Mark Mikofski

John, Sorry for my slow response. You can accomplish this the same way I zeroed out the last coefficient.

E.g. to force the 1st order coefficient to zero do the following:

% ...
x = x(:);
y = y(:);

% since you want might want to include the constant term,
% change "z" to be a matrix of ones, and make it one column wider
% to include the 0th-order term

% z = zeros(dim,degree); % comment out this line which doesn't include constant
z = ones(dim,degree+1); % add this line which now includes 0th-order term

for n = 1:degree
    z(:,n) = x.^(degree-n+1);
end

% you don't have to calculate the constant term,
% because it will be a column of ones (i.e. x^0 = 1)
% now remove any columns that you don't want to fit
% e.g. we want to force the 1st order coefficient to zero
orderOfZeroCoeffs = 1; % a vector of terms to omit from regression, e.g. [1,0],
% you could make "orderOfZeroCoeffs" an input to the function

% now, remove the terms whose coeffs you want to zero
orderOfNonZeroCoeffs= ~ismember(degree:-1:0, orderOfZeroCoeffs);
z = z(:,orderOfNonZeroCoeffs); % replace z with the columns removed
% there are a 1000 other ways to write this code!

% comment out the following lines
% because now it's more complicated
% pZero = z\y;
% pZero = [pZero;0]';

% instead create a vector of zeros
% any terms not calculated are already set to zero
pZero = zeros(1,degree+1);
% substitute the coefficients directly into "pZero" by index assignment
pZero(orderOfNonZeroCoeffs) = z\y;

% ...

Try that out. I'm curious what you're using this for. Also check out the other polyfit0 (fex272) function that Jennifer Sanders found above. You can modify it in exactly the same way I show here, but you will also have to modify the other output parameters.

Thank you Q. Fang for this excellent program. As an alternative anyone could just use the org.json files directly from java. they are here:
https://github.com/douglascrockford/JSON-java
and directions are here:
http://www.json.org/java/index.html
You need to compile them or just export them to a jar file which requires jdk. I have compiled it already for you here:
http://dl.dropbox.com/u/19049582/JSON.jar
Before you can use the org.json library you have to add to your java class path (either dynamic or static) by following the directions here:
http://www.mathworks.com/help/techdoc/matlab_external/f4863.html
For example: javaaddpath('full-path\JSON.jar') will add the jar file to your dynamic path.
Then you can use java which is native to MATLAB to use the org.json library.
For example:
jsonObj = org.json.JSONObject('{myKey:myVal}')

Great suggestions Jonathan. I have added them to the issues list on Github here:
https://github.com/mikofski/iapws_if97/issues
Also, I cp is available as a function of p & h (but not p & T as you pointed out), if that would suit your needs.

I wonder if you could modify the routine so that higher powers could also be forced to be zero. For example, the current routine set the constant coefficient to zero. But, can the 1st order coefficient also be forced to be zero. And so on...

Gahh! It didn't post my initial message which was asking how to generate the structure S as you can ordinarily so with polyfit. Thus allowing you to calculate the error on the gradient. And then I found a file that does just that on the file exchange (See above post: which it posted twice?!).