Javadoc fixes.
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/7b62d015 Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/7b62d015 Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/7b62d015 Branch: refs/heads/master Commit: 7b62d0155efebb2748918a5e4f67ac0ee2e759da Parents: 85a4fdd Author: Phil Steitz <phil.ste...@gmail.com> Authored: Mon Dec 28 08:29:28 2015 -0700 Committer: Phil Steitz <phil.ste...@gmail.com> Committed: Mon Dec 28 08:29:28 2015 -0700 ---------------------------------------------------------------------- .../gauss/LegendreHighPrecisionRuleFactory.java | 2 +- .../interpolation/LoessInterpolator.java | 26 ++--- .../interpolation/SplineInterpolator.java | 2 +- .../polynomials/PolynomialFunction.java | 10 +- .../polynomials/PolynomialSplineFunction.java | 4 +- .../analysis/polynomials/PolynomialsUtils.java | 100 +++++++++---------- 6 files changed, 71 insertions(+), 73 deletions(-) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/commons-math/blob/7b62d015/src/main/java/org/apache/commons/math4/analysis/integration/gauss/LegendreHighPrecisionRuleFactory.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math4/analysis/integration/gauss/LegendreHighPrecisionRuleFactory.java b/src/main/java/org/apache/commons/math4/analysis/integration/gauss/LegendreHighPrecisionRuleFactory.java index 81e6727..e4108a2 100644 --- a/src/main/java/org/apache/commons/math4/analysis/integration/gauss/LegendreHighPrecisionRuleFactory.java +++ b/src/main/java/org/apache/commons/math4/analysis/integration/gauss/LegendreHighPrecisionRuleFactory.java @@ -27,7 +27,7 @@ import org.apache.commons.math4.util.Pair; * In this implementation, the lower and upper bounds of the natural interval * of integration are -1 and 1, respectively. * The Legendre polynomials are evaluated using the recurrence relation - * presented in <a href="http://en.wikipedia.org/wiki/Abramowitz_and_Stegun"; + * presented in <a href="http://en.wikipedia.org/wiki/Abramowitz_and_Stegun";> * Abramowitz and Stegun, 1964</a>. * * @since 3.1 http://git-wip-us.apache.org/repos/asf/commons-math/blob/7b62d015/src/main/java/org/apache/commons/math4/analysis/interpolation/LoessInterpolator.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math4/analysis/interpolation/LoessInterpolator.java b/src/main/java/org/apache/commons/math4/analysis/interpolation/LoessInterpolator.java index f256c17..1209df5 100644 --- a/src/main/java/org/apache/commons/math4/analysis/interpolation/LoessInterpolator.java +++ b/src/main/java/org/apache/commons/math4/analysis/interpolation/LoessInterpolator.java @@ -36,14 +36,14 @@ import org.apache.commons.math4.util.MathUtils; * Implements the <a href="http://en.wikipedia.org/wiki/Local_regression";> * Local Regression Algorithm</a> (also Loess, Lowess) for interpolation of * real univariate functions. - * <p/> + * <p> * For reference, see - * <a href="http://www.math.tau.ac.il/~yekutiel/MA seminar/Cleveland 1979.pdf"> + * <a href="http://amstat.tandfonline.com/doi/abs/10.1080/01621459.1979.10481038";> * William S. Cleveland - Robust Locally Weighted Regression and Smoothing - * Scatterplots</a> - * <p/> + * Scatterplots</a></p> + * <p> * This class implements both the loess method and serves as an interpolation - * adapter to it, allowing one to build a spline on the obtained loess fit. + * adapter to it, allowing one to build a spline on the obtained loess fit.</p> * * @since 2.0 */ @@ -65,16 +65,16 @@ public class LoessInterpolator * a particular point, this fraction of source points closest * to the current point is taken into account for computing * a least-squares regression. - * <p/> - * A sensible value is usually 0.25 to 0.5. + * <p> + * A sensible value is usually 0.25 to 0.5.</p> */ private final double bandwidth; /** * The number of robustness iterations parameter: this many * robustness iterations are done. - * <p/> + * <p> * A sensible value is usually 0 (just the initial fit without any - * robustness iterations) to 4. + * robustness iterations) to 4.