MATLAB: Reversing the inverse hyperbolic sine function

data

Y = asinh(X) 
to get Y which is the inverse hyperbolic sine value. I have Y , how can I get x?

Best Answer

MATLAB also has hyperbolic sin sinh() function.

y = asinh(x);
sinh(y)

sinh(y) will give back x.

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MATLAB: Transform a discontinuous function to continuous form

There are a few transforms available in the Symbolic Math Toolbox, but I am not sure that they would show you continuity or not.

fourier

laplace

Z-transform

MATLAB: Hyperbolic Least Squares Interpolation

You can use core MATLAB functions to do the regression:

x = ...;                                                    % Independent Variable
y = ...;                                                    % Dependent Variable
fcn1 = @(b,x) b(1)./(b(2).*x + b(3));                       % Objective Function #1
fcn2 = @(b,x) b(1)./(b(2).*x);                              % Objective Function #2
SSECF = @(b) sum((y - fcn2(b,x)).^2);                       % Sum-Squared-Error Cost Function (Use ‘fcn2’ Here)
B0 = [1; 1];                                                % Initial Parameter Estimates
[B,SSE] = fminsearch(SSECF, [1; 1]);                        % Estimate Parameters
xv = linspace(min(x), max(x));
figure(1)
plot(x, y, 'bp')
hold on
plot(xv, fcn2(B,xv), '-r')
hold off
grid

I tested this with random vectors and it ran without error.

EDIT — Note that the two-parameter model you want requires only one parameter. A simple ratio (or product) of parameters will not uniquely identify either of them, only the ratio (or product). The three-parameter model actually makes sense.

Best Answer

Related Solutions

MATLAB: Transform a discontinuous function to continuous form

MATLAB: Hyperbolic Least Squares Interpolation

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