rounding

Functions for rounding numbers.

UncertainQtty

Data container associating uncertainty (confidence) to a quantity.

Includes intelligent rounding and printing functionality.

Usually, the precision parameter will be set to the (potentially estimated) standard deviation of an uncertain quantity. However, this class in itself does not define the prec attribute by anything else than what it does: impact the rounding & printing of val.

Examples:

>>> for c in [.01, .1, .2, .9, 1]:
...    print(UncertainQtty(1.2345, c))
1.23 ±0.01
1.2 ±0.1
1.2 ±0.2
1.2 ±0.9
1 ±1

>>> for c in [.01, 1e-10, 1e-17, 0]:
...    print(UncertainQtty(1.2, c))
1.20 ±0.01
1.2000000000 ±1e-10
1.19999999999999996 ±1e-17
1.2000000000 ±0

Note that in the case of a confidence of exactly 0, it defaults to 10 decimal places. Meanwhile, a NaN confidence yields printing using rc.sigfig:

>>> print(UncertainQtty(1.234567, np.nan))
1.235 ±nan

Also note the effect of large uncertainty:

>>> for c in [1, 9, 10, 11, 20, 100, np.inf]:
...    print(UncertainQtty(12, c))
12 ±1
12 ±9
10 ±10
10 ±10
10 ±20
0 ±100
0 ±inf

__repr__()

Essentially the same as __str__.

__str__()

Returns 'val ±prec', using tools.rounding.UncertainQtty.round

and some finesse.

round()

Round intelligently.

• prec to 1 sig.fig.
• val to round2(val, prec).

is_whole(x, **kwargs)

Check if a number is a whole/natural number to precision given by np.isclose.

For actual type checking, use isinstance(x, (int, np.integer)).

Parameters:

Name	Type	Description	Default
x	float or ndarray	Values to be checked	required

Returns:

Name	Type	Description
l	bool	True if rounded x is close to x, otherwise False

log10int(x)

Compute decimal order, rounded down.

Conversion to int means that we cannot return nan's or ± infinity, even though this could be meaningful. Instead, we return integers of magnitude a little less than IEEE floating point max/min-ima instead. This avoids a lot of clauses in the parent/callers to this function.

Examples:

>>> log10int([1e-1, 1e-2, 1, 3, 10, np.inf, -np.inf, np.nan])
array([  -1,   -2,    0,    0,    1,  300, -300, -300])

np_vectorize(f)

Like np.vectorize, but with some embellishments.

• Includes functools.wraps
• Applies .item() to output if input was a scalar.

Parameters:

Name	Type	Description	Default
f	callable	Your function.	required

Returns:

Name	Type	Description
vectorized	callable	Your function, now element-wise applicable to an iterable.

round2(x, prec=1.0)

Round x to the decimal order appropriate for the precision.

Parameters:

Name	Type	Description	Default
x	array_like	Value to be rounded.	required
prec	float	Precision, before prettify, which is given by $$ \text{prec} = 10^{\text{floor}(-\log_{10}|\text{prec}|)} $$	1.0

Returns:

Type	Description
Rounded value (always a float).

See Also

round2sigfig

Examples:

>>> round2(1.65, 0.543)
1.6
>>> round2(1.66, 0.543)
1.7
>>> round2(1.65, 1.234)
2.0

round2sigfig(x, sigfig=1)

Round to significant figures.

Parameters:

Name	Type	Description	Default
x		Value to be rounded.	required
sigfig		Number of significant figures to include.	1

Returns:

Type	Description
rounded value (always a float).

See Also

np.round : rounds to a given number of decimals. round2 : rounds to a given precision.

Examples:

>>> round2sigfig(1234.5678, 1)
1000.0
>>> round2sigfig(1234.5678, 4)
1235.0
>>> round2sigfig(1234.5678, 6)
1234.57