Matrix operations performance benchmarks

Customer Comments:

"Let me begin by saying that you have developed a fantastic piece of software ... "

Gary Ray

Benchmark Analysis
Testing the speed of .NET Matrix Library (NML™)

The following tables lists timings in seconds and operations per second for some common matrix operations. They have been produced by the benchmark program that is included in the samples folder.

The machine used was an Intel Quad Core running at 2.4 MHz with 2Gb or RAM capable of running either Windows Vista 32-bit or Windows Vista 64-bit (dual boot).

.NET Matrix Library 4.3 (32-bit)

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|                Multiplication                 |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    2.2670E-004 |    4.4111E+003 |
|        100  |    4.9440E-004 |    2.0227E+003 |
|        250  |    0.0033      |  302.2335      |
|        500  |    0.0142      |   70.4543      |
|       1000  |    0.0817      |   12.2333      |
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|                Solve A * X = B                |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    0.0025      |  400.2241      |
|        100  |    5.6380E-004 |    1.7737E+003 |
|        250  |    0.0017      |  598.0504      |
|        500  |    0.0079      |  126.9358      |
|       1000  |    0.0629      |   15.8982      |
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|               LU Decomposition                |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    1.0900E-004 |    9.1743E+003 |
|        100  |    2.6810E-004 |    3.7300E+003 |
|        250  |    0.0015      |  656.5988      |
|        500  |    0.0093      |  108.0976      |
|       1000  |    0.0428      |   23.3661      |
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|               QR Decomposition                |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    0.0012      |  856.6778      |
|        100  |    6.2080E-004 |    1.6108E+003 |
|        250  |    0.0024      |  409.6514      |
|        500  |    0.0127      |   78.7185      |
|       1000  |    0.0857      |   11.6689      |
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|               SVD Decomposition               |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    0.0028      |  358.1021      |
|        100  |    0.0064      |  155.8069      |
|        250  |    0.0516      |   19.3709      |
|        500  |    0.2234      |    4.4765      |
|       1000  |    1.2465      |    0.8023      |
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|                   Inversion                   |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    0.0012      |  836.8901      |
|        100  |    9.0310E-004 |    1.1073E+003 |
|        250  |    0.0058      |  171.3238      |
|        500  |    0.0287      |   34.7923      |
|       1000  |    0.1579      |    6.3346      |
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|  Eigenvalues eigenvectors (Symmetric matrix)  |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    0.0017      |  580.0128      |
|        100  |    0.0038      |  264.3894      |
|        250  |    0.0297      |   33.6519      |
|        500  |    0.1691      |    5.9146      |
|       1000  |    1.3545      |    0.7383      |
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|   Eigenvalues eigenvectors (General matrix)   |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    0.0047      |  213.9220      |
|        100  |    0.0185      |   54.0640      |
|        250  |    0.2658      |    3.7622      |
|        500  |    0.7799      |    1.2823      |
|       1000  |    5.4839      |    0.1824      |
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.NET Matrix Library 4.3 (64-bit)

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|                Multiplication                 |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    1,3930E-004 |    7,1788E+003 |
|        100  |    7,3310E-004 |    1,3641E+003 |
|        250  |    0,0031      |  318,6032      |
|        500  |    0,0117      |   85,6597      |
|       1000  |    0,0752      |   13,3026      |
-------------------------------------------------

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|                Solve A * X = B                |
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| Matrix Size |       Duration | Operations/sec |
-------------------------------------------------
|         50  |    0,0051      |  196,3865      |
|        100  |    5,3880E-004 |    1,8560E+003 |
|        250  |    0,0018      |  549,4807      |
|        500  |    0,0072      |  137,9405      |
|       1000  |    0,0446      |   22,4182      |
-------------------------------------------------

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|               LU Decomposition                |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    9,6500E-005 |    1,0363E+004 |
|        100  |    2,4570E-004 |    4,0700E+003 |
|        250  |    0,0012      |  820,6812      |
|        500  |    0,0065      |  153,5155      |
|       1000  |    0,0425      |   23,5138      |
-------------------------------------------------

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|               QR Decomposition                |
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| Matrix Size |       Duration | Operations/sec |
-------------------------------------------------
|         50  |    0,0023      |  439,4445      |
|        100  |    6,0400E-004 |    1,6556E+003 |
|        250  |    0,0021      |  481,8348      |
|        500  |    0,0114      |   87,4730      |
|       1000  |    0,0663      |   15,0775      |
-------------------------------------------------

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|               SVD Decomposition               |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    0,0040      |  249,3020      |
|        100  |    0,0059      |  168,7280      |
|        250  |    0,0429      |   23,3263      |
|        500  |    0,1842      |    5,4301      |
|       1000  |    0,9317      |    1,0734      |
-------------------------------------------------

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|                   Inversion                   |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    0,0026      |  380,4306      |
|        100  |    9,5790E-004 |    1,0440E+003 |
|        250  |    0,0115      |   87,3286      |
|        500  |    0,0254      |   39,4041      |
|       1000  |    0,1537      |    6,5068      |
-------------------------------------------------

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|  Eigenvalues eigenvectors (Symmetric matrix)  |
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| Matrix Size |       Duration | Operations/sec |
-------------------------------------------------
|         50  |    0,0029      |  342,3954      |
|        100  |    0,0041      |  243,7360      |
|        250  |    0,0259      |   38,6221      |
|        500  |    0,1243      |    8,0428      |
|       1000  |    0,8220      |    1,2165      |
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|   Eigenvalues eigenvectors (General matrix)   |
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| Matrix Size |       Duration | Operations/sec |
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|         50  |    0,0070      |  142,8592      |
|        100  |    0,0188      |   53,2884      |
|        250  |    0,1510      |    6,6213      |
|        500  |    0,7645      |    1,3081      |
|       1000  |    6,7776      |    0,1475      |
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Benchmark Analysis Testing the speed of .NET Matrix Library (NML™)

.NET Matrix Library 4.3 (32-bit)

.NET Matrix Library 4.3 (64-bit)

Benchmark Analysis
Testing the speed of .NET Matrix Library (NML™)