From b35e3998333e8190bf07ade51dba30773b3a3d0b Mon Sep 17 00:00:00 2001
From: Elizabeth Hunt <elizabeth.hunt@simponic.xyz>
Date: Wed, 27 Sep 2023 10:10:33 -0600
Subject: [PATCH] fix bug in which err = 0

---
 homeworks/hw-2.org     |  80 ++++++-----------------------------------
 homeworks/hw-2.pdf     | Bin 65550 -> 68368 bytes
 homeworks/hw-2.tex     |  37 +++++++++----------
 src/approx/maceps.lisp |   1 +
 4 files changed, 31 insertions(+), 87 deletions(-)

diff --git a/homeworks/hw-2.org b/homeworks/hw-2.org
index 9dad2d3..29502d7 100644
--- a/homeworks/hw-2.org
+++ b/homeworks/hw-2.org
@@ -45,7 +45,6 @@ Computing $\epsilon_{\text{mac}}$ for single precision numbers
 | 1.0 | 4.7683716e-07 | 4.7683716e-07 |
 | 1.0 | 2.3841858e-07 | 2.3841858e-07 |
 | 1.0 | 1.1920929e-07 | 1.1920929e-07 |
-| 1.0 | 5.9604645e-08 |           0.0 |
 
 (with many rows truncated)
 
@@ -54,14 +53,14 @@ Computing $\epsilon_{\text{mac}}$ for single precision numbers
 | 1.0 |          0.25 |          0.25 |
 | 1.0 |         0.125 |         0.125 |
 | 1.0 |        0.0625 |        0.0625 |
+| 1.0 |       0.03125 |       0.03125 |
 | 1.0 | 1.9073486e-06 | 1.9073486e-06 |
 | 1.0 |  9.536743e-07 |  9.536743e-07 |
 | 1.0 | 4.7683716e-07 | 4.7683716e-07 |
 | 1.0 | 2.3841858e-07 | 2.3841858e-07 |
 | 1.0 | 1.1920929e-07 | 1.1920929e-07 |
-| 1.0 | 5.9604645e-08 |           0.0 |
 
-$\epsilon_{\text{mac}}$ \approx 5.9604 \cdot 10^{-8}
+$\epsilon_{\text{mac single precision}}$ \approx 1.192(10^-7)
 
 * Question Two
 Computing $\epsilon_{\text{mac}}$ for double precision numbers:
@@ -75,62 +74,6 @@ Computing $\epsilon_{\text{mac}}$ for double precision numbers:
                          :domain-values domain-values)))
 #+END_SRC
 
