MatFlat

This library aims to provide a subset of BLAS and LAPACK routines implemented in pure C#.

This library was created as a matrix decomposition implementation for NumFlat, a general purpose numerical computing library written in pure C#. If you're interested in numerical computing with C#, please check out NumFlat.

This library is based on the following great projects:

• Math.NET Numerics
• Accord.NET
• Mapack Matrix Package

Currently the following routines are implemented:

• LU decomposition
• Cholesky decomposition
• QR decomposition
• Singular value decomposition
• Eigenvalue decomposition
• Generalized eigenvalue decomposition
• Forward and backward substitution
• Inverse matrix
• Matrix-vector multiplication
• Matrix-matrix multiplication
• Dot and outer product
• Vector norm

Features

• Supports float, double, and Complex matrices.
• Faster than the managed matrix decompositions in Math.NET in many cases.
• Small code size, with no dependencies other than .NET 8.
• No internal multi-threaded optimization, making it safe to use in any multi-threaded code.
• BLAS and LAPACK-like interface that allows arbitrary leading dimension.

Limitations

• Unsafe pointers are required, similar to the original BLAS and LAPACK routines.
• Only column-major order is supported.
• EVD and GEVD support only symmetric (Hermitian) matrices.

Installation

.NET 8 is required.

The NuGet package is available.

Install-Package MatFlat

All the classes are in the MatFlat namespace.

using MatFlat;

Performance

The performance of MatFlat is compared with that of Math.NET Numerics and OpenBLAS below. The execution times of various double matrix decompositions for square matrices were measured. The matrix sizes range from 10x10 to 100x100. The plots show the execution times, with the execution time of Math.NET Numerics considered as 1.

Measurement condition

The benchmarks were run under the following condition:

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.3447/23H2/2023Update/SunValley3)
12th Gen Intel Core i7-12700K, 1 CPU, 20 logical and 12 physical cores
.NET SDK 8.0.202
  [Host]     : .NET 8.0.3 (8.0.324.11423), X64 RyuJIT AVX2
  DefaultJob : .NET 8.0.3 (8.0.324.11423), X64 RyuJIT AVX2

LU decomposition

Method	Order	Mean	Error	StdDev	Allocated
MathNet	10	356.3 ns	1.03 ns	0.91 ns	104 B
MatFlat	10	318.4 ns	1.55 ns	1.45 ns	-
OpenBlas	10	632.7 ns	3.47 ns	3.25 ns	-
MathNet	20	1,884.5 ns	9.26 ns	8.66 ns	184 B
MatFlat	20	1,511.7 ns	9.80 ns	9.17 ns	-
OpenBlas	20	1,731.4 ns	8.02 ns	7.50 ns	-
MathNet	30	6,141.2 ns	22.08 ns	20.65 ns	264 B
MatFlat	30	4,062.0 ns	24.81 ns	23.21 ns	-
OpenBlas	30	4,109.6 ns	9.17 ns	8.13 ns	-
MathNet	40	12,300.8 ns	53.74 ns	47.64 ns	344 B
MatFlat	40	8,590.4 ns	41.08 ns	38.43 ns	-
OpenBlas	40	5,613.0 ns	11.54 ns	10.80 ns	-
MathNet	50	25,438.9 ns	112.91 ns	105.61 ns	424 B
MatFlat	50	15,788.6 ns	69.35 ns	64.87 ns	-
OpenBlas	50	9,751.5 ns	21.30 ns	19.92 ns	-
MathNet	60	39,288.8 ns	151.06 ns	141.30 ns	504 B
MatFlat	60	25,824.7 ns	81.10 ns	75.86 ns	-
OpenBlas	60	14,091.9 ns	28.01 ns	26.20 ns	-
MathNet	70	69,376.4 ns	315.96 ns	280.09 ns	584 B
MatFlat	70	39,621.0 ns	173.00 ns	161.82 ns	-
OpenBlas	70	18,460.6 ns	34.77 ns	32.52 ns	-
MathNet	80	101,273.9 ns	329.08 ns	307.82 ns	664 B
MatFlat	80	54,074.5 ns	273.94 ns	256.24 ns	-
OpenBlas	80	22,488.7 ns	64.39 ns	60.23 ns	-
MathNet	90	131,540.5 ns	671.69 ns	628.30 ns	744 B
MatFlat	90	82,170.1 ns	422.07 ns	394.81 ns	-
OpenBlas	90	30,344.1 ns	46.13 ns	40.89 ns	-
MathNet	100	180,358.0 ns	359.72 ns	336.48 ns	824 B
MatFlat	100	111,801.6 ns	136.84 ns	128.00 ns	-
OpenBlas	100	396,249.3 ns	7,715.05 ns	7,922.79 ns	-

