Source code for sas.sascalc.data_util.formatnum

# This program is public domain
# Author: Paul Kienzle
"""
Format values and uncertainties nicely for printing.

:func:`format_uncertainty_pm` produces the expanded format v +/- err.

:func:`format_uncertainty_compact` produces the compact format v(##),
where the number in parenthesis is the uncertainty in the last two digits of v.

:func:`format_uncertainty` uses the compact format by default, but this
can be changed to use the expanded +/- format by setting 
format_uncertainty.compact to False.
    
The formatted string uses only the number of digits warranted by
the uncertainty in the measurement.

If the uncertainty is 0 or not otherwise provided, the simple
%g floating point format option is used.

Infinite and indefinite numbers are represented as inf and NaN.

Example::

    >>> v,dv = 757.2356,0.01032
    >>> print format_uncertainty_pm(v,dv)
    757.236 +/- 0.010
    >>> print format_uncertainty_compact(v,dv)
    757.236(10)
    >>> print format_uncertainty(v,dv)
    757.236(10)
    >>> format_uncertainty.compact = False
    >>> print format_uncertainty(v,dv)
    757.236 +/- 0.010

UncertaintyFormatter() returns a private formatter with its own
formatter.compact flag.
"""
from __future__ import division

import math
import numpy
__all__ = ['format_uncertainty', 'format_uncertainty_pm',
           'format_uncertainty_compact']

# Coordinating scales across a set of numbers is not supported.  For easy
# comparison a set of numbers should be shown in the same scale.  One could
# force this from the outside by adding scale parameter (either 10**n, n, or
# a string representing the desired SI prefix) and having a separate routine
# which computes the scale given a set of values.

# Coordinating scales with units offers its own problems.  Again, the user
# may want to force particular units.  This can be done by outside of the
# formatting routines by scaling the numbers to the appropriate units then
# forcing them to print with scale 10**0.  If this is a common operation,
# however, it may want to happen inside.

# The value e<n> is currently formatted into the number.  Alternatively this
# scale factor could be returned so that the user can choose the appropriate
# SI prefix when printing the units.  This gets tricky when talking about
# composite units such as 2.3e-3 m**2 -> 2300 mm**2, and with volumes
# such as 1 g/cm**3 -> 1 kg/L.


