree * (degree + 1) / 2; - - RationalNumber[] a = new RationalNumber[degree + 1]; - for (int i = 0; i <= degree; ++i) { - a[i] = (RationalNumber) l.get(start + i); - } - - return a; - - } - - /** List holding the coefficients of the polynomials computed so far. */ - private ArrayList l; - - /** Maximal degree of the polynomials computed so far. */ - private int maxDegree; - - /** b2,k coefficient to initialize - * (b2,k = a2,k / a1,k). */ - private RationalNumber b2k; - - /** b3,k coefficient to initialize - * (b3,k = a3,k / a1,k). */ - private RationalNumber b3k; - - /** b4,k coefficient to initialize - * (b4,k = a4,k / a1,k). */ - private RationalNumber b4k; - -} diff --git a/src/mantissa/src/org/spaceroots/mantissa/algebra/Hermite.java b/src/mantissa/src/org/spaceroots/mantissa/algebra/Hermite.java deleted file mode 100644 index 37d56a35e..000000000 --- a/src/mantissa/src/org/spaceroots/mantissa/algebra/Hermite.java +++ /dev/null @@ -1,69 +0,0 @@ -// 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.spaceroots.mantissa.algebra; - -/** - * This class implements Hermite polynomials. - - *

Hermite polynomials can be defined by the following recurrence - * relations: - * 

- *  H0(X)   = 1
- *  H1(X)   = 2X
- *  Hk+1(X) = 2X Hk(X) - 2k Hk-1(X)
- *

- - * @version $Id$ - * @author L. Maisonobe - - */ -public class Hermite - extends OrthogonalPolynomial { - - /** Generator for the Hermite polynomials. */ - private static final CoefficientsGenerator generator = - new CoefficientsGenerator(new RationalNumber(1l), - new RationalNumber(0l), - new RationalNumber(2l)) { - public void setRecurrenceCoefficients(int k) { - // the recurrence relation is - // Hk+1(X) = 2X Hk(X) - 2k Hk-1(X) - setRecurrenceCoefficients(new RationalNumber(0l), - new RationalNumber(2l), - new RationalNumber(k * 2l)); - } - }; - - /** Simple constructor. - * Build a degree 0 Hermite polynomial - */ - public Hermite() { - super(0, generator); - } - - /** Simple constructor. - * Build a degree d Hermite polynomial - * @param degree degree of the polynomial - */ - public Hermite(int degree) { - super(degree, generator); - } - - private static final long serialVersionUID = 7910082423686662133L; - -} diff --git a/src/mantissa/src/org/spaceroots/mantissa/algebra/Laguerre.java b/src/mantissa/src/org/spaceroots/mantissa/algebra/Laguerre.java deleted file mode 100644 index d3c5f41f1..000000000 --- a/src/mantissa/src/org/spaceroots/mantissa/algebra/Laguerre.java +++ /dev/null @@ -1,70 +0,0 @@ -// 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.spaceroots.mantissa.algebra; - -/** - * This class implements Laguerre polynomials. - - *

Laguerre polynomials can be defined by the following recurrence - * relations: - * 

- *        L0(X)   = 1
- *        L1(X)   = 1 - X
- *  (k+1) Lk+1(X) = (2k + 1 - X) Lk(X) - k Lk-1(X)
- *

