Array manipulation and booleans in numpy, hunting for what went wrong

Recently I was doing some raster processing with but I was getting some surprising results.
The goal was to convert some continuous value into a binary value based on a treshold and then detect places where only A was True (value: -1), where only B was True (value: 1) and where both A and B where True (value: 0). With a treshold set to 2 I came with the following formula:

(A > 2) - (B > 2)

But after calling the with my formula and inspecting the results I only got values of 0 and 1.
After inspecting I noticed that it uses numpy and more specifically numpy arrays for the raster manipulation.

This how my python shell session went (

>>> import numpy as np
>>> a = np.array([1,2,3,4])
>>> b = np.array([1,5,3,2])
>>> print(a > 2)
[False False  True  True]
>>> print(b > 2)
[False  True  True False]
>>> print(True-False)
>>> print(False-True)
>>> print((a>2)-(b>2))
[False  True False  True]
>>> print((a>2)*1-(b>2))  # we got a winner
[ 0 -1  0  1]

The problem was that boolean substraction in Python does generate the expected numeric results but the results where converted back into a boolean array by numpy after the substraction. And indeed converting -1, 1 or any other non zero number to a boolean generates a True which when converted back to number for writing the raster to disk gives you the value 1.
The solution was to force at least one of the arrays to be numeric so that we substract numeric values.

>>> bool(1)
>>> bool(2)
>>> bool(-1)
>>> bool(0)
>>> print((a>2)*1)
[0 0 1 1]

If you want to try this yourself on Windows then the easiest way to install gdal is with the OSGeo4W installer. A windows installer for numpy can be found on the website by Christopher Golke but consider also installing the full SciPy stack with one of the Scientific Python distributions.

What surprising results have you encountered with numpy.array or gdal_calc ?

Minimal introduction to Python

A few years ago I gave a short introduction to Python to some of my former colleagues and this was the result (also on github):

""" minimal introduction to python """

# 1) data basics

# numbers
i = 1234    # integer
f = 1.234   # float

# operators
a = 12 + 5  # = 17
b = 3 * 4   # = 12
c = 6 / 3   # = 2
d = 46 % 5  # = 1 (=> modulo operator)

a += 1      # = 18
a -= 2      # = 16
a *= 2      # = 32
a /= 2      # = 16
a %= 5      # = 1

# text
s = 'string'                
s = s.upper()               # 'STRING'
s = s.lower()               # 'string'
s.startswith('s')           # true
s.endswith('ng')             # true
s = s.replace('str', 'bl')  # 'bling'
l = s.split('i')            # list ['bl', 'ng']
strings = ['s', "t", "r'i'n", 'g"s"tring', "3"]

## add the prefix r for e.g. paths to files to escape the backslash character

testdoc = r'test\test.txt' ## same as : 'test\\test.txt'

# list
l = ['a1']
l[0] # 'a1'

mixed = ['3', 'abc', 3, 4.56]

d = {} # dictionary (key-value pairs)

d = {'a' : 'blabla',
     'b' : 1,
     3 : 'ablabl',
     4 : 12.3,
     16.9 : 'dif3'}

d['a'] # 'blabla'

# 2) conditions, loops and functions

# indentation is required !!!

if 3 > 2:
    print('3 > 2')
elif 1 == 0:
    print('1 = 0')
    print('else clause')

if d.has_key('a'):
    print('not found')

for x in range(0, 5):  # from 0 to 5 (0, 1, 2, 3 ,4)

letters = ['a', 'b', 'c']
for letter in letters:

# list comprehension
upper_letters = [letter.upper() for letter in letters]

d = { 1:'a', 2:'b', 3:'c'}
for key, value in d.iteritems():
    print(str(key), value)
for key in d.keys():
    print('key :', str(key))
for value in d.values():
    print('value :', value)

def special_sum(numberlist):
    total = 0
    for element in numberlist:
        if element < 5:
            continue # go to the next element
        elif total > 100:
            break # stop the loop
            total += element
    return total

print(special_sum([1,2,2,4,8,50, 60])) # = 118

# 3) using os and shutil

# import modules

import os
import shutil

def setup_test(directory):
    if not os.path.isdir(directory):
    file1 = os.path.join(directory, 'file1_test.dll')
    open(file1, 'a').close() # create empty file and close it
    file2 = os.path.join(directory, 'file2_test.txt')
    open(file2, 'a').close() # 'a' creates a file for appending (doesn't overwrite)

# looping over files in dir and subdirs and renaming some of them
def list_files(startdir):
    for element in os.listdir(startdir):
        path = os.path.join(startdir, element)
        if os.path.isfile(path):
            print path
            root, extension = os.path.splitext(path)
            if extension.lower() == '.dll': # add an extra extension to dll's
                shutil.copyfile(path, path + '.REMOVETHIS')
                # with os.rename you can replace the file
                ## os.rename(path, path + '.REMOVETHIS')

startdir = r'test'

# or you can loop with os.walk

for root, directories, files in os.walk(startdir, topdown=True):
    print 'dir : %s' % root
    if files:
        print 'files :'
        for f in files:
            print '\t', os.path.join(root, f)

# 4) reading, parsing and writing files

def create_tab_test(inputpath):
    with open(inputpath, 'w') as inputfile: # 'w' creates a file for (over)writing
        # create some dummy content separated by tabs and with newlines at the end
        lines = ['\t'.join([str(1*i),str(2*i)])+'\n' for i in range(5)]
        # write to the file
def tab_to_csv(inputpath, outputpath): # only for small files
    lines = []
    with open(inputpath) as inputfile:
        for line in inputfile:
            line = line.replace('\n', '')
            columns = line.split('\t')
            line = ';'.join(columns)
    with open(outputpath, 'w') as outputfile: # overwrites the outputfile if it exists
inputpath = r'test\test.txt' ## or r'D:\temp\test.txt'
outputpath = r'test\test.csv'

tab_to_csv(inputpath, outputpath)

Want to learn more or need some help ?
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BIOMOD2: invalid term in model formula

While trying out BIOMOD2 for species distribution modeling I encountered the following error when trying to create a random forest (RF) model:

Error in terms.formula(formula, data = data) : 
  invalid term in model formula
Error in predict(, Data[, expl_var_names, drop = FALSE], on_0_1000 = TRUE) : 
  error in evaluating the argument 'object' in selecting a method for function 'predict': Error: object '' not found

After lots of digging in the source code of BIOMOD I discovered what happened and how to fix it.

The line where the error was occurring looked like this:

model.sp <- try(randomForest(formula = makeFormula(resp_name, 
    head(Data), "simple", 0), data = Data[calibLines, 
    ], ntree = Options@RF$ntree, importance = FALSE, 
    norm.votes = TRUE, strata = factor(c(0, 1)), 
    nodesize = Options@RF$nodesize, maxnodes = Options@RF$maxnodes))

As you can see a formula is created from our data. The generated formula looked like this:

654987634 ~ 1 + nitrate_mean + par_mean + sst_mean + sst_range

The number 654987634 is my response variable name that I set when calling BIOMOD_FormatingData which apparently has been added to the Data data.frame as the first column. 

Solution: adding a letter prefix to my response variable name fixed my issue.

Lessons learned:
  1. It's incredibly useful that you can take a look at external source code in an RSession by typing its name, for iternals you add the package name and 3 double dots e.g. biomod2:::.Biomod.Models. Generics functions can be fetched with getMethod e.g. getMethod(biomod2::predict, signature="RF_biomod2_model")
  2. Read the docs very carefully: this is the description for response variable name (character). The species name.
  3. An assertion in BIOMOD_FormatingData would have saved me an hour or two. But note that a naive check like is.character( wouldn't work in this case, because once the formula is made it isn't a character anymore.
  4. Adding more diagnostic information in your error messages saves people time. If the generated formula would have been printed as well then I would probably have noticed the issue directly.
  5. Libraries make you win time, but you lose some as well.
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Creating a kernel density estimate map in R