[docs]def format_uncertainty_pm(value, uncertainty): """ Given *value* v and *uncertainty* dv, return a string v +/- dv. """ return _format_uncertainty(value, uncertainty, compact=False)
[docs]def format_uncertainty_compact(value, uncertainty): """ Given *value* v and *uncertainty* dv, return the compact representation v(##), where ## are the first two digits of the uncertainty. """ return _format_uncertainty(value, uncertainty, compact=True)
class UncertaintyFormatter: """ Value and uncertainty formatter. The *formatter* instance will use either the expanded v +/- dv form or the compact v(##) form depending on whether *formatter.compact* is True or False. The default is True. """ compact = True def __call__(self, value, uncertainty): """ Given *value* and *uncertainty*, return a string representation. """ return _format_uncertainty(value, uncertainty, self.compact) format_uncertainty = UncertaintyFormatter() def _format_uncertainty(value, uncertainty, compact): """ Implementation of both the compact and the +/- formats. """ # Handle indefinite value if numpy.isinf(value): return "inf" if value > 0 else "-inf" if numpy.isnan(value): return "NaN" # Handle indefinite uncertainty if uncertainty is None or uncertainty <= 0 or numpy.isnan(uncertainty): return "%g" % value if numpy.isinf(uncertainty): if compact: return "%.2g(inf)" % value else: return "%.2g +/- inf" % value # Handle zero and negative values sign = "-" if value < 0 else "" value = abs(value) # Determine scale of value and error err_place = int(math.floor(math.log10(uncertainty))) if value == 0: val_place = err_place - 1 else: val_place = int(math.floor(math.log10(value))) if err_place > val_place: # Degenerate case: error bigger than value # The mantissa is 0.#(##)e#, 0.0#(##)e# or 0.00#(##)e# val_place = err_place + 2 elif err_place == val_place: # Degenerate case: error and value the same order of magnitude # The value is ##(##)e#, #.#(##)e# or 0.##(##)e# val_place = err_place + 1 elif err_place <= 1 and val_place >= -3: # Normal case: nice numbers and errors # The value is ###.###(##) val_place = 0 else: # Extreme cases: zeros before value or after error # The value is ###.###(##)e#, ##.####(##)e# or #.#####(##)e# pass # Force engineering notation, with exponent a multiple of 3 val_place = int(math.floor(val_place / 3.)) * 3 # Format the result digits_after_decimal = abs(val_place - err_place + 1) val_str = "%.*f" % (digits_after_decimal, value / 10.**val_place) exp_str = "e%d" % val_place if val_place != 0 else "" if compact: err_str = "(%2d)" % int(uncertainty / 10.**(err_place - 1) + 0.5) result = "".join((sign, val_str, err_str, exp_str)) else: err_str = "%.*f" % (digits_after_decimal, uncertainty / 10.**val_place) result = "".join((sign, val_str, exp_str + " +/- ", err_str, exp_str)) return result def test_compact(): # Oops... renamed function after writing tests value_str = format_uncertainty_compact # val_place > err_place assert value_str(1235670,766000) == "1.24(77)e6" assert value_str(123567.,76600) == "124(77)e3" assert value_str(12356.7,7660) == "12.4(77)e3" assert value_str(1235.67,766) == "1.24(77)e3" assert value_str(123.567,76.6) == "124(77)" assert value_str(12.3567,7.66) == "12.4(77)" assert value_str(1.23567,.766) == "1.24(77)" assert value_str(.123567,.0766) == "0.124(77)" assert value_str(.0123567,.00766) == "0.0124(77)" assert value_str(.00123567,.000766) == "0.00124(77)" assert value_str(.000123567,.0000766) == "124(77)e-6" assert value_str(.0000123567,.00000766) == "12.4(77)e-6" assert value_str(.00000123567,.000000766) == "1.24(77)e-6" assert value_str(.000000123567,.0000000766) == "124(77)e-9" assert value_str(.00000123567,.0000000766) == "1.236(77)e-6" assert