- - * @version $Id$ - * @author L. Maisonobe - - */ -public class Laguerre - extends OrthogonalPolynomial { - - /** Generator for the Laguerre polynomials. */ - private static final CoefficientsGenerator generator = - new CoefficientsGenerator(new RationalNumber(1l), - new RationalNumber(1l), - new RationalNumber(-1l)) { - public void setRecurrenceCoefficients(int k) { - // the recurrence relation is - // (k+1) Lk+1(X) = (2k + 1 - X) Lk(X) - k Lk-1(X) - long kP1 = k + 1; - setRecurrenceCoefficients(new RationalNumber(2 * k + 1, kP1), - new RationalNumber(-1l, kP1), - new RationalNumber(k, kP1)); - } - }; - - /** Simple constructor. - * Build a degree 0 Laguerre polynomial - */ - public Laguerre() { - super(0, generator); - } - - /** Simple constructor. - * Build a degree d Laguerre polynomial - * @param degree degree of the polynomial - */ - public Laguerre(int degree) { - super(degree, generator); - } - - private static final long serialVersionUID = 3213856667479179710L; - -} diff --git a/src/mantissa/src/org/spaceroots/mantissa/algebra/Legendre.java b/src/mantissa/src/org/spaceroots/mantissa/algebra/Legendre.java deleted file mode 100644 index 8288d68f8..000000000 --- a/src/mantissa/src/org/spaceroots/mantissa/algebra/Legendre.java +++ /dev/null @@ -1,71 +0,0 @@ -// 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.spaceroots.mantissa.algebra; - -/** - * This class implements Legendre polynomials. - - *

Legendre polynomials can be defined by the following recurrence - * relations: - * 

- *        P0(X)   = 1
- *        P1(X)   = X
- *  (k+1) Pk+1(X) = (2k+1) X Pk(X) - k Pk-1(X)
- *

- - * @version $Id$ - * @author L. Maisonobe - - */ - -public class Legendre - extends OrthogonalPolynomial { - - /** Generator for the Legendre polynomials. */ - private static final CoefficientsGenerator generator = - new CoefficientsGenerator(new RationalNumber(1l), - new RationalNumber(0l), - new RationalNumber(1l)) { - public void setRecurrenceCoefficients(int k) { - // the recurrence relation is - // (k+1) Pk+1(X) = (2k+1) X Pk(X) - k Pk-1(X) - long kP1 = k + 1; - setRecurrenceCoefficients(new RationalNumber(0l), - new RationalNumber(2 * k + 1, kP1), - new RationalNumber(k, kP1)); - } - }; - - /** Simple constructor. - * Build a degree 0 Legendre polynomial - */ - public Legendre() { - super(0, generator); - } - - /** Simple constructor. - * Build a degree d Legendre polynomial - * @param degree degree of the polynomial - */ - public Legendre(int degree) { - super(degree, generator); - } - - private static final long serialVersionUID = 4014485393845978429L; - -} diff --git a/src/mantissa/src/org/spaceroots/mantissa/algebra/OrthogonalPolynomial.java b/src/mantissa/src/org/spaceroots/mantissa/algebra/OrthogonalPolynomial.java deleted file mode 100644 index 32264ab04..000000000 --- a/src/mantissa/src/org/spaceroots/mantissa/algebra/OrthogonalPolynomial.java +++ /dev/null @@ -1,49 +0,0 @@ -// 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.spaceroots.mantissa.algebra; - -/** - * This class is the base class for orthogonal polynomials. - - *

Orthogonal polynomials can be defined by recurrence relations like: - * 

- *      O0(X)   = some 0 degree polynomial
- *      O1(X)   = some first degree polynomial
- *  a1,k Ok+1(X) = (a2,k + a3,k X) Ok(X) - a4,k Ok-1(X)
- *
- * where a1,k, a2,k, a3,k and - * a4,k are simple expressions which either are - * constants or depend on k.

