# Monotonic Functions

## Monotonic function:

A function, whose value is constant or increases or decreases as the input to the function increases or decreases.

## Example:

 import pandas as pds   sequence = [1,1,1,1,1,1]; series   = pds.Series(sequence);   # Check the is_monotonic attribute isMonotonic = series.is_monotonic;   result = "non-monotonic"; if isMonotonic:     result = "monotonic";   print("The series:"); print(series); print("is %s."%result);

## Output:

 The series: 0    1 1    1 2    1 3    1 4    1 5    1 dtype: int64 is monotonic.

## Monotonically increasing function:

A monotonically increasing function is a function whose output increases in value as the input value to the function increases. This rate of increase may not be constant over the distribution. Real world examples of monotonically increasing functions include knowledge available in the universe and the age of the universe.

## Example:

 import pandas as pds   # Function to print the result of whether # the series is monotonically increasing def printResults(series, testResult):     print("The series:");     print(series);     result = "monotonically not-increasing.";     if testResult:         result = "monotonically increasing.";     print("is %s"%result);   # Sequences as Python lists numberSequence1 = [4,5,5.1,5.2,7.01,8.95]; numberSequence2 = [1,2,1.9,3,4];   # Create pandas series instances series1 = pds.Series(numberSequence1); series2 = pds.Series(numberSequence2);   # Get the value of the monotonically-increasing property/attribute monoIncS1 = series1.is_monotonic_increasing; monoIncS2 = series2.is_monotonic_increasing;   # Print the results printResults(series1, monoIncS1); printResults(series2, monoIncS2);

## Output:

 The series: 0    4.00 1    5.00 2    5.10 3    5.20 4    7.01 5    8.95 dtype: float64 is monotonically increasing. The series: 0    1.0 1    2.0 2    1.9 3    3.0 4    4.0 dtype: float64 is monotonically not-increasing.

## Monotonically decreasing function:

A monotonically decreasing function is a function whose output decreases in value as the input value to the function decreases. This rate of decrease may not be constant over the distribution. Real world example of monotonically decreasing functions is life available for living beings to acquire knowledge.

## Example:

 import pandas as pds   # Create pandas series instance with number sequences s1 = pds.Series([1, 0.75, 0.7499, 0.2, -.5, -2.5]); s2 = pds.Series([10, 9, 8, 11, 7, 6, 12]);   # Check for the property: monotonically decreasing monoDecr_s1 = s1.is_monotonic_decreasing; monoDecr_s2 = s2.is_monotonic_decreasing;   print("The series:"); print(s1); print("is monotonically decreasing: %s" % monoDecr_s1);   print("The series:"); print(s2); print("is monotonically decreasing: %s" % monoDecr_s2);

## Output:

 The series: 0    1.0000 1    0.7500 2    0.7499 3    0.2000 4   -0.5000 5   -2.5000 dtype: float64 is monotonically decreasing: True The series: 0    10 1     9 2     8 3    11 4     7 5     6 6    12 dtype: int64 is monotonically decreasing: False