value_str(.0000123567,.0000000766) == "12.357(77)e-6" assert value_str(.000123567,.0000000766) == "123.567(77)e-6" assert value_str(.00123567,.000000766) == "0.00123567(77)" assert value_str(.0123567,.00000766) == "0.0123567(77)" assert value_str(.123567,.0000766) == "0.123567(77)" assert value_str(1.23567,.000766) == "1.23567(77)" assert value_str(12.3567,.00766) == "12.3567(77)" assert value_str(123.567,.0764) == "123.567(76)" assert value_str(1235.67,.764) == "1235.67(76)" assert value_str(12356.7,7.64) == "12356.7(76)" assert value_str(123567,76.4) == "123567(76)" assert value_str(1235670,764) == "1.23567(76)e6" assert value_str(12356700,764) == "12.35670(76)e6" assert value_str(123567000,764) == "123.56700(76)e6" assert value_str(123567000,7640) == "123.5670(76)e6" assert value_str(1235670000,76400) == "1.235670(76)e9" # val_place == err_place assert value_str(123567,764000) == "0.12(76)e6" assert value_str(12356.7,76400) == "12(76)e3" assert value_str(1235.67,7640) == "1.2(76)e3" assert value_str(123.567,764) == "0.12(76)e3" assert value_str(12.3567,76.4) == "12(76)" assert value_str(1.23567,7.64) == "1.2(76)" assert value_str(.123567,.764) == "0.12(76)" assert value_str(.0123567,.0764) == "12(76)e-3" assert value_str(.00123567,.00764) == "1.2(76)e-3" assert value_str(.000123567,.000764) == "0.12(76)e-3" # val_place == err_place-1 assert value_str(123567,7640000) == "0.1(76)e6" assert value_str(12356.7,764000) == "0.01(76)e6" assert value_str(1235.67,76400) == "0.001(76)e6" assert value_str(123.567,7640) == "0.1(76)e3" assert value_str(12.3567,764) == "0.01(76)e3" assert value_str(1.23567,76.4) == "0.001(76)e3" assert value_str(.123567,7.64) == "0.1(76)" assert value_str(.0123567,.764) == "0.01(76)" assert value_str(.00123567,.0764) == "0.001(76)" assert value_str(.000123567,.00764) == "0.1(76)e-3" # val_place == err_place-2 assert value_str(12356700,7640000000) == "0.0(76)e9" assert value_str(1235670,764000000) == "0.00(76)e9" assert value_str(123567,76400000) == "0.000(76)e9" assert value_str(12356,7640000) == "0.0(76)e6" assert value_str(1235,764000) == "0.00(76)e6" assert value_str(123,76400) == "0.000(76)e6" assert value_str(12,7640) == "0.0(76)e3" assert value_str(1,764) == "0.00(76)e3" assert value_str(0.1,76.4) == "0.000(76)e3" assert value_str(0.01,7.64) == "0.0(76)" assert value_str(0.001,0.764) == "0.00(76)" assert value_str(0.0001,0.0764) == "0.000(76)" assert value_str(0.00001,0.00764) == "0.0(76)e-3" # val_place == err_place-3 assert value_str(12356700,76400000000) == "0.000(76)e12" assert value_str(1235670,7640000000) == "0.0(76)e9" assert value_str(123567,764000000) == "0.00(76)e9" assert value_str(12356,76400000) == "0.000(76)e9" assert value_str(1235,7640000) == "0.0(76)e6" assert value_str(123,764000) == "0.00(76)e6" assert value_str(12,76400) == "0.000(76)e6" assert value_str(1,7640) == "0.0(76)e3" assert value_str(0.1,764) == "0.00(76)e3" assert value_str(0.01,76.4) == "0.000(76)e3" assert value_str(0.001,7.64) == "0.0(76)" assert value_str(0.0001,0.764) == "0.00(76)" assert value_str(0.00001,0.0764) == "0.000(76)" assert value_str(0.000001,0.00764) == "0.0(76)e-3" # Zero values assert value_str(0,7640000) == "0.0(76)e6" assert value_str(0, 764000) == "0.00(76)e6" assert value_str(0, 76400) == "0.000(76)e6" assert value_str(0, 7640) == "0.0(76)e3" assert value_str(0, 764) == "0.00(76)e3" assert value_str(0, 76.4) == "0.000(76)e3" assert value_str(0, 7.64) == "0.0(76)" assert value_str(0, 0.764) == "0.00(76)" assert value_str(0, 0.0764) == "0.000(76)" assert value_str(0, 0.00764) == "0.0(76)e-3" assert value_str(0, 0.000764) == "0.00(76)e-3" assert value_str(0, 0.0000764) == "0.000(76)e-3" # negative values assert value_str(-1235670,765000) == "-1.24(77)e6" assert