Why is this code so slow? The 2019 Stack Overflow Developer Survey Results Are InWhy is...
What do these terms in Caesar's Gallic Wars mean?
How come people say “Would of”?
Worn-tile Scrabble
How did passengers keep warm on sail ships?
"as much details as you can remember"
Button changing its text & action. Good or terrible?
Why is this code so slow?
What is the motivation for a law requiring 2 parties to consent for recording a conversation
Why are there uneven bright areas in this photo of black hole?
Did any laptop computers have a built-in 5 1/4 inch floppy drive?
Can there be female White Walkers?
Is an up-to-date browser secure on an out-of-date OS?
Does adding complexity mean a more secure cipher?
Why doesn't UInt have a toDouble()?
Likelihood that a superbug or lethal virus could come from a landfill
How do I free up internal storage if I don't have any apps downloaded?
What must someone know in statistics and machine learning?
Why did Peik say, "I'm not an animal"?
Is bread bad for ducks?
How can I define good in a religion that claims no moral authority?
Accepted by European university, rejected by all American ones I applied to? Possible reasons?
What does もの mean in this sentence?
Old scifi movie from the 50s or 60s with men in solid red uniforms who interrogate a spy from the past
How to type a long/em dash `—`
Why is this code so slow?
The 2019 Stack Overflow Developer Survey Results Are InWhy is FindRoot initial value far from the specified one?Newton-Raphson Method and the Van der Waal Equation Coding questionWhat are the hidden specifications for FindRootHow can I resolve the insufficient memory to complete the computation problem for solving function with iterated variables?Why does this function inside FindRoot fail to evaluate?Very slow mathematica finite differencesManipulate+FindRoot+Plot3D very slow/crashAttacking a “Mathematica can't solve” problemErrors using FindRoot on slow numerical functionAvoiding a for loop to create a list
$begingroup$
This code for the first five iterations the speed is okay , but after that the speed is very slow, I cannot understand what is wrong with this? Would you please help me fix it?
Clear[A, r, x, s, e]
s := 0.3405
e := 1.6539*10^-21
u[0] := 0.
u[1] := 0.1
A[r_] := A[r] =
Piecewise[{{r - 2.5 s - 48*e *s^12*r^-13 + 24*e*s^6*r^-7,
r > 2.5 s}, {-48*e*s^12*r^-13 + 24*e*s^6*r^-7,
s [LessSlantEqual] r [LessSlantEqual] 2.5 s}, {r - s -
24*e*s^-1, r < s}}]
For[i = 2, i < 101,
i++, { u[i_] :=
x /. FindRoot[
u[i - 1] +
1/(i^2 (u[i - 1] - u[i - 2])^2) (u[i - 1] - u[i - 2]) -
0.9 A[x] == x , {x, 1.}]; Print[u[i]]}]
equation-solving iteration
asked 2 hours ago
morapimorapi
203
$endgroup$
add a comment |
$begingroup$
This code for the first five iterations the speed is okay , but after that the speed is very slow, I cannot understand what is wrong with this? Would you please help me fix it?
Clear[A, r, x, s, e]
s := 0.3405
e := 1.6539*10^-21
u[0] := 0.
u[1] := 0.1
A[r_] := A[r] =
Piecewise[{{r - 2.5 s - 48*e *s^12*r^-13 + 24*e*s^6*r^-7,
r > 2.5 s}, {-48*e*s^12*r^-13 + 24*e*s^6*r^-7,
s [LessSlantEqual] r [LessSlantEqual] 2.5 s}, {r - s -
24*e*s^-1, r < s}}]
For[i = 2, i < 101,
i++, { u[i_] :=
x /. FindRoot[
u[i - 1] +
1/(i^2 (u[i - 1] - u[i - 2])^2) (u[i - 1] - u[i - 2]) -
0.9 A[x] == x , {x, 1.}]; Print[u[i]]}]
equation-solving iteration
asked 2 hours ago
morapimorapi
203
$endgroup$
add a comment |
$begingroup$
This code for the first five iterations the speed is okay , but after that the speed is very slow, I cannot understand what is wrong with this? Would you please help me fix it?
