Simple tricks to make your C/C++ code run faster

Us, engineers with no formal computer science training, for a myriad of good reasons tend to favor friendly programming languages such as Python over evil C/C++. However, when our application is performance sensitive and we cannot wait for results sitting in our chairs for as long as a Python code would require us to, we are sometimes forced to us C/C++. Why then not making the most of it when it this is the case?

Here are some simple tips to make your C/C++ code run even faster, and how to get some advice about further performance improvements. The last idea (data locality) is transferable to Python and other languages.

Most important trick

Improve your algorithm. Thinking if there is a simpler way of doing what you coded may reduce your algorithm’s complexity (say, from say n3 to n*log(n)), which would:

  • yield great speed-up when you have lots of data or needs to run a computation several times in a row, and
  • make you look smarter.

Compiler flags

First and foremost, the those who know what they are doing — compiler developers — do the work for you by calling the compiler with the appropriate flags. There are an incredible amount of flags you can call for that, but I would say that the ones you should have on whenever possible are -O3 and –march=native.

The optimization flags (-O1 to -O3, the latter more aggressive than the former) will perform a series of modification on your code behind the scenes to speed it up, some times by more than an order of magnitude. The issue is that this modifications may eventually make your code behave differently than you expected, so it’s always good to do a few smaller runs with -O0 and -O3 and compare their results before getting into production mode.

The –march=native flag will make the compiler fine tune your code to the processor it is being compiled on (conversely, –march=haswell would fine tune it to haswell architectures, for example). This is great if you are only going to run your code on your own machine or in another machine known to have a similar architecture, but if you try to run the binary on a machine with a different architecture, specially if it is an older one, you may end up with illegal instruction errors.

Restricted pointer array

When declaring a pointer array which you are sure will not be subject to pointer aliasing — namely there will be no other pointer pointing to the same memory address –, you can declare that pointer as a restrict pointer, as below:

  • GCC: double* __restrict__ my_pointer_array
  • Intel compiler: double* restrict my_pointer_array

This will let the compiler know that it can change order of certain operations involving my_pointer_array to make your code faster without changing some read/write order that may change your results. If you want to use the restricted qualifier with the intel compiler the flag -restrict must be passed as an argument to the compiler.

Aligned pointer array

By aligning an array, you are making sure the data is going to lie in the ideal location in memory for the processor to fetch it and perform the calculations it needs based on that array. To help your compiler optimize your data alignment, you need to (1) align your array when it is declared by a specific number of bytes and (2) tell your the compiler the array is aligned when using it to perform calculations — the compiler has no idea whether or not arrays received as arguments in function are aligned. Below are examples in C, although the same ideas apply to C++ as well.

GCC

#include <stdio.h>
#include <omp.h>

#define SIZE_ARRAY 100000
#define ALIGN 64

void sum(double *__restrict__ a, double *__restrict__ b, double *__restrict__ c, int n) {
    a = (double*) __builtin_assume_aligned(a, ALIGN);
    b = (double*) __builtin_assume_aligned(b, ALIGN);
    c = (double*) __builtin_assume_aligned(c, ALIGN);
    for (int i = 0; i < n; ++i)
        c[i] = a[i] + b[i];
}

int main(void) {

    double a[SIZE_ARRAY] __attribute__((aligned(ALIGN )));
    double b[SIZE_ARRAY] __attribute__((aligned(ALIGN )));
    double c[SIZE_ARRAY] __attribute__((aligned(ALIGN )));

    for (int i = 0; i < SIZE_ARRAY; ++i) {
        a[i] = 5.;
        b[i] = 2.;
    }
    double start_time = omp_get_wtime();
    sum(a, b, c, SIZE_ARRAY);
    double time = omp_get_wtime() - start_time;
    printf("%0.6fs", time);
}