value_str(-1.23567,.766) == "-1.24(77)" assert value_str(-.00000123567,.0000000766) == "-1.236(77)e-6" assert value_str(-12356.7,7.64) == "-12356.7(76)" assert value_str(-123.567,764) == "-0.12(76)e3" assert value_str(-1235.67,76400) == "-0.001(76)e6" assert value_str(-.000123567,.00764) == "-0.1(76)e-3" assert value_str(-12356,7640000) == "-0.0(76)e6" assert value_str(-12,76400) == "-0.000(76)e6" assert value_str(-0.0001,0.764) == "-0.00(76)" # non-finite values assert value_str(-numpy.inf,None) == "-inf" assert value_str(numpy.inf,None) == "inf" assert value_str(numpy.NaN,None) == "NaN" # bad or missing uncertainty assert value_str(-1.23567,numpy.NaN) == "-1.23567" assert value_str(-1.23567,-numpy.inf) == "-1.23567" assert value_str(-1.23567,-0.1) == "-1.23567" assert value_str(-1.23567,0) == "-1.23567" assert value_str(-1.23567,None) == "-1.23567" assert value_str(-1.23567,numpy.inf) == "-1.2(inf)" def test_pm(): # Oops... renamed function after writing tests value_str = format_uncertainty_pm # val_place > err_place assert value_str(1235670,766000) == "1.24e6 +/- 0.77e6" assert value_str(123567., 76600) == "124e3 +/- 77e3" assert value_str(12356.7, 7660) == "12.4e3 +/- 7.7e3" assert value_str(1235.67, 766) == "1.24e3 +/- 0.77e3" assert value_str(123.567, 76.6) == "124 +/- 77" assert value_str(12.3567, 7.66) == "12.4 +/- 7.7" assert value_str(1.23567, .766) == "1.24 +/- 0.77" assert value_str(.123567, .0766) == "0.124 +/- 0.077" assert value_str(.0123567, .00766) == "0.0124 +/- 0.0077" assert value_str(.00123567, .000766) == "0.00124 +/- 0.00077" assert value_str(.000123567, .0000766) == "124e-6 +/- 77e-6" assert value_str(.0000123567, .00000766) == "12.4e-6 +/- 7.7e-6" assert value_str(.00000123567, .000000766) == "1.24e-6 +/- 0.77e-6" assert value_str(.000000123567,.0000000766) == "124e-9 +/- 77e-9" assert value_str(.00000123567, .0000000766) == "1.236e-6 +/- 0.077e-6" assert value_str(.0000123567, .0000000766) == "12.357e-6 +/- 0.077e-6" assert value_str(.000123567, .0000000766) == "123.567e-6 +/- 0.077e-6" assert value_str(.00123567, .000000766) == "0.00123567 +/- 0.00000077" assert value_str(.0123567, .00000766) == "0.0123567 +/- 0.0000077" assert value_str(.123567, .0000766) == "0.123567 +/- 0.000077" assert value_str(1.23567, .000766) == "1.23567 +/- 0.00077" assert value_str(12.3567, .00766) == "12.3567 +/- 0.0077" assert value_str(123.567, .0764) == "123.567 +/- 0.076" assert value_str(1235.67, .764) == "1235.67 +/- 0.76" assert value_str(12356.7, 7.64) == "12356.7 +/- 7.6" assert value_str(123567, 76.4) == "123567 +/- 76" assert value_str(1235670, 764) == "1.23567e6 +/- 0.00076e6" assert value_str(12356700, 764) == "12.35670e6 +/- 0.00076e6" assert value_str(123567000, 764) == "123.56700e6 +/- 0.00076e6" assert value_str(123567000,7640) == "123.5670e6 +/- 0.0076e6" assert value_str(1235670000,76400) == "1.235670e9 +/- 0.000076e9" # val_place == err_place assert value_str(123567,764000) == "0.12e6 +/- 0.76e6" assert value_str(12356.7,76400) == "12e3 +/- 76e3" assert value_str(1235.67,7640) == "1.2e3 +/- 7.6e3" assert value_str(123.567,764) == "0.12e3 +/- 0.76e3" assert value_str(12.3567,76.4) == "12 +/- 76" assert value_str(1.23567,7.64) == "1.2 +/- 7.6" assert value_str(.123567,.764) == "0.12 +/- 0.76" assert value_str(.0123567,.0764) == "12e-3 +/- 76e-3" assert value_str(.00123567,.00764) == "1.2e-3 +/- 7.6e-3" assert value_str(.000123567,.000764) == "0.12e-3 +/- 0.76e-3" # val_place == err_place-1 assert value_str(123567,7640000) == "0.1e6 +/- 7.6e6" assert value_str(12356.7,764000) == "0.01e6 +/- 0.76e6" assert value_str(1235.67,76400) == "0.001e6 +/- 0.076e6" assert value_str(123.567,7640) == "0.1e3 +/- 7.6e3" assert value_str(12.3567,764) == "0.01e3 +/- 0.76e3" assert