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17.1 Exponents and Logarithms ¶

 

: y = exp (x) ¶

Compute e^x for each element of x.

To compute the matrix exponential, see Linear Algebra.

See also: log.

 

: y = expm1 (x) ¶

Compute exp (x) - 1 accurately in the neighborhood of zero.

See also: exp.

 

: y = log (x) ¶

Compute the natural logarithm, ln (x), for each element of x.

To compute the matrix logarithm, see Linear Algebra.

See also: exp, log1p, log2, log10, logspace.

 

: y = 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: log, realpow, realsqrt.

 

: y = log1p (x) ¶

Compute log (1 + x) accurately in the neighborhood of zero.

See also: log, exp, expm1.

 

: y = log10 (x) ¶

Compute the base-10 logarithm of each element of x.

See also: log, log2, logspace, exp.

 

: y = log2 (x) ¶

: [f, e] = log2 (x) ¶

Compute the base-2 logarithm of each element of x.

If called with one output, compute the base-2 logarithm such that 2^y = x.

If called with two output arguments, split x into binary mantissa (f) and exponent (e) such that x = f * 2^e where 1/2 <= abs (f) < 1 and e is an integer. If x = 0, f = e = 0.

See also: pow2, log, log10, exp.

 

: y = pow2 (x) ¶

: y = pow2 (f, e) ¶

With one input argument, compute y = 2 .^ x for each element of x.

With two input arguments, return y = f .* (2 .^ e). where for complex inputs only the real part of both inputs is regarded and from e only the real integer part. This calling form corresponds to C/C++ standard function ldexp().

See also: log2, nextpow2, power.

 

: n = 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: pow2, log2.

 

: z = 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: power, reallog, realsqrt.

 

: y = 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 Linear Algebra.

See also: realsqrt, nthroot.

 

: y = 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: sqrt, realpow, reallog.

 

: y = cbrt (x) ¶

Compute the real-valued cube root of each element of x.

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

If any element of x is complex, cbrt aborts with an error.

See also: nthroot.

 

: y = 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: realsqrt, sqrt, cbrt.