Cholesky decomposition

Method	Order	Mean	Error	StdDev	Allocated
MathNet	10	200.9 ns	0.60 ns	0.54 ns	664 B
MatFlat	10	163.4 ns	0.85 ns	0.79 ns	-
OpenBlas	10	592.0 ns	2.33 ns	2.18 ns	24 B
MathNet	20	1,074.6 ns	5.24 ns	4.91 ns	1304 B
MatFlat	20	907.6 ns	4.37 ns	4.08 ns	-
OpenBlas	20	704.4 ns	2.83 ns	2.65 ns	24 B
MathNet	30	3,289.6 ns	15.63 ns	14.62 ns	1944 B
MatFlat	30	2,469.6 ns	12.36 ns	11.56 ns	-
OpenBlas	30	1,486.7 ns	2.35 ns	2.20 ns	24 B
MathNet	40	7,381.9 ns	29.87 ns	27.94 ns	2584 B
MatFlat	40	5,024.0 ns	25.70 ns	24.04 ns	-
OpenBlas	40	3,076.4 ns	5.84 ns	5.47 ns	24 B
MathNet	50	14,076.3 ns	70.74 ns	66.17 ns	3224 B
MatFlat	50	8,803.8 ns	46.68 ns	43.66 ns	-
OpenBlas	50	4,668.1 ns	9.87 ns	9.23 ns	24 B
MathNet	60	25,819.8 ns	81.21 ns	75.97 ns	3864 B
MatFlat	60	14,346.9 ns	36.56 ns	34.20 ns	-
OpenBlas	60	7,256.3 ns	12.05 ns	11.27 ns	24 B
MathNet	70	38,900.2 ns	145.13 ns	135.76 ns	4504 B
MatFlat	70	21,853.4 ns	119.00 ns	111.31 ns	-
OpenBlas	70	52,870.4 ns	1,056.20 ns	2,707.44 ns	24 B
MathNet	80	62,603.4 ns	358.44 ns	335.29 ns	5144 B
MatFlat	80	31,830.3 ns	149.25 ns	139.61 ns	-
OpenBlas	80	73,786.8 ns	609.29 ns	508.78 ns	24 B
MathNet	90	83,681.4 ns	286.78 ns	268.26 ns	5784 B
MatFlat	90	44,244.4 ns	223.02 ns	208.62 ns	-
OpenBlas	90	84,149.8 ns	1,003.21 ns	938.41 ns	24 B
MathNet	100	115,551.9 ns	672.86 ns	596.47 ns	6424 B
MatFlat	100	59,350.4 ns	334.89 ns	313.25 ns	-
OpenBlas	100	89,611.6 ns	1,711.85 ns	1,681.26 ns	24 B

QR decomposition

Method	Order	Mean	Error	StdDev	Allocated
MathNet	10	16,395.9 ns	60.26 ns	53.41 ns	29206 B
MatFlat	10	680.4 ns	1.53 ns	1.43 ns	-
OpenBlas	10	1,655.8 ns	4.50 ns	4.21 ns	-
MathNet	20	54,226.6 ns	549.03 ns	513.57 ns	68867 B
MatFlat	20	4,645.9 ns	22.98 ns	21.49 ns	-
OpenBlas	20	5,148.5 ns	20.61 ns	19.28 ns	-
MathNet	30	118,586.5 ns	668.11 ns	592.27 ns	114887 B
MatFlat	30	12,199.9 ns	56.84 ns	53.17 ns	-
OpenBlas	30	10,844.1 ns	37.50 ns	35.08 ns	-
MathNet	40	200,877.5 ns	430.67 ns	381.78 ns	156810 B
MatFlat	40	26,532.9 ns	163.90 ns	153.31 ns	-
OpenBlas	40	19,615.5 ns	42.48 ns	37.66 ns	-
MathNet	50	302,011.2 ns	1,808.26 ns	1,691.45 ns	201012 B
MatFlat	50	47,273.9 ns	308.30 ns	288.38 ns	-
OpenBlas	50	30,619.7 ns	61.78 ns	54.77 ns	-
MathNet	60	426,465.4 ns	7,785.35 ns	7,282.42 ns	242501 B
MatFlat	60	80,619.4 ns	307.43 ns	272.53 ns	-
OpenBlas	60	45,598.1 ns	74.76 ns	69.93 ns	-
MathNet	70	584,892.0 ns	5,543.57 ns	4,914.23 ns	286236 B
MatFlat	70	135,624.1 ns	526.02 ns	492.04 ns	-
OpenBlas	70	66,024.7 ns	143.80 ns	134.51 ns	-
MathNet	80	764,410.9 ns	14,198.79 ns	14,581.12 ns	324848 B
MatFlat	80	187,239.2 ns	1,068.00 ns	999.00 ns	-
OpenBlas	80	93,071.6 ns	261.52 ns	244.62 ns	-
MathNet	90	1,025,887.2 ns	8,722.75 ns	8,159.26 ns	366159 B
MatFlat	90	264,657.7 ns	509.46 ns	451.62 ns	-
OpenBlas	90	130,194.9 ns	392.21 ns	366.88 ns	-
MathNet	100	1,270,333.6 ns	17,520.01 ns	16,388.22 ns	406464 B
MatFlat	100	345,101.4 ns	2,451.92 ns	2,293.52 ns	-
OpenBlas	100	650,895.2 ns	10,389.01 ns	8,675.29 ns	-

