Why is this recursive code so slow? The 2019 Stack Overflow Developer Survey Results Are In ...
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Why is this recursive code so slow?
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)What are the hidden specifications for FindRootWhy does this function inside FindRoot fail to evaluate?Very slow mathematica finite differencesUsing Mathematica to solve a recursive system of differential equationsImproving the speed on an iterated differential systemForward iterations of coupled recursion equationsManipulate+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 <= r <= 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 recursion
edited yesterday
Roman
5,24511131
asked 2 days ago
morapimorapi
355
$endgroup$
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 <= r <= 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 recursion
edited yesterday
Roman
5,24511131
asked 2 days ago
morapimorapi
355
$endgroup$
$begingroup$
How slow? How many minutes/seconds?
$endgroup$
– JonyD
yesterday
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 <= r <= 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 recursion
edited yesterday
Roman
5,24511131
asked 2 days ago
morapimorapi
355
$endgroup$
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 <= r <= 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 recursion
equation-solving recursion
edited yesterday
Roman
5,24511131
asked 2 days ago
morapimorapi
355
edited yesterday
Roman
5,24511131
asked 2 days ago
morapimorapi
355
edited yesterday
Roman
5,24511131
edited yesterday
Roman
5,24511131
edited yesterday
Roman
5,24511131
5,24511131
asked 2 days ago
morapimorapi
355
asked 2 days ago
morapimorapi
355
asked 2 days ago
morapimorapi
355
355
$begingroup$
How slow? How many minutes/seconds?
$endgroup$
– JonyD
yesterday
add a comment |
$begingroup$
How slow? How many minutes/seconds?
$endgroup$
– JonyD
yesterday
$begingroup$
How slow? How many minutes/seconds?
$endgroup$
– JonyD
yesterday
$begingroup$
How slow? How many minutes/seconds?
$endgroup$
– JonyD
yesterday
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 1.3 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 yesterday
RomanRoman
5,24511131
$endgroup$
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
yesterday
$begingroup$
delayedassignments definitely sound slower thanimmediate, even if I have never worked with Mathematica
$endgroup$
– Roland
yesterday
2
$begingroup$
@Roland it's not just that one is necessarily faster or slower than the other, it's more that they are completely different things with very different applications. For some reason this point is often overlooked by beginners in Mathematica.
$endgroup$
– Roman
yesterday
add a comment |
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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 1.3 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 yesterday
RomanRoman
5,24511131
$endgroup$
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
yesterday
$begingroup$
delayedassignments definitely sound slower thanimmediate, even if I have never worked with Mathematica
$endgroup$
– Roland
yesterday
2
$begingroup$
@Roland it's not just that one is necessarily faster or slower than the other, it's more that they are completely different things with very different applications. For some reason this point is often overlooked by beginners in Mathematica.
$endgroup$
– Roman
yesterday
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 1.3 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 yesterday
RomanRoman
5,24511131
$endgroup$
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
yesterday
$begingroup$
delayedassignments definitely sound slower thanimmediate, even if I have never worked with Mathematica
$endgroup$
– Roland
yesterday
2
$begingroup$
@Roland it's not just that one is necessarily faster or slower than the other, it's more that they are completely different things with very different applications. For some reason this point is often overlooked by beginners in Mathematica.
$endgroup$
– Roman
yesterday
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 1.3 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 yesterday
RomanRoman
5,24511131
$endgroup$
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 1.3 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 yesterday
RomanRoman
5,24511131
edited yesterday
answered yesterday
RomanRoman
5,24511131
answered yesterday
RomanRoman
5,24511131
answered yesterday
RomanRoman
5,24511131
5,24511131
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thank you very much. I really appreciate it.
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– morapi
yesterday
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delayedassignments definitely sound slower thanimmediate, even if I have never worked with Mathematica
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– Roland
yesterday
2
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@Roland it's not just that one is necessarily faster or slower than the other, it's more that they are completely different things with very different applications. For some reason this point is often overlooked by beginners in Mathematica.
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– Roman
yesterday
add a comment |
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
yesterday
$begingroup$
delayedassignments definitely sound slower thanimmediate, even if I have never worked with Mathematica
$endgroup$
– Roland
yesterday
2
$begingroup$
@Roland it's not just that one is necessarily faster or slower than the other, it's more that they are completely different things with very different applications. For some reason this point is often overlooked by beginners in Mathematica.
$endgroup$
– Roman
yesterday
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
yesterday
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
yesterday
$begingroup$
delayed assignments definitely sound slower than immediate, even if I have never worked with Mathematica$endgroup$
– Roland
yesterday
$begingroup$
delayed assignments definitely sound slower than immediate, even if I have never worked with Mathematica$endgroup$
– Roland
yesterday
2
2
$begingroup$
@Roland it's not just that one is necessarily faster or slower than the other, it's more that they are completely different things with very different applications. For some reason this point is often overlooked by beginners in Mathematica.
$endgroup$
– Roman
yesterday
$begingroup$
@Roland it's not just that one is necessarily faster or slower than the other, it's more that they are completely different things with very different applications. For some reason this point is often overlooked by beginners in Mathematica.
$endgroup$
– Roman
yesterday
add a comment |
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How slow? How many minutes/seconds?
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– JonyD
yesterday