- - * @version $Id$ - * @author L. Maisonobe - - */ -public abstract class OrthogonalPolynomial - extends Polynomial.Rational { - - /** Simple constructor. - * Build a degree d orthogonal polynomial - * @param degree degree of the polynomial - * @param generator coefficients generator for the current type of polynomials - */ - protected OrthogonalPolynomial(int degree, CoefficientsGenerator generator) { - a = generator.getCoefficients(degree); - } - -} diff --git a/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/AllTests.java b/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/AllTests.java index a840155f3..9f7d5bea5 100644 --- a/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/AllTests.java +++ b/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/AllTests.java @@ -28,10 +28,6 @@ public class AllTests { suite.addTest(RationalNumberTest.suite()); suite.addTest(PolynomialRationalTest.suite()); suite.addTest(PolynomialDoubleTest.suite()); - suite.addTest(ChebyshevTest.suite()); - suite.addTest(HermiteTest.suite()); - suite.addTest(LegendreTest.suite()); - suite.addTest(LaguerreTest.suite()); suite.addTest(PolynomialFractionTest.suite()); return suite; diff --git a/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/ChebyshevTest.java b/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/ChebyshevTest.java deleted file mode 100644 index 19ea9a20d..000000000 --- a/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/ChebyshevTest.java +++ /dev/null @@ -1,85 +0,0 @@ -// 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.spaceroots.mantissa.algebra; - -import junit.framework.*; - -public class ChebyshevTest - extends TestCase { - - public ChebyshevTest(String name) { - super(name); - } - - public void testOne() { - assertTrue(new Chebyshev().isOne()); - } - - public void testFirstPolynomials() { - - checkPolynomial(new Chebyshev(3), "-3 x + 4 x^3"); - checkPolynomial(new Chebyshev(2), "-1 + 2 x^2"); - checkPolynomial(new Chebyshev(1), "x"); - checkPolynomial(new Chebyshev(0), "1"); - - checkPolynomial(new Chebyshev(7), "-7 x + 56 x^3 - 112 x^5 + 64 x^7"); - checkPolynomial(new Chebyshev(6), "-1 + 18 x^2 - 48 x^4 + 32 x^6"); - checkPolynomial(new Chebyshev(5), "5 x - 20 x^3 + 16 x^5"); - checkPolynomial(new Chebyshev(4), "1 - 8 x^2 + 8 x^4"); - - } - - public void testBounds() { - for (int k = 0; k < 12; ++k) { - OrthogonalPolynomial Tk = new Chebyshev(k); - for (double x = -1.0; x <= 1.0; x += 0.02) { - assertTrue(Math.abs(Tk.valueAt(x)) < (1.0 + 1.0e-12)); - } - } - } - - public void testDifferentials() { - for (int k = 0; k < 12; ++k) { - - Polynomial.Rational Tk0 = new Chebyshev(k); - Polynomial.Rational Tk1 = (Polynomial.Rational) Tk0.getDerivative(); - Polynomial.Rational Tk2 = (Polynomial.Rational) Tk1.getDerivative(); - - Polynomial.Rational g0 = new Polynomial.Rational(k * k); - Polynomial.Rational g1 = new Polynomial.Rational(-1l, 0l); - Polynomial.Rational g2 = new Polynomial.Rational(-1l, 0l, 1l); - - Polynomial.Rational Tk0g0 = Tk0.multiply(g0); - Polynomial.Rational Tk1g1 = Tk1.multiply(g1); - Polynomial.Rational Tk2g2 = Tk2.multiply(g2); - - Polynomial.Rational d = Tk0g0.add(Tk1g1.add(Tk2g2)); - assertTrue(d.isZero()); - - } - } - - public void checkPolynomial(Polynomial.Rational p, String reference) { - assertTrue(p.toString().equals(reference)); - } - - public static Test suite() { - return new TestSuite(ChebyshevTest.class); - } - -} diff --git a/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/HermiteTest.java b/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/HermiteTest.java deleted file mode 100644 index 9d69fa6a5..000000000 --- a/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/HermiteTest.java +++ /dev/null @@ -1,76 +0,0 @@ -// 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.spaceroots.mantissa.algebra; - -import junit.framework.