Clear[A, r, x, s, e]
s := 0.3405
e := 1.6539*10^-21
u[0] := 0.
u[1] := 0.1
A[r_] := A[r] =
Piecewise[{{r - 2.5 s - 48*e *s^12*r^-13 + 24*e*s^6*r^-7,
r > 2.5 s}, {-48*e*s^12*r^-13 + 24*e*s^6*r^-7,
s [LessSlantEqual] r [LessSlantEqual] 2.5 s}, {r - s -
24*e*s^-1, r < s}}]
For[i = 2, i < 101,
i++, { u[i_] :=
x /. FindRoot[
u[i - 1] +
1/(i^2 (u[i - 1] - u[i - 2])^2) (u[i - 1] - u[i - 2]) -
0.9 A[x] == x , {x, 1.}]; Print[u[i]]}]
equation-solving iteration
asked 2 hours ago
morapimorapi
203
$endgroup$
This code for the first five iterations the speed is okay , but after that the speed is very slow, I cannot understand what is wrong with this? Would you please help me fix it?
Clear[A, r, x, s, e]
s := 0.3405
e := 1.6539*10^-21
u[0] := 0.
u[1] := 0.1
A[r_] := A[r] =
Piecewise[{{r - 2.5 s - 48*e *s^12*r^-13 + 24*e*s^6*r^-7,
r > 2.5 s}, {-48*e*s^12*r^-13 + 24*e*s^6*r^-7,
s [LessSlantEqual] r [LessSlantEqual] 2.5 s}, {r - s -
24*e*s^-1, r < s}}]
For[i = 2, i < 101,
i++, { u[i_] :=
x /. FindRoot[
u[i - 1] +
1/(i^2 (u[i - 1] - u[i - 2])^2) (u[i - 1] - u[i - 2]) -
0.9 A[x] == x , {x, 1.}]; Print[u[i]]}]
equation-solving iteration
equation-solving iteration
asked 2 hours ago
morapimorapi
203
asked 2 hours ago
morapimorapi
203
asked 2 hours ago
morapimorapi
203
asked 2 hours ago
morapimorapi
203
asked 2 hours ago
morapimorapi
203
203
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I recommend you learn the distinction between immediate (=) and delayed (:=) assignments. They make the difference between slow and fast code here. Start with this tutorial or this book chapter, then look at memoization.
s = 0.3405;
e = 1.6539*10^-21;
u[0] = 0.;
u[1] = 0.1;
A[r_] = Piecewise[{{r - 2.5 s - 48*e*s^12*r^-13 + 24*e*s^6*r^-7, r > 2.5 s},
{-48*e*s^12*r^-13 + 24*e*s^6*r^-7, s <= r <= 2.5 s},
{r - s - 24*e*s^-1, r < s}}];
u[i_] := u[i] = x /. FindRoot[
u[i - 1] + 1/(i^2 (u[i - 1] - u[i - 2])^2) (u[i - 1] - u[i - 2]) - 0.9 A[x] == x, {x, 1.}]
Array[u, 100]
{0.1, 1.77164, 1.37065, 1.04259, 0.887781, 0.708344, 0.59461,
0.457228, 0.367364, 0.296071, 0.256104, 0.20463, 0.208487, 1.20917,
1.04197, 0.939331, 0.879865, 0.827963, 0.774591, 0.72775, 0.67934,
0.63666, 0.592369, 0.553172, 0.512352, 0.476112, 0.438261, 0.404563,
0.369277, 0.339073, 0.321616, 0.301118, 0.296195, 0.224688, 0.273538,
0.31357, 0.33593, 0.366902, 0.38813, 0.417572, 0.437777, 0.465834,
0.48511, 0.511907, 0.530336, 0.55598, 0.573633, 0.598219, 0.615159,
0.638772, 0.655054, 0.677768, 0.693441, 0.715321, 0.73043, 0.751535,
0.766118, 0.786503, 0.800596, 0.820306, 0.833941, 0.852182, 0.85901,
0.874152, 0.871531, 0.78396, 0.781416, 0.696402, 0.693931, 0.611329,
0.608927, 0.528603, 0.526267, 0.448099, 0.445825, 0.369701, 0.367485,
0.315658, 0.325798, 0.341207, 0.351098, 0.366134, 0.375788, 0.390468,
0.399897, 0.414237, 0.42345, 0.437466, 0.446473, 0.46018, 0.46899,
0.4824, 0.491022, 0.504149, 0.51259, 0.525444, 0.533712, 0.546306,
0.554408, 0.56675}
(takes about 5 seconds)
Alternatively, use
Table[u[i], {i, 1, 100}]
(same result). Your combination of For and Print shows the results but doesn't let you keep using them for more calculations.
