jmabuin / matrix-market-suite

Matrix Market Suite

Matrix Market Suite

1. Description

The Matrix Market format is a widely used format when working with dense and sparse matrices. Typically, when measuring performance of linear algebra programs or testing scientific simulation software, matrices from collections such as The University of Florida Sparse Matrix Collection or The Harwell-Boeing Collection. These collections use the Matrix Market format as one of their formats.

But sometimes, these matrices are not enough, or don't adapt to certain kind of problems. So, in order to create and test these data, we have created Matrix Market Suite. Matrix Market Suite is a tool that creates and operates over matrices with the Matrix Market format.

2. Installation

2.1 Dependencies

Matrix Market Suite depends on the openblas and lapacke libraries.

To install them Debian:

sudo aptitude install libopenblas-base libopenblas-dev liblapacke liblapacke-dev

Also, the compiler used to build the tool is gcc.

2.2 Compiling

In order to compile Matrix Market Suite, the user only has to execute:

make

This command creates the MM-Suite executable.

3. Commands

Available commands are:

Input/Output

• CreateDenseMatrix - creates a dense matrix. It can be a symmetric, generic or diagonally dominant matrix, or a combination of all of them, depending on the arguments.
• CreateDenseVector - creates a dense vector.
• CreateSparseMatrix - creates a sparse matrix.

Basic operations

• DMxV - Dense matrix dot vector operation.
• DMxDM - Dense matrix dot dense matrix operation.
• LUDecomposition - LU factorization of a matrix using partial pivoting.

Solvers

• ConjugateGradient - Solves a system by using the conjugate gradient method.
• Jacobi - Solves a system by using the Jacobi method.

To check the available options for a given command, execute:

MM-Suite <Command-name>

4. Versions

4.1. MPI version

This version is a parallel implementation of the methods from Matrix Market Suite that allows parallelization. Nowadays, these methods are:

• DMxV
• ConjugateGradient

The DMxDM is not yet implemented with MPI.

4.1.2. Build MPI version

To build the parallel MPI version, the user has to enter the MPI directory and run:

make

Dependencies for this versions are only openmpi

sudo aptitude install libopenmpi-dev openmpi-common openmpi-bin libopenmpi2

5. Examples

5.1. Create a dense symmetrix matrix

In this example a dense symmetrix matrix of dimensions 10x10 is created.

./MM-Suite CreateDenseMatrix -o Matrix-Example-10x10.mtx -s 10 10  87

Where:

• -o Matrix-Example-10x10.mtx Is the option and the file name of the result matrix.
• -s Indicates that we want to create a symmetric matrix.
• 10 Is the number of rows.
• 10 Is the number of cols.
• 87 Is the seed used to fill the matrix.

The result is:

%%MatrixMarket matrix coordinate real symmetric
10 10 100
1 1 0.163865
1 2 0.921726
1 3 0.831328
...
10 7 0.084717
10 8 0.240895
10 9 0.700352
10 10 0.318448

5.2. Create a dense vector

In this example a vector of 10 elements is created.

./MM-Suite CreateDenseVector 10 Vector-B-10.mtx 55

Where:

• 10 Is the number of elements.
• Vector-B-10.mtx Is the file name of the result vector.
• 55 Is the seed used to fill the vector.

The result is:

%%MatrixMarket matrix array real general
10 1
0.193523
0.200518
0.625800
0.585233
0.849371
0.121675
0.331428
0.199876
0.774032
0.127585

5.3. Solve a system by using the conjugate gradient method

In this example we will use the matrix and vector created previouslly to solve a system. For that:

./MM-Suite ConjugateGradient Matrix-Example-10x10.mtx Vector-B-10.mtx

Where:

• Matrix-Example-10x10.mtx Is the file name of the matrix.
• Vector-B-10.mtx Is the file name of the vector

The result is:

%%MatrixMarket matrix array real general
10 1
0.159064
-1.07431
1.60824
3.59025
-1.91339
1.62213
1.11456
-1.29864
-0.0936935
-2.45013

5.4. Multiply a dense matrix and a vector.

To check if the result obtained from the conjugate gradient method is correct, we can perform a multiplication with the input matrix and the result obtained in the previous example. The result must be the vector used also in the previous example.

./MM-Suite DMxV Matrix-Example-10x10.mtx Result-CG.mtx

Where:

• Matrix-Example-10x10.mtx Is the same matrix used in these examples.
• Result-CG.mtx Is the result from the previous example.

The result is:

%%MatrixMarket matrix array real general
10 1
0.193531
0.200523
0.625799
0.585231
0.849374
0.121682
0.331433
0.199879
0.774031
0.127583

Which is the input vector from the conjugate gradient example.