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Archive for January, 2011

C# & Science: A 2D Heatmap Visualization Function (PNG)

without comments

Today, let’s take advantage of the bitmap writing ability of C# and output some heatmaps. Heatmaps are a nice visualization tool as they allow you to summarize numeric continuous values as colour intensities or hue spectra. It’s far easier for the human to grasp a general trend in data via a 2D image than it is to interpret a giant rectangular matrix of numbers. I’ll use two examples to demonstrate my heatmap code. The function provided is generalizable to all 2D arrays of doubles so I welcome you to download it and try it yourself.

>>> Attached: ( tgz | zip — C# source: demo main, example data used below, makefile ) <<<

Let’s start by specifying the two target colour schemes.

  • RGB-faux-colour {blue = cold, green = medium, red = hot} for web display
  • greyscale {white = cold, black = hot} suitable for print

Next, let’s take a look at the two examples.

Example Heat Maps 1: Bioinformatics Sequence Alignments — Backtrace Matrix

Here’s an application of heat maps to sequence alignments. We’ve visualized the alignment traces in the dynamic programming score matrices of local alignments. Here, a pair of tryptophan-aspartate-40 protein sequences are aligned so that you can quickly pick out two prominent traces with your eyes. The highest scoring spot is in red — the highest scoring trace carries backward and upward on a diagonal from that spot.

The left heatmap is shown in RGB-faux-colour decorated with a white diagonal. The center heatmap is shown in greyscale with no decorations. The right heatmap is decorated with a major diagonal, borders, lines every 100 values and ticks every ten values. Values correspond to amino acid positions where the top left is (0, 0) of the alignment.

Example Heat Maps 2: Feed Forward Back Propagation Network — Weight Training

Here’s another application of heat maps. This time we’ve visualized the training of neural network weight values. The weights are trained over 200 epochs to their final values. This visualization allows us to see the movement of weights from pseudorandom noise (top) to their final values (bottom).

Shown above are the weight and bias values for a 2-input, 4-hidden-node, 4-hidden-node, 2-output back-propagation feed-forward ANN trained on the toy XOR-EQ problem. The maps are rendered as RGB-faux-colour (left); greyscale (center); and RGB-faux-colour decorated with horizontal lines every 25 values (=50px) (right). Without going into detail, the leftmost 12 columns bridge inputs to the first hidden layer, the next 20 columns belong to the next weight layer, and the last 10 columns bridge to the output layer.

Update: I changed the height of the images of this example to half their original height — the horizontal lines now occur every 25 values (=25px).

C# Functions

This code makes use of two C# features — (1) function delegates and (2) optional arguments. If you also crack open the main file attached, you’ll notice I also make use of a third feature — (3) named arguments. A function delegate is used so that we can define and select which heat function to use to transform a three-tuple of double values (real, min, max) into a three-tuple of byte values (R, G, B). Optional arguments are used because the function signature has a total of twelve arguments. Leaving some out with sensible default values makes a lot of sense. Finally, I use named arguments in the main function because they allow me to (1) specify my optional arguments in a logical order and (2) read which arguments have been assigned without looking at the function signature.

Heat Functions

For this code to work, heat functions must match this delegate signature. Arguments: val is the current value, min is the lowest value in the matrix and max is the highest value in the matrix; we use min and max for normalization of val.

public delegate byte[] ValueToPixel(double val, double min, double max);

This is the RGB-faux-colour function that breaks apart the domain of heats and assigns it some amount of blue, green and red.

public static byte[] FauxColourRGB(double val, double min, double max) {
    byte r = 0;
    byte g = 0;
    byte b = 0;
    val = (val - min) / (max - min);
           if(               val <= 0.2) {
        b = (byte)((val / 0.2) * 255);
    } else if(val >  0.2 &&  val <= 0.7) {
        b = (byte)((1.0 - ((val - 0.2) / 0.5)) * 255);
           if(val >= 0.2 &&  val <= 0.6) {
        g = (byte)(((val - 0.2) / 0.4) * 255);
    } else if(val >  0.6 &&  val <= 0.9) {
        g = (byte)((1.0 - ((val - 0.6) / 0.3)) * 255);
           if(val >= 0.5               ) {
        r = (byte)(((val - 0.5) / 0.5) * 255);
    return new byte[]{r, g, b};

This is a far simpler greyscale function.

public static byte[] Greyscale(double val, double min, double max) {
    byte y = 0;
    val = (val - min) / (max - min);
    y = (byte)((1.0 - val) * 255);
    return new byte[]{y, y, y};

Heatmap Writer

The function below is split into a few logical parts: (1) we get the minimum and maximum heat values to normalize intensities against; (2) we set the pixels to the colours we want; (3) we add the decorations (borders, ticks etc.); (4) we save the file.

public static void SaveHeatmap(
    string fileName, double[,] matrix, ValueToPixel vtp,
    int pixw = 1, int pixh = 1,
    Color? decorationColour = null,
    bool drawBorder = false, bool drawDiag = false,
    int hLines = 0, int vLines = 0, int hTicks = 0, int vTicks = 0)
    var rows = matrix.GetLength(0);
    var cols = matrix.GetLength(1);
    var bitmap = new Bitmap(rows * pixw, cols * pixh);

    //Get min and max values ...
    var min = Double.PositiveInfinity;
    var max = Double.NegativeInfinity;
    for(int i = 0; i < matrix.GetLength(0); i ++) {
        for(int j = 0; j < matrix.GetLength(1); j ++) {
            max = matrix[i,j] > max? matrix[i,j]: max;
            min = matrix[i,j] < min? matrix[i,j]: min;
    //Set pixels ...
    for(int j = 0; j < bitmap.Height; j ++) {
        for(int i = 0; i < bitmap.Width; i ++) {
            var triplet = vtp(matrix[i / pixw, j / pixh], min, max);
            var color = Color.FromArgb(triplet[0], triplet[1], triplet[2]);
            bitmap.SetPixel(i, j, color);
    //Decorations ...
    var dc = decorationColour ?? Color.Black;
    for(int i = 0; i < bitmap.Height; i ++) {
        for(int j = 0; j < bitmap.Width; j ++) {
            if(drawBorder) {
                if(i == 0 || i == bitmap.Height -1) {
                    // Top and Bottom Borders ...
                    bitmap.SetPixel(j, i, dc);
                } else if(j == 0 || j == bitmap.Width -1) {
                    // Left and Right Borders ...
                    bitmap.SetPixel(j, i, dc);
            if(bitmap.Width == bitmap.Height && drawDiag && (i % 2 == 0)) {
                // Major Diagonal ... (only draw if square image +explicit)
                bitmap.SetPixel(i, i, dc);
            //Zeroed lines and zeroed ticks are turned off.
            if(hLines != 0 && i % (hLines*pixh) == 0) {
                if(j % (2*pixw) == 0) {
                    //Horizontal Bars ...
                    bitmap.SetPixel(j, i, dc);
            } else if(hTicks != 0 && i % (hTicks*pixh) == 0) {
                // Dots: H-Spacing
                if(vTicks != 0 && j % (vTicks*pixw) == 0) {
                    // Dots: V-Spacing
                    bitmap.SetPixel(j, i, dc);
            } else if(i % (2*pixh) == 0) {
                if(vLines != 0 && j % (vLines*pixw) == 0) {
                    //Vertical Bars
                    bitmap.SetPixel(j, i, dc);

    //Save file...
    bitmap.Save(fileName, ImageFormat.Png);

Happy mapping 😀

Compatibility Notes: The C# code discussed was developed with Mono using Monodevelop. All code is compatible with the C#.NET 4.0 specification and is forward compatible. I’ve linked in two assemblies — (1) -r:System.Core for general C#.Net 3.5~4.0 features, and (2) r:System.Drawing to write out PNG files. If you need an overview of how to set up Monodevelop to use the System.Drawing assembly, see C Sharp PNG Bitmap Writing with System.Drawing in my notebook.

Eddie Ma

January 21st, 2011 at 1:20 pm

Simple Interactive Phylogenetic Tree Sketches JS+SVG+XHTML

without comments

>>> Attached: ( parse_newick_xhtml.js | draw_phylogeny.js — implementation in JS | index.html — demo with IL-1 ) <<<
>>> Attached: ( auto_phylo_diagram.tgz — includes all above, a python script, a demo makefile and IL-1 data ) <<<

In this post, I discuss a Python script I wrote that will convert a Newick Traversal and a FASTA file into a browser-viewable interactive diagram using SVG+JS+XHTML. This method is compatible with WebKit (Safari, Chrome) and Mozilla (Firefox) renderers but not Opera. XHTML doesn’t work with IE, so we’ll have to wait for massive adoption of HTML5 before I can make this work for everyone — don’t worry, it’s coming.

To the left is what the rendered tree looks like (shown as a screen captured PNG).

I recommend looking at the demo index.xhtml above if your browser supports it now. The demo will do a far better job than text in explaining exactly what features are possible using this method.

Try clicking on the different nodes and hyperlinks in the demo — notice that the displayed alignment strips away sites (columns) that are 100% gaps so that each node displays only a profile relevant for itself.

I originally intended to explain all the details of the JavaScripts that render and drive the diagram, but I think it’d be more useful to first focus on the Python script and the data input and output from the script.

The Attached Python Script to_xhtml.py found in auto_phylo_diagram.tgz

I’ll explain how to invoke to_xhtml.py with an example below.

python to_xhtml.py IL1fasta.txt IL1tree2.txt "IL-1 group from NCBI CDD (15)" > index.xhtml

Arguments …

  1. Plain Text FASTA file — IL1fasta.txt
  2. Plain Text Newick Traversal file — IL1tree2.txt
  3. Title of the generated XHTML — “IL-1 group from NCBI CDD (15)”

The data I used was generated with MUSCLE with default parameters. I specified the output FASTA with -out and the output second iteration tree with -tree2.

The Attached makefile found in auto_phylo_diagram.tgz

The makefile has two actual rules. If index.html does not exist, it will be regenerated with the above Python script and IL1fasta.txt and IL1tree2.txt. If either IL1fasta.txt or IL1tree2.txt or both do not exist, these files are regenerated using MUSCLE with default parameters on the included example data file ncbi.IL1.cl00094.15.fasta.txt. Running make on the included package shouldn’t do anything since all of the files are included.

The Example Data

The example data comes from the Interleukin-1 group (cd00100) from the NCBI Conserved Domains Database (CDD).

Finally, I’ll discuss briefly the nitty gritty of the JavaScripts found as stand-alones above that are also included in the package.

Part Two of Two

As is the nature of programatically drawing things, this particular task comes with its share of prerequisites.

In a previous — Part 1, I covered Interactive Diagrams Using Inline JS+SVG+XHTML — see that post for compatibility notes and the general method (remember, this technique is a holdover that will eventually be replaced with HTML5 and that the scripts in this post are not compatible with Opera anymore).

In this current post — Part 2, I’ll also assume you’ve seen Parsing a Newick Tree with recursive descent (you don’t need to know it inside and out, since we’ll only use these functions) — if you look at the example index.html attached, you’ll see that we actually parse the Newick Traversal using two functions in parse_newick_xhtml.jstree_builder() then traverse_tree(). The former converts the traversal to an in-memory binary tree while the latter accepts the root node of said tree and produces an array. This array is read in draw_phylogeny.js by fdraw_tree_svg() which does the actual rendering along with attaching all of the dynamic behaviour.

Parameters ( What are we drawing? )

To keep things simple, let’s focus on three requirements: (1) the tree will me sketched top-down with the root on top and its leaves below; (2) the diagram must make good use of the window width and avoid making horizontal scroll bars (unless it’s absolutely necessary); (3) the drawing function must make the diagram compatible with the overall document object model (DOM) so that we can highlight nodes and know what nodes were clicked to show the appropriate data.

Because of the second condition, all nodes in a given depth of the tree will be drawn at the same time. A horizontal repulsion will be applied so that each level will appear to be centre-justified.

General Strategy

Because we are centre-justifying the tree, we will be drawing each level of the tree simultaneously to calculate the offsets we want for each node. We perform this iteratively for each level of depth of the tree in the function fdraw_tree_svg(). Everything that is written dynamically by JavaScript goes to a div with a unique id. All of the SVG goes to id=”tree_display” and all of the textual output including raster images, text and alignments goes to id=”thoughts”. To attach behaviour to hyperlinks, whether it’s within the SVG or using standard anchor tags, the “onclick” property is defined. In this case, we always call the same function “onclick=javascript:select_node()“. This function accepts a single parameter: the integer serial number that has been clicked.

Additional Behaviour — Images and Links to Databases

After I wrote the first drafts of the JavaScripts, I decided to add two more behaviours in the current version. First, if a particular node name has the letters “GI” in it, the script will attempt to hyperlink it with the proceeding serial number against NCBI. Second, if a particular node name has the letters “PDB” in it, the script will attempt to hyperlink the following identifier against RSCB Protein Database and also pull the first thumbnail with an img tag for the 3D protein structure.


This was done because I wanted to show a custom alignment algorithm to my advisors. In this demo, I’ve stripped away the custom alignment leaving behind a more general yet pleasing visualizer. I hope that the Python script and JavaScripts are useful to you. Enjoy!

Eddie Ma

January 1st, 2011 at 11:55 pm