Create a function with the header: function [Y] = myinterpfunction(x,y,X,method)

Question

Create a function with the header:

function [Y] = myinterpfunction(x,y,X,method)

Where x and y are column vectors containing experimental data points, and X is an array. Assume that x and X are in ascending order and have unique elements. The output argument, Y, should be a vector, the same size as X, where Y(i) is the interpolation of X(i) using the method specified.

The options for method should be

‘linear’ : uses linear interpolation

‘spline’ : uses cubic spline interpolation

‘nearest’ : uses nearest neighbor interpolation

Hint1: you should use the function strcmp to compare the given method to the different options. If the output of strcmp is = 1, then the two strings are the same.

   Example: if strcmp(method, ‘linear’) == 1 %the method is linear

Hint2: for the spline method, you may want to start with a matrix of zeros sized 4(n-1) x 4(n-1) - you can use the zeros(rows, columns) function for this

Your function should plot the data points (x,y) as open circles and should plot the interpolation as a black line. Be sure to include a title, legend, and axis labels.

You can use the test case and plots below to test your function:

Type the following into the command window (or into a new script)-

x = [0 0.1 0.15 0.35 0.6 0.7 0.95 1];

y = [1 0.8187 0.7408 0.4966 0.3012 0.2466 0.1496 0.1353];

X = linspace(0,1,100);

[Y] = myinterpfunction(x,y,X, ‘nearest’)

-without using matlab built in interp1 function

Explanation / Answer

#include <iostream>

using namespace std;

#define m 3

#define n 3

int main()

{

     int i, j;

     int x[m][n]={{10,25,33}, {21,32,43},{20,42,51}};

     cout<<" 3x3 arrays' subscripts and ";

     cout<<"their respective elements ";

     cout<<"-------------------------- ";

     // the outer for loop, reading the row by row...

     for(i=0; i<m; i++)

            // the inner loop, for every row, read every column by column...

            for(j=0; j<n; j++)

                  cout<<"["<<i<<"]"<<"["<<j<<"]"<<"="<<x[i][j]<<" ";

     return 0;

}

#include <iostream>

   using namespace std;

#define   m 4

#define   n 5

int main()

{

   int i, j, total = 0;

   // a 4x5 or [4][5] array variable...

   int q[m][n]={{4,5,6,2,12},{10,25,33,22,11},

                 {21,32,43,54,65},{3,2,1,5,6}};

   float average;

   // the outer for loop, read row by row...

   for(i=0; i<m; i++)

          // the inner for loop, for every row, read column by column

          for(j=0; j<n; j++)

          // the get the summation of the array elements.

          {

                 // the display the array...

                 cout<<"q["<<i<<"]["<<j<<"] = "<<q[i][j]<<endl;

                 total=total + q[i][j];

          }

   // calculate the average, notice the simple typecast casted from int to float...

   average = (float)total/(float) (m*n);

   cout<<" This program will calculate the average of the";

   cout<<" 4 x 5 array, which means the sum of the";

   cout<<" array's element, divide the number of the";

   cout<<" array's element....";

   cout<<" Processing.... PLEASE WAIT ";

   // display the average

   cout<<"Average = "<<total<<"/"<<m*n<<endl;

   cout<<" The Average = "<<average<<endl;

   return 0;

}

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