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Posted to commits@commons.apache.org by er...@apache.org on 2021/06/10 14:15:29 UTC
[commons-math] 05/05: MATH-1603: Userguide update.
This is an automated email from the ASF dual-hosted git repository.
erans pushed a commit to branch master
in repository https://gitbox.apache.org/repos/asf/commons-math.git
commit c67bf75076860be55ae78e7eebeacd8074b808e0
Author: Gilles Sadowski <gi...@gmail.com>
AuthorDate: Thu Jun 10 15:57:18 2021 +0200
MATH-1603: Userguide update.
---
src/site/apt/userguide/special.apt | 136 -------------------------------------
1 file changed, 136 deletions(-)
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-~~
-~~ 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.
-~~
-
- -----------------------------------------------
- The Commons Math User Guide - Special Functions
- -----------------------------------------------
-
-5 Special Functions
-
-* 5.1 Overview
-
- The <<<special>>> package of Commons-Math gathers several useful special
- functions not provided by <<<java.lang.Math>>>.
-
-* 5.2 Erf functions
-
- {{{../apidocs/org/apache/commons/math4/special/Erf.html}Erf}} contains
- several useful functions involving the Error Function, Erf.
-
-*----------------+---------+-------------------------------------------------------------------+
-|| Function || Method || Reference |
-*----------------+---------+-------------------------------------------------------------------+
-| Error Function |erf | See {{{http://mathworld.wolfram.com/Erf.html}Erf}} from MathWorld |
-*----------------+---------+-------------------------------------------------------------------+
-
-* 5.3 Gamma functions
-
- Class {{{../apidocs/org/apache/commons/math4/special/Gamma.html}<<<Gamma>>>}}
- contains several useful functions involving the Gamma Function.
-
-** Gamma
-
- <<<Gamma.gamma(x)>>> computes the Gamma function, Γ(x)
- (see {{{http://mathworld.wolfram.com/GammaFunction.html}MathWorld}},
- {{{http://dlmf.nist.gov/5}DLMF}}). The accuracy of the Commons-Math
- implementation is assessed by comparison with high precision values computed
- with the {{{http://maxima.sourceforge.net/}Maxima}} Computer Algebra System.
-
-*----------------+-----------------------------------------------+-----------------+----------------------+----------------+
-|| Interval || Values tested || Average error || Standard deviation || Maximum error |
-*----------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| -5 \< x \< -4 | <<<x[i] = i / 1024, i = -5119, ..., -4097>>> | 0.49 ulps | 0.57 ulps | 3.0 ulps |
-*----------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| -4 \< x \< -3 | <<<x[i] = i / 1024, i = -4095, ..., -3073>>> | 0.36 ulps | 0.51 ulps | 2.0 ulps |
-*----------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| -3 \< x \< -2 | <<<x[i] = i / 1024, i = -3071, ..., -2049>>> | 0.41 ulps | 0.53 ulps | 2.0 ulps |
-*----------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| -2 \< x \< -1 | <<<x[i] = i / 1024, i = -2047, ..., -1025>>> | 0.37 ulps | 0.50 ulps | 2.0 ulps |
-*----------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| -1 \< x \< 0 | <<<x[i] = i / 1024, i = -1023, ..., -1>>> | 0.46 ulps | 0.54 ulps | 2.0 ulps |
-*----------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| 0 \< x ≤ 8 | <<<x[i] = i / 1024, i = 1, ..., 8192>>> | 0.33 ulps | 0.48 ulps | 2.0 ulps |
-*----------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| 8 \< x ≤ 141 | <<<x[i] = i / 64, i = 513, ..., 9024>>> | 1.32 ulps | 1.19 ulps | 7.0 ulps |
-*----------------+-----------------------------------------------+-----------------+----------------------+----------------+
-
-** Log Gamma
-
- <<<Gamma.logGamma(x)>>> computes the natural logarithm of the Gamma function,
- log \u0393(x), for x > 0
- (see {{{http://mathworld.wolfram.com/LogGammaFunction.html}MathWorld}},
- {{{http://dlmf.nist.gov/5}DLMF}}). The accuracy of the Commons-Math
- implementation is assessed by comparaison with high precision values computed
- with the {{{http://maxima.sourceforge.net/}Maxima}} Computer Algebra System.