*; - -public class HermiteTest - extends TestCase { - - public HermiteTest(String name) { - super(name); - } - - public void testOne() { - assertTrue(new Hermite().isOne()); - } - - public void testFirstPolynomials() { - - checkPolynomial(new Hermite(3), "-12 x + 8 x^3"); - checkPolynomial(new Hermite(2), "-2 + 4 x^2"); - checkPolynomial(new Hermite(1), "2 x"); - checkPolynomial(new Hermite(0), "1"); - - checkPolynomial(new Hermite(7), "-1680 x + 3360 x^3 - 1344 x^5 + 128 x^7"); - checkPolynomial(new Hermite(6), "-120 + 720 x^2 - 480 x^4 + 64 x^6"); - checkPolynomial(new Hermite(5), "120 x - 160 x^3 + 32 x^5"); - checkPolynomial(new Hermite(4), "12 - 48 x^2 + 16 x^4"); - - } - - public void testDifferentials() { - for (int k = 0; k < 12; ++k) { - - Polynomial.Rational Hk0 = new Hermite(k); - Polynomial.Rational Hk1 = (Polynomial.Rational) Hk0.getDerivative(); - Polynomial.Rational Hk2 = (Polynomial.Rational) Hk1.getDerivative(); - - Polynomial.Rational g0 = new Polynomial.Rational(2l * k); - Polynomial.Rational g1 = new Polynomial.Rational(-2l, 0l); - Polynomial.Rational g2 = new Polynomial.Rational(1l); - - Polynomial.Rational Hk0g0 = Hk0.multiply(g0); - Polynomial.Rational Hk1g1 = Hk1.multiply(g1); - Polynomial.Rational Hk2g2 = Hk2.multiply(g2); - - Polynomial.Rational d = Hk0g0.add(Hk1g1.add(Hk2g2)); - assertTrue(d.isZero()); - - } - } - - public void checkPolynomial(Polynomial.Rational p, String reference) { - assertTrue(p.toString().equals(reference)); - } - - public static Test suite() { - return new TestSuite(HermiteTest.class); - } - -} diff --git a/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/LaguerreTest.java b/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/LaguerreTest.java deleted file mode 100644 index a7be6e58b..000000000 --- a/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/LaguerreTest.java +++ /dev/null @@ -1,82 +0,0 @@ -// 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.spaceroots.mantissa.algebra; - -import junit.framework.*; - -public class LaguerreTest - extends TestCase { - - public LaguerreTest(String name) { - super(name); - } - - public void testOne() { - assertTrue(new Laguerre().isOne()); - } - - public void testFirstPolynomials() { - - checkLaguerre(new Laguerre(3), 6l, "6 - 18 x + 9 x^2 - x^3"); - checkLaguerre(new Laguerre(2), 2l, "2 - 4 x + x^2"); - checkLaguerre(new Laguerre(1), 1l, "1 - x"); - checkLaguerre(new Laguerre(0), 1l, "1"); - - checkLaguerre(new Laguerre(7), 5040l, - "5040 - 35280 x + 52920 x^2 - 29400 x^3" - + " + 7350 x^4 - 882 x^5 + 49 x^6 - x^7"); - checkLaguerre(new Laguerre(6), 720l, - "720 - 4320 x + 5400 x^2 - 2400 x^3 + 450 x^4" - + " - 36 x^5 + x^6"); - checkLaguerre(new Laguerre(5), 120l, - "120 - 600 x + 600 x^2 - 200 x^3 + 25 x^4 - x^5"); - checkLaguerre(new Laguerre(4), 24l, - "24 - 96 x + 72 x^2 - 16 x^3 + x^4"); - - } - - public void testDifferentials() { - for (int k = 0; k < 12; ++k) { - - Polynomial.Rational Lk0 = new Laguerre(k); - Polynomial.Rational Lk1 = (Polynomial.Rational) Lk0.getDerivative(); - Polynomial.Rational Lk2 = (Polynomial.Rational) Lk1.getDerivative(); - - Polynomial.Rational g0 = new Polynomial.Rational(k); - Polynomial.Rational g1 = new Polynomial.Rational(-1l, 1l); - Polynomial.Rational g2 = new Polynomial.Rational(1l, 0l); - - Polynomial.Rational Lk0g0 = Lk0.multiply(g0); - Polynomial.Rational Lk1g1 = Lk1.multiply(g1); - Polynomial.Rational Lk2g2 = Lk2.multiply(g2); - - Polynomial.Rational d = Lk0g0.add(Lk1g1.add(Lk2g2)); - assertTrue(d.isZero()); - - } - } - - public void checkLaguerre(Laguerre p, long denominator, String reference) { - assertTrue(p.multiply(denominator).toString().equals(reference)); - } - - public static Test suite() { - return new TestSuite(LaguerreTest.class); - } - -} diff --git a/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/LegendreTest.java b/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/LegendreTest.java deleted file mode 100644 index 27bb57137..000000000 --- a/src/mantissa/tests-src/org/spaceroots/mantissa/algebra/LegendreTest.java +++ /dev/null @@ -1,101 +0,0 @@ -// 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.spaceroots.mantissa.algebra; - -import junit.framework.