21.2.2  Finding and removing leading/trailing zeros

You can find leading and/or trailing zeros in a vector and remove them by using the trim command (see Section 5.2.5, Section 28.1.9 and Section 28.2.2 for other usages of trim).

• trim takes one mandatory argument and up to three optional arguments:
  • v, a vector of real or complex numbers.
  • Optionally, threshold, a positive real number specifying the threshold for zeros (by default, threshold=epsilon(), the working precision).
  • Optionally, either left or right, the symbol specifiying one-sided trimming.
  • Optionally, index, the symbol.
• trim(v ⟨,threshold  ⟩ ⟨,left|right ⟩ ⟨,index ⟩) finds the index l of the first nonzero element in v and the index u of the first trailing zero in v. A number z is considered to be zero if |z|≤threshold. If index is given, then the return value is either l if left is given, u if right is given, or (l,u−l) otherwise (the last sequence contains the start and length of the truncated vector). If index is omitted, then the return value is the portion of v between v[l] (inclusive) and v[u] (exclusive); if left is given, then u=length(v), and if right is given, then l=0.

Example

To remove leading zeros from v:

To remove leading and trailing zeros with threshold set to 10⁻¹⁴ (the default is the value of epsilon(), which is 10⁻¹² in this case):

To return the start and length of the nonzero part of v:

Now, enter

to obtain the trimmed variant of v.