Difference between revisions of "EGR 103/Fall 2017/Lab 7"

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== Chapra 7.23, 7.24, and 7.25(b/c) ==
 
== Chapra 7.23, 7.24, and 7.25(b/c) ==
 
* These problems will require [[MATLAB:Fminbnd_and_fminsearch|fminsearch]] to find the extremes, as well as <code>meshgrid</code> and <code>surfc</code> to make the plots; more on that at [[MATLAB:Plotting_Surfaces|Plotting Surfaces]]
 
* These problems will require [[MATLAB:Fminbnd_and_fminsearch|fminsearch]] to find the extremes, as well as <code>meshgrid</code> and <code>surfc</code> to make the plots; more on that at [[MATLAB:Plotting_Surfaces|Plotting Surfaces]]
 +
 +
== General Notes - Code from Lab ==
 +
First, you need to think about what it is you are being asked to do:
 +
* Find a single value of a single variable that sets a function equal to zero (or sets a function equal to a particular value, such that the difference between the function and the particular value is zero):
 +
** Use fzero
 +
** First argument is an anonymous function calculating the function you want to be set to zero
 +
** Second argument is either a valid bracket surrounding the root of interest (preferred) or a single initial guess from which MATLAB will try to build a bracket.
 +
* Find a single value of a single variable that minimizes a function within a particular bounded range:
 +
** Use fminbnd
 +
** First argument is an anonymous function calculating the function you want to minimize
 +
** Second argument is the left end of the bounded range
 +
** Third argument is the right end of the bounded range
 +
** '''The bounds are in two different argument!'''
 +
** If you want to ''maximize'' something, use the negative of the function ar the first argument (so you are minimizing the negative); note however that the function's value as given by fminbnd will have the wrong sign
 +
* Find a single vector of values of a single variable that minimizes a function within a particular bounded range:
 +
** Use fminsearch
 +
** First argument is an anonymous function calculating the function you want to minimize; this function must be of a single '''variable''' but you may use different entries within that variable
 +
** Second argument is an initial guess which must have as many entries as the number of entries used in the function
 +
** If you want to ''maximize'' something, use the negative of the function ar the first argument (so you are minimizing the negative); note however that the function's value as given by fminbnd will have the wrong sign
 +
** Because you are giving an initial guess versus a boundary, you must be careful in picking the initial guess

Revision as of 15:03, 17 October 2017

Basic Root-Finding Problems

  • Main thing is to look at MATLAB:Fzero and the different ways of calling it.
  • The sign plots are really helpful.
  • The last equation has three sign changes but only two roots

Basic Min/Max Finding Problems

  • Main thing is to look at MATLAB:Fminbnd and the different ways of calling it.

Chapra Problem 6.16

Chapra 6.20

Chapra 6.21

  • This simply requires using fzero twice - just be careful on how you initialize fzero and also be careful about units for the angles.

Chapra 7.23, 7.24, and 7.25(b/c)

  • These problems will require fminsearch to find the extremes, as well as meshgrid and surfc to make the plots; more on that at Plotting Surfaces

General Notes - Code from Lab

First, you need to think about what it is you are being asked to do:

  • Find a single value of a single variable that sets a function equal to zero (or sets a function equal to a particular value, such that the difference between the function and the particular value is zero):
    • Use fzero
    • First argument is an anonymous function calculating the function you want to be set to zero
    • Second argument is either a valid bracket surrounding the root of interest (preferred) or a single initial guess from which MATLAB will try to build a bracket.
  • Find a single value of a single variable that minimizes a function within a particular bounded range:
    • Use fminbnd
    • First argument is an anonymous function calculating the function you want to minimize
    • Second argument is the left end of the bounded range
    • Third argument is the right end of the bounded range
    • The bounds are in two different argument!
    • If you want to maximize something, use the negative of the function ar the first argument (so you are minimizing the negative); note however that the function's value as given by fminbnd will have the wrong sign
  • Find a single vector of values of a single variable that minimizes a function within a particular bounded range:
    • Use fminsearch
    • First argument is an anonymous function calculating the function you want to minimize; this function must be of a single variable but you may use different entries within that variable
    • Second argument is an initial guess which must have as many entries as the number of entries used in the function
    • If you want to maximize something, use the negative of the function ar the first argument (so you are minimizing the negative); note however that the function's value as given by fminbnd will have the wrong sign
    • Because you are giving an initial guess versus a boundary, you must be careful in picking the initial guess