Why is this code so slow? The 2019 Stack Overflow Developer Survey Results Are InWhy is...
ELI5: Why they say that Israel would have been the fourth country to land a spacecraft on the Moon and why they call it low cost?
Why don't hard Brexiteers insist on a hard border to prevent illegal immigration after Brexit?
How do you keep chess fun when your opponent constantly beats you?
Did Scotland spend $250,000 for the slogan "Welcome to Scotland"?
Is an up-to-date browser secure on an out-of-date OS?
Finding the area between two curves with Integrate
Why can't devices on different VLANs, but on the same subnet, communicate?
Pokemon Turn Based battle (Python)
Is it okay to consider publishing in my first year of PhD?
What does もの mean in this sentence?
Are there any other methods to apply to solving simultaneous equations?
Is it ethical to upload a automatically generated paper to a non peer-reviewed site as part of a larger research?
Kerning for subscripts of sigma?
How to support a colleague who finds meetings extremely tiring?
How come people say “Would of”?
Why couldn't they take pictures of a closer black hole?
Getting crown tickets for Statue of Liberty
Will it cause any balance problems to have PCs level up and gain the benefits of a long rest mid-fight?
Can we generate random numbers using irrational numbers like π and e?
Can an undergraduate be advised by a professor who is very far away?
How to type a long/em dash `—`
How can I define good in a religion that claims no moral authority?
Short story: man watches girlfriend's spaceship entering a 'black hole' (?) forever
If my opponent casts Ultimate Price on my Phantasmal Bear, can I save it by casting Snap or Curfew?
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