*; - -public class LegendreTest - extends TestCase { - - public LegendreTest(String name) { - super(name); - } - - public void testOne() { - assertTrue(new Legendre().isOne()); - } - - public void testFirstPolynomials() { - - checkLegendre(new Legendre(3), 2l, "-3 x + 5 x^3"); - checkLegendre(new Legendre(2), 2l, "-1 + 3 x^2"); - checkLegendre(new Legendre(1), 1l, "x"); - checkLegendre(new Legendre(0), 1l, "1"); - - checkLegendre(new Legendre(7), 16l, "-35 x + 315 x^3 - 693 x^5 + 429 x^7"); - checkLegendre(new Legendre(6), 16l, "-5 + 105 x^2 - 315 x^4 + 231 x^6"); - checkLegendre(new Legendre(5), 8l, "15 x - 70 x^3 + 63 x^5"); - checkLegendre(new Legendre(4), 8l, "3 - 30 x^2 + 35 x^4"); - - } - - public void testDifferentials() { - for (int k = 0; k < 12; ++k) { - - Polynomial.Rational Pk0 = new Legendre(k); - Polynomial.Rational Pk1 = (Polynomial.Rational) Pk0.getDerivative(); - Polynomial.Rational Pk2 = (Polynomial.Rational) Pk1.getDerivative(); - - Polynomial.Rational g0 = new Polynomial.Rational(k * (k + 1)); - Polynomial.Rational g1 = new Polynomial.Rational(-2l, 0l); - Polynomial.Rational g2 = new Polynomial.Rational(-1l, 0l, 1l); - - Polynomial.Rational Pk0g0 = Pk0.multiply(g0); - Polynomial.Rational Pk1g1 = Pk1.multiply(g1); - Polynomial.Rational Pk2g2 = Pk2.multiply(g2); - - Polynomial.Rational d = Pk0g0.add(Pk1g1.add(Pk2g2)); - assertTrue(d.isZero()); - - } - } - - public void testHighDegree() { - checkLegendre(new Legendre(40), 274877906944l, - "34461632205" - + " - 28258538408100 x^2" - + " + 3847870979902950 x^4" - + " - 207785032914759300 x^6" - + " + 5929294332103310025 x^8" - + " - 103301483474866556880 x^10" - + " + 1197358103913226000200 x^12" - + " - 9763073770369381232400 x^14" - + " + 58171647881784229843050 x^16" - + " - 260061484647976556945400 x^18" - + " + 888315281771246239250340 x^20" - + " - 2345767627188139419665400 x^22" - + " + 4819022625419112503443050 x^24" - + " - 7710436200670580005508880 x^26" - + " + 9566652323054238154983240 x^28" - + " - 9104813935044723209570256 x^30" - + " + 6516550296251767619752905 x^32" - + " - 3391858621221953912598660 x^34" - + " + 1211378079007840683070950 x^36" - + " - 265365894974690562152100 x^38" - + " + 26876802183334044115405 x^40"); - } - - public void checkLegendre(Legendre p, long denominator, String reference) { - assertTrue(p.multiply(denominator).toString().equals(reference)); - } - - public static Test suite() { - return new TestSuite(LegendreTest.class); - } - -} diff --git a/src/site/xdoc/changes.xml b/src/site/xdoc/changes.xml index f189b53b1..bae4e6c66 100644 --- a/src/site/xdoc/changes.xml +++ b/src/site/xdoc/changes.xml @@ -39,6 +39,9 @@ The type attribute can be add,update,fix,remove. + + Added factory methods to create Chebyshev, Hermite, Laguerre and Legendre polynomials. + Added add, subtract, negate, multiply and toString methods to PolynomialFunction. diff --git a/src/site/xdoc/userguide/analysis.xml b/src/site/xdoc/userguide/analysis.xml index 77db52c01..687138a9b 100644 --- a/src/site/xdoc/userguide/analysis.xml +++ b/src/site/xdoc/userguide/analysis.xml @@ -319,10 +319,20 @@ System.out println("f(" + interpolationX + ") = " + interpolatedY);