In this post I'm going to create a kernel density estimate map in R from a file with latitude/longitude coordinates. WARNING: depending on your application the following gives incorrect results because a non-spherical kernel density estimator is used with spherical data (big thanks too Brian Rowlingson for pointing that out). I didn't find any spherical kernel density estimation implementation in R but if you know any please let me know. While exploring this issue I also wrote a similar implementation as the below code for the generation of a kernel density estimate with the spatial statistics package splancs instead of KernSmooth (splancs_kernel_density.R).

To create this map we'll use the bkde2D function in the KernSmooth package to generate the kernel density estimates and the raster package for outputting a raster file. If you don't have the KernSmooth and raster packages then they can as usually be installed with:


In order to create the 2D binned kernel density map I first loaded the KernSmooth and raster package.


Then we read the input file with the coordinates of the points that we want to generate the kernel density estimate off. This input file is an export from the Ocean Biographic Information System (OBIS) and represents distribution records from the seaweed Alaria esculenta.

input <- "Alaria_esculenta.csv"
output <- "Alaria_esculenta_density.asc"

# get the coordinates
records <- read.csv(input)
coordinates <- records[,2:3]

Next we compute the 2D binned kernel density estimate. In order to limit the size of the generated output files I set all values smaller then 0.00001 to 0.

# compute the 2D binned kernel density estimate
est <- bkde2D(coordinates, 
est$fhat[est$fhat<0.00001] <- 0 ## ignore very small values

Finally we create a raster file from the output of bkde2D, inspect it visually and export it as an ascii file.

# create raster
est.raster = raster(list(x=est$x1,y=est$x2,z=est$fhat))
projection(est.raster) <- CRS("+init=epsg:4326")
xmin(est.raster) <- -180
xmax(est.raster) <- 180
ymin(est.raster) <- -90
ymax(est.raster) <- 90
# visually inspect the raster output
# write an ascii file

And the output looks like this. As you can see most records are located near 50°N and 0° which corresponds to the distribution records map generated by OBIS.
The output ascii raster file can be used as an input file for OccurrenceThinner which uses the kernel density estimate grid for filtering out records from densely sampled regions in order to avoid overfitting while building species distribution models (SDM).

Code and data for this post are in my blog github repository.

Azimuthal equidistant projection: An implementation in F#, Python and Julia

Recently I needed to calculate distance from one point to another set of points in order to find the nearest point and its distance to the origin point. I opted to project all points to the azimuthal equidistant projection. The most important property of this projection is that all distances from the center of the projection to all other points represents the true distance (assuming a spheric earth) to all other projected points. To calculate the distance you just have to calculate the euclidean distance and multiply it with the average earth radius (6371000.0 meters).

The formulas for the azimuthal equidistant projection can be found at This formula can then be directly translated into F# like this:

open System
module AzimuthalEquidistantProjection =

    let inline degToRad d = 0.0174532925199433 * d; // (1.0/180.0 * Math.PI) * d

    let project centerlon centerlat lon lat =
        let t:float = degToRad lat
        let l:float = degToRad lon
        let t1 = degToRad centerlat // latitude center of projection
        let l0 = degToRad centerlon // longitude center of projection
        let c = acos ((sin t1) * (sin t) + (cos t1) * (cos t) * (cos (l-l0)))
        let k = c / (sin c)
        let x = k * (cos t) * (sin (l-l0))
        let y = k * (cos t1) * (sin t) - (sin t1) * (cos t) * (cos (l-l0))
        (x, y)

I also implemented the azimuthal equidistant projection by using units of measure. I create one set of measures to distinguish between degrees and radians and another one to distinguish between x and y.