answered 1 hour ago
RomanRoman
5,11011130
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "387"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f195054%2fwhy-is-this-code-so-slow%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I recommend you learn the distinction between immediate (=) and delayed (:=) assignments. They make the difference between slow and fast code here. Start with this tutorial or this book chapter, then look at memoization.
s = 0.3405;
e = 1.6539*10^-21;
u[0] = 0.;
u[1] = 0.1;
A[r_] = Piecewise[{{r - 2.5 s - 48*e*s^12*r^-13 + 24*e*s^6*r^-7, r > 2.5 s},
{-48*e*s^12*r^-13 + 24*e*s^6*r^-7, s <= r <= 2.5 s},
{r - s - 24*e*s^-1, r < s}}];
u[i_] := u[i] = x /. FindRoot[
u[i - 1] + 1/(i^2 (u[i - 1] - u[i - 2])^2) (u[i - 1] - u[i - 2]) - 0.9 A[x] == x, {x, 1.}]
Array[u, 100]
{0.1, 1.77164, 1.37065, 1.04259, 0.887781, 0.708344, 0.59461,
0.457228, 0.367364, 0.296071, 0.256104, 0.20463, 0.208487, 1.20917,
1.04197, 0.939331, 0.879865, 0.827963, 0.774591, 0.72775, 0.67934,
0.63666, 0.592369, 0.553172, 0.512352, 0.476112, 0.438261, 0.404563,
0.369277, 0.339073, 0.321616, 0.301118, 0.296195, 0.224688, 0.273538,
0.31357, 0.33593, 0.366902, 0.38813, 0.417572, 0.437777, 0.465834,
0.48511, 0.511907, 0.530336, 0.55598, 0.573633, 0.598219, 0.615159,
0.638772, 0.655054, 0.677768, 0.693441, 0.715321, 0.73043, 0.751535,
0.766118, 0.786503, 0.800596, 0.820306, 0.833941, 0.852182, 0.85901,
0.874152, 0.871531, 0.78396, 0.781416, 0.696402, 0.693931, 0.611329,
0.608927, 0.528603, 0.526267, 0.448099, 0.445825, 0.369701, 0.367485,
0.315658, 0.325798, 0.341207, 0.351098, 0.366134, 0.375788, 0.390468,
0.399897, 0.414237, 0.42345, 0.437466, 0.446473, 0.46018, 0.46899,
0.4824, 0.491022, 0.504149, 0.51259, 0.525444, 0.533712, 0.546306,
0.554408, 0.56675}
(takes about 5 seconds)
Alternatively, use
Table[u[i], {i, 1, 100}]
(same result). Your combination of For and Print shows the results but doesn't let you keep using them for more calculations.
answered 1 hour ago
RomanRoman
5,11011130
$endgroup$
add a comment |
$begingroup$
I recommend you learn the distinction between immediate (=) and delayed (:=) assignments. They make the difference between slow and fast code here. Start with this tutorial or this book chapter, then look at memoization.
