From 52e0139b259503d7e2aa3debd0c9307797d8a0d7 Mon Sep 17 00:00:00 2001 From: Lakshmi Krishnamurthy Date: Sat, 16 Mar 2024 20:25:03 -0400 Subject: [PATCH] Features: Bug Fixes/Re-organization: - Special Function Property Digamma Equality Lemma - Summation Identity 10 #1 (1, 2, 3) - Special Function Property Digamma Equality Lemma - Summation Identity 10 #2 (4, 5) - Special Function Property Digamma Equality Lemma - Summation Identity 10 #3 (6, 7) - Special Function Property Digamma Inequality Lemma (8, 9, 10) - Special Function Property Digamma Inequality Lemma - Left Asymptote #1 (11, 12, 13) - Special Function Property Digamma Inequality Lemma - Left Asymptote #2 (14, 15, 16) - Special Function Property Digamma Inequality Lemma - Right Asymptote #1 (17, 18, 19) - Special Function Property Digamma Inequality Lemma - Right Asymptote #2 (20, 21, 22) - Special Function Property Digamma Inequality Lemma - Zero One Left Bound #1 (23, 24, 25) - Special Function Property Digamma Inequality Lemma - Zero One Left Bound #2 (26, 27, 28) - Special Function Property Digamma Inequality Lemma - Zero One Right Bound #1 (29, 30, 31) - Special Function Property Digamma Inequality Lemma - Zero One Right Bound #2 (32, 33, 34) - Special Function Property Digamma Inequality Lemma - Bernstein Binet Left Bound #1 (35, 36, 37) - Special Function Property Digamma Inequality Lemma - Bernstein Binet Left Bound #2 (38, 39, 40) - Special Function Property Digamma Inequality Lemma - Bernstein Binet Right Bound #1 (41, 42, 43) - Special Function Property Digamma Inequality Lemma - Bernstein Binet Right Bound #2 (44, 45, 46) - Special Function Property Digamma Inequality Lemma - Elezovic Giordano Pecaric Right Bound #1 (47, 48, 49) - Special Function Property Digamma Inequality Lemma - Elezovic Giordano Pecaric Right Bound #2 (50, 51, 52) - Special Function Property Digamma Inequality Lemma - Elezovic Giordano Pecaric Left Bound #1 (53, 54, 55) - Special Function Property Digamma Inequality Lemma - Elezovic Giordano Pecaric Left Bound #2 (56, 57, 58) - Special Function Property Digamma Inequality Lemma - Alzer Difference 1997 (59, 60) Samples: IdeaDRIP: --- ReleaseNotes/08_28_2023.txt | 31 ++ ScheduleSheet.xlsx | Bin 56217 -> 56111 bytes .../property/DigammaInequalityLemma.java | 467 +++++++++--------- 3 files changed, 255 insertions(+), 243 deletions(-) create mode 100644 ReleaseNotes/08_28_2023.txt diff --git a/ReleaseNotes/08_28_2023.txt b/ReleaseNotes/08_28_2023.txt new file mode 100644 index 000000000000..34200dbff6ff --- /dev/null +++ b/ReleaseNotes/08_28_2023.txt @@ -0,0 +1,31 @@ + +Features: + +Bug Fixes/Re-organization: + + - Special Function Property Digamma Equality Lemma - Summation Identity 10 #1 (1, 2, 3) + - Special Function Property Digamma Equality Lemma - Summation Identity 10 #2 (4, 5) + - Special Function Property Digamma Equality Lemma - Summation Identity 10 #3 (6, 7) + - Special Function Property Digamma Inequality Lemma (8, 9, 10) + - Special Function Property Digamma Inequality Lemma - Left Asymptote #1 (11, 12, 13) + - Special Function Property Digamma Inequality Lemma - Left Asymptote #2 (14, 15, 16) + - Special Function Property Digamma Inequality Lemma - Right Asymptote #1 (17, 18, 19) + - Special Function Property Digamma Inequality Lemma - Right Asymptote #2 (20, 21, 22) + - Special Function Property Digamma Inequality Lemma - Zero One Left Bound #1 (23, 24, 25) + - Special Function Property Digamma Inequality Lemma - Zero One Left Bound #2 (26, 27, 28) + - Special Function Property Digamma Inequality Lemma - Zero One Right Bound #1 (29, 30, 31) + - Special Function Property Digamma Inequality Lemma - Zero One Right Bound #2 (32, 33, 34) + - Special