# This program is public domain
# Author Paul Kienzle
"""
Format numbers nicely for printing.
Usage::
>> from danse.common.util.formatnum import *
>> v,dv = 757.2356,0.01032
>> print format_uncertainty_pm(v,dv)
757.235 +/- 0.010
>> format_uncertainty_compact(v,dv)
757.235(10)
>> format_uncertainty(v,dv)
757.235(10)
Set format_uncertainty.compact to False to use the +/-
format by default, otherwise leave it at True for compact
value(##) format.
"""
from __future__ import division
import math
import numpy
__all__ = ['format_uncertainty', 'format_uncertainty_pm',
'format_uncertainty_compact']
# These routines need work for +/- formatting::
# - pm formats are not rigorously tested
# - pm formats do not try to align the scale to multiples of 1000
# - pm formats do not try to align the value scale to uncertainty scale
# 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 appriate
# 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.
class FormatUncertainty:
"""
Given *value* and *uncertainty*, return a concise string representation.
This will either by the +/- form of :func:`format_uncertainty_pm` or
the compact form of :func:`format_uncertainty_compact` depending on
whether *compact* is specified or whether *format_uncertainty.compact*
is True or False.
"""
compact = True
def __call__(self, value, uncertainty):
return _format_uncertainty(value, uncertainty, self.compact)
format_uncertainty = FormatUncertainty()
def _format_uncertainty(value,uncertainty,compact):
"""
Implementation of both the compact and the +/- formats.
"""
if numpy.isinf(value):
return "inf" if value > 0 else "-inf"
if numpy.isnan(value):
return "NaN"
# Uncertainty check must come after indefinite check since the %g
# format string doesn't handle indefinite numbers consistently
# across platforms.
if uncertainty == None or uncertainty <= 0 or numpy.isnan(uncertainty):
return "%g"%value
if numpy.isinf(uncertainty):
if compact:
return "%g(inf)"%value
else:
return "%g +/- inf"%value
# Process sign
sign = "-" if value < 0 else ""
value = abs(value)
# Determine the number of digits in the value and the error
# Note that uncertainty <= 0 is handled above
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 pm, return a simple v +/- dv
if not compact:
scale = 10**(err_place-1)
val_digits = val_place-err_place+2
return "%s%.*g +/- %.2g"%(sign,val_digits,value,uncertainty)
# The remainder is for the v(dv) case
err_str = "(%2d)"%int(uncertainty/10.**(err_place-1)+0.5)
if err_place > val_place:
# Degenerate case: error bigger than value
# The mantissa is 0.#(##)e#, 0.0#(##)e# or 0.00#(##)e#
if err_place - val_place > 2: value = 0
val_place = int(math.floor((err_place+2)/3.))*3
digits_after_decimal = val_place - err_place + 1
val_str = "%.*f%s"%(digits_after_decimal,value/10.**val_place,err_str)
if val_place != 0: val_str += "e%d"%val_place
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 = int(math.floor((err_place+1)/3.))*3
digits_after_decimal = val_place - err_place + 1
val_str = "%.*f%s"%(digits_after_decimal,value/10.**val_place,err_str)
if val_place != 0: val_str += "e%d"%val_place
elif err_place <= 1 and val_place >= -3:
# Normal case: nice numbers and errors
# The value is ###.###(##)
digits_after_decimal = abs(err_place-1)
val_str = "%.*f%s"%(digits_after_decimal,value,err_str)
else:
# Extreme cases: zeros before value or after error
# The value is ###.###(##)e#, ##.####(##)e# or #.#####(##)e#
total_digits = val_place - err_place + 2
val_place = int(math.floor(val_place/3.))*3
val_str = "%.*g%se%d"%(total_digits,
value/10.**val_place,
err_str,val_place)
return sign+val_str
def test():
# 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) == "12.3567(76)e6"
assert value_str(123567000,7640) == "123.567(76)e6"
assert value_str(1235670000,76400) == "1.23567(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"
# negative values
assert value_str(-1235670,765000) == "-1.24(77)e6"
assert value_str(-1.23567,.765) == "-1.24(77)"
assert value_str(-.00000123567,.0000000765) == "-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)"
# zero values
assert value_str(0,0) == "0"
assert value_str(-1.23567,0) == "-1.23567"
assert value_str(0,765000) == "0.00(77)e6"
assert value_str(0,.765) == "0.00(77)"
assert value_str(0,.000000765) == "0.00(77)e-6"
assert value_str(0,76400) == "0.000(76)e6"
assert value_str(0,7640) == "0.0(76)e3"
# marked values
assert value_str(-numpy.inf,None) == "-inf"
assert value_str(numpy.inf,None) == "inf"
assert value_str(numpy.NaN,None) == "NaN"
# plus/minus form
assert format_uncertainty_pm(-1.23567,0.765) == "-1.24 +/- 0.77"
assert format_uncertainty_compact(-1.23567,0.765) == "-1.24(77)"
assert format_uncertainty_pm(752.3567,0.01) == "752.357 +/- 0.01"
assert format_uncertainty(-1.23567,0.765) == "-1.24(77)"
# bad uncertainty
assert format_uncertainty_pm(-1.23567,numpy.NaN) == "-1.23567"
assert format_uncertainty_pm(-1.23567,-numpy.inf) == "-1.23567"
assert format_uncertainty_pm(-1.23567,-0.1) == "-1.23567"
assert format_uncertainty_compact(-1.23567,numpy.NaN) == "-1.23567"
assert format_uncertainty_compact(-1.23567,-numpy.inf) == "-1.23567"
assert format_uncertainty_compact(-1.23567,-0.1) == "-1.23567"
# no uncertainty
assert format_uncertainty_pm(-1.23567,0) == "-1.23567"
assert format_uncertainty_compact(-1.23567,0) == "-1.23567"
assert format_uncertainty_pm(-1.23567,None) == "-1.23567"
assert format_uncertainty_compact(-1.23567,None) == "-1.23567"
# inf uncertainty
assert format_uncertainty_pm(-1.23567,numpy.inf) == "-1.23567 +/- inf"
assert format_uncertainty_compact(-1.23567,numpy.inf) == "-1.23567(inf)"
if __name__ == "__main__": test()