Lesson 3. Run Calculations and Summary Statistics on Numpy Arrays


Learning Objectives

After completing this page, you will be able to:

  • Check the dimensions and shape of numpy arrays.
  • Run calculations and summary statistics (e.g. mean, minimum, maximum) on one-dimensional and two-dimensional numpy arrays.

Import Python Packages and Get Data

Begin by importing the necessary Python packages and downloading and importing the data into numpy arrays.

As you learned previously in this chapter, you will use the earthpy package to download the data files, os to set the working directory, and numpy to import the data files into numpy arrays.

# Import necessary packages
import os
import numpy as np
import earthpy as et
# Download .txt with avg monthly precip (inches)
monthly_precip_url = 'https://ndownloader.figshare.com/files/12565616'
et.data.get_data(url=monthly_precip_url)

# Download .csv of precip data for 2002 and 2013 (inches)
precip_2002_2013_url = 'https://ndownloader.figshare.com/files/12707792'
et.data.get_data(url=precip_2002_2013_url)
Downloading from https://ndownloader.figshare.com/files/12565616
Downloading from https://ndownloader.figshare.com/files/12707792
'/root/earth-analytics/data/earthpy-downloads/monthly-precip-2002-2013.csv'
# Set working directory to earth-analytics
os.chdir(os.path.join(et.io.HOME, 'earth-analytics'))
# Import average monthly precip to numpy array
fname = os.path.join("data", "earthpy-downloads",
                     "avg-monthly-precip.txt")

avg_monthly_precip = np.loadtxt(fname)

print(avg_monthly_precip)
[0.7  0.75 1.85 2.93 3.05 2.02 1.93 1.62 1.84 1.31 1.39 0.84]
# Import monthly precip for 2002 and 2013 to numpy array
fname = os.path.join("data", "earthpy-downloads",
                     "monthly-precip-2002-2013.csv")

precip_2002_2013 = np.loadtxt(fname, delimiter = ",")

print(precip_2002_2013)
[[ 1.07  0.44  1.5   0.2   3.2   1.18  0.09  1.44  1.52  2.44  0.78  0.02]
 [ 0.27  1.13  1.72  4.14  2.66  0.61  1.03  1.4  18.16  2.24  0.29  0.5 ]]

Check Dimensions and Shape of Numpy Arrays

Before you begin to use the data in numpy arrays, it can be helpful to check the dimensions and shape of numpy arrays (e.g. the number of rows and columns of a two-dimensional array).

Numpy arrays have two attributes (i.e. built-in characteristics automatically assigned to objects) that provide useful information on their dimensions and shape: ndim and .shape.

You can use .ndim attribute of numpy arrays (e.g. array.ndim) to get the number dimensions of the numpy array.

For example, you can check the dimensions of avg_monthly_precip and precip_2002_2013 to check that they are one-dimensional and two-dimensional, respectively.

# Check dimensions of avg_monthly_precip
avg_monthly_precip.ndim
1
# Check dimensions of precip_2002_2013
precip_2002_2013.ndim
2

Another useful attribute of numpy arrays is the .shape attribute, which provides specific information on how the data is stored within the numpy array.

For an one-dimensional numpy array, the .shape attribute returns the number of elements, while for a two-dimensional numpy array, the .shape attribute returns the number of rows and columns.

For example, the .shape attribute of precip_2002_2013 tells us that it has two dimensions because there are two values returned. The first value is the number of rows, while the second value is the number of columns.

# Check shape of precip_2002_2013
precip_2002_2013.shape
(2, 12)

This result is expected given what you know about the data. Recall that precip_2002_2013 contains 2 years of data (one in each row) with 12 values for average monthly precipitation in each year (one month in each column).

Next, check the .shape for avg_monthly_precip.

# Check shape of avg_monthly_precip
avg_monthly_precip.shape
(12,)

The .shape attribute of avg_monthly_precip tells us that it is an one-dimensional numpy array, as only one value was returned: the number of elements, or values.

In the case of avg_monthly_precip, there are only 12 elements, one value of average monthly precipitation for each month (an average value across all years of data).