Function Property Digamma Inequality Lemma - Bernstein Binet Left Bound #1 (35, 36, 37) + - Special Function Property Digamma Inequality Lemma - Bernstein Binet Left Bound #2 (38, 39, 40) + - Special Function Property Digamma Inequality Lemma - Bernstein Binet Right Bound #1 (41, 42, 43) + - Special Function Property Digamma Inequality Lemma - Bernstein Binet Right Bound #2 (44, 45, 46) + - Special Function Property Digamma Inequality Lemma - Elezovic Giordano Pecaric Right Bound #1 (47, 48, 49) + - Special Function Property Digamma Inequality Lemma - Elezovic Giordano Pecaric Right Bound #2 (50, 51, 52) + - Special Function Property Digamma Inequality Lemma - Elezovic Giordano Pecaric Left Bound #1 (53, 54, 55) + - Special Function Property Digamma Inequality Lemma - Elezovic Giordano Pecaric Left Bound #2 (56, 57, 58) + - Special Function Property Digamma Inequality Lemma - Alzer Difference 1997 (59, 60) + + +Samples: + +IdeaDRIP: diff --git a/ScheduleSheet.xlsx b/ScheduleSheet.xlsx index cd4766187707ce718aab10e5a3f025dc486cdf2a..f68d23e1eec0094ab4c15956fcf48f20a1d4b20f 100644 GIT binary patch delta 3951 zcmY*cbyO3K*B&uOhk!6ZI+T!x5gSM-FeH^u=^P=Wgb@l7A}|;+N*YB$M|Y=;X23uc z5Jd!)5Ty3=egF90^W8u0x#!$?o_p>&_uQM;Oi|ZFQU9F^g__kNP*DH?2UGw66951R 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ze)2Y0FdvPa(ga)8qF+p@63wDJrjTIxSM;w=7If+q1buy)gXkeTVVVnVF)aP5eq zHU!&Z(AO|G(3Dsa@NWO#ry$w_3nvOi$6y8iE7IsHEHlw6x)-ZL^b}1tBS0oK`48#8 E0F9^Do&W#< diff --git a/src/main/java/org/drip/specialfunction/property/DigammaInequalityLemma.java b/src/main/java/org/drip/specialfunction/property/DigammaInequalityLemma.java index 9a0602f0736d..ef597fbd6206 100644 --- a/src/main/java/org/drip/specialfunction/property/DigammaInequalityLemma.java +++ b/src/main/java/org/drip/specialfunction/property/DigammaInequalityLemma.java @@ -1,11 +1,20 @@ package org.drip.specialfunction.property; +import org.drip.function.definition.R1ToR1; +import org.drip.function.definition.R1ToR1Property; +import org.drip.numerical.common.NumberUtil; +import org.drip.specialfunction.digamma.CumulativeSeriesEstimator; +import org.drip.specialfunction.gamma.Definitions; + /* * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ /*! + * Copyright (C) 2025 Lakshmi Krishnamurthy + * Copyright (C) 2024 Lakshmi Krishnamurthy + * Copyright (C) 2023 Lakshmi Krishnamurthy * Copyright (C) 2022 Lakshmi Krishnamurthy * Copyright (C) 2021 Lakshmi Krishnamurthy * Copyright (C) 2020 Lakshmi Krishnamurthy @@ -78,7 +87,7 @@ /** * DigammaInequalityLemma contains the Verifiable Inequality Lemmas for the Digamma Function. The - * References are: + * References are: * *

*
    @@ -102,15 +111,36 @@ * Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function * *
+ * + * It provides the following functionality: * - *

*
    - *
  • Module = Computational Core Module
    • - *
  • Library = Function Analysis Library
    • - *
  • Project = Special Function Implementation Analysis
    • - *
  • Package = Special Function Property Lemma Verifiers
    • + *
  • Generate the Digamma Asymptotic Left Inequality Verifier
    • + *
  • Generate the Digamma Asymptotic Right Inequality Verifier
    • + *
  • Generate the Digamma (0, 1) Left Bound Inequality Verifier
    • + *
  • Generate the Digamma (0, 1) Right Bound Verifier
    • + *
  • Generate the Bernstein-Binet Left Bound Inequality Verifier
    • + *
  • Generate the Bernstein-Binet Right Bound Inequality Verifier
    • + *
  • Generate the Elezovic-Giordano-Pecaric Left Bound Inequality Verifier
    • + *
  • Generate the Elezovic-Giordano-Pecaric Right Bound Inequality Verifier
    • + *
  • Generate the Alzer (1997) Digamma Difference Lemma Verifier
    • + *
