Mdthbs

How to count the number of function evaluations in NIntegrate

Can I separate garlic into cloves for storage?

The relationship of noch nicht and the passive voice

Is a global DNS record a security risk for phpMyAdmin?

Quick Kurodoko Puzzle: Threes and Triples

Is Zack Morris's 'time stop' ability in "Saved By the Bell" a supernatural ability?

Floating Point XOR

Did HaShem ever command a Navi (Prophet) to break a law?

All numbers in a 5x5 Minesweeper grid

How does one calculate the distribution of the Matt Colville way of rolling stats?

What do solvers like Gurobi and CPLEX do when they run into hard instances of MIP

Find all files in directories named foo

Solving a nonhomogeneous linear recurrence relation

How do rulers get rich from war?

What did the controller say during my approach to land (audio clip)?

How is underwater propagation of sound possible?

Flying pigs arrive

4h 40m delay caused by aircraft inspection, Norwegian refuses EU 261/2004 compensation because it turned out there was nothing wrong with the aircraft

Algorithm for competing cells of 0s and 1s

Who are the people reviewing far more papers than they're submitting for review?

Is it possible that the shadow of The Moon is a single dot during solar eclipse?

EU compensation - fire alarm at the Flight Crew's hotel

Integrability of log of distance function

Is there a comprehensive book, contains (algebra, trig, calculus, differential equations, statistics, ...)?

How to count the number of function evaluations in NIntegrate

Differences between ParametricPlot3D and NIntegrateDetermining which rule NIntegrate selects automaticallyWeighted mean of complex exponential function using NIntegrateProblems with NIntegrateNIntegrate fails to converge under almost any PrecisionGoal, MinRecursion etc. How can I trust the result?Match NIntegrate vs Integrate with HighPrecision

.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0;
}

3

1

$begingroup$

I expect the following code to count the number of function calls in NIntegrate.

i = 0;

f[x_] := (i += 1; Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]])

Print[NIntegrate[f[x], {x, -2, 1}]] 

Print[i]

However, the output is

0.0901049

2

which means only 2 function calls in NIntegrate. It's hard to believe converged result can be obtained by merely two function calls. What's happening here?

numerical-integration

share|improve this question

asked 8 hours ago

Chong WangChong Wang

25922 silver badges88 bronze badges

$endgroup$

add a comment
 | 

3

1

$begingroup$

I expect the following code to count the number of function calls in NIntegrate.

i = 0;

f[x_] := (i += 1; Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]])

Print[NIntegrate[f[x], {x, -2, 1}]] 

Print[i]

However, the output is

0.0901049

2

which means only 2 function calls in NIntegrate. It's hard to believe converged result can be obtained by merely two function calls. What's happening here?

numerical-integration

share|improve this question

asked 8 hours ago

Chong WangChong Wang

25922 silver badges88 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

I expect the following code to count the number of function calls in NIntegrate.

i = 0;

f[x_] := (i += 1; Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]])

Print[NIntegrate[f[x], {x, -2, 1}]] 

Print[i]

However, the output is

0.0901049

2

which means only 2 function calls in NIntegrate. It's hard to believe converged result can be obtained by merely two function calls. What's happening here?

numerical-integration

share|improve this question

asked 8 hours ago

Chong WangChong Wang

25922 silver badges88 bronze badges

$endgroup$

i = 0;

f[x_] := (i += 1; Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]])

Print[NIntegrate[f[x], {x, -2, 1}]] 

Print[i]

0.0901049

2

share|improve this question

asked 8 hours ago

Chong WangChong Wang

25922 silver badges88 bronze badges

share|improve this question

asked 8 hours ago

Chong WangChong Wang

25922 silver badges88 bronze badges

asked 8 hours ago

Chong WangChong Wang

25922 silver badges88 bronze badges

asked 8 hours ago

Chong WangChong Wang

25922 silver badges88 bronze badges

2 Answers
2

active

oldest

votes

2

$begingroup$

Try the option EvaluationMonitor

Block[{k = 0}, {NIntegrate[f[x], {x, -2, 1}, EvaluationMonitor :> k++], k}]

{0.0901049, 121}

Without using EvaluationMonitor you can do

ClearAll[f, ff]

f[x_] := Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]]



i = 0;

ff[y_?NumberQ] := Block[{x = y}, i++; f[x]]



{NIntegrate[ff[x], {x, -2, 1}], i}

{0.0901049, 121}

share|improve this answer

edited 8 hours ago

answered 8 hours ago

kglrkglr

217k1010 gold badges247247 silver badges497497 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yeah, that works. But what's wrong with my approach?
  $endgroup$
  – Chong Wang
  8 hours ago
  

  
  
  
  

add a comment
 | 

2

$begingroup$

A very simple modification (adding ?NumericQ) achieves the result you expected.

i = 0;

f[x_?NumericQ] := (i += 1; Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]])

Print[NIntegrate[f[x], {x, -2, 1}]]

Print[i]



(* 0.0901049*)



(*122*)

The issue is that NIntegrate tries to evaluate f[x] symbolically. In your version, it is called only once and is replaced by Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]. In my version, the f[x] is returned unchanged until specific numerical values are given to x.

share|improve this answer

answered 7 hours ago

mikadomikado

7,63711 gold badge99 silver badges2929 bronze badges

$endgroup$

add a comment
 | 

Your Answer

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/4.0/"u003ecc by-sa 4.0 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
});


}
});

draft saved

draft discarded

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

Name

Email

Required, but never shown

StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f206391%2fhow-to-count-the-number-of-function-evaluations-in-nintegrate%23new-answer', 'question_page');
}
);

