scinum 1.0.2

Scientific numbers with multiple uncertainties and correlation-aware, gaussian propagation.

scinum provides a simple Number class that wraps plain floats or NumPy arrays and adds support for multiple uncertainties, automatic (gaussian) error propagation, and scientific rounding.

Usage

The following examples demonstrate the most common use cases. For more info, see the API documentation or open the example.ipynb notebook on binder:

Number definition

from scinum import Number, UP, DOWN

num = Number(5, (2, 1))
print(num)                    # -> 5.00 +2.00-1.00

# get the nominal value
print(num.nominal)            # -> 5.0
print(num.n)                  # -> 5.0 (shorthand)
print(num())                  # -> 5.0 (shorthand)

# get uncertainties
print(num.get_uncertainty())  # -> (2.0, 1.0)
print(num.u())                # -> (2.0, 1.0) (shorthand)
print(num.u(direction=UP))    # -> 2.0

# get shifted values
print(num.get())              # -> 5.0 (no shift)
print(num.get(UP))            # -> 7.0 (up shift)
print(num(UP))                # -> 7.0 (up shift, shorthand)
print(num.get(DOWN))          # -> 4.0 (down shift)
print(num(DOWN))              # -> 4.0 (down shift, shorthand)

Multiple uncertainties

from scinum import Number, ABS, REL

num = Number(2.5, {
    "sourceA": 0.5,                  # absolute 0.5, both up and down
    "sourceB": (1.0, 1.5),           # absolute 1.0 up, 1.5 down
    "sourceC": (REL, 0.1),           # relative 10%, both up and down
    "sourceD": (REL, 0.1, 0.2),      # relative 10% up, 20% down
    "sourceE": (1.0, REL, 0.2),      # absolute 1.0 up, relative 20% down
    "sourceF": (REL, 0.3, ABS, 0.3)  # relative 30% up, absolute 0.3 down
})

Formatting and rounding

Number.str() provides some simple formatting tools, including latex and root latex support, as well as scientific rounding rules:

# output formatting
n = Number(8848, 10)
n.str(unit="m")                          # -> "8848.0 +- 10.0 m"
n.str(unit="m", force_asymmetric=True)   # -> "8848.0 +10.0-10.0 m"
n.str(unit="m", scientific=True)         # -> "8.848 +- 0.01 x 1E3 m"
n.str(unit="m", si=True)                 # -> "8.848 +- 0.01 km"
n.str(unit="m", style="latex")           # -> "$8848.0 \pm 10.0\,m$"
n.str(unit="m", style="latex", si=True)  # -> "8.848 \pm 0.01\,km"
n.str(unit="m", style="root")            # -> "8848.0 #pm 10.0 m"
n.str(unit="m", style="root", si=True)   # -> "8.848 #pm 0.01 km"

# output rounding
n = Number(17.321, {"a": 1.158, "b": 0.453})
n.str()               # -> '17.321 +- 1.158 (a) +- 0.453 (b)'
n.str("%.1f")         # -> '17.3 +- 1.2 (a) +- 0.5 (b)'
n.str("publication")  # -> '17.32 +- 1.16 (a) +- 0.45 (b)'
n.str("pdg")          # -> '17.3 +- 1.2 (a) +- 0.5 (b)'

For situations that require more sophisticated rounding and formatting rules, you might want to checkout:

• sn.split_value()
• sn.match_precision()
• sn.round_uncertainty()
• sn.round_value()
• sn.infer_si_prefix()

NumPy arrays

from scinum import Number, ABS, REL
import numpy as np

num = Number(np.array([3, 4, 5]), 2)
print(num)
# [ 3.  4.  5.]
# + [ 2.  2.  2.]
# - [ 2.  2.  2.]

num = Number(np.array([3, 4, 5]), {
    "sourceA": (np.array([0.1, 0.2, 0.3]), REL, 0.5)  # absolute values for up, 50% down
})
print(num)
# [ 3.  4.  5.]
# + sourceA [ 0.1  0.2  0.3]
# - sourceA [ 1.5  2.   2.5]

Uncertainty propagation

from scinum import Number

num = Number(5, 1)
print(num + 2)  # -> '7.0 +- 1.0'
print(num * 3)  # -> '15.0 +- 3.0'

num2 = Number(2.5, 1.5)
print(num + num2)  # -> '7.5 +- 1.80277563773'
print(num * num2)  # -> '12.5 +- 7.90569415042'

# add num2 to num and consider their uncertainties to be fully correlated, i.e. rho = 1
num.add(num2, rho=1)
print(num)  # -> '7.5 +- 2.5'

Math operations

As a drop-in replacement for the math module, scinum provides an object ops that contains math operations that are aware of guassian error propagation.

from scinum import Number, ops

num = ops.log(Number(5, 2))
print(num)  # -> 1.61 (+0.40, -0.40)

num = ops.exp(ops.tan(Number(5, 2)))
print(num)  # -> 0.03 (+0.85, -0.85)

Custom operations

There might be situations where a specific operation is not (yet) contained in the ops object. In this case, you can easily register a new one via:

from scinum import Number, ops

@ops.register
def my_op(x):
    return x * 2 + 1

@my_op.derive
def my_op(x):
    return 2

num = ops.my_op(Number(5, 2))
print(num)  # -> 11.00 (+4.00, -4.00)

Please note that there is no need to register simple functions like in the particular example above as most of them are just composite operations whose propagation rules (derivatives) are already known.

Installation and dependencies

Via pip

pip install scinum

or by simply copying the file into your project.

Numpy is an optional dependency.

Contributing

If you like to contribute, I'm happy to receive pull requests. Just make sure to add a new test cases and run them via:

> python -m unittest tests

Testing

In general, tests should be run for different environments:

• Python 2.7
• Python 3.X (X ≥ 5)

Docker

To run tests in a docker container, do:

git clone https://github.com/riga/scinum.git
cd scinum

docker run --rm -v `pwd`:/scinum -w /scinum python:3.6 python -m unittest tests

Development

• Source hosted at GitHub
• Report issues, questions, feature requests on GitHub Issues