simponic/lizfcm
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
1a8c81d07e
lizfcm/homeworks/hw-2.org

265 lines
10 KiB
Org Mode
Raw Normal View History

add september notes & hw2 code / pdf
2023-09-25 12:36:23 -04:00
#+TITLE: HW 02
#+AUTHOR: Elizabeth Hunt
#+STARTUP: entitiespretty fold inlineimages
#+LATEX_HEADER: \notindent \notag \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
#+LATEX: \setlength\parindent{0pt}
#+OPTIONS: toc:nil
* Question One
Computing $\epsilon_{\text{mac}}$ for single precision numbers
#+BEGIN_SRC lisp :session t :results table
keep unit tests but make directory structure more consistent with requirements i did not read
2023-09-27 11:53:37 -04:00
(load "../lizfcm.asd")
add september notes & hw2 code / pdf
2023-09-25 12:36:23 -04:00
(ql:quickload :lizfcm)
fix compute-maceps arguments
2023-09-27 11:38:55 -04:00
(let ((domain-values (lizfcm.approx:compute-maceps (lambda (x) x)
1.0
1.0)))
add september notes & hw2 code / pdf
2023-09-25 12:36:23 -04:00
(lizfcm.utils:table (:headers '("a" "h" "err")
:domain-order (a h err)
:domain-values domain-values)))
#+END_SRC
fix compute-maceps arguments
2023-09-27 11:38:55 -04:00
#+RESULTS:
| a | h | err |
| 1.0 | 0.5 | 0.5 |
| 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 | 0.015625 | 0.015625 |
| 1.0 | 0.0078125 | 0.0078125 |
| 1.0 | 0.00390625 | 0.00390625 |
| 1.0 | 0.001953125 | 0.001953125 |
| 1.0 | 0.0009765625 | 0.0009765625 |
| 1.0 | 0.00048828125 | 0.00048828125 |
| 1.0 | 0.00024414063 | 0.00024414063 |
| 1.0 | 0.00012207031 | 0.00012207031 |
| 1.0 | 6.1035156e-05 | 6.1035156e-05 |
| 1.0 | 3.0517578e-05 | 3.0517578e-05 |
| 1.0 | 1.5258789e-05 | 1.5258789e-05 |
| 1.0 | 7.6293945e-06 | 7.6293945e-06 |
| 1.0 | 3.8146973e-06 | 3.8146973e-06 |
| 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 |
add september notes & hw2 code / pdf
2023-09-25 12:36:23 -04:00
(with many rows truncated)
| a | h | err |
| 1.0 | 0.5 | 0.5 |
| 1.0 | 0.25 | 0.25 |
| 1.0 | 0.125 | 0.125 |
| 1.0 | 0.0625 | 0.0625 |
| 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}
* Question Two
Computing $\epsilon_{\text{mac}}$ for double precision numbers:
#+BEGIN_SRC lisp :session t :results table
fix compute-maceps arguments
2023-09-27 11:38:55 -04:00
(let ((domain-values (lizfcm.approx:compute-maceps (lambda (x) x)
1.0d0
1.0d0)))
add september notes & hw2 code / pdf
2023-09-25 12:36:23 -04:00
(lizfcm.utils:table (:headers '("a" "h" "err")
:domain-order (a h err)
:domain-values domain-values)))
#+END_SRC
fix compute-maceps arguments
2023-09-27 11:38:55 -04:00
#+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 |
add september notes & hw2 code / pdf
2023-09-25 12:36:23 -04:00
(with many rows truncated)
| 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 | 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 |
Thus, $\epsilon_{\text{mac}}$ \approx 1.1102 \cdot 10^{-16}
* Question Three - |v|_2
#+BEGIN_SRC lisp :session t
(let ((vs '((1 1) (2 3) (4 5) (-1 2)))
(2-norm (lizfcm.vector:p-norm 2)))
(lizfcm.utils:table (:headers '("x" "y" "2norm")
:domain-order (x y)
:domain-values vs)
(funcall 2-norm (list x y))))
#+END_SRC
| x | y | 2norm |
| 1 | 1 | 1.4142135 |
| 2 | 3 | 3.6055512 |
| 4 | 5 | 6.4031243 |
| -1 | 2 | 2.236068 |
* Question Four - |v|_1
#+BEGIN_SRC lisp :session t
(let ((vs '((1 1) (2 3) (4 5) (-1 2)))
(1-norm (lizfcm.vector:p-norm 1)))
(lizfcm.utils:table (:headers '("x" "y" "1norm")
:domain-order (x y)
:domain-values vs)
(funcall 1-norm (list x y))))
#+END_SRC
| x | y | 1norm |
| 1 | 1 | 2 |
| 2 | 3 | 5 |
| 4 | 5 | 9 |
| -1 | 2 | 3 |
* Question Five - |v|_{\infty}
#+BEGIN_SRC lisp :session t
(let ((vs '((1 1) (2 3) (4 5) (-1 2))))
(lizfcm.utils:table (:headers '("x" "y" "max-norm")
:domain-order (x y)
:domain-values vs)
(lizfcm.vector:max-norm (list x y))))
#+END_SRC
| x | y | infty-norm |
| 1 | 1 | 1 |
| 2 | 3 | 3 |
| 4 | 5 | 5 |
| -1 | 2 | 2 |
* 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)))
(lizfcm.utils:table (:headers '("v1" "v2" "2-norm-d")
:domain-order (v1 v2)
:domain-values (mapcar (lambda (v1 v2)
(list v1 v2))
vs
vs2))
(lizfcm.vector:distance v1 v2 2-norm)))
#+END_SRC
| v1 | v2 | 2-norm |
| (1 1) | (7 9) | 10.0 |
| (2 3) | (2 2) | 1.0 |
| (4 5) | (8 -1) | 7.2111025 |
| (-1 2) | (4 4) | 5.3851647 |
* 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)))
(lizfcm.utils:table (:headers '("v1" "v2" "1-norm-d")
:domain-order (v1 v2)
:domain-values (mapcar (lambda (v1 v2)
(list v1 v2))
vs
vs2))
(lizfcm.vector:distance v1 v2 1-norm)))
#+END_SRC
| v1 | v2 | 1-norm-d |
| (1 1) | (7 9) | 14 |
| (2 3) | (2 2) | 1 |
| (4 5) | (8 -1) | 10 |
| (-1 2) | (4 4) | 7 |
* 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))))
(lizfcm.utils:table (:headers '("v1" "v2" "max-norm-d")
:domain-order (v1 v2)
:domain-values (mapcar (lambda (v1 v2)
(list v1 v2))
vs
vs2))
(lizfcm.vector:distance v1 v2 'lizfcm.vector:max-norm)))
#+END_SRC
| v1 | v2 | max-norm-d |
| (1 1) | (7 9) | -6 |
| (2 3) | (2 2) | 1 |
| (4 5) | (8 -1) | 6 |
| (-1 2) | (4 4) | -2 |
Reference in New Issue Copy Permalink