s = 0.3405;
e = 1.6539*10^-21;
u[0] = 0.;
u[1] = 0.1;
A[r_] = Piecewise[{{r - 2.5 s - 48*e*s^12*r^-13 + 24*e*s^6*r^-7, r > 2.5 s},
{-48*e*s^12*r^-13 + 24*e*s^6*r^-7, s <= r <= 2.5 s},
{r - s - 24*e*s^-1, r < s}}];
u[i_] := u[i] = x /. FindRoot[
u[i - 1] + 1/(i^2 (u[i - 1] - u[i - 2])^2) (u[i - 1] - u[i - 2]) - 0.9 A[x] == x, {x, 1.}]
Array[u, 100]
{0.1, 1.77164, 1.37065, 1.04259, 0.887781, 0.708344, 0.59461,
0.457228, 0.367364, 0.296071, 0.256104, 0.20463, 0.208487, 1.20917,
1.04197, 0.939331, 0.879865, 0.827963, 0.774591, 0.72775, 0.67934,
0.63666, 0.592369, 0.553172, 0.512352, 0.476112, 0.438261, 0.404563,
0.369277, 0.339073, 0.321616, 0.301118, 0.296195, 0.224688, 0.273538,
0.31357, 0.33593, 0.366902, 0.38813, 0.417572, 0.437777, 0.465834,
0.48511, 0.511907, 0.530336, 0.55598, 0.573633, 0.598219, 0.615159,
0.638772, 0.655054, 0.677768, 0.693441, 0.715321, 0.73043, 0.751535,
0.766118, 0.786503, 0.800596, 0.820306, 0.833941, 0.852182, 0.85901,
0.874152, 0.871531, 0.78396, 0.781416, 0.696402, 0.693931, 0.611329,
0.608927, 0.528603, 0.526267, 0.448099, 0.445825, 0.369701, 0.367485,
0.315658, 0.325798, 0.341207, 0.351098, 0.366134, 0.375788, 0.390468,
0.399897, 0.414237, 0.42345, 0.437466, 0.446473, 0.46018, 0.46899,
0.4824, 0.491022, 0.504149, 0.51259, 0.525444, 0.533712, 0.546306,
0.554408, 0.56675}
(takes about 5 seconds)
Alternatively, use
Table[u[i], {i, 1, 100}]
(same result). Your combination of For and Print shows the results but doesn't let you keep using them for more calculations.
answered 1 hour ago
RomanRoman
5,11011130
$endgroup$
add a comment |
$begingroup$
I recommend you learn the distinction between immediate (=) and delayed (:=) assignments. They make the difference between slow and fast code here. Start with this tutorial or this book chapter, then look at memoization.
s = 0.3405;
e = 1.6539*10^-21;
u[0] = 0.;
u[1] = 0.1;
A[r_] = Piecewise[{{r - 2.5 s - 48*e*s^12*r^-13 + 24*e*s^6*r^-7, r > 2.5 s},
{-48*e*s^12*r^-13 + 24*e*s^6*r^-7, s <= r <= 2.5 s},
{r - s - 24*e*s^-1, r < s}}];
u[i_] := u[i] = x /. FindRoot[
u[i - 1] + 1/(i^2 (u[i - 1] - u[i - 2])^2) (u[i - 1] - u[i - 2]) - 0.9 A[x] == x, {x, 1.}]
Array[u, 100]
{0.1, 1.77164, 1.37065, 1.04259, 0.887781, 0.708344, 0.59461,
0.457228, 0.367364, 0.296071, 0.256104, 0.20463, 0.208487, 1.20917,
1.04197, 0.939331, 0.879865, 0.827963, 0.774591, 0.72775, 0.67934,
0.63666, 0.592369, 0.553172, 0.512352, 0.476112, 0.438261, 0.404563,
0.369277, 0.339073, 0.321616, 0.301118, 0.296195, 0.224688, 0.273538,
0.31357, 0.33593, 0.366902, 0.38813, 0.417572, 0.437777, 0.465834,
0.48511, 0.511907, 0.530336, 0.55598, 0.573633, 0.598219, 0.615159,
0.638772, 0.655054, 0.677768, 0.693441, 0.715321, 0.73043, 0.751535,
0.766118, 0.786503, 0.800596, 0.820306, 0.833941, 0.852182, 0.85901,
0.874152, 0.871531, 0.78396, 0.781416, 0.696402, 0.693931, 0.611329,
0.608927, 0.528603, 0.526267, 0.448099, 0.445825, 0.369701, 0.367485,
0.315658, 0.325798, 0.341207, 0.351098, 0.366134, 0.375788, 0.390468,
0.399897, 0.414237, 0.42345, 0.437466, 0.446473, 0.46018, 0.46899,
0.4824, 0.491022, 0.504149, 0.51259, 0.525444, 0.533712, 0.546306,
0.554408, 0.56675}
(takes about 5 seconds)
Alternatively, use
Table[u[i], {i, 1, 100}]
(same result). Your combination of For and Print shows the results but doesn't let you keep using them for more calculations.