Intel compiler

#include <stdio.h>
#include <omp.h>

#define SIZE_ARRAY 100000
#define ALIGN 64

void sum(double* restrict a, double* restrict b, double* restrict c, int n) {
    __assume_aligned(a, ALIGN);
    __assume_aligned(b, ALIGN);
    __assume_aligned(c, ALIGN);
    for (int i = 0; i < n; ++i)
        c[i] = a[i] + b[i];
}

int main(void) {

    __declspec(align(ALIGN )) float a[SIZE_ARRAY];
    __declspec(align(ALIGN )) float b[SIZE_ARRAY];
    __declspec(align(ALIGN )) float c[SIZE_ARRAY];

    for (int i = 0; i < SIZE_ARRAY; ++i) {
        a[i] = 5.;
        b[i] = 2.;
    }
    double start_time = omp_get_wtime();
    sum(a, b, c, SIZE_ARRAY);
    double time = omp_get_wtime() - start_time;

    printf("%0.6fs", time);
}

Edit: In a comment to this post, Krister Walfridsson not only caught an issue with my GCC code, for which mention I thank him, but he also shows the differences in machine code generated with and without alignment.

Data Locality

Computers are physical things, which means that data is physically stored and needs to be physically moved around in memory and between cache and processor in order to be used in calculations. This means that, if your data is stored all over the place in memory — e.g. in multiple pointer arrays in different parts of memory –, the processor will have to reach out to several parts of memory to fetch all your data before performing any computations. By having the data intelligently laid out in memory you ensure all data required for each computation is stored close to each other and in cache at the same time, which becomes even more important if your code uses too much data to fit in the cache at once.

In order to making your processor’s life easier, it is a good idea to ensure that all data required for a calculation step is close together. For example, if a given computation required three arrays of fixed sizes, it is always a good idea to merge them into one long array, as in the example below for the Intel compiler.

#include <stdio.h>
#include <omp.h>

#define SIZE_ARRAY 100000
#define ALIGN 64

void sum(double* restrict a, double* restrict b, double* restrict c, int n) {
    __assume_aligned(a, ALIGN);
    __assume_aligned(b, ALIGN);
    __assume_aligned(c, ALIGN);
    for (int i = 0; i < n; ++i)
        c[i] = a[i] + b[i];
}

int main(void) {

    __declspec(align(ALIGN )) float abc[3 * SIZE_ARRAY];

    for (int i = 0; i < 2 * SIZE_ARRAY; ++i) {
        a[i] = 5.;
        b[i] = 2.;
    }
    double start_time = omp_get_wtime();
    sum(abc, abc + SIZE_ARRAY, abc + 2 * ARRAY, SIZE_ARRAY);
    double time = omp_get_wtime() - start_time;

    printf("%0.6fs", time);
}

or even, since c[i] depends only on b[i] and a[i], we can have the values of a, b and c intercalated to assure that all computations will be performed on data that is right next to each other in memory:

#include <stdio.h>
#include <omp.h>

#define SIZE_ARRAY 100000
#define ALIGN 64
#define STRIDE 3

void sum(double* restrict abc, int n, int stride) {
    __assume_aligned(abc, ALIGN);

    for (int i = 0; i < n; i += stride)
        abc[i+2] = abc[i] + abc[i+1];
}

int main(void) {
    __declspec(align(ALIGN )) double abc[3 * SIZE_ARRAY];

    for (int i = 0; i < 3 * SIZE_ARRAY; i += STRIDE) {
        abc[i] = 5.;
        abc[i+1] = 2.;
                                            }
    double start_time = omp_get_wtime();
    sum(abc, SIZE_ARRAY, STRIDE );
    double time = omp_get_wtime() - start_time;

    printf("%0.6fs", time);
}

Conclusion

According a class project in which we had to write C code to perform matrix multiplication, the improvements suggested should may improve the performance of your code by 5 or 10 times. Also, the idea of data locality can be transferred to other languages, such as Python.

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Web Scraping: Constructing URLs, Downloading and Unpacking Zipped Files in Python and R

Introduction

Being able to automate data retrieval helps alleviate encountering irritating, repetitive tasks. Often times, these data files can be separated by a range of times, site locations, or even type of measurement, causing them to be cumbersome to download manually. This blog post outlines how to download multiple zipped csv files from a webpage using both R and Python.

