linear interpolation of function handle

Question

Gianluca Angelini 2023-11-29

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2053932-linear-interpolation-of-function-handle

回答： Nipun 2023-12-21

Hi everybody, I need to calculate the value in the range pi <= wave_angle < pi/2 of the a function handle @(freq_wave,wave_angle) which is defined as:

((log(B/T))^-1).*(0.87/CB).^((1+Fn).*cos(wave_angle)).*(1/3-(2/3).*cos(wave_angle))

in the range ((wave_angle >=0) & (wave_angle <= pi/2))

((log(B/T))^-1).*(0.87/CB).^(1+Fn) in the range (wave_angle=pi)&(vel_nave>V_G(freq_wave)./2)&(Fn_rel(freq_wave)>=0.12)

((log(B/T))^-1).*(0.87/CB) in the range (wave_angle=pi)&(vel_nave<V_G(freq_wave)./2)+ ((log(B/T))^-1).*(0.87/CB) .*(wave_angle=pi)&(Fn_rel(freq_wave)<0.12);

but I don't konw which function is the best to use. Thanks in advance for your help.

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Torsten 2023-11-29

编辑：Torsten 2023-11-29

在 MATLAB Online 中打开

As you can see, none of the four conditions is satisfied for your inputs. Thus the result is logical 0.

(Note that I added additional brackets around your conditions).

Extrapolating values for a1 over the limits where a1 is defined is completely arbitrary and thus nonsense.

B=22.5; T=7; CB=0.59; Fn=0.2; vel_nave=10.28; g=1;Lpp=1;
V_G=@(freq_wave) g/(2*freq_wave);
Fn_rel=@(freq_wave) (vel_nave-V_G(freq_wave)/2)/(g*Lpp)^0.5;
a1=@(freq_wave,wave_angle) ((log(B/T))^-1).*(0.87/CB).^((1+Fn).*cos(wave_angle)).*(1/3-(2/3).*cos(wave_angle)).*((wave_angle >=0) & (wave_angle <= pi/2)) +...
((log(B/T))^-1).*(0.87/CB).^(1+Fn) .*((wave_angle==pi)&(vel_nave>V_G(freq_wave)./2)&(Fn_rel(freq_wave)>=0.12)) +...
((log(B/T))^-1).*(0.87/CB) .*((wave_angle==pi)&(vel_nave<V_G(freq_wave)./2))+...
((log(B/T))^-1).*(0.87/CB) .*((wave_angle==pi)&(Fn_rel(freq_wave)<0.12));
freq_wave = 5;
wave_angle = 2.09;
((wave_angle >=0) & (wave_angle <= pi/2))
ans = logical
   0
((wave_angle==pi)&(vel_nave>V_G(freq_wave)./2)&(Fn_rel(freq_wave)>=0.12))
ans = logical
   0
((wave_angle==pi)&(vel_nave<V_G(freq_wave)./2))
ans = logical
   0
((wave_angle==pi)&(Fn_rel(freq_wave)<0.12))
ans = logical
   0
a1(5,2.09)
ans = 0

Gianluca Angelini 2023-11-29

在 MATLAB Online 中打开

Hi Torsten, thanks for you support. Your results are exactlay what the code do at this moment: I need to fill the empty space where the function a1 is not defined by interporlating its defintion between

((log(B/T))^-1).*(0.87/CB).^((1+Fn).*cos(wave_angle)).*(1/3-(2/3).*cos(wave_angle))

valid only for

((wave_angle >=0) & (wave_angle <= pi/2))

and

((log(B/T))^-1).*(0.87/CB).^(1+Fn) .*(vel_nave>V_G(freq_wave)./2)&(Fn_rel(freq_wave)>=0.12)) +...
((log(B/T))^-1).*(0.87/CB) .*((vel_nave<V_G(freq_wave)./2))+...
((log(B/T))^-1).*(0.87/CB) .*((Fn_rel(freq_wave)<0.12));

valid only for

(wave_angle==pi)

Torsten 2023-11-29

编辑：Torsten 2023-11-29

And what should be the "interpolating" function ? It's completely arbitrary at the moment.

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Answer 1

Nipun 2023-12-21

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https://ww2.mathworks.cn/matlabcentral/answers/2053932-linear-interpolation-of-function-handle#answer_1375382

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Hi Gianluca,

I understand that you are trying to evaluate a semantic relation, given the variable values. In the illustrated case, the equation to be used changes according to the range of the input.

It seems like you have a piecewise function defined over different ranges of wave_angle. In MATLAB, you can use the if, elseif, and else statements to define a piecewise function. The if statements can be used to check the conditions for each range and evaluate the corresponding expression.

Here is a code snippet to help you with the same:

function result = your_function(freq_wave, wave_angle, B, T, CB, Fn, vel_nave)
    if wave_angle >= 0 && wave_angle < pi/2
        result = ((log(B/T))^-1) .* (0.87/CB).^((1+Fn).*cos(wave_angle)) .* (1/3 - (2/3) .* cos(wave_angle));
    elseif wave_angle == pi && vel_nave > V_G(freq_wave)/2 && Fn_rel(freq_wave) >= 0.12
        result = ((log(B/T))^-1) .* (0.87/CB).^(1+Fn);
    elseif wave_angle == pi && vel_nave < V_G(freq_wave)/2
        result = ((log(B/T))^-1) .* (0.87/CB);
    elseif wave_angle == pi && Fn_rel(freq_wave) < 0.12
        result = ((log(B/T))^-1) .* (0.87/CB) .* (wave_angle == pi) .* (Fn_rel(freq_wave) < 0.12);
    else
        % Define default behavior if none of the conditions are met
        result = NaN; % or any default value you prefer
    end
end

This function checks the conditions for each range of wave_angle and evaluates the corresponding expression. You can adjust the conditions and expressions based on your specific requirements. The result variable holds the final value of the function for a given set of input parameters.

Since the signature and description of functions "Fn_rel" and others were not provided, I assume that they work as expected.

Hope this helps.

Regards,

Nipun