answered 1 hour ago
RomanRoman
5,11011130
$endgroup$
I recommend you learn the distinction between immediate (=) and delayed (:=) assignments. They make the difference between slow and fast code here. Start with this tutorial or this book chapter, then look at memoization.
s = 0.3405;
e = 1.6539*10^-21;
u[0] = 0.;
u[1] = 0.1;
A[r_] = Piecewise[{{r - 2.5 s - 48*e*s^12*r^-13 + 24*e*s^6*r^-7, r > 2.5 s},
{-48*e*s^12*r^-13 + 24*e*s^6*r^-7, s <= r <= 2.5 s},
{r - s - 24*e*s^-1, r < s}}];
u[i_] := u[i] = x /. FindRoot[
u[i - 1] + 1/(i^2 (u[i - 1] - u[i - 2])^2) (u[i - 1] - u[i - 2]) - 0.9 A[x] == x, {x, 1.}]
Array[u, 100]
{0.1, 1.77164, 1.37065, 1.04259, 0.887781, 0.708344, 0.59461,
0.457228, 0.367364, 0.296071, 0.256104, 0.20463, 0.208487, 1.20917,
1.04197, 0.939331, 0.879865, 0.827963, 0.774591, 0.72775, 0.67934,
0.63666, 0.592369, 0.553172, 0.512352, 0.476112, 0.438261, 0.404563,
0.369277, 0.339073, 0.321616, 0.301118, 0.296195, 0.224688, 0.273538,
0.31357, 0.33593, 0.366902, 0.38813, 0.417572, 0.437777, 0.465834,
0.48511, 0.511907, 0.530336, 0.55598, 0.573633, 0.598219, 0.615159,
0.638772, 0.655054, 0.677768, 0.693441, 0.715321, 0.73043, 0.751535,
0.766118, 0.786503, 0.800596, 0.820306, 0.833941, 0.852182, 0.85901,
0.874152, 0.871531, 0.78396, 0.781416, 0.696402, 0.693931, 0.611329,
0.608927, 0.528603, 0.526267, 0.448099, 0.445825, 0.369701, 0.367485,
0.315658, 0.325798, 0.341207, 0.351098, 0.366134, 0.375788, 0.390468,
0.399897, 0.414237, 0.42345, 0.437466, 0.446473, 0.46018, 0.46899,
0.4824, 0.491022, 0.504149, 0.51259, 0.525444, 0.533712, 0.546306,
0.554408, 0.56675}
(takes about 5 seconds)
Alternatively, use
Table[u[i], {i, 1, 100}]
(same result). Your combination of For and Print shows the results but doesn't let you keep using them for more calculations.
answered 1 hour ago
RomanRoman
5,11011130
edited 1 hour ago
answered 1 hour ago
RomanRoman
5,11011130
answered 1 hour ago
RomanRoman
5,11011130
answered 1 hour ago
RomanRoman
5,11011130
5,11011130
add a comment |
add a comment |
Thanks for contributing an answer to Mathematica Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f195054%2fwhy-is-this-code-so-slow%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