Run Calculations on Numpy Arrays

A key benefit of numpy arrays is that they support mathematical operations on an element-by-element basis, meaning that you can actually run one operation (e.g. array *= 25.4) on the entire array with a single line of code.

For example, you can run a calculation to convert the values avg_monthly_precip from inches to millimeters (1 inch = 25.4 millimeters) and save it to a new numpy array as follows:

avg_monthly_precip_mm = avg_monthly_precip * 25.4

Or, if you do not need to retain the original numpy array, you can use an assignment operator as shown below to assign the new values to the original variable.

# Check the original values
print(avg_monthly_precip)
[0.7  0.75 1.85 2.93 3.05 2.02 1.93 1.62 1.84 1.31 1.39 0.84]
# Use assignment operator to convert values from in to mm
avg_monthly_precip *= 25.4

# Print new values
print(avg_monthly_precip)
[17.78  19.05  46.99  74.422 77.47  51.308 49.022 41.148 46.736 33.274
 35.306 21.336]

These arithmetic calculations will work on any numpy array, including two-dimensional and multi-dimensional numpy arrays.

# Check the original values
print(precip_2002_2013)
[[ 1.07  0.44  1.5   0.2   3.2   1.18  0.09  1.44  1.52  2.44  0.78  0.02]
 [ 0.27  1.13  1.72  4.14  2.66  0.61  1.03  1.4  18.16  2.24  0.29  0.5 ]]
# Use assignment operator to convert values from in to mm
precip_2002_2013 *= 25.4

# Print new values
print(precip_2002_2013)
[[ 27.178  11.176  38.1     5.08   81.28   29.972   2.286  36.576  38.608
   61.976  19.812   0.508]
 [  6.858  28.702  43.688 105.156  67.564  15.494  26.162  35.56  461.264
   56.896   7.366  12.7  ]]

Revisit Python Lists Versus Numpy Arrays

Running these types of calculations on numpy arrays highlight one key difference between Python lists and numpy arrays.

Recall that when working with variables and lists, you created separate variables for each monthly average precipitation value to convert values (e.g. jan *= 25.4), and then you created a new list containing all of these converted monthly values.

You had to complete that longer workflow because you cannot complete the same mathematical operations on Python lists.

For example, try to run the code below:

precip_list = [0.70, 0.75, 1.85, 2.93, 3.05, 2.02, 
              1.93, 1.62, 1.84, 1.31, 1.39, 0.84]

precip_list *=  25.4

You will receive an error that this type of operation is not allowed on lists:

TypeError: can't multiply sequence by non-int of type 'float'

As you can see, using numpy arrays makes it very easy to run calculations on scientific data. Next, you will learn how numpy arrays can be used to calculate summary statistics of data such as identifying mean, maximum, and minimum values.

Run Summary Statistics on One-dimensional Numpy Arrays

Calculate Mean and Median

Another useful feature of numpy arrays is the ability to run summary statistics (e.g. calculating averages, finding minimum or maximum values) across the entire array of values.

For example, you can use the np.mean() function to calculate the average value across an array (e.g. np.mean(array)) or np.median() to identify the median value across an array (e.g. np.median(array)).

# Create variable with mean value
mean_avg_precip = np.mean(avg_monthly_precip)

print("mean average monthly precipitation:", mean_avg_precip)
mean average monthly precipitation: 42.820166666666665
# Create variable with median value
median_avg_precip = np.median(avg_monthly_precip)

print("median average monthly precipitation:", median_avg_precip)
median average monthly precipitation: 43.942

It can be useful to calculate both the mean and median of data, as sometimes the mean can be noticeably different from the median value (i.e. the middle value of the data at which exactly half of the values are lower or higher). This difference between the mean and median can occur when the data are skewed in one direction (e.g. skewed toward lower or higher values) or contain a few significant outliers (e.g. a few really low or really high values).

Find Other Summary Statistics Functions Including Minimum and Maximum Values

Recall that you can use tab complete to get a list of all available functions in any package.

This means you can get a list of the functions available in numpy (which you imported with the alias np) by typing np., and hitting the tab key. A list of callable functions will appear.

For example: np.std for identifying the standard deviation or np.sum for calculating the sum of elements.

