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
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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
204
$endgroup$
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
204
$endgroup$
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
204
$endgroup$
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
204
asked 2 hours ago
morapimorapi
204
asked 2 hours ago
morapimorapi
204
asked 2 hours ago
morapimorapi
204
asked 2 hours ago
morapimorapi
204
204
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 2 hours ago
RomanRoman
5,12011130
$endgroup$
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
12 mins ago
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
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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 2 hours ago
RomanRoman
5,12011130
$endgroup$
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
12 mins ago
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 2 hours ago
RomanRoman
5,12011130
$endgroup$
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
12 mins ago
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 2 hours ago
RomanRoman
5,12011130
$endgroup$
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 2 hours ago
RomanRoman
5,12011130
edited 1 hour ago
answered 2 hours ago
RomanRoman
5,12011130
answered 2 hours ago
RomanRoman
5,12011130
answered 2 hours ago
RomanRoman
5,12011130
5,12011130
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
12 mins ago
add a comment |
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
12 mins ago
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
12 mins ago
$begingroup$
thank you very much. I really appreciate it.
$endgroup$
– morapi
12 mins ago
add a comment |
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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
