Avoiding -0.0000 as an output

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Left Terry
Left Terry 2025-2-3
编辑： Left Terry 2025-2-3
Ran in:
Hello. I have the following script for differentiation and for some functions (e.g. f(x) = x) I get f'''(1) and f''''(1) equal to -0.0000. How can i avoid the minus sign when the reasult is zero ?
clear all, clc, format long e
f = @(x) x; %input('Enter f(x) = ');
x = 1; %input('Enter point: x = ');
tol = 1e-1; %input('Enter tolerance: ');
f3 = feval(f,x);
h = tol*f3;
f0 = feval(f,x-3*h);
f1 = feval(f,x-2*h);
f2 = feval(f,x-1*h);
f4 = feval(f,x+1*h);
f5 = feval(f,x+2*h);
f6 = feval(f,x+3*h);
d1f = (f1-8*f2+8*f4-f5)/12/h;
d2f = (-f1+16*f2-30*f3+16*f4-f5)/12/h^2;
d3f = (f0-8*f1+13*f2-13*f4+8*f5-f6)/8/h^3;
d4f = (-f0+12*f1-39*f2+56*f3-39*f4+12*f5-f6)/6/h^4;
p = [d1f;d2f;d3f;d4f];
fprintf('\nFirst derivative at x = %g:\tf''(%g) = %f\n',x,x,d1f);
First derivative at x = 1: f'(1) = 1.000000
fprintf('\nSecond derivative at x = %g:\tf''''(%g) = %f\n',x,x,d2f);
Second derivative at x = 1: f''(1) = 0.000000
fprintf('\nThird derivative at x = %g:\tf''''''(%g) = %f\n',x,x,d3f);
Third derivative at x = 1: f'''(1) = -0.000000
fprintf('\nFourth derivative at x = %g:\tf''''''''(%g) = %f\n',x,x,d4f);
Fourth derivative at x = 1: f''''(1) = -0.000000

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采纳的回答

Torsten
Torsten 2025-2-3
移动：Steven Lord 2025-2-3
The results for d2,...,d4 aren't exactly 0 because of floating point errors in their computation. So without artificially manipulating the results, you can't get rid of the minus sign.
  1 个评论
Left Terry
Left Terry 2025-2-3
编辑：Left Terry 2025-2-3
Ran in:
@Torsten That is true, i just discovered what you said by making a small change. The results are extremely small and negative.
clear all, clc, format long e
f = @(x) x; %input('Enter f(x) = ');
x = 1; %input('Enter point: x = ');
tol = 1e-1; %input('Enter tolerance: ');
f3 = feval(f,x);
h = tol*f3;
f0 = feval(f,x-3*h);
f1 = feval(f,x-2*h);
f2 = feval(f,x-1*h);
f4 = feval(f,x+1*h);
f5 = feval(f,x+2*h);
f6 = feval(f,x+3*h);
d1f = (f1-8*f2+8*f4-f5)/12/h;
d2f = (-f1+16*f2-30*f3+16*f4-f5)/12/h^2;
d3f = (f0-8*f1+13*f2-13*f4+8*f5-f6)/8/h^3;
d4f = (-f0+12*f1-39*f2+56*f3-39*f4+12*f5-f6)/6/h^4;
p = [d1f;d2f;d3f;d4f];
fprintf('\nFirst derivative at x = %g:\tf''(%g) = %g\n',x,x,d1f);
First derivative at x = 1: f'(1) = 1
fprintf('\nSecond derivative at x = %g:\tf''''(%g) = %g\n',x,x,d2f);
Second derivative at x = 1: f''(1) = 2.40548e-14
fprintf('\nThird derivative at x = %g:\tf''''''(%g) = %g\n',x,x,d3f);
Third derivative at x = 1: f'''(1) = -1.38778e-13
fprintf('\nFourth derivative at x = %g:\tf''''''''(%g) = %g\n',x,x,d4f);
Fourth derivative at x = 1: f''''(1) = -1.07322e-11

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