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

## 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.

**Note**: Support for Python versions 2.7 and 3.6 has been dropped starting from v2.0.0.
Checkout the legacy/v1.4 branch for legacy support.

### Usage

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

Use single values to denote symmetric uncertainties, and tuples for asymmetric ones. Float values refer to absolute values whereas complex numbers (only their imaginary part) define relative effects.

```
from scinum import Number
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": 0.1j, # relative 10%, both up and down
"sourceD": (0.1j, 0.2j), # relative 10% up, relative 20% down
"sourceE": (1.0, 0.2j), # absolute 1.0 up, relative 20% down
"sourceF": (0.3j, 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(style="fancy") # -> "$8848.0 ±10.0$"
n.str(unit="m", style="fancy") # -> "$8848.0 ±10.0\,m$"
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
num.add(num2, 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 gaussian 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
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]), 0.5j), # 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, pull requests are happily accepted. 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 all python versions ≥ 3.7.

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
```

### Development

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

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