  • Generate the Alzer-Jameson (2017) Inequality Verifier
    • *
* + *
+ * + * + * + * + * + * + * + *
Module Computational Core Module
Library Function Analysis Library
Project Special Function Implementation and Analysis
Package Special Function Property Lemma Verifiers
+ * * @author Lakshmi Krishnamurthy */ @@ -123,50 +153,45 @@ public class DigammaInequalityLemma * @return The Digamma Asymptotic Left Inequality Verifier */ - public static final org.drip.function.definition.R1ToR1Property LeftAsymptote() + public static final R1ToR1Property LeftAsymptote() { - final org.drip.specialfunction.digamma.CumulativeSeriesEstimator abramowitzStegun2007 = - org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); + final CumulativeSeriesEstimator abramowitzStegun2007 = + CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); - try - { - return new org.drip.function.definition.R1ToR1Property ( - org.drip.function.definition.R1ToR1Property.LT, - new org.drip.function.definition.R1ToR1 (null) - { + try { + return new R1ToR1Property ( + R1ToR1Property.LT, + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::LeftAsymptote::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::LeftAsymptote::evaluate => Invalid Inputs" + ); } - return java.lang.Math.log (z - 0.5); + return Math.log (z - 0.5); } }, - new org.drip.function.definition.R1ToR1 (null) - { + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::LeftAsymptote::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::LeftAsymptote::evaluate => Invalid Inputs" + ); } return abramowitzStegun2007.evaluate (z); } }, - org.drip.function.definition.R1ToR1Property.MISMATCH_TOLERANCE + R1ToR1Property.MISMATCH_TOLERANCE ); - } - catch (java.lang.Exception e) - { + } catch (Exception e) { e.printStackTrace(); } @@ -179,50 +204,45 @@ public static final org.drip.function.definition.R1ToR1Property LeftAsymptote() * @return The Digamma Asymptotic Right Inequality Verifier */ - public static final org.drip.function.definition.R1ToR1Property RightAsymptote() + public static final R1ToR1Property RightAsymptote() { - final org.drip.specialfunction.digamma.CumulativeSeriesEstimator abramowitzStegun2007 = - org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); + final CumulativeSeriesEstimator abramowitzStegun2007 = + CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); - try - { - return new org.drip.function.definition.R1ToR1Property ( - org.drip.function.definition.R1ToR1Property.GT, - new org.drip.function.definition.R1ToR1 (null) - { + try { + return new R1ToR1Property ( + R1ToR1Property.GT, + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::RightAsymptote::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::RightAsymptote::evaluate => Invalid Inputs" + ); } - return java.lang.Math.log (z); + return Math.log (z); } }, - new org.drip.function.definition.R1ToR1 (null) - { + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::RightAsymptote::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::RightAsymptote::evaluate => Invalid Inputs" + ); } return abramowitzStegun2007.evaluate (z); } }, - org.drip.function.definition.R1ToR1Property.MISMATCH_TOLERANCE + R1ToR1Property.MISMATCH_TOLERANCE ); - } - catch (java.lang.Exception e) - { + } catch (Exception e) { e.printStackTrace(); } @@ -235,50 +255,45 @@ public static final org.drip.function.definition.R1ToR1Property RightAsymptote() * @return The Digamma (0, 1) Left Bound Inequality Verifier */ - public static final org.drip.function.definition.R1ToR1Property ZeroOneLeftBound() + public static final R1ToR1Property ZeroOneLeftBound() { - final org.drip.specialfunction.digamma.CumulativeSeriesEstimator abramowitzStegun2007 = - org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); + final