Post as a guest

Name

Email

Required, but never shown

2

$begingroup$

Try the option EvaluationMonitor

Block[{k = 0}, {NIntegrate[f[x], {x, -2, 1}, EvaluationMonitor :> k++], k}]

{0.0901049, 121}

Without using EvaluationMonitor you can do

ClearAll[f, ff]

f[x_] := Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]]



i = 0;

ff[y_?NumberQ] := Block[{x = y}, i++; f[x]]



{NIntegrate[ff[x], {x, -2, 1}], i}

{0.0901049, 121}

share|improve this answer

edited 8 hours ago

answered 8 hours ago

kglrkglr

217k1010 gold badges247247 silver badges497497 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yeah, that works. But what's wrong with my approach?
  $endgroup$
  – Chong Wang
  8 hours ago
  

  
  
  
  

add a comment
 | 

2

$begingroup$

Try the option EvaluationMonitor

Block[{k = 0}, {NIntegrate[f[x], {x, -2, 1}, EvaluationMonitor :> k++], k}]

{0.0901049, 121}

Without using EvaluationMonitor you can do

ClearAll[f, ff]

f[x_] := Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]]



i = 0;

ff[y_?NumberQ] := Block[{x = y}, i++; f[x]]



{NIntegrate[ff[x], {x, -2, 1}], i}

{0.0901049, 121}

share|improve this answer

edited 8 hours ago

answered 8 hours ago

kglrkglr

217k1010 gold badges247247 silver badges497497 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yeah, that works. But what's wrong with my approach?
  $endgroup$
  – Chong Wang
  8 hours ago
  

  
  
  
  

add a comment
 | 

$begingroup$

Try the option EvaluationMonitor

Block[{k = 0}, {NIntegrate[f[x], {x, -2, 1}, EvaluationMonitor :> k++], k}]

{0.0901049, 121}

Without using EvaluationMonitor you can do

ClearAll[f, ff]

f[x_] := Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]]



i = 0;

ff[y_?NumberQ] := Block[{x = y}, i++; f[x]]



{NIntegrate[ff[x], {x, -2, 1}], i}

{0.0901049, 121}

share|improve this answer

edited 8 hours ago

answered 8 hours ago

kglrkglr

217k1010 gold badges247247 silver badges497497 bronze badges

$endgroup$

Block[{k = 0}, {NIntegrate[f[x], {x, -2, 1}, EvaluationMonitor :> k++], k}]

ClearAll[f, ff]

f[x_] := Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]]



i = 0;

ff[y_?NumberQ] := Block[{x = y}, i++; f[x]]



{NIntegrate[ff[x], {x, -2, 1}], i}

share|improve this answer

edited 8 hours ago

answered 8 hours ago

kglrkglr

217k1010 gold badges247247 silver badges497497 bronze badges

answered 8 hours ago

kglrkglr

217k1010 gold badges247247 silver badges497497 bronze badges

answered 8 hours ago

kglrkglr

217k1010 gold badges247247 silver badges497497 bronze badges

2

$begingroup$

A very simple modification (adding ?NumericQ) achieves the result you expected.

i = 0;

f[x_?NumericQ] := (i += 1; Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]])

Print[NIntegrate[f[x], {x, -2, 1}]]

Print[i]



(* 0.0901049*)



(*122*)

The issue is that NIntegrate tries to evaluate f[x] symbolically. In your version, it is called only once and is replaced by Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]. In my version, the f[x] is returned unchanged until specific numerical values are given to x.

share|improve this answer

answered 7 hours ago

mikadomikado

7,63711 gold badge99 silver badges2929 bronze badges

$endgroup$

add a comment
 | 

2

$begingroup$

A very simple modification (adding ?NumericQ) achieves the result you expected.

i = 0;

f[x_?NumericQ] := (i += 1; Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]])

Print[NIntegrate[f[x], {x, -2, 1}]]

Print[i]



(* 0.0901049*)



(*122*)

The issue is that NIntegrate tries to evaluate f[x] symbolically. In your version, it is called only once and is replaced by Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]. In my version, the f[x] is returned unchanged until specific numerical values are given to x.

share|improve this answer

answered 7 hours ago

mikadomikado

7,63711 gold badge99 silver badges2929 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

A very simple modification (adding ?NumericQ) achieves the result you expected.

i = 0;

f[x_?NumericQ] := (i += 1; Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]])

Print[NIntegrate[f[x], {x, -2, 1}]]

Print[i]



(* 0.0901049*)



(*122*)

The issue is that NIntegrate tries to evaluate f[x] symbolically. In your version, it is called only once and is replaced by Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]. In my version, the f[x] is returned unchanged until specific numerical values are given to x.

share|improve this answer

answered 7 hours ago

mikadomikado

7,63711 gold badge99 silver badges2929 bronze badges

$endgroup$

i = 0;

f[x_?NumericQ] := (i += 1; Tanh[x] Sin[Exp[x]] Exp[-0.55 x^2 Exp[x^2]])

Print[NIntegrate[f[x], {x, -2, 1}]]

Print[i]



(* 0.0901049*)



(*122*)

share|improve this answer

answered 7 hours ago

mikadomikado

7,63711 gold badge99 silver badges2929 bronze badges

answered 7 hours ago

mikadomikado

7,63711 gold badge99 silver badges2929 bronze badges

answered 7 hours ago

mikadomikado

7,63711 gold badge99 silver badges2929 bronze badges