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4-point Gauss Quadrature with MATLAB

  1. Dec 12, 2013 #1
    1. The problem statement, all variables and given/known data
    I need to evaluate a function using 4-point GQ.


    2. Relevant equations
    GQ theory


    3. The attempt at a solution
    I have got more of a programming issue in MATLAB. I am new to MATLAB. Actually this is for a numerical analysis course where we kind of learn MATLAB on the fly. First, I have 4 .m files to calculate the 4-point GQ which are listed below. Now, I have the program running for a specific function.m file and it calculates correctly. But I want to modify my existing GQ routine such that I can call any function.m file I want to. I think this is more of a syntax issue than anything. Since I have no experience with MATLAB any input or suggestions will be greatly appreciated.
    .m files:

    Main Program
    function gauss_quadFULL(a,b,'integrand')
    format longe;

    %fhandle = @integrand;
    reference_weights = [0.3478548 0.6521452 0.6521452 0.3478548];
    reference_nodes = [-0.861136312 -0.339981044 0.3399810436 0.8611363116];
    [New_weights, New_nodes] = gauss_quad(a,b,reference_weights,reference_nodes);
    FourPoint_Gauss = guass_quadSUM('integrand',New_weights,New_nodes)

    ---------------------------------------------------------------------------------------------
    %This function takes the reference weights/nodes and transforms them to the [-1,1] interval

    function [weights, nodes] = gauss_quad(a,b,reference_weights,reference_node)

    weights=1/2*(b-a)*reference_weights;
    nodes = 1/2*((b-a)*reference_node+(b+a));
    [weights, nodes]

    ---------------------------------------------------------------------------------------------
    %Does the sum for GQ using nodes and weights

    function result = guass_quadSUM(fhandle,New_weights,New_nodes)

    result = 0;
    nn = length(New_weights); % We choose weights here instead of nodes because
    % in multidemensions nodes is a matrix.
    for j=1:nn
    result = result + New_weights(j)*feval(fhandle,New_nodes(j));
    end

    ---------------------------------------------------------------------------------------------
    %example function
    function result = function_f_quad(x)

    result = cos(pi/4*x)/sin(pi/4*x)^2;

    ---------------------------------------------------------------------------------------------

    When I call the main function I get the following error:

    EDU>> gauss_quadFULL(0,1,function_f_quad)
    Error using function_f_quad (line 3)
    Not enough input arguments.


    Again, if I replace the loop sum by:
    result = result + New_weights(j)*function_f_quad(New_nodes(j));
    I get the correct answer. My question is how to pass the GQ main routine a new function, say f1.m, that does the same thing but for any function that I have in an .m file? I have tried messing with the handles and single quotes but I keep getting the same error in my program. Please help. Thank you in advance.
     
  2. jcsd
  3. Dec 12, 2013 #2
    I figured it out. Thanks.
     
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