-#+RESULTS:
-|     a |                      h |                    err |
-| 1.0d0 |                  0.5d0 |                  0.5d0 |
-| 1.0d0 |                 0.25d0 |                 0.25d0 |
-| 1.0d0 |                0.125d0 |                0.125d0 |
-| 1.0d0 |               0.0625d0 |               0.0625d0 |
-| 1.0d0 |              0.03125d0 |              0.03125d0 |
-| 1.0d0 |             0.015625d0 |             0.015625d0 |
-| 1.0d0 |            0.0078125d0 |            0.0078125d0 |
-| 1.0d0 |           0.00390625d0 |           0.00390625d0 |
-| 1.0d0 |          0.001953125d0 |          0.001953125d0 |
-| 1.0d0 |            9.765625d-4 |            9.765625d-4 |
-| 1.0d0 |           4.8828125d-4 |           4.8828125d-4 |
-| 1.0d0 |          2.44140625d-4 |          2.44140625d-4 |
-| 1.0d0 |         1.220703125d-4 |         1.220703125d-4 |
-| 1.0d0 |         6.103515625d-5 |         6.103515625d-5 |
-| 1.0d0 |        3.0517578125d-5 |        3.0517578125d-5 |
-| 1.0d0 |       1.52587890625d-5 |       1.52587890625d-5 |
-| 1.0d0 |       7.62939453125d-6 |       7.62939453125d-6 |
-| 1.0d0 |      3.814697265625d-6 |      3.814697265625d-6 |
-| 1.0d0 |     1.9073486328125d-6 |     1.9073486328125d-6 |
-| 1.0d0 |     9.5367431640625d-7 |     9.5367431640625d-7 |
-| 1.0d0 |    4.76837158203125d-7 |    4.76837158203125d-7 |
-| 1.0d0 |   2.384185791015625d-7 |   2.384185791015625d-7 |
-| 1.0d0 |  1.1920928955078125d-7 |  1.1920928955078125d-7 |
-| 1.0d0 |   5.960464477539063d-8 |   5.960464477539063d-8 |
-| 1.0d0 |  2.9802322387695313d-8 |  2.9802322387695313d-8 |
-| 1.0d0 |  1.4901161193847656d-8 |  1.4901161193847656d-8 |
-| 1.0d0 |   7.450580596923828d-9 |   7.450580596923828d-9 |
-| 1.0d0 |   3.725290298461914d-9 |   3.725290298461914d-9 |
-| 1.0d0 |   1.862645149230957d-9 |   1.862645149230957d-9 |
-| 1.0d0 |  9.313225746154785d-10 |  9.313225746154785d-10 |
-| 1.0d0 |  4.656612873077393d-10 |  4.656612873077393d-10 |
-| 1.0d0 | 2.3283064365386963d-10 | 2.3283064365386963d-10 |
-| 1.0d0 | 1.1641532182693481d-10 | 1.1641532182693481d-10 |
-| 1.0d0 |  5.820766091346741d-11 |  5.820766091346741d-11 |
-| 1.0d0 | 2.9103830456733704d-11 | 2.9103830456733704d-11 |
-| 1.0d0 | 1.4551915228366852d-11 | 1.4551915228366852d-11 |
-| 1.0d0 |  7.275957614183426d-12 |  7.275957614183426d-12 |
-| 1.0d0 |  3.637978807091713d-12 |  3.637978807091713d-12 |
-| 1.0d0 | 1.8189894035458565d-12 | 1.8189894035458565d-12 |
-| 1.0d0 |  9.094947017729282d-13 |  9.094947017729282d-13 |
-| 1.0d0 |  4.547473508864641d-13 |  4.547473508864641d-13 |
-| 1.0d0 | 2.2737367544323206d-13 | 2.2737367544323206d-13 |
-| 1.0d0 | 1.1368683772161603d-13 | 1.1368683772161603d-13 |
-| 1.0d0 |  5.684341886080802d-14 |  5.684341886080802d-14 |
-| 1.0d0 |  2.842170943040401d-14 |  2.842170943040401d-14 |
-| 1.0d0 | 1.4210854715202004d-14 | 1.4210854715202004d-14 |
-| 1.0d0 |  7.105427357601002d-15 |  7.105427357601002d-15 |
-| 1.0d0 |  3.552713678800501d-15 |  3.552713678800501d-15 |
-| 1.0d0 | 1.7763568394002505d-15 | 1.7763568394002505d-15 |
-| 1.0d0 |  8.881784197001252d-16 |  8.881784197001252d-16 |
-| 1.0d0 |  4.440892098500626d-16 |  4.440892098500626d-16 |
-| 1.0d0 |  2.220446049250313d-16 |  2.220446049250313d-16 |
-| 1.0d0 | 1.1102230246251565d-16 |                  0.0d0 |
-
 (with many rows truncated)
 |     a |                      h |                    err |
 | 1.0d0 |                  0.5d0 |                  0.5d0 |
@@ -148,9 +91,8 @@ Computing $\epsilon_{\text{mac}}$ for double precision numbers:
 | 1.0d0 |  8.881784197001252d-16 |  8.881784197001252d-16 |
 | 1.0d0 |  4.440892098500626d-16 |  4.440892098500626d-16 |
 | 1.0d0 |  2.220446049250313d-16 |  2.220446049250313d-16 |
-| 1.0d0 | 1.1102230246251565d-16 |                  0.0d0 |
 
-Thus, $\epsilon_{\text{mac}}$ \approx 1.1102 \cdot 10^{-16}
+Thus, $\epsilon_{\text{mac double precision}}$ \approx 2.220 \cdot 10^{-16}
 
 * Question Three - |v|_2
 #+BEGIN_SRC lisp :session t
@@ -204,9 +146,9 @@ Thus, $\epsilon_{\text{mac}}$ \approx 1.1102 \cdot 10^{-16}
 
