# breaks - Partitioning a scale for readability¶

All scales have a means by which the values that are mapped onto the scale are interpreted. Numeric digital scales put out numbers for direct interpretation, but most scales cannot do this. What they offer is named markers/ticks that aid in assessing the values e.g. the common odometer will have ticks and values to help gauge the speed of the vehicle.

The named markers are what we call breaks. Properly calculated breaks make interpretation straight forward. These functions provide ways to calculate good(hopefully) breaks.

class mizani.breaks.breaks_log(n: int = 5, base: = 10)[source]

Integer breaks on log transformed scales

Parameters:
n`int`

Desired number of breaks

base`int`

Base of logarithm

Examples

```>>> x = np.logspace(3, 6)
>>> limits = min(x), max(x)
>>> breaks_log()(limits)
array([     1000,    10000,   100000,  1000000])
>>> breaks_log(2)(limits)
array([  1000, 100000])
>>> breaks_log()([0.1, 1])
array([0.1, 0.3, 1. , 3. ])
```
__call__(limits: TupleFloat2) NDArrayFloat[source]

Compute breaks

Parameters:
limits`tuple`

Minimum and maximum values

Returns:
outarray_like

Sequence of breaks points

class mizani.breaks.minor_breaks(n: int = 1)[source]

Compute minor breaks

This is the naive method. It does not take into account the transformation.

Parameters:
n`int`

Number of minor breaks between the major breaks.

Examples

```>>> major = [1, 2, 3, 4]
>>> limits = [0, 5]
>>> minor_breaks()(major, limits)
array([0.5, 1.5, 2.5, 3.5, 4.5])
>>> minor_breaks()([1, 2], (1, 2))
array([1.5])
```

More than 1 minor break.

```>>> minor_breaks(3)([1, 2], (1, 2))
array([1.25, 1.5 , 1.75])
>>> minor_breaks()([1, 2], (1, 2), 3)
array([1.25, 1.5 , 1.75])
```
__call__(major: FloatArrayLike, limits: TupleFloat2 | None = None, n: = None) NDArrayFloat[source]

Minor breaks

Parameters:
majorarray_like

Major breaks

limits

Limits of the scale. If array_like, must be of size 2. If None, then the minimum and maximum of the major breaks are used.

n`int`

Number of minor breaks between the major breaks. If None, then self.n is used.

Returns:
outarray_like

Minor beraks

class mizani.breaks.minor_breaks_trans(trans: Trans, n: int = 1)[source]

Compute minor breaks for transformed scales

The minor breaks are computed in data space. This together with major breaks computed in transform space reveals the non linearity of of a scale. See the log transforms created with `log_trans()` like `log10_trans`.

Parameters:
trans`trans` or type

Trans object or trans class.

n`int`

Number of minor breaks between the major breaks.

Examples

```>>> from mizani.transforms import sqrt_trans
>>> major = [1, 2, 3, 4]
>>> limits = [0, 5]
>>> t1 = sqrt_trans()
>>> t1.minor_breaks(major, limits)
array([1.58113883, 2.54950976, 3.53553391])
```

# Changing the regular minor_breaks method

```>>> t2 = sqrt_trans()
>>> t2.minor_breaks = minor_breaks()
>>> t2.minor_breaks(major, limits)
array([0.5, 1.5, 2.5, 3.5, 4.5])
```

More than 1 minor break

```>>> major = [1, 10]
>>> limits = [1, 10]
>>> t2.minor_breaks(major, limits, 4)
array([2.8, 4.6, 6.4, 8.2])
```
__call__(major: FloatArrayLike, limits: TupleFloat2 | None = None, n: = None) NDArrayFloat[source]

Minor breaks for transformed scales

Parameters:
majorarray_like

Major breaks

limits

Limits of the scale. If array_like, must be of size 2. If None, then the minimum and maximum of the major breaks are used.

n`int`

Number of minor breaks between the major breaks. If None, then self.n is used.

Returns:
outarray_like

Minor breaks

class mizani.breaks.breaks_date(n: int = 5, width: = None)[source]

Regularly spaced dates

Parameters:
n

Desired number of breaks.

width

An interval specification. Must be one of [second, minute, hour, day, week, month, year] If `None`, the interval automatic.

Examples

```>>> from datetime import datetime
>>> limits = (datetime(2010, 1, 1), datetime(2026, 1, 1))
```

Default breaks will be regularly spaced but the spacing is automatically determined

```>>> breaks = breaks_date(9)
>>> [d.year for d in breaks(limits)]
[2010, 2012, 2014, 2016, 2018, 2020, 2022, 2024, 2026]
```

Breaks at 4 year intervals

```>>> breaks = breaks_date('4 year')
>>> [d.year for d in breaks(limits)]
[2010, 2014, 2018, 2022, 2026]
```
__call__(limits: TupleT2[datetime]) Sequence[datetime][source]

Compute breaks

Parameters:
limits`tuple`

Minimum and maximum `datetime.datetime` values.

Returns:
outarray_like

Sequence of break points.

class mizani.breaks.breaks_timedelta(n: int = 5, Q: Sequence[float] = (1, 2, 5, 10))[source]

Timedelta breaks

Returns:
out`callable()` `f(limits)`

A function that takes a sequence of two `datetime.timedelta` values and returns a sequence of break points.

Examples

```>>> from datetime import timedelta
>>> breaks = breaks_timedelta()
>>> x = [timedelta(days=i*365) for i in range(25)]
>>> limits = min(x), max(x)
>>> major = breaks(limits)
>>> [val.total_seconds()/(365*24*60*60)for val in major]
[0.0, 5.0, 10.0, 15.0, 20.0, 25.0]
```
__call__(limits: tuple[Timedelta, Timedelta]) NDArrayTimedelta[source]

Compute breaks

Parameters:
limits`tuple`

Minimum and maximum `datetime.timedelta` values.

Returns:
outarray_like

Sequence of break points.

class mizani.breaks.breaks_extended(n: int = 5, Q: Sequence[float] = (1, 5, 2, 2.5, 4, 3), only_inside: bool = False, w: Sequence[float] = (0.25, 0.2, 0.5, 0.05))[source]

An extension of Wilkinson's tick position algorithm

Parameters:
n`int`

Desired number of breaks

Q`list`

List of nice numbers

only_insidebool

If `True`, then all the breaks will be within the given range.

w`list`

Weights applied to the four optimization components (simplicity, coverage, density, and legibility). They should add up to 1.

References

• Talbot, J., Lin, S., Hanrahan, P. (2010) An Extension of Wilkinson's Algorithm for Positioning Tick Labels on Axes, InfoVis 2010.

Additional Credit to Justin Talbot on whose code this implementation is almost entirely based.

Examples

```>>> limits = (0, 9)
>>> breaks_extended()(limits)
array([  0. ,   2.5,   5. ,   7.5,  10. ])
>>> breaks_extended(n=6)(limits)
array([  0.,   2.,   4.,   6.,   8.,  10.])
```
__call__(limits: TupleFloat2) NDArrayFloat[source]

Calculate the breaks

Parameters:
limits`array`

Minimum and maximum values.

Returns:
outarray_like

Sequence of break points.