If you provide letter such as .np.m and hit the tab key, you will see options for other summary functions that begin with the letter m, such as np.min() and np.max() to find the minimum and maximum values in an array.

# Calculate and print minimum and maximum values
print("minimum average monthly precipitation:", np.min(avg_monthly_precip))
print("maximum average monthly precipitation:", np.max(avg_monthly_precip))
minimum average monthly precipitation: 17.779999999999998
maximum average monthly precipitation: 77.46999999999998

Run Summary Statistics Across Axes of Two-dimensional Numpy Arrays

In the examples above, you calculated summary statistics (e.g. mean, min, max) of one-dimensional numpy arrays, and you received one summary value for the whole array.

To calculate statistics on two-dimensional arrays, you can use the axis argument in the same functions (e.g. np.max) to specify which axis you would like to summarize:

  • vertical axis downwards, summarizing across rows (axis=0)
  • hortizontal axis, summarizing across columns (axis=1)

When using axis=0 to calculate summary statistics, you are requesting the summary of each column across all rows of data. For example, running axis=0 on an array with 2 rows and 12 columns will result in an output with 12 values: one value summarized across 2 rows for each column in the array. There are 12 columns, and thus, 12 summary values.

When using axis=1, you are requesting the summary of each row across all columns of data. For example, running axis=1 on an array with 2 rows and 12 columns will result in an output with 2 values: one value summarized across 12 columns for each row in the array. There are 2 rows, and thus, 2 summary values.

To better understand the axis argument and the resulting output, it can help to see it in action such as in the examples below with real data.

Calculate Summary Statistics Across Rows

Recall that precip_2002_2013 contained two rows of data: one for 2002 and one for 2013. It also contained twelve columns, one value for each month of the year.

By using np.max(array, axis=0), you are requesting the maximum value from each column across all rows (or years) of data. This means that you will receive twelve maximum values: one for each column (or month) of data.

Compare the output of np.max(precip_2002_2013, axis=0) to your visual inspection of the maximum value in each column. In the first column, the two values are 27.178 for 2002 and 6.858 for 2013.

# Visually identify max value across the rows of precip_2002_2013
print(precip_2002_2013)
[[ 27.178  11.176  38.1     5.08   81.28   29.972   2.286  36.576  38.608
   61.976  19.812   0.508]
 [  6.858  28.702  43.688 105.156  67.564  15.494  26.162  35.56  461.264
   56.896   7.366  12.7  ]]

The maximum value across the two rows is 27.178, which is the first value in the output of the function.

# Maximum value for each month across years 2002 and 2013
print(np.max(precip_2002_2013, axis=0))
[ 27.178  28.702  43.688 105.156  81.28   29.972  26.162  36.576 461.264
  61.976  19.812  12.7  ]

Note that you can then save the output to a new numpy arrays for additional use.

# Create new array of the maximum value for each month
precip_2002_2013_monthly_max = np.max(precip_2002_2013, axis=0)

type(precip_2002_2013_monthly_max)
numpy.ndarray

Calculate Summary Statistics Across Columns

You can use np.max(array, axis=1) to identify the maximum value from each row across all columns. In the case of precip_2002_2013, this identifies the maximum value for each row (or year) of data.

Again, compare the output of np.max(precip_2002_2013, axis=1) to your visual inspection of the maximum value in each row. In the first row, the maximum value is 81.28, while in the second row, the maximum value is 461.264.

# Visually identify max value across the rows of precip_2002_2013
print(precip_2002_2013)
[[ 27.178  11.176  38.1     5.08   81.28   29.972   2.286  36.576  38.608
   61.976  19.812   0.508]
 [  6.858  28.702  43.688 105.156  67.564  15.494  26.162  35.56  461.264
   56.896   7.366  12.7  ]]

Since you requested the maximum value of each row across all the columns, your output returns the maximum value for each row (or year) of data.

# Maximum value for each year 2002 and 2013
print(np.max(precip_2002_2013, axis=1))
[ 81.28  461.264]

These summary statistics make it easy to quickly summarize large amounts of data using numpy arrays. On the next page of this chapter, you will learn how to select (i.e. slice) data from numpy arrays.

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