 * Question Six - ||v - u|| via |v|_{2}
 #+BEGIN_SRC lisp :session t
-  (let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
-         (vs2 '((7 9) (2 2) (8 -1) (4 4)))
-         (2-norm (lizfcm.vector:p-norm 2)))
+  (let ((vs '((1 1) (2 3) (4 5) (-1 2)))
+        (vs2 '((7 9) (2 2) (8 -1) (4 4)))
+        (2-norm (lizfcm.vector:p-norm 2)))
     (lizfcm.utils:table (:headers '("v1" "v2" "2-norm-d")
                          :domain-order (v1 v2)
                          :domain-values (mapcar (lambda (v1 v2)
@@ -225,9 +167,9 @@ Thus, $\epsilon_{\text{mac}}$ \approx 1.1102 \cdot 10^{-16}
 
 * Question Seven - ||v - u|| via |v|_{1}
 #+BEGIN_SRC lisp :session t
-  (let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
-         (vs2 '((7 9) (2 2) (8 -1) (4 4)))
-         (1-norm (lizfcm.vector:p-norm 1)))
+  (let ((vs '((1 1) (2 3) (4 5) (-1 2)))
+        (vs2 '((7 9) (2 2) (8 -1) (4 4)))
+        (1-norm (lizfcm.vector:p-norm 1)))
     (lizfcm.utils:table (:headers '("v1" "v2" "1-norm-d")
                          :domain-order (v1 v2)
                          :domain-values (mapcar (lambda (v1 v2)
@@ -246,8 +188,8 @@ Thus, $\epsilon_{\text{mac}}$ \approx 1.1102 \cdot 10^{-16}
 
 * Question Eight - ||v - u|| via |v|_{\infty}
 #+BEGIN_SRC lisp :session t
-  (let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
-         (vs2 '((7 9) (2 2) (8 -1) (4 4))))
+  (let ((vs '((1 1) (2 3) (4 5) (-1 2)))
+        (vs2 '((7 9) (2 2) (8 -1) (4 4))))
     (lizfcm.utils:table (:headers '("v1" "v2" "max-norm-d")
                          :domain-order (v1 v2)
                          :domain-values (mapcar (lambda (v1 v2)
diff --git a/homeworks/hw-2.pdf b/homeworks/hw-2.pdf
index fed1f4400b8bca65529034e45c2cb0242918f351..b719796c0530fb1579f037fcf8703e0f087f7a43 100644
GIT binary patch
delta 10798
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diff --git a/homeworks/hw-2.tex b/homeworks/hw-2.tex
index 5155448..e0aa172 100644
--- a/homeworks/hw-2.tex
+++ b/homeworks/hw-2.tex
@@ -1,4 +1,4 @@
-% Created 2023-09-25 Mon 09:52
+% Created 2023-09-27 Wed 10:09
 % Intended LaTeX compiler: pdflatex
 \documentclass[11pt]{article}
 \usepackage[utf8]{inputenc}
@@ -29,15 +29,16 @@
 \setlength\parindent{0pt}
 
 \section{Question One}
-\label{sec:orga203815}
+\label{sec:orga21c813}
 Computing \(\epsilon_{\text{mac}}\) for single precision numbers
 
 \begin{verbatim}
-(load "../cl/lizfcm.asd")
+(load "../lizfcm.asd")
 (ql:quickload :lizfcm)
 
-(let ((domain-values (lizfcm.approx:compute-maceps 1.0
-                                                   (lambda (x) x))))
+(let ((domain-values (lizfcm.approx:compute-maceps (lambda (x) x)
+                                                   1.0
+                                                   1.0)))
   (lizfcm.utils:table (:headers '("a" "h" "err")
                        :domain-order (a h err)
                        :domain-values domain-values)))
@@ -52,24 +53,25 @@ a & h & err\\[0pt]
 1.0 & 0.25 & 0.25\\[0pt]
 1.0 & 0.125 & 0.125\\[0pt]
 1.0 & 0.0625 & 0.0625\\[0pt]
+1.0 & 0.03125 & 0.03125\\[0pt]
 1.0 & 1.9073486e-06 & 1.9073486e-06\\[0pt]
 1.0 & 9.536743e-07 & 9.536743e-07\\[0pt]
 1.0 & 4.7683716e-07 & 4.7683716e-07\\[0pt]
 1.0 & 2.3841858e-07 & 2.3841858e-07\\[0pt]
 1.0 & 1.1920929e-07 & 1.1920929e-07\\[0pt]
-1.0 & 5.9604645e-08 & 0.0\\[0pt]
 \end{tabular}
 \end{center}
 
