Examples: matices F# examples, similar to vectors examples

src/FSharpExamples/FSharpExamples.fsproj

@@ -49,6 +49,7 @@
     <None Include="Histogram.fsx" />
     <None Include="MCMC.fsx" />
     <None Include="Vectors.fsx" />
+    <None Include="Matrices.fsx" />
     <None Include="LinearRegression.fsx" />
     <None Include="Apply.fsx" />
   </ItemGroup>

src/FSharpExamples/Matrices.fsx

@@ -0,0 +1,89 @@
+// <copyright file="Matrices.fsx" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+//
+// Copyright (c) 2009-2013 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+#r "../../out/lib/Net40/MathNet.Numerics.dll"
+#r "../../out/lib/Net40/MathNet.Numerics.FSharp.dll"
+
+open MathNet.Numerics.LinearAlgebra
+open MathNet.Numerics.LinearAlgebra.Double
+open MathNet.Numerics.Distributions
+
+// Create a dense matrix directly from an array (by reference, without copy)
+// The array must be in column major order (column-by-column)
+let a1 = DenseMatrix(2, 3, [| 1.0; 2.0; 10.0; 20.0; 100.0; 300.0 |])
+let a2 = DenseMatrix.raw 2 3 [| 1.0; 2.0; 10.0; 20.0; 100.0; 300.0 |]
+
+// Create a matrix of size 3x4 (3 rows, 4 columns) with a given number for each value
+let b1 = DenseMatrix.zeroCreate 3 4
+let b2 = DenseMatrix.create 3 4 20.5
+let b3 = SparseMatrix.zeroCreate 3 4
+
+// Create a matrix of size 3x4 with random values sampled from a distribution
+let c = DenseMatrix.randomCreate 3 4 (Normal.WithMeanStdDev(2.0, 0.5))
+
+// Create a matrix of size 3x4 with each value initialized by a lambda function
+let d1 = DenseMatrix.init 3 4 (fun i j -> float i / 100.0 + float j)
+let d2 = SparseMatrix.init 3 4 (fun i j -> if i=j then float i / 100.0 + float j else 0.0)
+
+// Matrices can also be constructed from sequences of rows or of columns
+let e1 = DenseMatrix.ofRowSeq 20 10 (seq { for i in 1 .. 20 do yield Array.init 10 (fun j -> float j + 100.0 * float i) })
+let e2 = SparseMatrix.ofRowSeq 20 10 (seq { for i in 1 .. 20 do yield Array.init 10 (fun j -> if i%5 = 0 then float j + 100.0 * float i else 0.0) })
+let e3 = DenseMatrix.ofColumnSeq 20 10 (seq { for j in 1 .. 10 do yield Array.init 20 (fun i -> float j + 100.0 * float i) })
+let e4 = SparseMatrix.ofColumnSeq 20 10 (seq { for j in 1 .. 10 do yield Array.init 20 (fun i -> if i%5 = 0 then float j + 100.0 * float i else 0.0) })
+
+// Or from F# lists
+let f1 = DenseMatrix.ofRowList 20 10 [ for i in 1 .. 20 -> List.init 10 (fun j -> float j + 100.0 * float i) ]
+let f2 = SparseMatrix.ofRowList 20 10 [ for i in 1 .. 20 -> List.init 10 (fun j -> if i%5 = 0 then float j + 100.0 * float i else 0.0) ]
+let f3 = DenseMatrix.ofColumnList 20 10 [ for j in 1 .. 10 -> List.init 20 (fun i -> float j + 100.0 * float i) ]
+let f4 = SparseMatrix.ofColumnList 20 10 [ for j in 1 .. 10 -> List.init 20 (fun i -> if i%5 = 0 then float j + 100.0 * float i else 0.0) ]
+
+// Or from indexed lists or sequences where all other values are zero (useful mostly for sparse data)
+let g1 = DenseMatrix.ofListi 20 10 [(4,3,20.0); (18,9,3.0); (2,1,100.0)]
+let g2 = SparseMatrix.ofListi 20 10 [(4,3,20.0); (18,9,3.0); (2,1,100.0)]
+
+// Another way to create dense matrix is using the matrix function.
+let h = matrix [[1.0;  2.0;  3.0]
+                [10.0; 11.0; 12.0]]
+
+// Or create it from a multi-dimensional array
+let k = DenseMatrix.ofArray2 (array2D [[1.0;  2.0;  3.0]; [10.0; 11.0; 12.0]])
+
+// We can now add two matrices together ...
+let z = a1 + a2
+
+// ... or scale them in the process.
+let x = e1 + 3.0 * e4 - g2
+
+// "pretty" printing (configurable with the Control class):
+printfn "A: %A" e3
+printfn "B: %s" (e3.ToString())
+printfn "C: %s" (e3.ToTypeString())
+printfn "D:\n%s" (e3.ToMatrixString(20, 20))
+printfn "E:\n%s" (e3.ToMatrixString(4, 10))