Make very small numbers in complex matrix zero

format shortG

a11 = 0;
a12 = exp(-j*0.5*pi);
a21 = exp(-j*0.5*pi);
a22 = 0;

S = [a11, a12; a21, a22]

S = 
            0 +          0i   6.1232e-17 -          1i
   6.1232e-17 -          1i            0 +          0i

A = ((1+a11)*(1-a22)+a12*a21)/(2*a21);
B = ((1+a11)*(1+a22)-a12*a21)/(2*a21);
C = ((1-a11)*(1-a22)-a12*a21)/(2*a21);
D = ((1-a11)*(1+a22)+a12*a21)/(2*a21);

X = [A, B; C, D]

X = 
   6.1232e-17 - 3.7494e-33i            0 +          1i
            0 +          1i   6.1232e-17 - 3.7494e-33i

X_cleanup = X;
X_cleanup(abs(X_cleanup)<0.0001) = 0

X_cleanup = 
            0 +          0i            0 +          1i
            0 +          1i            0 +          0i

Is there a way to automatically ask matlab to output matrix like what's in the X_cleanup instead of X?

Is there anyting under 'format'?

[Mathieu NOE]

hi

why not simply make the clean up a function that you can call anytime ?

[Math Works]

It's just a bit annoying having to do that.

Answer 1

[Matt J]

Is there a way to automatically ask matlab to output matrix like what's in the X_cleanup instead of X?

No, but note that if you expect your input data to be integer-valued, you can avoid the issue by generating them in integer form directly:

format shortG

a11 = 0;
a12 = -1i;
a21 = -1i;
a22 = 0;

S = [a11, a12; a21, a22]

S = 
            0 +          0i            0 -          1i
            0 -          1i            0 +          0i

A = ((1+a11)*(1-a22)+a12*a21)/(2*a21);
B = ((1+a11)*(1+a22)-a12*a21)/(2*a21);
C = ((1-a11)*(1-a22)-a12*a21)/(2*a21);
D = ((1-a11)*(1+a22)+a12*a21)/(2*a21);

X = [A, B; C, D]

X = 
            0 +          0i            0 +          1i
            0 +          1i            0 +          0i

[Math Works]

No, they are obviously not integers. They are complex numbers with decimals.

[Matt J]

No, they are obviously not integers

No, that is not obvious. In your example, it is clear that the complex numbers are intended to have integer-valued real and imaginary parts. The function call,

a12 = exp(-j*0.5*pi);

would generate a12=-1i in an infinite precision computer.

[Math Works]

The formula must work for all inputs and outputs.

I am expecting sensible output matrices like ones in the picture below. I want decimals, but not "1e-32", because that's just zero from an Engineering perspective.

[Matt J]

Well like I said, you can't make Matlab truncate results to zero on autopilot.

I think you would regret it even if it were implementable. In the situation you describe, Matlab would have no way of knowing if a computation was the final one or just an intermediate step in a future computation you are planning, so basically truncation would occur at every step in your computational pipeline and accumulate unpredictably.

[Math Works]

Okay, that's a good point.