-\(\epsilon_{\text{mac}}\) \(\approx\) 5.9604 \(\cdot\) 10\textsuperscript{-8}
+\(\epsilon_{\text{mac single precision}}\) \(\approx\) 1.192(10\textsuperscript{-7})
 
 \section{Question Two}
-\label{sec:orgdd79be1}
+\label{sec:org06c4a23}
 Computing \(\epsilon_{\text{mac}}\) for double precision numbers:
 
 \begin{verbatim}
-(let ((domain-values (lizfcm.approx:compute-maceps 1.0d0
-                                                   (lambda (x) x))))
+(let ((domain-values (lizfcm.approx:compute-maceps (lambda (x) x)
+                                                   1.0d0
+                                                   1.0d0)))
   (lizfcm.utils:table (:headers '("a" "h" "err")
                        :domain-order (a h err)
                        :domain-values domain-values)))
@@ -94,14 +96,13 @@ a & h & err\\[0pt]
 1.0d0 & 8.881784197001252d-16 & 8.881784197001252d-16\\[0pt]
 1.0d0 & 4.440892098500626d-16 & 4.440892098500626d-16\\[0pt]
 1.0d0 & 2.220446049250313d-16 & 2.220446049250313d-16\\[0pt]
-1.0d0 & 1.1102230246251565d-16 & 0.0d0\\[0pt]
 \end{tabular}
 \end{center}
 
-Thus, \(\epsilon_{\text{mac}}\) \(\approx\) 1.1102 \(\cdot\) 10\textsuperscript{-16}
+Thus, \(\epsilon_{\text{mac double precision}}\) \(\approx\) 2.220 \(\cdot\) 10\textsuperscript{-16}
 
 \section{Question Three - |v|\textsubscript{2}}
-\label{sec:org04608d9}
+\label{sec:orgf181ba7}
 \begin{verbatim}
 (let ((vs '((1 1) (2 3) (4 5) (-1 2)))
       (2-norm (lizfcm.vector:p-norm 2)))
@@ -123,7 +124,7 @@ x & y & 2norm\\[0pt]
 \end{center}
 
 \section{Question Four - |v|\textsubscript{1}}
-\label{sec:orgfb57f3a}
+\label{sec:org2196087}
 \begin{verbatim}
 (let ((vs '((1 1) (2 3) (4 5) (-1 2)))
       (1-norm (lizfcm.vector:p-norm 1)))
@@ -145,7 +146,7 @@ x & y & 1norm\\[0pt]
 \end{center}
 
 \section{Question Five - |v|\textsubscript{\(\infty\)}}
-\label{sec:org7bbdf04}
+\label{sec:org11b8894}
 \begin{verbatim}
 (let ((vs '((1 1) (2 3) (4 5) (-1 2))))
   (lizfcm.utils:table (:headers '("x" "y" "max-norm")
@@ -166,7 +167,7 @@ x & y & infty-norm\\[0pt]
 \end{center}
 
 \section{Question Six - ||v - u|| via |v|\textsubscript{2}}
-\label{sec:orge36996c}
+\label{sec:orga2324b2}
 \begin{verbatim}
 (let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
        (vs2 '((7 9) (2 2) (8 -1) (4 4)))
@@ -192,7 +193,7 @@ v1 & v2 & 2-norm\\[0pt]
 \end{center}
 
 \section{Question Seven - ||v - u|| via |v|\textsubscript{1}}
-\label{sec:orgd1577f0}
+\label{sec:org388fbc7}
 \begin{verbatim}
 (let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
        (vs2 '((7 9) (2 2) (8 -1) (4 4)))
@@ -218,7 +219,7 @@ v1 & v2 & 1-norm-d\\[0pt]
 \end{center}
 
 \section{Question Eight - ||v - u|| via |v|\textsubscript{\(\infty\)}}
-\label{sec:org2661676}
+\label{sec:org6e77f76}
 \begin{verbatim}
 (let* ((vs '((1 1) (2 3) (4 5) (-1 2)))
        (vs2 '((7 9) (2 2) (8 -1) (4 4))))
diff --git a/src/approx/maceps.lisp b/src/approx/maceps.lisp
index ad234e8..debaa67 100644
--- a/src/approx/maceps.lisp
+++ b/src/approx/maceps.lisp
@@ -8,4 +8,5 @@
           (setf h (/ h 2)
                 err (abs (- (funcall f (+ a h))
                             (funcall f a))))
+          when (> err 0)
           collect (list a h err))))