0
# Scales and Transformations
1

2
Comprehensive axis scaling system including logarithmic, power, inverse, and custom scales with seamless integration into matplotlib's transformation pipeline. Proplot extends matplotlib's scale system with additional scales and enhanced functionality.
3

4
## Capabilities
5

6
### Built-in Scale Classes
7

8
```python { .api }
9
class LinearScale:
10
    """Linear axis scaling (default)."""
11

12
class LogScale:
13
    """Logarithmic axis scaling."""
14

15
class SymmetricalLogScale:
16
    """Symmetric logarithmic scaling for data crossing zero."""
17

18
class LogitScale:
19
    """Logit scaling for probability data."""
20

21
class PowerScale:
22
    """Power law scaling with configurable exponent."""
23
    
24
class InverseScale:
25
    """Inverse scaling (1/x transformation)."""
26

27
class ExpScale:
28
    """Exponential scaling."""
29

30
class CutoffScale:
31
    """Scale with arbitrary cutoff points for piecewise linear scaling."""
32

33
class FuncScale:
34
    """Scale with arbitrary forward and inverse functions."""
35

36
class SineLatitudeScale:
37
    """Sine latitude scaling for geographic data."""
38

39
class MercatorLatitudeScale:
40
    """Mercator latitude scaling for geographic projections."""
41
```
42

43
### Scale Constructor
44

45
```python { .api }
46
def Scale(*args, **kwargs):
47
    """
48
    Construct axis scale instances from various specifications.
49
    
50
    Parameters:
51
    - scale (str): Scale name ('linear', 'log', 'symlog', 'power', etc.)
52
    - **kwargs: Scale-specific parameters
53
    
54
    Scale Types:
55
    - 'linear': Linear scaling
56
    - 'log': Logarithmic scaling
57
    - 'symlog': Symmetric logarithmic scaling
58
    - 'logit': Logit scaling for probabilities
59
    - 'power': Power law scaling
60
    - 'inverse': Inverse (1/x) scaling
61
    - 'exp': Exponential scaling
62
    - 'cutoff': Piecewise linear with cutoffs
63
    - 'func': Custom function scaling
64
    - 'sine': Sine latitude scaling
65
    - 'mercator': Mercator latitude scaling
66
    
67
    Returns:
68
    Scale: Appropriate scale instance
69
    """
70
```
71

72
## Usage Examples
73

74
```python
75
import proplot as pplt
76
import numpy as np
77

78
# Logarithmic scaling
79
fig, ax = pplt.subplots()
80
ax.plot(x, y)
81
ax.format(yscale='log')
82

83
# Power scaling
84
ax.format(xscale='power', xscale_kw={'power': 0.5})
85

86
# Custom function scaling
87
from proplot import FuncScale
88
scale = FuncScale(lambda x: x**2, lambda x: np.sqrt(x))
89
ax.format(yscale=scale)
90

91
# Cutoff scaling for multi-range data
92
ax.format(yscale='cutoff', yscale_kw={'cutoffs': [1, 10, 100]})
93
```