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Interpolating X axis values using a Y axis value and interp1 command.

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% I need to interpolate this data using the interp1 command and find the X
% value (time) when the Y value is 105. I do not know how to
% reverse-interpolate this data to find the X value?
Ti=[0 1 2 3 4 5 6 7 8 9 10];
Temp=[72.5 78.1 86.4 92.3 110.6 111.5 109.3 110.2 110.5 109.9 110.2];
y=interp1(Ti,Temp,105,'pchip')
n=interp1(Temp,Ti,105,'pchip')
% I tried to reverse the axises in order to find the time value using an
% interp1 command, however it dosent work either? I have been told to use
% an fzero command however I am unsure of how to apply it?
  1 Comment
Stephen
Stephen on 17 Jul 2021
"I tried to reverse the axises in order to find the time value using an interp1 command, however it dosent work either"
Lets first have a look at your data:
Ti = [0,1,2,3,4,5,6,7,8,9,10];
Temp = [72.5,78.1,86.4,92.3,110.6,111.5,109.3,110.2,110.5,109.9,110.2];
plot(Ti,Temp)
Now answer this very simple question: what is the expected Ti value for Temp==110 ?

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Accepted Answer

Image Analyst
Image Analyst on 17 Jul 2021
Try this:
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format short g;
format compact;
fontSize = 15;
fprintf('Beginning to run %s.m ...\n', mfilename);
Ti=[0 1 2 3 4 5 6 7 8 9 10];
Temp=[72.5 78.1 86.4 92.3 110.6 111.5 109.3 110.2 110.5 109.9 110.2];
plot(Ti, Temp, 'b.', 'MarkerSize', 50);
xlabel('Ti', 'FontSize', fontSize);
ylabel('Temp', 'FontSize', fontSize);
xFit = linspace(min(Ti), max(Ti), 30000);
yFit = interp1(Ti, Temp, xFit, 'pchip');
hold on;
darkGreen = [0, 0.5, 0];
plot(xFit, yFit, '-', 'Color', darkGreen, 'LineWidth', 2);
index = find(yFit >= 105, 1, 'first')
x = xFit(index);
xline(x, 'Color', 'r', 'LineWidth', 2);
yline(105, 'Color', 'r', 'LineWidth', 2);
grid on;
str = sprintf('Ti = %.3f when Temp = %.2f', xFit(index), yFit(index));
title(str, 'FontSize', fontSize);

More Answers (1)

Torsten
Torsten on 17 Jul 2021
f = @(x) (interp1(Ti,Temp,x,'pchip') - 105);
x0 = 3;
Ti105 = fzero(f,x0)

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