From 692fd092d732daa72429119a0f4e455601bb6604 Mon Sep 17 00:00:00 2001
From: Christoph Ruegg <git@cdrnet.ch>
Date: Sun, 14 Apr 2013 14:53:04 +0200
Subject: [PATCH] Examples: extended F# vector examples

---
 src/FSharpExamples/FSharpExamples.fsproj      | 30 ++++++------
 .../{DenseVector.fsx => Vectors.fsx}          | 47 ++++++++++++++-----
 2 files changed, 50 insertions(+), 27 deletions(-)
 rename src/FSharpExamples/{DenseVector.fsx => Vectors.fsx} (53%)

diff --git a/src/FSharpExamples/FSharpExamples.fsproj b/src/FSharpExamples/FSharpExamples.fsproj
index f009133e..5f44b824 100644
--- a/src/FSharpExamples/FSharpExamples.fsproj
+++ b/src/FSharpExamples/FSharpExamples.fsproj
@@ -38,6 +38,20 @@
     <WarningLevel>3</WarningLevel>
     <OutputPath>bin\Release-Signed\</OutputPath>
   </PropertyGroup>
+  <PropertyGroup>
+    <MinimumVisualStudioVersion Condition="'$(MinimumVisualStudioVersion)' == ''">11</MinimumVisualStudioVersion>
+  </PropertyGroup>
+  <Import Project="$(MSBuildExtensionsPath32)\..\Microsoft SDKs\F#\3.0\Framework\v4.0\Microsoft.FSharp.Targets" Condition="Exists('$(MSBuildExtensionsPath32)\..\Microsoft SDKs\F#\3.0\Framework\v4.0\Microsoft.FSharp.Targets')" />
+  <Import Project="$(MSBuildExtensionsPath32)\..\Microsoft F#\v4.0\Microsoft.FSharp.Targets" Condition="(!Exists('$(MSBuildExtensionsPath32)\..\Microsoft SDKs\F#\3.0\Framework\v4.0\Microsoft.FSharp.Targets')) And (Exists('$(MSBuildExtensionsPath32)\..\Microsoft F#\v4.0\Microsoft.FSharp.Targets'))" />
+  <Import Project="$(MSBuildExtensionsPath32)\FSharp\1.0\Microsoft.FSharp.Targets" Condition="(!Exists('$(MSBuildExtensionsPath32)\..\Microsoft SDKs\F#\3.0\Framework\v4.0\Microsoft.FSharp.Targets')) And (!Exists('$(MSBuildExtensionsPath32)\..\Microsoft F#\v4.0\Microsoft.FSharp.Targets')) And (Exists('$(MSBuildExtensionsPath32)\FSharp\1.0\Microsoft.FSharp.Targets'))" />
+  <ItemGroup>
+    <None Include="RandomAndDistributions.fsx" />
+    <None Include="Histogram.fsx" />
+    <None Include="MCMC.fsx" />
+    <None Include="Vectors.fsx" />
+    <None Include="LinearRegression.fsx" />
+    <None Include="Apply.fsx" />
+  </ItemGroup>
   <ItemGroup>
     <Reference Include="FSharp.Core" />
     <Reference Include="mscorlib" />
@@ -46,8 +60,6 @@
       <RequiredTargetFramework>3.5</RequiredTargetFramework>
     </Reference>
     <Reference Include="System.Numerics" />
-  </ItemGroup>
-  <ItemGroup>
     <ProjectReference Include="..\FSharp\FSharp.fsproj">
       <Name>FSharp</Name>
       <Project>{37e8e802-a354-4114-bfc1-6e1357da605b}</Project>
@@ -59,20 +71,6 @@
       <Private>True</Private>
     </ProjectReference>
   </ItemGroup>
-  <ItemGroup>
-    <None Include="RandomAndDistributions.fsx" />
-    <None Include="Histogram.fsx" />
-    <None Include="MCMC.fsx" />
-    <None Include="DenseVector.fsx" />
-    <None Include="LinearRegression.fsx" />
-    <None Include="Apply.fsx" />
-  </ItemGroup>
-  <PropertyGroup>
-    <MinimumVisualStudioVersion Condition="'$(MinimumVisualStudioVersion)' == ''">11</MinimumVisualStudioVersion>
-  </PropertyGroup>
-  <Import Project="$(MSBuildExtensionsPath32)\..\Microsoft SDKs\F#\3.0\Framework\v4.0\Microsoft.FSharp.Targets" Condition="Exists('$(MSBuildExtensionsPath32)\..\Microsoft SDKs\F#\3.0\Framework\v4.0\Microsoft.FSharp.Targets')" />
-  <Import Project="$(MSBuildExtensionsPath32)\..\Microsoft F#\v4.0\Microsoft.FSharp.Targets" Condition="(!Exists('$(MSBuildExtensionsPath32)\..\Microsoft SDKs\F#\3.0\Framework\v4.0\Microsoft.FSharp.Targets')) And (Exists('$(MSBuildExtensionsPath32)\..\Microsoft F#\v4.0\Microsoft.FSharp.Targets'))" />
-  <Import Project="$(MSBuildExtensionsPath32)\FSharp\1.0\Microsoft.FSharp.Targets" Condition="(!Exists('$(MSBuildExtensionsPath32)\..\Microsoft SDKs\F#\3.0\Framework\v4.0\Microsoft.FSharp.Targets')) And (!Exists('$(MSBuildExtensionsPath32)\..\Microsoft F#\v4.0\Microsoft.FSharp.Targets')) And (Exists('$(MSBuildExtensionsPath32)\FSharp\1.0\Microsoft.FSharp.Targets'))" />
   <!-- To modify your build process, add your task inside one of the targets below and uncomment it. 
 	     Other similar extension points exist, see Microsoft.Common.targets.
 	<Target Name="BeforeBuild">
diff --git a/src/FSharpExamples/DenseVector.fsx b/src/FSharpExamples/Vectors.fsx
similarity index 53%
rename from src/FSharpExamples/DenseVector.fsx
rename to src/FSharpExamples/Vectors.fsx
index 8d209632..3610722b 100644
--- a/src/FSharpExamples/DenseVector.fsx
+++ b/src/FSharpExamples/Vectors.fsx
@@ -1,4 +1,4 @@
-// <copyright file="DenseVector.fsx" company="Math.NET">
+// <copyright file="Vectors.fsx" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -33,24 +33,49 @@
 