</p> */ private final int robustnessIters; /** @@ -109,10 +109,10 @@ public class LoessInterpolator * @param bandwidth when computing the loess fit at * a particular point, this fraction of source points closest * to the current point is taken into account for computing - * a least-squares regression.</br> + * a least-squares regression. * A sensible value is usually 0.25 to 0.5, the default value is * {@link #DEFAULT_BANDWIDTH}. - * @param robustnessIters This many robustness iterations are done.</br> + * @param robustnessIters This many robustness iterations are done. * A sensible value is usually 0 (just the initial fit without any * robustness iterations) to 4, the default value is * {@link #DEFAULT_ROBUSTNESS_ITERS}. @@ -130,10 +130,10 @@ public class LoessInterpolator * @param bandwidth when computing the loess fit at * a particular point, this fraction of source points closest * to the current point is taken into account for computing - * a least-squares regression.</br> + * a least-squares regression. * A sensible value is usually 0.25 to 0.5, the default value is * {@link #DEFAULT_BANDWIDTH}. - * @param robustnessIters This many robustness iterations are done.</br> + * @param robustnessIters This many robustness iterations are done. * A sensible value is usually 0 (just the initial fit without any * robustness iterations) to 4, the default value is * {@link #DEFAULT_ROBUSTNESS_ITERS}. http://git-wip-us.apache.org/repos/asf/commons-math/blob/7b62d015/src/main/java/org/apache/commons/math4/analysis/interpolation/SplineInterpolator.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math4/analysis/interpolation/SplineInterpolator.java b/src/main/java/org/apache/commons/math4/analysis/interpolation/SplineInterpolator.java index 99d725c..8de5532 100644 --- a/src/main/java/org/apache/commons/math4/analysis/interpolation/SplineInterpolator.java +++ b/src/main/java/org/apache/commons/math4/analysis/interpolation/SplineInterpolator.java @@ -29,7 +29,7 @@ import org.apache.commons.math4.util.MathArrays; * <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, - * x[0] < x[i] ... < x[n]. The x values are referred to as "knot points."</p> + * @code{x[0] < x[i] ... < x[n].} The x values are referred to as "knot points."</p> * <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 http://git-wip-us.apache.org/repos/asf/commons-math/blob/7b62d015/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialFunction.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialFunction.java b/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialFunction.java index 9d40a1b..9333c1e 100644 --- a/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialFunction.java +++ b/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialFunction.java @@ -79,8 +79,8 @@ public class PolynomialFunction implements UnivariateDifferentiableFunction, Ser /** * Compute the value of the function for the given argument. * <p> - * The value returned is <br/> - * <code>coefficients[n] * x^n + ... + coefficients[1] * x + coefficients[0]</code> + * The value returned is </p><p> + * {@code coefficients[n] * x^n + ... + coefficients[1] * x + coefficients[0]} * </p> * * @param x Argument for which the function value should be computed. @@ -189,7 +189,7 @@ public class PolynomialFunction implements UnivariateDifferentiableFunction, Ser * Subtract a polynomial from the instance. * * @param p Polynomial to subtract. - * @return a new polynomial which is the difference the instance minus {@code p}. + * @return a new polynomial which is the instance minus {@code p}. */ public PolynomialFunction subtract(final PolynomialFunction p) { // identify the lowest degree polynomial @@ -216,7 +216,7 @@ public class PolynomialFunction implements UnivariateDifferentiableFunction, Ser /** * Negate the instance. * - * @return a new polynomial. + * @return