Best method to define a linear piece-wise function given limits and line equations?

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David Hagan 2012-1-2

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https://ww2.mathworks.cn/matlabcentral/answers/25154-best-method-to-define-a-linear-piece-wise-function-given-limits-and-line-equations

I am writing a function(also new to matlab) that is fed the following:

 the x limits of each piece
 the slope and intercept values of each piece
 the y values for which I am trying to find corresponding x  values

How can I write a function that can take any number of pieces, and create a piece-wise function? I then would like to be able to feed it y values and return the corresponding x values. I currently can only write the function for a given number of pieces, not any number..?

My code thus far:

%%define the piecewise function
function x = peicewisehot(y,Hbreaks,slope)
      %y;        input from user
      %Hbreaks;  vertical breaks
      %slope;    slope of equation
      %x = (y-b)/m
for i = 1:length(y)   
    if y(i) >= Hbreaks(1) & y(i) < Hbreaks(2)
        x(i) = (y(i) - b(1))./slope(1);
      elseif y(i) >= Hbreaks(2) & y(i) < Hbreaks(3)
          x(i) = (y(i) - b(2))./slope(2);
      else
          x(i) = nan;
      end
  end

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Answer 1

Walter Roberson 2012-1-2

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https://ww2.mathworks.cn/matlabcentral/answers/25154-best-method-to-define-a-linear-piece-wise-function-given-limits-and-line-equations#answer_33009

Please see the following hints:

http://www.mathworks.com/matlabcentral/answers/24415-continuous-piecewise-function-in-anonymous-fittype-equation

http://www.mathworks.com/matlabcentral/answers/24573-how-to-use-the-output-function-of-a-cubic-spline-interpolation

Looks to me like you could use interp1() and ppval()

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David Hagan 2012-1-3

Thank you very much. I tried doing this and using interp1 seems to work great, however I am having issues using ppval to evaluate points. I am getting an error that says: "The input array does not seem to describe a pp function." The following is my code:

load HXData

B= unique(sort(TH(:)));

numsecB = size(B) - 1;

slopeB = zeros(1,numsecB);

s = [length(TC) length(TH)];

for i=1:numsecB

tester = (B(i)+B(i+1))/2;

for j=1:s(2)

if (tester >= TH(j,2) & tester <= TH(j,1))

checkB(i,j) = 1;

slopeB(i) = slopeB(i)+ KH(j);

else

checkB(i,j) = 0;

end

%Calculates the total enthalpy needed for each stream

Hhot=entHC1(B,slopeB); %enthalpy needed for each hot stream section

Hhotpt(1)=0; %calculates the y value of the hot stream at each point

for i=2:(length(Hhot)+1)

Hhotpt(i) = (Hhot(i-1)+Hhotpt(i-1));

end

u = linspace(B(1), B(end), 1000)';

[k,k] = histc(u,B);

n = length(B);

k(k == n) = n-1;

yinterp1 = interp1(B,Hhotpt,u, 'linear')';

I also was wondering if this is how i would correctly evaluate a point on the piecewise curve:

check = ppval(yinterp1, 40);

Walter Roberson 2012-1-3

yinterp1 = interp1(B, Hhotpt, 'linear', 'pp');

Notice the "u" is not passed, as you are not interpolating at specific points when you create the pp.

David Hagan 2012-1-3

Works like a charm!

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Best method to define a linear piece-wise function given limits and line equations?

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