 open MathNet.Numerics.LinearAlgebra
 open MathNet.Numerics.LinearAlgebra.Double
+open MathNet.Numerics.Distributions
 
-// Create a new 100 dimensional dense vector.
-let v = DenseVector.init 100 (fun i -> float i / 100.0)
+// Create a dense vector of length 3 directly from an array (by reference, without copy)
+let a1 = DenseVector [| 1.0; 2.0; 3.0 |]
+let a2 = DenseVector.raw [| 1.0; 2.0; 3.0 |]
 
-// Another way to create a 100 dimensional dense vector is using the vector function.
-let w = vector (List.init 100 (fun i -> float i ** 2.0))
+// Create a vector of length 100 with a given number for each value
+let b1 = DenseVector.zeroCreate 100
+let b2 = DenseVector.create 100 20.5
+let b3 = SparseVector.zeroCreate 100
+
+// Create a vector of length 100 with random values sampled from a distribution
+let c = DenseVector.randomCreate 100 (Normal.WithMeanStdDev(2.0, 0.5))
+
+// Create a vector of length 100 with each value initialized by a lambda function
+let d1 = DenseVector.init 100 (fun i -> float i / 100.0)
+let d2 = SparseVector.init 100 (fun i -> if i%5 = 0 then float i / 100.0 else 0.0)
+
+// Vectors can also be constructed from sequences
+let e = DenseVector.ofSeq (seq { for i in 1 .. 100 do yield float i })
 
-// Vectors can also be constructed from sequences.
-let t = DenseVector.ofSeq (seq { for i in 1 .. 100 do yield float i })
+// Or from F# lists
+let f = DenseVector.ofList [ for i in 1 .. 100 -> float i ]
+
+// Or from indexed lists or sequences where all other values are zero (useful mostly for sparse data)
+let g1 = DenseVector.ofListi 100 [(4,20.0); (18,3.0); (2,100.0)]
+let g2 = SparseVector.ofListi 100 [(4,20.0); (18,3.0); (2,100.0)]
+
+// Another way to create a 100 dimensional dense vector is using the vector function.
+let h = vector (List.init 100 (fun i -> float i ** 2.0))
 
 // We can now add two vectors together ...
-let z = v + w
+let z = a1 + a2
 
 // ... or scale them in the process.
-let x = v + 3.0 * t
+let x = d2 + 3.0 * e - g2
 
 // We can create a vector from an integer range (in this case, 5 and 10 inclusive) ...
-let s = DenseVector.range 5 10
+let u = DenseVector.range 5 10
 
 // ... or we can create a vector from a double range with a particular step size.
-let r = DenseVector.rangef 0.0 0.1 10.0
+let v = DenseVector.rangef 0.0 0.1 10.0
+
+// "pretty" printing (configurable with the Control class):
+printfn "%s" (v.ToString())
+// "printfn "%A" v" doesn't work yet because FSI treats it as sequence