-
-*------------------------------------------------+-----------------------------------------------+-----------------+----------------------+----------------+
-|| Interval || Values tested || Average error || Standard deviation || Maximum error |
-*------------------------------------------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| 0 \< x ≤ 8 | <<<x[i] = i / 1024, i = 1, ..., 8192>>> | 0.32 ulps | 0.50 ulps | 4.0 ulps |
-*------------------------------------------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| 8 \< x ≤ 1024 | <<<x[i] = i / 8, i = 65, ..., 8192>>> | 0.43 ulps | 0.53 ulps | 3.0 ulps |
-*------------------------------------------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| 1024 \< x ≤ 8192 | <<<x[i], i = 1025, ..., 8192>>> | 0.53 ulps | 0.56 ulps | 3.0 ulps |
-*------------------------------------------------+-----------------------------------------------+-----------------+----------------------+----------------+
-| 8933.439345993791 ≤ x ≤ 1.75555970201398e+305 | <<<x[i] = 2**(i / 8), i = 105, ..., 8112>>> | 0.35 ulps | 0.49 ulps | 2.0 ulps |
-*------------------------------------------------+-----------------------------------------------+-----------------+----------------------+----------------+
-
-** Regularized Gamma
-
- <<<Gamma.regularizedGammaP(a, x)>>> computes the value of the regularized
- Gamma function, P(a, x)
- (see {{{http://mathworld.wolfram.com/RegularizedGammaFunction.html}MathWorld}}).
-
-* 5.4 Beta functions
-
- {{{../apidocs/org/apache/commons/math4/special/Beta.html}Beta}} contains
- several useful functions involving the Beta Function.
-
-** Log Beta
-
- <<<Beta.logBeta(a, b)>>> computes the value of the natural logarithm of the
- Beta function, log B(a, b).
- (see {{{http://mathworld.wolfram.com/BetaFunction.html}MathWorld}},
- {{{http://dlmf.nist.gov/5.12}DLMF}}). The accuracy of the Commons-Math
- implementation is assessed by comparison with high precision values computed
- with the {{{http://maxima.sourceforge.net/}Maxima}} Computer Algebra System.
-
-*----------------+-----------------------------------------+-----------------+----------------------+----------------+
-|| Interval || Values tested || Average error || Standard deviation || Maximum error |
-*----------------+-----------------------------------------+-----------------+----------------------+-----------------+
-| 0 \< x ≤ 8\ | <<<x[i] = i / 32, i = 1, ..., 256>>>\ | 1.80 ulps | 81.08 ulps | 14031.0 ulps |
-| 0 \< y ≤ 8 | <<<y[j] = j / 32, j = 1, ..., 256>>> | | | |
-*----------------+-----------------------------------------+-----------------+----------------------+-----------------+
-| 0 \< x ≤ 8\ | <<<x[i] = i / 32, i = 1, ..., 256>>>\ | 0.50 ulps | 3.64 ulps | 694.0 ulps |
-| 8 \< y ≤ 16 | <<<y[j] = j / 32, j = 257, ..., 512>>> | | | |
-*----------------+-----------------------------------------+-----------------+----------------------+-----------------+
-| 0 \< x ≤ 8\ | <<<x[i] = i / 32, i = 1, ..., 256>>>\ | 1.04 ulps | 139.32 ulps | 34509.0 ulps |
-| 16 \< y ≤ 256 | <<<y[j] = j, j = 17, ..., 256>>> | | | |
-*----------------+-----------------------------------------+-----------------+----------------------+-----------------+
-| 8 \< x ≤ 16\ | <<<x[i] = i / 32, i = 257, ..., 512>>>\ | 0.35 ulps | 0.48 ulps | 2.0 ulps |
-| 8 \< y ≤ 16 | <<<y[j] = j / 32, j = 257, ..., 512>>> | | | |
-*----------------+-----------------------------------------+-----------------+----------------------+-----------------+
-| 8 \< x ≤ 16\ | <<<x[i] = i / 32, i = 257, ..., 512>>>\ | 0.31 ulps | 0.47 ulps | 2.0 ulps |
-| 16 \< y ≤ 256 | <<<y[j] = j, j = 17, ..., 256>>> | | | |
-*----------------+-----------------------------------------+-----------------+----------------------+-----------------+
-| 16 \< x ≤ 256\ | <<<x[i] = i, i = 17, ..., 256>>>\ | 0.35 ulps | 0.49 ulps | 2.0 ulps |
-| 16 \< y ≤ 256 | <<<y[j] = j, j = 17, ..., 256>>> | | | |
-*----------------+-----------------------------------------+-----------------+----------------------+-----------------+
-
-** Regularized Beta
-
- (see {{{http://mathworld.wolfram.com/RegularizedBetaFunction.html}MathWorld}})