open System
module AzimuthalEquidistantProjectionWithMeasures = 
    [<Measure>] type deg // degrees
    [<Measure>] type rad // radians
    [<Measure>] type x
    [<Measure>] type y
    type lon = float<x deg>
    type lat = float<y deg>
    let inline degToRad (d:float<'u deg>) = d*0.0174532925199433<rad/deg>
    let cos (d:float<'u rad>) = Math.Cos(float d)
    let sin (d:float<'u rad>) = Math.Sin(float d)
    let project (centerlon:lon) (centerlat:lat) (lon:lon) (lat:lat) =
        let t = degToRad lat
        let l = degToRad lon
        let t1 = degToRad centerlat // latitude center of projection
        let l0 = degToRad centerlon // longitude center of projection
        let c = acos ((sin t1) * (sin t) + (cos t1) * (cos t) * (cos (l-l0)))
        let k = c / (sin c)
        let x:float<x> = k * (cos t) * (sin (l-l0)) 
                         |> LanguagePrimitives.FloatWithMeasure
        let y:float<y> = k * (cos t1) * (sin t) - (sin t1) * (cos t) * (cos (l-l0)) 
                         |> LanguagePrimitives.FloatWithMeasure
        (x, y)

In the past I've used the python OGR bindings and the ESRI Projection Engine for my map projection needs but this time I needed a pure python implementation so I translated the above code and optimized it a bit by precalculating some values that we'll need when we project the points during the initialization of my projection class. A similarly optimized version in F# is on

from math import cos, sin, acos, radians

class Point(object):
    def __init__(self,x,y):
        self.x = x
        self.y = y       

class AzimuthalEquidistantProjection(object):
    def __init__(self, center): = center
        self.t1 = radians(center.y) ## latitude center of projection
        self.l0 = radians(center.x) ## longitude center of projection
        self.cost1 = cos(self.t1)
        self.sint1 = sin(self.t1)
    def project(self, point):
        t = radians(point.y)
        l = radians(point.x)
        costcosll0 = cos(t) * cos(l-self.l0)
        sint = sin(t)
        c = acos ((self.sint1) * (sint) + (self.cost1) * costcosll0)
        k = c / sin(c)
        x = k * cos(t) * sin(l-self.l0)
        y = k * self.cost1 * sint - self.sint1 * costcosll0
        return Point(x, y)

import unittest
class Test_AzimuthalEquidistantProjection(unittest.TestCase):
    def test_project(self):
        p = AzimuthalEquidistantProjection(Point(0.0,0.0))
        r = p.project(Point(1.0,1.0))
        self.assertAlmostEqual(0.01745152022, r.x)
        self.assertAlmostEqual(0.01745417858, r.y)

        p = AzimuthalEquidistantProjection(Point(1.0,2.0))
        r = p.project(Point(3.0,4.0))
        self.assertAlmostEqual(0.03482860733, r.x)
        self.assertAlmostEqual(0.03494898734, r.y)

        p = AzimuthalEquidistantProjection(Point(-10.0001, 80.0001))
        r = p.project(Point(7.935, 63.302))
        self.assertAlmostEqual(0.1405127567, r.x)
        self.assertAlmostEqual(-0.263406547, r.y)

if __name__ == '__main__':

I've also implemented the straightforward projection code in Julia. Julia is a promising language built for technical computing. It's still only on version 0.2 but a lot of packages have already been created for the language.

function degToRad(d)

function project(centerlon, centerlat, lon, lat)
  t = degToRad(lat)
  l = degToRad(lon)
  t1 = degToRad(centerlat)
  l0 = degToRad(centerlon)
  c = acos(sin(t1) * sin(t) + cos(t1) * cos(t) * cos(l-l0))
  k = c / sin(c)
  x = k * cos(t) * sin(l-l0)
  y = k * cos(t1) * sin(t) - sin(t1) * cos(t) * cos(l-l0)
  x, y

More Python, F#, Julia and geospatial code will be posted here so make sure to subscribe to my e-mail updates on the left. I also occasionally tweet as @gissolved.