- The + The org.apache.commons.math.analysis.polynomials package provides real coefficients polynomials.

+

+ The + org.apache.commons.math.analysis.polynomials.PolynomialFunction class is the most general + one, using traditional coefficients arrays. The + org.apache.commons.math.analysis.polynomials.PolynomialsUtils utility class provides static + factory methods to build Chebyshev, Hermite, Lagrange and Legendre polynomials. Beware that due + to overflows in the coefficients computations, these factory methods can only build low degrees + polynomials yet. +

diff --git a/src/test/org/apache/commons/math/analysis/polynomials/PolynomialsUtilsTest.java b/src/test/org/apache/commons/math/analysis/polynomials/PolynomialsUtilsTest.java new file mode 100644 index 000000000..a0265f0c3 --- /dev/null +++ b/src/test/org/apache/commons/math/analysis/polynomials/PolynomialsUtilsTest.java @@ -0,0 +1,225 @@ +/* + * 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.polynomials; + +import junit.framework.TestCase; + +/** + * Tests the PolynomialsUtils class. + * + * @version $Revision$ $Date$ + */ +public class PolynomialsUtilsTest extends TestCase { + + public void testFirstChebyshevPolynomials() { + + checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(3), "-3.0 x + 4.0 x^3"); + checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(2), "-1.0 + 2.0 x^2"); + checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(1), "x"); + checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(0), "1.0"); + + checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(7), "-7.0 x + 56.0 x^3 - 112.0 x^5 + 64.0 x^7"); + checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(6), "-1.0 + 18.0 x^2 - 48.0 x^4 + 32.0 x^6"); + checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(5), "5.0 x - 20.0 x^3 + 16.0 x^5"); + checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(4), "1.0 - 8.0 x^2 + 8.0 x^4"); + + } + + public void testChebyshevBounds() { + for (int k = 0; k < 12; ++k) { + PolynomialFunction Tk = PolynomialsUtils.createChebyshevPolynomial(k); + for (double x = -1.0; x <= 1.0; x += 0.02) { + assertTrue(k + " " + Tk.value(x), Math.abs(Tk.value(x)) < (1.0 + 1.0e-12)); + } + } + } + + public void testChebyshevDifferentials() { + for (int k = 0; k < 12; ++k) { + + PolynomialFunction Tk0 = PolynomialsUtils.createChebyshevPolynomial(k); + PolynomialFunction Tk1 = Tk0.polynomialDerivative(); + PolynomialFunction Tk2 = Tk1.polynomialDerivative(); + + PolynomialFunction g0 = new PolynomialFunction(new double[] { k * k }); + PolynomialFunction g1 = new PolynomialFunction(new double[] { 0, -1}); + PolynomialFunction g2 = new PolynomialFunction(new double[] { 1, 0, -1 }); + + PolynomialFunction Tk0g0 = Tk0.multiply(g0); + PolynomialFunction Tk1g1 = Tk1.multiply(g1); + PolynomialFunction Tk2g2 = Tk2.multiply(g2); + + checkNullPolynomial(Tk0g0.add(Tk1g1.add(Tk2g2))); + + } + } + + public void testFirstHermitePolynomials() { + + checkPolynomial(PolynomialsUtils.createHermitePolynomial(3), "-12.0 x + 8.0 