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

## Project description 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

Number.default_format = "%.2f"

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
})

###### Correlation handling

When two numbers are combined by means of an operator, the correlation between equally named uncertainties is assumed to be 1. The example above shows how to configure this correlation coefficient rho when used with explicit operator methods defined on a number, such as num.add() or num.mul().

However, it is probably more convenient to use Correlation objects:

from scinum import Number, Correlation

num = Number(2, 5)
print(num * num)  # -> '4.0 +- 20.0', fully correlated by default
# same as
# print(num**2)
# print(num.pow(2, inplace=False))

print(num * Correlation(0) * num)  # -> '4.0 +- 14.14', no correlation
# same as
# print(num.pow(2, rho=0, inplace=False))


The correlation object is combined with a number through multiplication, resulting in a DeferredResult object. The deferred result is used to resolve the actual uncertainty combination once it is applied to another number instance which happens in a second step. Internally, the above example is handled as

deferred = num * Correlation(0)
print(deferred * num)


and similarly, adding two numbers without correlation can be expressed as

(num * Correlation(0)) + num


When combining numbers with multiple, named uncertainties, correlation coefficients can be controlled per uncertainty by passing names to the Correlation constructor.

Correlation(1, sourceA=0)  # zero correlation for sourceA, all others default to 1
Correlation(sourceA=0)     # zero correlation for sourceA, no default

###### 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:

###### 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 +- 2.5'
print(num * num2)  # -> '12.5 +- 10.0'

# add num2 to num and consider their uncertainties to be fully uncorrelated, i.e. rho = 0
print(num)  # -> '7.5 +- 1.80277563773'

###### 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)  # -> 1.60943791243 +- 0.4

num = ops.exp(ops.tan(Number(5, 2)))
print(num)  # -> 0.0340299245972 +- 0.845839754815
print(num.str("%.2f"))  # -> 0.03 +- 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.

###### 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]


### 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:3.8 python -m unittest tests


## Project details

This version 1.4.1 1.4.0 1.3.0 1.2.0 1.1.4 1.1.3 1.1.2 1.1.1 1.1.0 1.0.2 1.0.1 1.0.0 0.2.8 0.2.7 0.2.6 0.2.5 0.2.4 0.2.3 0.2.2 0.2.1 0.2.0 0.1.1 0.1.0 0.0.1

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