a new polynomial with all coefficients negated */ public PolynomialFunction negate() { double[] newCoefficients = new double[coefficients.length]; @@ -230,7 +230,7 @@ public class PolynomialFunction implements UnivariateDifferentiableFunction, Ser * Multiply the instance by a polynomial. * * @param p Polynomial to multiply by. - * @return a new polynomial. + * @return a new polynomial equal to this times {@code p} */ public PolynomialFunction multiply(final PolynomialFunction p) { double[] newCoefficients = new double[coefficients.length + p.coefficients.length - 1]; http://git-wip-us.apache.org/repos/asf/commons-math/blob/7b62d015/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialSplineFunction.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialSplineFunction.java b/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialSplineFunction.java index afa7eef..b842a40 100644 --- a/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialSplineFunction.java +++ b/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialSplineFunction.java @@ -57,8 +57,8 @@ import org.apache.commons.math4.util.MathArrays; * than the largest one, an <code>IllegalArgumentException</code> * is thrown.</li> * <li> Let <code>j</code> be the index of the largest knot point that is less - * than or equal to <code>x</code>. The value returned is <br> - * <code>polynomials[j](x - knot[j])</code></li></ol></p> + * than or equal to <code>x</code>. The value returned is + * {@code polynomials[j](x - knot[j])}</li></ol> * */ public class PolynomialSplineFunction implements UnivariateDifferentiableFunction { http://git-wip-us.apache.org/repos/asf/commons-math/blob/7b62d015/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialsUtils.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialsUtils.java b/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialsUtils.java index 346644e..c406979 100644 --- a/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialsUtils.java +++ b/src/main/java/org/apache/commons/math4/analysis/polynomials/PolynomialsUtils.java @@ -90,14 +90,15 @@ public class PolynomialsUtils { /** * Create a Chebyshev polynomial of the first kind. - * <p><a href="http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html";>Chebyshev + * <p><a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials";>Chebyshev * polynomials of the first kind</a> are orthogonal polynomials. - * They can be defined by the following recurrence relations: - * <pre> - * T<sub>0</sub>(X) = 1 - * T<sub>1</sub>(X) = X - * T<sub>k+1</sub>(X) = 2X T<sub>k</sub>(X) - T<sub>k-1</sub>(X) - * </pre></p> + * They can be defined by the following recurrence relations:</p><p> + * \( + * T_0(x) = 1 \\ + * T_1(x) = x \\ + * T_{k+1}(x) = 2x T_k(x) - T_{k-1}(x) + * \) + * </p> * @param degree degree of the polynomial * @return Chebyshev polynomial of specified degree */ @@ -118,12 +119,13 @@ public class PolynomialsUtils { * Create a Hermite polynomial. * <p><a href="http://mathworld.wolfram.com/HermitePolynomial.html";>Hermite * polynomials</a> are orthogonal polynomials. - * They can be defined by the following recurrence relations: - * <pre> - * H<sub>0</sub>(X) = 1 - * H<sub>1</sub>(X) = 2X - * H<sub>k+1</sub>(X) = 2X H<sub>k</sub>(X) - 2k H<sub>k-1</sub>(X) - * </pre></p> + * They can be defined by the following recurrence relations:</p><p> + * \( + * H_0(x) = 1 \\ + * H_1(x) = 2x \\ + * H_{k+1}(x) = 2x H_k(X) - 2k H_{k-1}(x) + * \) + * </p> * @param degree degree of the polynomial * @return Hermite polynomial of specified degree @@ -146,12 +148,13 @@ public class PolynomialsUtils { * Create a Laguerre polynomial. * <p><a href="http://mathworld.wolfram.com/LaguerrePolynomial.html";>Laguerre * polynomials</a> are orthogonal polynomials. - * They can be defined by the following recurrence relations: - * <pre> - * L<sub>0</sub>(X) = 1 - * L<sub>1</sub>(X) = 1 - X - * (k+1) L<sub>k+1</sub>(X) = (2k + 1 - X) L<sub>k</sub>(X) - k L<sub>k-1</sub>(X) - * </pre></p> + * They can be defined by the following recurrence relations:</p><p> + * \( + * L_0(x) = 1 \\ + * L_1(x) = 1 - x \\ + * (k+1) L_{k+1}(x) = (2k + 1 - x) L_k(x) - k L_{k-1}(x) + * \) + * </p> * @param degree degree of the polynomial * @return Laguerre polynomial of specified degree */ @@ -174,12 +177,13 @@ public class PolynomialsUtils { * Create a Legendre polynomial. * <p><a href="http://mathworld.wolfram.com/LegendrePolynomial.html";>Legendre * polynomials</a> are orthogonal polynomials. - * They can be defined by the following recurrence relations: - * <pre> - * P<sub>0</sub>(X) = 1 - * P<sub>1</sub>(X) = X - * (k+1) P<sub>k+1</sub>(X) = (2k+1) X P<sub>k</sub>(X) - k P<sub>k-1</sub>(X) - * </pre></p> + * They can be defined by the following recurrence relations:</p><p> + * \( + * P_0(x) = 1 \\ + * P_1(x) = x \\ + * (k+1) P_{k+1}(x) = (2k+1) x P_k(x) - k P_{k-1}(x) + * \) + * </p> * @param degree degree of the polynomial * @return Legendre polynomial of specified degree */ @@ -202,14 +206,15 @@ public class PolynomialsUtils { * Create a Jacobi polynomial. * <p><a href="http://mathworld.wolfram.com/JacobiPolynomial.html";>Jacobi * polynomials</a> are orthogonal polynomials. - * They can be defined by the following recurrence relations: - * <pre> - * P<sub>0</sub><sup>vw</sup>(X) = 1 - * P<sub>-1</sub><sup>vw</sup>(X) = 0 - * 2k(k + v + w)(2k + v + w - 2) P<sub>k</sub><sup>vw</sup>(X) = - * (2k + v + w - 1)[(2k + v + w)(2k + v + w - 2) X + v<sup>2</sup> - w<sup>2</sup>] P<sub>k-1</sub><sup>vw</sup>(X) - * - 2(k + v - 1)(k + w - 1)(2k + v + w) P<sub>k-2</sub><sup>vw</sup>(X) - * </pre></p> + * They can be defined by the following recurrence relations:</p><p> + * \( + * P_0^{vw}(x) = 1 \\ + * P_{-1}^{vw}(x) = 0 \\ + * 2k(k + v + w)(2k + v + w - 2) P_k^{vw}(x) = \\ + * (2k + v + w - 1)[(2k + v + w)(2k + v + w - 2) x + v^2 - w^2] P_{k-1}^{vw}(x) \\ + * - 2(k + v - 1)(k + w - 1)(2k + v + w) P_{k-2}^{vw}(x) + * \) + * </p> * @param degree degree of the polynomial * @param v first exponent * @param w second exponent @@ -301,27 +306,20 @@ public class PolynomialsUtils { } /** - * Compute the coefficients of the polynomial <code>P<sub>s</sub>(x)</code> + * Compute the coefficients of the polynomial \(P_s(x)\) * whose values at point {@code x} will be the same as the those from the - * original polynomial <code>P(x)</code> when computed at {@code x + shift}. - * Thus, if <code>P(x) = Σ<sub>i</sub> a<sub>i</sub> x<sup>i</sup></code>, - * then - * <pre> - * <table> - * <tr> - * <td><code>P<sub>s</sub>(x)</td> - * <td>= Σ<sub>i</sub> b<sub>i</sub> x<sup>i</sup></code></td> - * </tr> - * <tr> - * <td></td> - * <td>= Σ<sub>i</sub> a<sub>i</sub> (x + shift)<sup>i</sup></code></td> - * </tr> - * </table> - * </pre> + * original polynomial \(P(x)\) when computed at {@code x + shift}. + * <p> + * More precisely, let \(\Delta = \) {@code shift} and let + * \(P_s(x) = P(x + \Delta)\). The returned array + * consists of the coefficients of \(P_s\). So if \(a_0, ..., a_{n-1}\) + * are the coefficients of \(P\), then the returned array + * \(b_0, ..., b_{n-1}\) satisfies the identity + * \(\sum_{i=0}^{n-1} b_i x^i = \sum_{i=0}^{n-1} a_i (x + \Delta)^i\) for all \(x\). * * @param coefficients Coefficients of the original polynomial. * @param shift Shift value. - * @return the coefficients <code>b<sub>i</sub></code> of the shifted + * @return the coefficients \(b_i\) of the shifted * polynomial. */ public static double[] shift(final double[] coefficients, @@ -444,7 +442,7 @@ public class PolynomialsUtils { * Generate recurrence coefficients. * @param k highest degree of the polynomials used in the recurrence * @return an array of three coefficients such that - * P<sub>k+1</sub>(X) = (a[0] + a[1] X) P<sub>k</sub>(X) - a[2] P<sub>k-1</sub>(X) + * \( P_{k+1}(x) = (a[0] + a[1] x) P_k(x) - a[2] P_{k-1}(x) \) */ BigFraction[] generate(int k); }