x^3"); + checkPolynomial(PolynomialsUtils.createHermitePolynomial(2), "-2.0 + 4.0 x^2"); + checkPolynomial(PolynomialsUtils.createHermitePolynomial(1), "2.0 x"); + checkPolynomial(PolynomialsUtils.createHermitePolynomial(0), "1.0"); + + checkPolynomial(PolynomialsUtils.createHermitePolynomial(7), "-1680.0 x + 3360.0 x^3 - 1344.0 x^5 + 128.0 x^7"); + checkPolynomial(PolynomialsUtils.createHermitePolynomial(6), "-120.0 + 720.0 x^2 - 480.0 x^4 + 64.0 x^6"); + checkPolynomial(PolynomialsUtils.createHermitePolynomial(5), "120.0 x - 160.0 x^3 + 32.0 x^5"); + checkPolynomial(PolynomialsUtils.createHermitePolynomial(4), "12.0 - 48.0 x^2 + 16.0 x^4"); + + } + + public void testHermiteDifferentials() { + for (int k = 0; k < 12; ++k) { + + PolynomialFunction Hk0 = PolynomialsUtils.createHermitePolynomial(k); + PolynomialFunction Hk1 = Hk0.polynomialDerivative(); + PolynomialFunction Hk2 = Hk1.polynomialDerivative(); + + PolynomialFunction g0 = new PolynomialFunction(new double[] { 2 * k }); + PolynomialFunction g1 = new PolynomialFunction(new double[] { 0, -2 }); + PolynomialFunction g2 = new PolynomialFunction(new double[] { 1 }); + + PolynomialFunction Hk0g0 = Hk0.multiply(g0); + PolynomialFunction Hk1g1 = Hk1.multiply(g1); + PolynomialFunction Hk2g2 = Hk2.multiply(g2); + + checkNullPolynomial(Hk0g0.add(Hk1g1.add(Hk2g2))); + + } + } + + public void testFirstLaguerrePolynomials() { + + checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(3), 6l, "6.0 - 18.0 x + 9.0 x^2 - x^3"); + checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(2), 2l, "2.0 - 4.0 x + x^2"); + checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(1), 1l, "1.0 - x"); + checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(0), 1l, "1.0"); + + checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(7), 5040l, + "5040.0 - 35280.0 x + 52920.0 x^2 - 29400.0 x^3" + + " + 7350.0 x^4 - 882.0 x^5 + 49.0 x^6 - x^7"); + checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(6), 720l, + "720.0 - 4320.0 x + 5400.0 x^2 - 2400.0 x^3 + 450.0 x^4" + + " - 36.0 x^5 + x^6"); + checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(5), 120l, + "120.0 - 600.0 x + 600.0 x^2 - 200.0 x^3 + 25.0 x^4 - x^5"); + checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(4), 24l, + "24.0 - 96.0 x + 72.0 x^2 - 16.0 x^3 + x^4"); + + } + + public void testLaguerreDifferentials() { + for (int k = 0; k < 12; ++k) { + + PolynomialFunction Lk0 = PolynomialsUtils.createLaguerrePolynomial(k); + PolynomialFunction Lk1 = Lk0.polynomialDerivative(); + PolynomialFunction Lk2 = Lk1.polynomialDerivative(); + + PolynomialFunction g0 = new PolynomialFunction(new double[] { k }); + PolynomialFunction g1 = new PolynomialFunction(new double[] { 1, -1 }); + PolynomialFunction g2 = new PolynomialFunction(new double[] { 0, 1 }); + + PolynomialFunction Lk0g0 = Lk0.multiply(g0); + PolynomialFunction Lk1g1 = Lk1.multiply(g1); + PolynomialFunction Lk2g2 = Lk2.multiply(g2); + + checkNullPolynomial(Lk0g0.add(Lk1g1.add(Lk2g2))); + + } + } + + public void testFirstLegendrePolynomials() { + + checkPolynomial(PolynomialsUtils.createLegendrePolynomial(3), 