Lagrange Interpolation Code Error/Help

Hello! I am to graph an interpolating polynomial and the data points. The data points are from a file which I will provide. I keep running into an error which is "Array indices must be positive integers or logical values." for my variable ys. I would love to use polyval however I am not allowed in this assignment. Any idea how to fix this or what I need to change?? I know that p is not the right thing to do...Thanks in advance!

data file (first line are the x values, second line is the y values, and third line is N which will be the number of points to use to graph the polynomial which is found in xs)

1 2 3 4 5 6 7
1 4 9 16 25 36 49
101

code:

clear;
clf;

%reading from dot_data file
fid = fopen('data_file.m','r');
x = str2num(fgetl(fid)); %reads in first line of data
n = length(x); %length of x
tline = fgets(fid); %reads in the second line of data
y = str2num(tline); %converts to numbers
tline = fgets(fid, 3); %reads in last line of data
N = str2num(tline); %N, also converts to number
fclose(fid); %close file

xx = [x];
yy = [y];

deg = n - 1;

%lagrange
sum=0;
for i=1:length(x)
    p=1;
    for j=1:length(x)
        if j~=i
            c = poly(x(j))/(x(i)-x(j));
            p = conv(p,c);
        end
    end
    term = p*y(i);
    sum= sum + term;
end

%max x value
x_n = max(x);

%plotting the polynomial and data points
xs = linspace(x(1), x_n, N);
ys = p(xs); %this is where I have a mistake when using p
plot(xx,ys, 'r'); %plotting the curve/line
hold on;
plot(x, y, '-o');%plotting the points

Answer 1

[KSSV]

You can evaluate polyval using:

deg = length(p)-1 ; % degree of he polynomial 
% get powers of x till deg 
X = xs'.^(deg:-1:0) ; 
y = sum(p.*X,2) ; % assuming p has coefficients are in decresing powers of n

[Manny]

Thank you! How would I go about implementing that in my code? I am still getting errors when I copy and pasted it and change it to the variables in my code.

[Walter Roberson]

You would replace your

ys = p(xs); %this is where I have a mistake when using p

with

deg = length(p)-1 ; % degree of he polynomial 
% get powers of x till deg 
X = xs'.^(deg:-1:0) ; 
ys = sum(p.*X,2) ; % assuming p has coefficients are in decresing powers of n

[Manny]

Thank you! I am still getting an error with the variable ys and unsure why that is :/ Matlab keeps saying

"Error in HW_7 (line 43)

ys = sum(p.*X,2) ; % assuming p has coefficients are in decresing powers of n"

[KSSV]

Show the whole code.....don't include file reading.....give the values of inputs instead.

[Manny]

x = [1 2 3 4 5 6 7];
y = [1 4 9 16 25 36 49];

n = length(x); %length of x
deg = n - 1; %deg of polynomial

sum=0;
for i=1:length(x)
    p=1;
    for j=1:length(x)
        if j~=i
            c = poly(x(j))/(x(i)-x(j));
            p = conv(p,c);
        end
    end
    term = p*y(i);
    sum= sum + term;
end

x_n = max(x); %max x value

%plotting the polynomial and data points
xs = linspace(x(1), x_n, N);

%deg = n-1 ; % degree of he polynomial 
% get powers of x till deg 
X = xs'.^(deg:-1:0); 
ys = sum(x.*X,2) ; % assuming p has coefficients are in decresing powers of n

plot(xx, ys, 'r');
hold on;
plot(x, y, '-o');

[Walter Roberson]

Is your p a row or a column?

    sum= sum + term;

What are you doing with that variable named sum ?

 p = conv(p,c);

You are overwriting p for each x value, so it is going to end up holding the value it was last assigned, the one for i = length(x). Are you sure that is what you want?

[KSSV]

You should not use the variable names as inbuilt functions. Check the variable sum = 0, this is not allowed.

clear all ;
x = [1 2 3 4 5 6 7];
y = [1 4 9 16 25 36 49];

n = length(x); %length of x
deg = n - 1; %deg of polynomial

thesum=0;
for i=1:length(x)
    p=1;
    for j=1:length(x)
        if j~=i
            c = poly(x(j))/(x(i)-x(j));
            p = conv(p,c);
        end
    end
    term = p*y(i);
    thesum= thesum + term;
end

x_n = max(x); %max x value

%plotting the polynomial and data points
N = 100 ;
xs = linspace(x(1), x_n,N);

%deg = n-1 ; % degree of he polynomial 
% get powers of x till deg 
X = xs'.^(deg:-1:0); 
ys = sum(x.*X,2) ; % assuming p has coefficients are in decresing powers of n

plot(xs, ys, 'r');
hold on;
plot(x, y, '-o');

[Walter Roberson]

Using sum as a variable name leads to problems more often than not, as it is very common to want to use sum as a function in the same section of code. We advise to never use sum as the name of a variable.

[Manny]

That makes so much sense! I didn't realize sum was already a variable name so now understand why there were so many issues.

Now the only issue left that I can see is that my data points are being plotted on a straight line and not on the curve. I notice the x axis with 10^4 on the top.

I apologize for asking so many questions and I appreciate all of the help!!