CumulativeSeriesEstimator abramowitzStegun2007 = + CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); - try - { - return new org.drip.function.definition.R1ToR1Property ( - org.drip.function.definition.R1ToR1Property.LT, - new org.drip.function.definition.R1ToR1 (null) - { + try { + return new R1ToR1Property ( + R1ToR1Property.LT, + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::ZeroOneLeftBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::ZeroOneLeftBound::evaluate => Invalid Inputs" + ); } - return -1. / z - org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI; + return -1. / z - Definitions.EULER_MASCHERONI; } }, - new org.drip.function.definition.R1ToR1 (null) - { + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::ZeroOneLeftBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::ZeroOneLeftBound::evaluate => Invalid Inputs" + ); } return abramowitzStegun2007.evaluate (z); } }, - org.drip.function.definition.R1ToR1Property.MISMATCH_TOLERANCE + R1ToR1Property.MISMATCH_TOLERANCE ); - } - catch (java.lang.Exception e) - { + } catch (Exception e) { e.printStackTrace(); } @@ -291,50 +306,45 @@ public static final org.drip.function.definition.R1ToR1Property ZeroOneLeftBound * @return The Digamma (0, 1) Right Bound Verifier */ - public static final org.drip.function.definition.R1ToR1Property ZeroOneRightBound() + public static final R1ToR1Property ZeroOneRightBound() { - final org.drip.specialfunction.digamma.CumulativeSeriesEstimator abramowitzStegun2007 = - org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); + final CumulativeSeriesEstimator abramowitzStegun2007 = + CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); - try - { - return new org.drip.function.definition.R1ToR1Property ( - org.drip.function.definition.R1ToR1Property.GT, - new org.drip.function.definition.R1ToR1 (null) - { + try { + return new R1ToR1Property ( + R1ToR1Property.GT, + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::ZeroOneRightBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::ZeroOneRightBound::evaluate => Invalid Inputs" + ); } - return 1. - 1. / z - org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI; + return 1. - 1. / z - Definitions.EULER_MASCHERONI; } }, - new org.drip.function.definition.R1ToR1 (null) - { + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::ZeroOneRightBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::ZeroOneRightBound::evaluate => Invalid Inputs" + ); } return abramowitzStegun2007.evaluate (z); } }, - org.drip.function.definition.R1ToR1Property.MISMATCH_TOLERANCE + R1ToR1Property.MISMATCH_TOLERANCE ); - } - catch (java.lang.Exception e) - { + } catch (Exception e) { e.printStackTrace(); } @@ -347,50 +357,45 @@ public static final org.drip.function.definition.R1ToR1Property ZeroOneRightBoun * @return The Bernstein-Binet Left Bound Inequality Verifier */ - public static final org.drip.function.definition.R1ToR1Property BernsteinBinetLeftBound() + public static final R1ToR1Property BernsteinBinetLeftBound() { - final org.drip.specialfunction.digamma.CumulativeSeriesEstimator abramowitzStegun2007 = - org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); + final CumulativeSeriesEstimator abramowitzStegun2007 = + CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); - try - { - return new org.drip.function.definition.R1ToR1Property ( - org.drip.function.definition.R1ToR1Property.LT, - new org.drip.function.definition.R1ToR1 (null) - { + try { + return new R1ToR1Property ( + R1ToR1Property.LT, + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::BernsteinBinetLeftBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::BernsteinBinetLeftBound::evaluate => Invalid Inputs" + ); } - return java.lang.Math.log (z) - 1. / z; + return Math.log (z) - 1. / z; } }, - new org.drip.function.definition.R1ToR1 (null) - { + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::BernsteinBinetLeftBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::BernsteinBinetLeftBound::evaluate => Invalid Inputs" + ); } return abramowitzStegun2007.evaluate (z); } }, - org.drip.function.definition.R1ToR1Property.MISMATCH_TOLERANCE + R1ToR1Property.MISMATCH_TOLERANCE ); - } - catch (java.lang.Exception e) - { + } catch (Exception e) { e.printStackTrace(); } @@ -403,50 +408,45 @@ public static final org.drip.function.definition.R1ToR1Property BernsteinBinetLe * @return The Bernstein-Binet Right Bound Inequality Verifier */ - public static final org.drip.function.definition.R1ToR1Property BernsteinBinetRightBound() + public static final R1ToR1Property BernsteinBinetRightBound() { - final org.drip.specialfunction.digamma.CumulativeSeriesEstimator abramowitzStegun2007 = - org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); + final CumulativeSeriesEstimator abramowitzStegun2007 = + CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); - try - { - return new org.drip.function.definition.R1ToR1Property ( - org.drip.function.definition.R1ToR1Property.GT, - new org.drip.function.definition.R1ToR1 (null) - { + try { + return new R1ToR1Property ( + R1ToR1Property.GT, + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::BernsteinBinetRightBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::BernsteinBinetRightBound::evaluate => Invalid Inputs" + ); } - return java.lang.Math.log (z) - 0.5 / z; + return Math.log (z) - 0.5 / z; } }, - new org.drip.function.definition.R1ToR1 (null) - { + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::BernsteinBinetRightBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::BernsteinBinetRightBound::evaluate => Invalid Inputs" + ); } return abramowitzStegun2007.evaluate (z); } }, - org.drip.function.definition.R1ToR1Property.MISMATCH_TOLERANCE + R1ToR1Property.MISMATCH_TOLERANCE ); - } - catch (java.lang.Exception e) - { + } catch (Exception e) { e.printStackTrace(); } @@ -459,50 +459,45 @@ public static final org.drip.function.definition.R1ToR1Property BernsteinBinetRi * @return The Elezovic-Giordano-Pecaric Left Bound Inequality Verifier */ - public static final org.drip.function.definition.R1ToR1Property ElezovicGiordanoPecaricLeftBound() + public static final R1ToR1Property ElezovicGiordanoPecaricLeftBound() { - final org.drip.specialfunction.digamma.CumulativeSeriesEstimator abramowitzStegun2007 = - org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); + final CumulativeSeriesEstimator abramowitzStegun2007 = + CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); - try - { - return new org.drip.function.definition.R1ToR1Property ( - org.drip.function.definition.R1ToR1Property.LT, - new org.drip.function.definition.R1ToR1 (null) - { + try { + return new R1ToR1Property ( + R1ToR1Property.LT, + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::ElezovicGiordanoPecaricLeftBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::ElezovicGiordanoPecaricLeftBound::evaluate => Invalid Inputs" + ); } - return java.lang.Math.log (z + 0.5) - 1. / z; + return Math.log (z + 0.5) - 1. / z; } }, - new org.drip.function.definition.R1ToR1 (null) - { + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::ElezovicGiordanoPecaricLeftBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::ElezovicGiordanoPecaricLeftBound::evaluate => Invalid Inputs" + ); } return abramowitzStegun2007.evaluate (z); } }, - org.drip.function.definition.R1ToR1Property.MISMATCH_TOLERANCE + R1ToR1Property.MISMATCH_TOLERANCE ); - } - catch (java.lang.Exception e) - { + } catch (Exception e) { e.printStackTrace(); } @@ -515,54 +510,45 @@ public static final org.drip.function.definition.R1ToR1Property ElezovicGiordano * @return The Elezovic-Giordano-Pecaric Right Bound Inequality Verifier */ - public static final org.drip.function.definition.R1ToR1Property ElezovicGiordanoPecaricRightBound() + public static final R1ToR1Property ElezovicGiordanoPecaricRightBound() { - final org.drip.specialfunction.digamma.CumulativeSeriesEstimator abramowitzStegun2007 = - org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); + final CumulativeSeriesEstimator abramowitzStegun2007 = + CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); - try - { - return new org.drip.function.definition.R1ToR1Property ( - org.drip.function.definition.R1ToR1Property.GT, - new org.drip.function.definition.R1ToR1 (null) - { + try { + return new R1ToR1Property ( + R1ToR1Property.GT, + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::ElezovicGiordanoPecaricRightBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::ElezovicGiordanoPecaricRightBound::evaluate => Invalid Inputs" + ); } - return java.lang.Math.log ( - z + java.lang.Math.exp ( - -org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI - ) - ) - 1. / z; + return Math.log (z + Math.exp (Definitions.EULER_MASCHERONI)) - 1. / z; } }, - new org.drip.function.definition.R1ToR1 (null) - { + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::ElezovicGiordanoPecaricRightBound::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::ElezovicGiordanoPecaricRightBound::evaluate => Invalid Inputs" + ); } return abramowitzStegun2007.evaluate (z); } }, - org.drip.function.definition.R1ToR1Property.MISMATCH_TOLERANCE + R1ToR1Property.MISMATCH_TOLERANCE ); - } - catch (java.lang.Exception e) - { + } catch (Exception e) { e.printStackTrace(); } @@ -577,51 +563,46 @@ public static final org.drip.function.definition.R1ToR1Property ElezovicGiordano * @return The Alzer (1997) Digamma Difference Lemma Verifier */ - public static final org.drip.function.definition.R1ToR1Property AlzerDifference1997 ( + public static final R1ToR1Property AlzerDifference1997 ( final double s) { - final org.drip.specialfunction.digamma.CumulativeSeriesEstimator abramowitzStegun2007 = - org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); + final CumulativeSeriesEstimator abramowitzStegun2007 = + CumulativeSeriesEstimator.AbramowitzStegun2007 (1638400); - try - { - return new org.drip.function.definition.R1ToR1Property ( - org.drip.function.definition.R1ToR1Property.LT, - new org.drip.function.definition.R1ToR1 (null) - { + try { + return new R1ToR1Property ( + R1ToR1Property.LT, + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::AlzerDifference1997::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::AlzerDifference1997::evaluate => Invalid Inputs" + ); } return (1. - s) / (z + s); } }, - new org.drip.function.definition.R1ToR1 (null) - { + new R1ToR1 (null) { @Override public double evaluate ( final double z) - throws java.lang.Exception + throws Exception { - if (!org.drip.numerical.common.NumberUtil.IsValid (z)) - { - throw new java.lang.Exception - ("DigammaInequalityLemma::AlzerDifference1997::evaluate => Invalid Inputs"); + if (!NumberUtil.IsValid (z)) { + throw new Exception ( + "DigammaInequalityLemma::AlzerDifference1997::evaluate => Invalid Inputs" + ); } return abramowitzStegun2007.evaluate (z + 1) - abramowitzStegun2007.evaluate (z + s); } }, - org.drip.function.definition.R1ToR1Property.MISMATCH_TOLERANCE + R1ToR1Property.MISMATCH_TOLERANCE ); - } - catch (java.lang.Exception e) - { + } catch (Exception e) { e.printStackTrace(); }