(octave.info)Exponents and Logarithms

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17.1 Exponents and Logarithms
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 -- : exp (X)
     Compute ‘e^x’ for each element of X.

     To compute the matrix exponential, see Note: Linear Algebra.

     See also: Note: log.

 -- : expm1 (X)
     Compute ‘exp (X) - 1’ accurately in the neighborhood of zero.

     See also: Note: exp.

 -- : log (X)
     Compute the natural logarithm, ‘ln (X)’, for each element of X.

     To compute the matrix logarithm, see Note: Linear Algebra.

     See also: Note: exp, Note: log1p, *note log2:
     XREFlog2, Note: log10, Note: logspace.

 -- : reallog (X)
     Return the real-valued natural logarithm of each element of X.

     If any element results in a complex return value ‘reallog’ aborts
     and issues an error.

     See also: Note: log, Note: realpow, Note:
     realsqrt.

 -- : log1p (X)
     Compute ‘log (1 + X)’ accurately in the neighborhood of zero.

     See also: Note: log, Note: exp, *note expm1:
     XREFexpm1.

 -- : log10 (X)
     Compute the base-10 logarithm of each element of X.

     See also: Note: log, Note: log2, *note logspace:
     XREFlogspace, Note: exp.

 -- : log2 (X)
 -- : [F, E] = log2 (X)
     Compute the base-2 logarithm of each element of X.

     If called with two output arguments, split X into binary mantissa
     and exponent so that ‘1/2 <= abs(f) < 1’ and E is an integer.  If
     ‘x = 0’, ‘f = e = 0’.

     See also: Note: pow2, Note: log, *note log10:
     XREFlog10, Note: exp.

 -- : pow2 (X)
 -- : pow2 (F, E)
     With one input argument, compute 2 .^ x for each element of X.

     With two input arguments, return f .* (2 .^ e).

     See also: Note: log2, Note: nextpow2, Note:
     power.

 -- : nextpow2 (X)
     Compute the exponent for the smallest power of two larger than the
     input.

     For each element in the input array X, return the first integer N
     such that 2^n ≥ abs (x).

     See also: Note: pow2, Note: log2.

 -- : realpow (X, Y)
     Compute the real-valued, element-by-element power operator.

     This is equivalent to ‘X .^ Y’, except that ‘realpow’ reports an
     error if any return value is complex.

     See also: Note: power, Note: reallog, Note:
     realsqrt.

 -- : sqrt (X)
     Compute the square root of each element of X.

     If X is negative, a complex result is returned.

     To compute the matrix square root, see Note: Linear Algebra.

     See also: Note: realsqrt, Note: nthroot.

 -- : realsqrt (X)
     Return the real-valued square root of each element of X.

     If any element results in a complex return value ‘realsqrt’ aborts
     and issues an error.

     See also: Note: sqrt, Note: realpow, Note:
     reallog.

 -- : cbrt (X)
     Compute the real cube root of each element of X.

     Unlike ‘X^(1/3)’, the result will be negative if X is negative.

     See also: Note: nthroot.

 -- : nthroot (X, N)

     Compute the real (non-complex) N-th root of X.

     X must have all real entries and N must be a scalar.  If N is an
     even integer and X has negative entries then ‘nthroot’ aborts and
     issues an error.

     Example:

          nthroot (-1, 3)
          ⇒ -1
          (-1) ^ (1 / 3)
          ⇒ 0.50000 - 0.86603i

     See also: Note: realsqrt, Note: sqrt, Note:
     cbrt.