Singular value decomposition

Method	Order	Mean	Error	StdDev	Allocated
MathNet	10	10.369 μs	0.0390 μs	0.0365 μs	1136 B
MatFlat	10	6.261 μs	0.0190 μs	0.0168 μs	-
OpenBlas	10	8.218 μs	0.0441 μs	0.0413 μs	48 B
MathNet	20	60.701 μs	0.2754 μs	0.2576 μs	3776 B
MatFlat	20	34.161 μs	0.1679 μs	0.1570 μs	-
OpenBlas	20	32.076 μs	0.1371 μs	0.1282 μs	48 B
MathNet	30	165.329 μs	0.6463 μs	0.5729 μs	8016 B
MatFlat	30	97.288 μs	0.2930 μs	0.2741 μs	-
OpenBlas	30	80.800 μs	0.2287 μs	0.2028 μs	48 B
MathNet	40	359.838 μs	1.3219 μs	1.2365 μs	13856 B
MatFlat	40	212.872 μs	0.6934 μs	0.6486 μs	-
OpenBlas	40	159.768 μs	0.3706 μs	0.3285 μs	48 B
MathNet	50	660.509 μs	2.0123 μs	1.8823 μs	21296 B
MatFlat	50	392.559 μs	1.3545 μs	1.2670 μs	-
OpenBlas	50	261.269 μs	1.3967 μs	1.3064 μs	48 B
MathNet	60	1,144.149 μs	4.0893 μs	3.8251 μs	30337 B
MatFlat	60	664.029 μs	3.4705 μs	3.2463 μs	1 B
OpenBlas	60	431.300 μs	0.8319 μs	0.7782 μs	48 B
MathNet	70	1,832.909 μs	9.0039 μs	8.4223 μs	40976 B
MatFlat	70	1,073.801 μs	3.6979 μs	3.4590 μs	1 B
OpenBlas	70	642.370 μs	1.4747 μs	1.3794 μs	48 B
MathNet	80	2,600.145 μs	16.8514 μs	15.7628 μs	53218 B
MatFlat	80	1,542.437 μs	8.6110 μs	8.0548 μs	1 B
OpenBlas	80	918.765 μs	2.7510 μs	2.5733 μs	48 B
MathNet	90	3,615.089 μs	16.6810 μs	15.6034 μs	67058 B
MatFlat	90	2,136.354 μs	12.5674 μs	11.7555 μs	3 B
OpenBlas	90	1,319.471 μs	2.5227 μs	2.3597 μs	49 B
MathNet	100	4,905.273 μs	28.3718 μs	26.5390 μs	82499 B
MatFlat	100	3,036.419 μs	13.4627 μs	11.9343 μs	3 B
OpenBlas	100	2,625.432 μs	33.5104 μs	31.3456 μs	50 B

Todo

• ✅ LU decomposition
• ✅ Cholesky decomposition
• ✅ QR decomposition
• ✅ Singular value decomposition
• ✅ Eigenvalue decomposition
• ✅ Generalized eigenvalue decomposition
• ✅ Forward and backward substitution
• ✅ Inverse matrix
• ✅ Matrix-vector multiplication
• ✅ Matrix-matrix multiplication
• ✅ Dot and outer product
• ✅ Vector norm

License

MatFlat is available under the MIT license.