Optimizing Mathematica Calculations: Faster Plotting with Delayed Expressions

[member 428835]

Hi PF!

I have a series of calculations I'm executing in Mathematica, and all expressions use the delayed := equality. At the end I am trying to plot a function, and for this example let's say it's

f[x_]:=x

When I plot, I am forced to plot in the form

Plot[f[x]/.x->y , {y,-1,1}

This method takes FOREVER! However, if I first evaluate f[x], copy-paste it into the plot, this happens much quicker (the evaluation takes some time and obviously the plot is instantaneous, but both are so much faster than the y-plot technique).

Anyone know how I can speed this up without doing the manual inputs?

 

[jedishrfu]

Did you check on the Mathematica forum? I’m sure others have experienced this same problem.

How many numbers in x array are we talking about? How slow is it really?

Mathematica isn’t the fastest tool on the block so you may be expecting too much from it performance wise.

I know many folks use Matlab for computations over Mathematica and use Mathematica when symbolic math is needed.

Heres some tips for speeding things up:

http://blog.wolfram.com/2011/12/07/10-tips-for-writing-fast-mathematica-code/

 

[DrClaude]

When I plot, I am forced to plot in the form

Plot[f[x]/.x->y , {y,-1,1}

Why are you doing that? The plot command should simply be

Plot[f[y], {y,-1,1}]

 

[member 428835]

Why are you doing that? The plot command should simply be

Plot[f[y], {y,-1,1}]

When I try this I receive the error message "y is not a valid variable".

Perhaps related, but in the past I've seen other code where f is defined slightly different. For example, if $f = x^2$ I've seen

f[x_]:=f[x_]=x^2

Any idea why this is done?

Edit: I just read jedishrfu's link, and it explains the above question on the := to the = example. Thanks!

 

[DrClaude]

When I try this I receive the error message "y is not a valid variable".

Are you using y before in the Notebook? Because you shouldn't get such an error.

 

[member 428835]

Are you using y before in the Notebook? Because you shouldn't get such an error.

Nope, I'm not. Want me to send you the notebook and you can check it out? It's pretty short.

 

[DrClaude]

Nope, I'm not. Want me to send you the notebook and you can check it out? It's pretty short.

Yes, I can check it out.