Editing Symbolic package

Jump to navigation Jump to search

Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.

The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.

Latest revision Your text
Line 1: Line 1:
The {{Forge|symbolic|symbolic package}} is part of the [[Octave Forge]] project.
+
The {{Forge|symbolic|symbolic package}} is part of the octave-forge project.
  
[[Category:Octave Forge]]
+
[[Category:Octave-Forge]]
  
 
=== Demos and usage examples ===
 
=== Demos and usage examples ===
 
* '''I'm trying to substitute a double value into an expression.  How can I avoid getting "warning: Using rat() heuristics for double-precision input (is this what you wanted?)".'''
 
 
In general, you should be very careful when converting floating point ("doubles") to symbolic variables, that's why the warning is bothering you.
 
 
<source lang="octave">
 
 
## Demo of how to use a number (which was calculated in an octave
 
## variable) in a symbolic calculation, without getting a warning.
 
 
## use octave to calculate some number:
 
a = pi/2
 
 
## now do some work with the symbolic pkg
 
syms x
 
f = x * cos (x)
 
df = diff (f)
 
 
## Now we want to evaluate df at a:
 
 
# subs (df, x, a)    # this gives the "rats" warning (and gives a symbolic answer)
 
 
## So instead, try
 
 
dfh = function_handle (df)
 
 
dfh (a)
 
 
ans = -1.5708
 
 
 
## And you can evaluate dfh at an array of "double" values:
 
 
dfh ([1.23 12.3 pi/2])
 
 
ans =
 
  -0.82502  4.20248  -1.57080
 
 
</source>
 
 
 
 
* '''Demo of how to graph symbolic functions (by converting SYMBOLIC functions into ANONYMOUS functions)'''
 
 
<source lang="octave">
 
 
## The following code will produce the same vector field plot as Figure 1.14 from Example 1.6 (pg. 39) from A Student's Guide to Maxwell's Equations by Dr. Daniel Fleisch.
 
 
## Make sure symbolic package is loaded and symbolic variables declared.
 
pkg load symbolic
 
syms x y
 
 
## Write a Vector Field Equation in terms of symbolic variables
 
vectorfield = [sin(pi*y/2); -sin(pi*x/2)];
 
 
## Vector components are converted from symbolic into "anonymous functions" which allows them to be graphed.
 
## The "'vars', [x y]" syntax ensures each component is a function of both 'x' & 'y'
 
iComponent = function_handle (vectorfield(1), 'vars', [x y]);
 
jComponent = function_handle (vectorfield(2), 'vars', [x y]);
 
 
## Setup a 2D grid
 
[X,Y] = meshgrid ([-0.5:0.05:0.5]);
 
 
figure
 
quiver (X, Y, iComponent (X, Y), jComponent (X,Y))
 
 
</source>
 
 
  
 
* '''Demo of Anonymous function to symbolic function and back to anonymous function and then the use of the interval pkg.'''
 
* '''Demo of Anonymous function to symbolic function and back to anonymous function and then the use of the interval pkg.'''
Line 79: Line 11:
 
% have fun and change it if you want to.
 
% have fun and change it if you want to.
  
f = @(x) x.^2 + 3*x - 1 + 5*x.*sin(x);
+
f=@(x) x.^2 +3*x-1 + 5*x.*sin(x);
  
% these next lines take the Anonymous function into a symbolic formula
+
% the next 2 line take the Anonymous function into a symbolic formula
  
pkg load symbolic
 
 
syms x;
 
syms x;
ff = f(x);
+
 
 +
ff=formula(f(x));
  
 
% now calculate the derivative of the function
 
% now calculate the derivative of the function
  
ffd = diff(ff, x);
+
ffd=diff(ff);
  
 
% and convert it back to an Anonymous function
 
% and convert it back to an Anonymous function
  
df = function_handle(ffd)
+
df=function_handle(ffd)
  
  
% this uses the interval pkg to find all the roots between -15 an 10  
+
% this uses the interval pkg. to find all the roots between -15 an 10  
  
pkg load interval
 
 
fzero (f, infsup (-15, 10), df)
 
fzero (f, infsup (-15, 10), df)
  
Line 107: Line 38:
 
     [-0.777688831121563, -0.7776888311215626]
 
     [-0.777688831121563, -0.7776888311215626]
 
     [0.22911205809043574, 0.2291120580904359]
 
     [0.22911205809043574, 0.2291120580904359]
</source>
 
 
 
* '''Demo of inputting a function at the input prompt and making an Anonymous function.'''
 
 
<source lang="octave">
 
# This prog. shows how to take a
 
# string input and make it into an anonymous function
 
# this uses the symbolic pkg.
 
disp("Example input")
 
disp("x^2 + 3*x - 1 + 5*x*sin(x)")
 
str_fucn=input("please enter your function  ","s")
 
fucn_sym=sym(str_fucn)
 
f=function_handle(fucn_sym)
 
# now back to symbolic
 
syms x;
 
ff=formula(f(x));
 
% now calculate the derivative of the function
 
ffd=diff(ff);
 
% and convert it back to an Anonymous function
 
df=function_handle(ffd)
 
% now lets do the second derivative
 
ffdd=diff(ffd);
 
ddf=function_handle(ffdd)
 
% and now plot them all
 
x1=-2:.0001:2;
 
plot(x1,f(x1),x1,df(x1),x1,ddf(x1))
 
grid minor on
 
legend("f","f '", "f '' ")
 
 
</source>
 
</source>
  
Line 160: Line 62:
 
  ##
 
  ##
 
  syms y(x)  
 
  syms y(x)  
sqrt2=sym(1.41421);
+
  de =diff(y, 3 ) +sqrt(2)*diff(y,2) + diff(y) == 0;
  de =diff(y, 3 ) +sqrt2*diff(y,2) + diff(y) == 0;
 
 
  f = dsolve(de, y(0) == 0, diff(y,1)(0) == 0 , diff(y,2)(0) == 1)
 
  f = dsolve(de, y(0) == 0, diff(y,1)(0) == 0 , diff(y,2)(0) == 1)
 
  ff=function_handle(rhs(f))
 
  ff=function_handle(rhs(f))
Line 168: Line 69:
 
  plot(x1,y)
 
  plot(x1,y)
 
  grid minor on  
 
  grid minor on  
 
 
</source>
 
</source>

Please note that all contributions to Octave may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Octave:Copyrights for details). Do not submit copyrighted work without permission!

To edit this page, please answer the question that appears below (more info):

Cancel Editing help (opens in new window)

Template used on this page: