Plotting Parallel Data (PGraph)

Overview

This document exists to outline the mechanism for plotting data that comes from distributed parallel sources within ParaQ. We dub the collection of code for parallel plotting as PGraph, although the implementation will actually be set of smaller, distinct pieces. Because two of the main design criteria for ParaQ are the ability to scale well on parallel machines and provide quantitative information, the design of PGraph is critical.

Use Cases

The overall goal of PGraph is to provide plot-style visualizations of distributed VTK objects. In this section we list the types of plots users may wish to perform on their data. I encourage other ParaQ developers to contribute to this list as they see fit.

Immediately below is a table listing the types of abstract visualizations with plots users may wish to create. The "Plot Type" column refers to one of the types of plots, which are listed further below in the Plot Types table.

Abstract Visualizations with Plots

Name	Description	Plot Type
Histogram	Given a data array (usually point scalars or cell scalars), returns a discrete function with <math>N</math> items or bins. Each bin has an assigned range and contains the count of entries in the data array that fall within that range.	Bar Chart or X-Y Plot
Time Plot	Given a point or cell, show the values of some scalar over time.	X-Y Plot
Line Probe	Given a line in space, plot the value of a scalar field defined by a data set along the line.	X-Y Plot
Plane Probe	Given a plane in space, plot the value of a scalar field defined by a data set along the line.	X-Y-Z Plot
Scatter Plot	Like a histogram, except that two scalars are selected and the bins are set into a 2D grid with each bin representing a range in each scalar.	Density Plot

Plot Types

Name	Input Dimensions	Description
Bar Chart	1	Shows discrete values with bars with heights proportional to the values.
X-Y Plot	1	A traditional graph of a function with the variables on the X axis and the value on the Y axis.
X-Y-Z Plot	2	This plot shows a surface in 3-space. The X and Y axis represent two input variables. The position of the surface in Z corresponds to the value for the variables at the given X and Y position.
Density Plot	2	A 2D plot with both the X and Y axis representing input variables. Every point in the image shaded (or colored) to represent the value at that point.

Approach

Our approach is based on the fact that the input for all of the plots given in Plot Types can be represented as either 1D or 2D arrays. Furthermore, because the resolution of the displays is limited to what representable by the display media, the size of these arrays Thus, to simplify things and enable us to break this problem into manageable pieces, we represent the plot data in simple arrays.

The image below shows the basic units of PGraph. The Sampling unit takes VTK objects, which may be distributed, and performs some sort of sampling to generate arrays of data. The Parallel Reduction unit combines array distributed across processes to a single array. The Server to Client unit transfers data from the root of the data server to the client. Finally, Qt Plotting Components are components that represent the arrays a plots. They are Qt components.

Obviously, some of these units may not be necessary. For example, Server to Client is only necessary in client/server mode. Parallel Reduction is only necessary in a parallel job.

Sampling

The sampling unit takes a vtkDataSet and generates data in 1D or 2D arrays. It comprises a collection of vtkImageAlgorithm classes. There will be a separate vtkImageAlgorithm class for each type of sampling performed. In general, we will probably need a separate image algorithm for each type of plot visualization, although similar ones may be combined.

Using vtkImageAlgorithm objects to perform the sampling provides many advantages. A vtkImageAlgorithm can interface directly with a vtkDataSet or within any VTK pipeline. The output of the vtkImageAlgorithm, a vtkImage, can also be used with other VTK components or passed downstream to another pipeline. Also, using a vtkImageAlgorithm makes controling the system with ParaView's server manager objects easy. Finally, using a vtkImageAlgorithm does no harm as it is not difficult to get the raw array data from a vtkImage object.

The algorithms used for sampling are not parallel algorithms, even though they run in a parallel job. Instead, the algorithm on each process runs independently on each piece of data. It is up to the Parallel Reduction unit to combine the results.

Parallel Reduction

If the Sampling occurs in parallel, the resulting arrays on each process need to be combined into a single array. The combining follows the following algorithm:

for each array index <math>i</math>
  <math>A_1[i] \leftarrow A_1[i] \oplus A_2[i] \oplus A_3[i] \oplus \ldots \oplus A_N[i]</math>

where <math>A_j[i]</math> is the <math>i</math>th element of the array on process <math>j</math> and <math>\oplus</math> is some mathematical binary operation. In words, it is a piecewise "sum" of elements across processes, except that the operation used to combine numbers may be something other than plus. This operation can changed based on the plot visualization type. For histograms, the operation would be an actual sum. For line probes, the operation would be to select a single value that is not undefined.

In parallel computing, this is called a reduction. In fact, MPI has a function specifically designed to do a reduction. For smaller sized data, simply using this MPI function may be sufficient. In fact, the function may be sufficient for larger 2D arrays.

Another option to do the reduction is to consider our parallel rendering code. If you think about it, image compositing is really just a reduction operation with special depth-test or color-blending operations. We have at our disposal a very efficient library to do these reductions: IceT. It may be worthwhile to leverage the IceT code to do reduction of larger data.

Whatever code we use to perform the parallel reduction, we can wrap it up in a parallel vtkImageAlgorithm class. We should do this for all the advantages listed in #Sampling.

Server to Client

If the original data resides on a server, and the plotting component resides on the client, at some point the data must be moved.