We will specifically explore downloading historical hourly locational marginal pricing (LMP) data files from PJM, a regional transmission organization coordinating a wholesale electricity market across 13 Midwestern, Southeastern, and Northeastern states. The files in question are located here.

First, Using Python

A distinct advantage of using Python over R is being able to write fewer lines for the same results. However, the differences in the time required to execute the code are generally minimal between the two languages.

Constructing URLs

The URL for the most recent file from the webpage for August 2017 has the following format: “http://www.pjm.com/pub/account/lmpmonthly/201708-da.csv
Notably, the URL is straightforward in its structure and allows for a fairly simple approach in attempting to create this URL from scratch.

To begin, we can deconstruct the URL into three aspects: the base URL, the date, and the file extension.
The base URL is fairly straightforward because it is constant: “http://www.pjm.com/pub/account/lmpmonthly/
As is the file extension: “-da.csv”

However, the largest issue presented is how to approach recreating the date: “201708”
It is in the form “yyyymm”, requiring a reconstruction of a 4-digit year (luckily these records don’t go back to the first millennium) and a 2-digit month.

In Python, this is excessively easy to reconstruct using the .format() string modifying method. All that is required is playing around with the format-specification mini-language within the squiggly brackets. Note that the squiggly brackets are inserted within the string with the following form: {index:modifyer}

In this example, we follow the format above and deconstruct the URL then reassemble it within one line in Python. Assigning this string to a variable allows for easy iterations through the code by simply changing the inputs. So let’s create a quick function named url_creator that allows for the input of a date in the format (yyyy, mm) and returns the constructed URL as a string:

def url_creator(date):
    """
    Input is list [yyyy, mm]
    """
    yyyy, mm = date

    return "http://www.pjm.com/pub/account/lmpmonthly/{0:}{1:02d}-da.zip".format(yyyy, mm)

To quickly generate a list of the dates we’re interested in, creating a list of with entries in the format (yyyy, mm) for each of the month’s we’re interested in is easy enough using a couple of imbedded for loops. If you need alternative dates, you can easily alter this loop around or manually create a list of lists to accommodate your needs:

#for loop method
dates = []
for i in range(17):
    for j in range(12):
        dates.append([2001 + i, j + 1])

#alternative manual method
dates = [[2011, 1], [2011, 2], [2011, 3]]

Retrieving and Unpacking Zipped Files

Now that we can create the URL for this specific file type by calling the url_creator function and have all of the dates we may be interested in, we need to be able to access, download, unzip/extract, and subsequently save these files. Utilizing the urllib library, we can request and download the zipped file. Note that urllib.request.urlretrieve only retrieves the files and does not attempt to read it. While we could simply save the zipped file at this step, it is preferred to extract it to prevent headaches down the line.

Utilizing the urllib library, we can extract the downloaded files to the specified folder. Notably, I use the operating system interface method getcwd while extracting the file to save the resulting csv file into the directory where this script is running. Following this, the extracted file is closed.

import zipfile, urllib, os
from urllib.request import Request,urlopen, urlretrieve

for date in dates:
    baseurl = url_creator(date)

    local_filename, headers = urllib.request.urlretrieve(url = baseurl)
    zip_ref = zipfile.ZipFile(file = local_filename, mode = 'r')
    zip_ref.extractall(path = os.getcwd())     #os.getcwd() directs to current working directory
    zip_ref.close()

At this point, the extracted csv files will be located in the directory where this script was running.

Alternatively, Using R

We will be using an csv files to specify date ranges instead of for loops as shown in the Python example above. The advantage of using the csv files rather than indexing i=2001:2010 is that if you have a list of non-consecutive months or years, it is sometimes easier to just make a list of the years and cycle through all of the elements of the list rather than trying to figure out how to index the years directly. However, in this example, it would be just as easy to index through the years and month rather than the csv file.

This first block of code sets the working directory and reads in two csv files from the directory. The first csv file contains a list of the years 2001-2010. The second CSV file lists out the months January-December as numbers.

#Set working directory
#specifically specified for the directory where we want to "dump" the data
setwd("E:/Data/WebScraping/PJM/Markets_and_operations/Energy/Real_Time_Monthly/R")

#Create csv files with a list of the relevant years and months
years=read.csv("Years.csv")
months=read.csv("Months.csv")

The breakdown of the URL was previously shown. To create this in R, we will generate a for-loop that will change this link to cycle through all the years and months listed in the csv files. The index i and j iterate through the elements in the year and month csv file respectively. (The if statement will be discussed at the end of this section). We then use the “downloadurl” and “paste” functions to turn the entire link into a string. The parts of the link surrounded in quotes are unchanging and denoted in green. The “as.character” function is used to cycle in the elements from the csv files and turn them into characters. Finally, the sep=’’ is used to denote that there should be no space separating the characters. The next two lines download the file into R as a temporary file.

#i indexes through the years and j indexes through the months
for (i in (1:16)){
  for( j in (1:12)){
      if (j>9){

    #dowload the url and save it as a temporary file

    downloadurl=paste("http://www.pjm.com/pub/account/lmpmonthly/",as.character(years[i,1]),as.character(months[j,1]),"-da.zip",sep="")
    temp="tempfile"
    download.file(downloadurl,temp)

Next, we unzip the temporary file and finds the csv (which is in the form: 200101-da.csv), reading in the csv file into the R environment as “x”. We assign the name “200101-da” to “x”. Finally, it is written as a csv file and stored in the working directory, the temporary file is deleted, and the for-loop starts over again.

    #read in the csv into the global environment
    x=read.csv((unz(temp,paste(as.character(years[i,1]),as.character(months[j,1]),"-da.csv",sep=""))))
    #Assign a name to the csv "x"
    newname=paste(as.character(years[i,1]),as.character(months[j,1]),sep="")
    assign(newname,x)
    #create a csv that is stored in your working directory
    write.csv(x,file=paste(newname,".csv",sep=""))

    unlink(temp) #deletetempfile
      }

    #If j is between 1 and 10, the only difference is that a "0" has to be added
    #in front of the month number

Overcoming Formatting

The reason for the “if” statement is that it is not a trivial process to properly format the dates in Excel when writing to a csv to create the list of dates. When inputing “01”, the entry is simply changed to “1” when the file is saved as a csv. However, note that in the name of the files, the first nine months have a 0 preceding their number. Therefore, the URL construct must be modified for these months. The downloadurl has been changed so that a 0 is added before the month number if j < 10. Aside from the hard-coded zeroes, the block of code is the same as the one above.

else { 

        downloadurl=paste("http://www.pjm.com/pub/account/lmpmonthly/",as.character(years[i,1]),"0",as.character(months[j,1]),"-da.zip",sep="")

        temp="tempfile"
        download.file(downloadurl,temp)

        #x=read.csv(url(paste("http://www.pjm.com/pub/account/lmpmonthly/",as.character(years[i,1],as.character(months[j,1],sep=""))))
        x=read.csv((unz(temp,paste(as.character(years[i,1]),"0",as.character(months[j,1]),"-da.csv",sep=""))))
        newname=paste(as.character(years[i,1]),"0",as.character(months[j,1]),sep="")
        assign(newname,x)
        write.csv(x,file=paste(newname,".csv",sep=""))

        unlink(temp) #deletetempfile

}

Acknowledgements

Many thanks to Rohini Gupta for contributing to this post by defining the problem and explaining her approach in R.

Versions: R = 3.4.1 Python = 3.6.2
To see the code in its entirety, please visit the linked GitHub Repository.

Generating Interactive Visuals in R

Visuals vs. Visual Analytics 

How do visuals differ from visual analytics? In a scientific sense, a visual is a broad term for any picture, illustration, or graph that can be used to convey an idea. However, visual analytics is more than just generating a graph of complex data and handing it to a decision maker. Visual analytic tools help create graphs that allow the user to interact with the data, whether that involves manipulating a graph in three-dimensional space or allowing users to filter or brush for solutions that match certain criteria. Ultimately, visual analytics seeks to help in making decisions as fast as possible and to “enable learning through continual [problem] reformulation” (Woodruff et al., 2013) by presenting large data sets in an organized way so that the user can better recognize patterns and make inferences.

My goal with this blog post is to introduce two R libraries that are particularly useful to develop interactive graphs that will allow for better exploration of a three-dimensional space. I have found that documentation on these libraries and potential errors was sparse, so this post will consolidate my hours of Stack Overflow searching into a step-by-step process to produce beautiful graphs!

R Libraries

            Use rgl to create a GIF of a 3D graph

Spinning graphs can be especially useful to visualize a 3D Pareto front and a nice visualization for a Power Point presentation. I will be using an example three-objective Pareto set from Julie’s work on the Red River Basin for this tutorial. The script has been broken down and explained in the following sections.


#Set working directory
setwd("C:/Users/Me/Folder/Blog_Post_1")

#Read in in csv of pareto set
data=read.csv("pareto.csv")

#Create three vectors for the three objectives
hydropower=data$WcAvgHydro
deficit=data$WcAvgDeficit
flood=data$WcAvgFlood

In this first block of code, the working directory is set, the data set is imported from a CSV file, and each column of the data frame is saved as a vector that is conveniently named. Now we will generate the plot.


#call the rgl library
library(rgl)

#Adjust the size of the window
par3d(windowRect=c(0,0,500,500))

If the rgl package isn’t installed on your computer yet, simply type install.packages(“rgl”) into the console. Otherwise, use the library function in line 2 to call the rgl package. The next line of code is used to adjust the window that the graph will pop up in. The default window is very small and as such, the movie will have a small resolution if the window is not adjusted!


#Plot the set in 3D space

plot3d(hydropower,deficit,flood,col=brewer.pal(8,"Blues"), size=2, type='s', alpha=0.75)

Let’s plot these data in 3D space. The first three components of the plot3d function are the x,y, and z vectors respectively. The rest of the parameters are subject to your personal preference. I used the Color Brewer (install package “RColorBrewer”) to color the data points in different blue gradients. The first value is the number of colors that you want, and the second value is the color set. Color Brewer sets can be found here: http://www.datavis.ca/sasmac/brewerpal.html. My choice of colors is random, so I opted not to create a color scale. Creating a color scale is more involved in rgl. One option is to split your data into classes and to use legend3d and the cut function to cut your legend into color levels. Unfortunately, there simply isn’t an easy way to create a color scale in rgl. Finally, I wanted my data points to be spheres, of size 2, that were 50% transparent, which is specified with type, size, and alpha respectively. Plot3d will open a window with your graph. You can use your mouse to rotate it.

Now, let’s make  a movie of the graph. The movie3d function requires that you install ImageMagick, a software that allows you to create a GIF from stitching together multiple pictures. ImageMagick also has cool functionalities like editing, resizing, and layering pictures. It can be installed into your computer through R using the first two lines of code below. Make sure not to re-run these lines once ImageMagick is installed.  Note that ImageMagick doesn’t have to be installed in your directory, just on your computer.


require(installr)
install.ImageMagick()

#Create a spinning movie of your plot
movie3d(spin3d(axis = c(0, 0, 1)), duration = 20,
 dir = getwd())

Finally, the last line of code is used to generate the movie. I have specified that I want the plot to spin about the z axis, specified a duration (you can play around with the number to see what suits your data), and that I want the movie to be saved in my current working directory. The resulting GIF is below. If the GIF has stopped running, reload the page and scroll down to this section again.

movie.gif

I have found that creating the movie can be a bit finicky and the last step is where errors usually occur. When you execute your code, make sure that you keep the plot window open while ImageMagick stitches together the snapshots otherwise you will get an error. If you have errors, please feel free to share because I most likely had them at one point and was able to ultimately fix them.