value_str(1.23567,76.4) == "0.001e3 +/- 0.076e3" assert value_str(.123567,7.64) == "0.1 +/- 7.6" assert value_str(.0123567,.764) == "0.01 +/- 0.76" assert value_str(.00123567,.0764) == "0.001 +/- 0.076" assert value_str(.000123567,.00764) == "0.1e-3 +/- 7.6e-3" # val_place == err_place-2 assert value_str(12356700,7640000000) == "0.0e9 +/- 7.6e9" assert value_str(1235670,764000000) == "0.00e9 +/- 0.76e9" assert value_str(123567,76400000) == "0.000e9 +/- 0.076e9" assert value_str(12356,7640000) == "0.0e6 +/- 7.6e6" assert value_str(1235,764000) == "0.00e6 +/- 0.76e6" assert value_str(123,76400) == "0.000e6 +/- 0.076e6" assert value_str(12,7640) == "0.0e3 +/- 7.6e3" assert value_str(1,764) == "0.00e3 +/- 0.76e3" assert value_str(0.1,76.4) == "0.000e3 +/- 0.076e3" assert value_str(0.01,7.64) == "0.0 +/- 7.6" assert value_str(0.001,0.764) == "0.00 +/- 0.76" assert value_str(0.0001,0.0764) == "0.000 +/- 0.076" assert value_str(0.00001,0.00764) == "0.0e-3 +/- 7.6e-3" # val_place == err_place-3 assert value_str(12356700,76400000000) == "0.000e12 +/- 0.076e12" assert value_str(1235670,7640000000) == "0.0e9 +/- 7.6e9" assert value_str(123567,764000000) == "0.00e9 +/- 0.76e9" assert value_str(12356,76400000) == "0.000e9 +/- 0.076e9" assert value_str(1235,7640000) == "0.0e6 +/- 7.6e6" assert value_str(123,764000) == "0.00e6 +/- 0.76e6" assert value_str(12,76400) == "0.000e6 +/- 0.076e6" assert value_str(1,7640) == "0.0e3 +/- 7.6e3" assert value_str(0.1,764) == "0.00e3 +/- 0.76e3" assert value_str(0.01,76.4) == "0.000e3 +/- 0.076e3" assert value_str(0.001,7.64) == "0.0 +/- 7.6" assert value_str(0.0001,0.764) == "0.00 +/- 0.76" assert value_str(0.00001,0.0764) == "0.000 +/- 0.076" assert value_str(0.000001,0.00764) == "0.0e-3 +/- 7.6e-3" # Zero values assert value_str(0,7640000) == "0.0e6 +/- 7.6e6" assert value_str(0, 764000) == "0.00e6 +/- 0.76e6" assert value_str(0, 76400) == "0.000e6 +/- 0.076e6" assert value_str(0, 7640) == "0.0e3 +/- 7.6e3" assert value_str(0, 764) == "0.00e3 +/- 0.76e3" assert value_str(0, 76.4) == "0.000e3 +/- 0.076e3" assert value_str(0, 7.64) == "0.0 +/- 7.6" assert value_str(0, 0.764) == "0.00 +/- 0.76" assert value_str(0, 0.0764) == "0.000 +/- 0.076" assert value_str(0, 0.00764) == "0.0e-3 +/- 7.6e-3" assert value_str(0, 0.000764) == "0.00e-3 +/- 0.76e-3" assert value_str(0, 0.0000764) == "0.000e-3 +/- 0.076e-3" # negative values assert value_str(-1235670,766000) == "-1.24e6 +/- 0.77e6" assert value_str(-1.23567,.766) == "-1.24 +/- 0.77" assert value_str(-.00000123567,.0000000766) == "-1.236e-6 +/- 0.077e-6" assert value_str(-12356.7,7.64) == "-12356.7 +/- 7.6" assert value_str(-123.567,764) == "-0.12e3 +/- 0.76e3" assert value_str(-1235.67,76400) == "-0.001e6 +/- 0.076e6" assert value_str(-.000123567,.00764) == "-0.1e-3 +/- 7.6e-3" assert value_str(-12356,7640000) == "-0.0e6 +/- 7.6e6" assert value_str(-12,76400) == "-0.000e6 +/- 0.076e6" assert value_str(-0.0001,0.764) == "-0.00 +/- 0.76" # non-finite values assert value_str(-numpy.inf,None) == "-inf" assert value_str(numpy.inf,None) == "inf" assert value_str(numpy.NaN,None) == "NaN" # bad or missing uncertainty assert value_str(-1.23567,numpy.NaN) == "-1.23567" assert value_str(-1.23567,-numpy.inf) == "-1.23567" assert value_str(-1.23567,-0.1) == "-1.23567" assert value_str(-1.23567,0) == "-1.23567" assert value_str(-1.23567,None) == "-1.23567" assert value_str(-1.23567,numpy.inf) == "-1.2 +/- inf" def test_default(): # Check that the default is the compact format assert format_uncertainty(-1.23567,0.766) == "-1.24(77)" def main(): """ Run all tests. This is equivalent to "nosetests --with-doctest" """ test_compact() test_pm() test_default() import doctest doctest.testmod() if __name__ == "__main__": main()