2l, "-3.0 x + 5.0 x^3"); + checkPolynomial(PolynomialsUtils.createLegendrePolynomial(2), 2l, "-1.0 + 3.0 x^2"); + checkPolynomial(PolynomialsUtils.createLegendrePolynomial(1), 1l, "x"); + checkPolynomial(PolynomialsUtils.createLegendrePolynomial(0), 1l, "1.0"); + + checkPolynomial(PolynomialsUtils.createLegendrePolynomial(7), 16l, "-35.0 x + 315.0 x^3 - 693.0 x^5 + 429.0 x^7"); + checkPolynomial(PolynomialsUtils.createLegendrePolynomial(6), 16l, "-5.0 + 105.0 x^2 - 315.0 x^4 + 231.0 x^6"); + checkPolynomial(PolynomialsUtils.createLegendrePolynomial(5), 8l, "15.0 x - 70.0 x^3 + 63.0 x^5"); + checkPolynomial(PolynomialsUtils.createLegendrePolynomial(4), 8l, "3.0 - 30.0 x^2 + 35.0 x^4"); + + } + + public void testLegendreDifferentials() { + for (int k = 0; k < 12; ++k) { + + PolynomialFunction Pk0 = PolynomialsUtils.createLegendrePolynomial(k); + PolynomialFunction Pk1 = Pk0.polynomialDerivative(); + PolynomialFunction Pk2 = Pk1.polynomialDerivative(); + + PolynomialFunction g0 = new PolynomialFunction(new double[] { k * (k + 1) }); + PolynomialFunction g1 = new PolynomialFunction(new double[] { 0, -2 }); + PolynomialFunction g2 = new PolynomialFunction(new double[] { 1, 0, -1 }); + + PolynomialFunction Pk0g0 = Pk0.multiply(g0); + PolynomialFunction Pk1g1 = Pk1.multiply(g1); + PolynomialFunction Pk2g2 = Pk2.multiply(g2); + + checkNullPolynomial(Pk0g0.add(Pk1g1.add(Pk2g2))); + + } + } + + public void testHighDegreeLegendre() { + try { + PolynomialsUtils.createLegendrePolynomial(40); + fail("an exception should have been thrown"); + } catch (ArithmeticException ae) { + // expected + } +// checkPolynomial(PolynomialsUtils.createLegendrePolynomial(40), 274877906944l, +// "34461632205.0" +// + " - 28258538408100.0 x^2" +// + " + 3847870979902950.0 x^4" +// + " - 207785032914759300.0 x^6" +// + " + 5929294332103310025.0 x^8" +// + " - 103301483474866556880.0 x^10" +// + " + 1197358103913226000200.0 x^12" +// + " - 9763073770369381232400.0 x^14" +// + " + 58171647881784229843050.0 x^16" +// + " - 260061484647976556945400.0 x^18" +// + " + 888315281771246239250340.0 x^20" +// + " - 2345767627188139419665400.0 x^22" +// + " + 4819022625419112503443050.0 x^24" +// + " - 7710436200670580005508880.0 x^26" +// + " + 9566652323054238154983240.0 x^28" +// + " - 9104813935044723209570256.0 x^30" +// + " + 6516550296251767619752905.0 x^32" +// + " - 3391858621221953912598660.0 x^34" +// + " + 1211378079007840683070950.0 x^36" +// + " - 265365894974690562152100.0 x^38" +// + " + 26876802183334044115405.0 x^40"); + } + + private void checkPolynomial(PolynomialFunction p, long denominator, String reference) { + PolynomialFunction q = new PolynomialFunction(new double[] { denominator}); + assertEquals(reference, p.multiply(q).toString()); + } + + private void checkPolynomial(PolynomialFunction p, String reference) { + assertEquals(reference, p.toString()); + } + + private void checkNullPolynomial(PolynomialFunction p) { + for (double coefficient : p.getCoefficients()) { + assertEquals(0.0, coefficient, 1.0e-13); + } + } + +}