Overall, I found this package to be useful for a quick overview of the 3D space, but I wasn’t pleased with the way the axes values and titles overlap sometimes when the graph spins. The way to work around this is to set the labels and title to NULL and insert your own non-moving labels and title when you add the GIF to a PowerPoint presentation.

            Use plotly to create an interactive scatter

I much prefer the plotly package to rgl for the aesthetic value, ease of creating a color scale, and the ability to mouse-over points to obtain coordinate values in a scatter plot. Plotly is an open source JavaScript graphing library but has an R API. The first step is to create a Plotly account at: https://plot.ly/. Once you have confirmed your email address, head to https://plot.ly/settings/api to get an API key. Click the “regenerate key” button and you’ll get a 20 character key that will be used to create a shareable link to your chart. Perfect, now we’re ready to get started!

setwd("C:/Users/Me/Folder/Blog_Post_1")

library(plotly)
library(ggplot2)

#Set environment variables

Sys.setenv("plotly_username"="rg727")
Sys.setenv("plotly_api_key"="insert key here")

#Read in pareto set data

pareto=read.csv("ieee_synthetic_thinned.csv")

Set the working directory, install the relevant libraries, set the environment variables and load in the data set. Be sure to insert your API key. You will need to regenerate a new key every time you make a new graph. Also, note that your data must be in the form of a data frame for plotly to work.

#Plot your data

plot= plot_ly(pareto, x = ~WcAvgHydro, y = ~WcAvgDeficit, z = ~WcAvgFlood, color = ~WcAvgFlood, colors = c('#00d6f7', '#ebfc2f'))
add_markers()

#Add axes titles
layout(title="Pareto Set", scene = list(xaxis = list(title = 'Hydropower'),yaxis = list(title = 'Deficit'), zaxis = list(title = 'Flood')))
#call the name of your plot to appear in the viewer
plot

To correctly use the plotly command, the first input needed is the data frame, followed by the column names of the x,y, and z columns in the data frame. Precede each column name with a “~”.

I decided that I wanted the colors to scale with the value of the z variable. The colors were defined using color codes available at http://www.color-hex.com/. Use the layout function to add a main title and axis labels. Finally call the name of your plot and you will see it appear in the viewer at the lower right of your screen.If your viewer shows up blank with only the color scale, click on the viewer or click “zoom”. Depending on how large the data set is, it may take some time for the graph to load.


#Create a link to your chart and call it to launch the window
chart_link = api_create(plot, filename = "public-graph")
chart_link

Finally create the chart link using the first line of code above and the next line will launch the graph in Plotly. Copy and save the URL and anyone with it can access your graph, even if they don’t have a Plotly account. Play around with the cool capabilities of my Plotly graph, like mousing over points, rotating, and zooming!

https://plot.ly/~rg727/1/

 

Sources: 

http://www.sthda.com/english/wiki/a-complete-guide-to-3d-visualization-device-system-in-r-r-software-and-data-visualization

https://plot.ly/r/3d-scatter-plots/

Woodruff, M.J., Reed, P.M. & Simpson, T.W. Struct Multidisc Optim (2013) 48: 201. https://doi.org/10.1007/s00158-013-0891-z

James J. Thomas and Kristin A. Cook (Ed.) (2005). Illuminating the Path: The R&D Agenda for Visual Analytics National Visualization and Analytics Center.

Python example: Hardy Cross method for pipe networks

I teach a class called Water Resources Engineering at the University of Colorado Boulder, and I have often added in examples where students use Python to perform the calculations.  For those of you who are new to programming, you might get a kick out of this example since it goes through an entire procedure of how to solve an engineering problem using Python, and the numpy library.  The example is two YouTube videos embedded below! The best way to watch them, though, is in full screen, which you can get to by clicking the name of the video, opening up a new YouTube tab in your browser.

Let us know if you have any questions in the comments section below. For more on Python from this blog, search “Python” in the search box.