100 FSharp exercises

This is FSharp version of 100 numpy exercises

Latest version of 100 numpy excercises are available at this repository.

The source of this document is available at https://github.com/teramonagi/fsharp-100-exercises . And your pull request is always welcome!!!

In this document, F# core library and Math.NET Numerics are used.

Neophyte

1. Import the numpy package under the name `np`

We use Math.NET Numerics libraries instead of numpy.

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open MathNet.Numerics.LinearAlgebra
open MathNet.Numerics.LinearAlgebra.Double
open MathNet.Numerics.Statistics
open MathNet.Numerics.Data.Text;

2. Print the Fsharp version and the configuration.

1:	printfn "%A" (System.Reflection.Assembly.GetExecutingAssembly().ImageRuntimeVersion)

"v4.0.30319"

3. Create a null vector of size 10

F# Core Library

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let Z = Array.zeroCreate<float>(10)
printfn "%A" Z

[|0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0|]

Math.NET Numerics

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let Z = DenseVector.zero<float>(10)
printfn "%A" (Z.ToArray())

[|0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0|]

4. Create a null vector of size 10 but the fifth value which is 1

F# Core Library

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let Z = Array.zeroCreate<float>(10)
Z.[4] <- 1.0
printfn "%A" Z

[|0.0; 0.0; 0.0; 0.0; 1.0; 0.0; 0.0; 0.0; 0.0; 0.0|]

Math.NET Numerics

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let Z = DenseVector.zero<float>(10)
Z.[4] <- 1.0
printfn "%A" (Z.ToArray())

[|0.0; 0.0; 0.0; 0.0; 1.0; 0.0; 0.0; 0.0; 0.0; 0.0|]

5. Create a vector with values ranging from 10 to 49

F# Core Library

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let Z = (Array.init 40 (fun index -> index+10))
printfn "%A" Z

[|10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29;
  30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49|]

Math.NET Numerics

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let Z = DenseVector.range 10 1 49
printfn "%A" (Z.ToArray())

[|10.0; 11.0; 12.0; 13.0; 14.0; 15.0; 16.0; 17.0; 18.0; 19.0; 20.0; 21.0; 22.0;
  23.0; 24.0; 25.0; 26.0; 27.0; 28.0; 29.0; 30.0; 31.0; 32.0; 33.0; 34.0; 35.0;
  36.0; 37.0; 38.0; 39.0; 40.0; 41.0; 42.0; 43.0; 44.0; 45.0; 46.0; 47.0; 48.0;
  49.0|]

6. Create a 3x3 matrix with values ranging from 0 to 8

F# Core Library

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let Z = Array2D.init 3 3 (fun i j -> 3*i + j)
printfn "%A" Z

[[0; 1; 2]
 [3; 4; 5]
 [6; 7; 8]]

Math.NET Numerics

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let Z = DenseMatrix.init 3 3 (fun i j -> float i * 3.0 + float j)
printfn "%A" (Z.ToArray())

[[0.0; 1.0; 2.0]
 [3.0; 4.0; 5.0]
 [6.0; 7.0; 8.0]]

7. Find indices of non-zero elements from [1,2,0,0,4,0]

F# Core Library

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let Z = [|1; 2; 0; 0; 4; 0|] |> Array.mapi (fun i x -> (x<>0, i)) |> Array.filter fst |> Array.map snd
printfn "%A" Z

[|0; 1; 4|]

...Or, you can write as the following:

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let Z = [|1; 2; 0; 0; 4; 0|] |> Array.mapi (fun i x -> (x<>0, i)) |> Array.choose (fun x -> if fst x then Some(snd x) else None)
printfn "%A" Z

[|0; 1; 4|]

Math.NET Numerics

You can use "Find" method implemented in Vector class directly if you can use MathNet.Numerics.FSharp 3.6.0. (My current MathNet.Numerics(.FSharp) is 3.5.0...)

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let Z = vector [1.; 2.; 0.; 0.; 4.; 0.] |> 
    Vector.foldi (fun i x y -> if y <> 0.0 then Array.append x [|y|] else x) [||]
printfn "%A" Z

[|1.0; 2.0; 4.0|]

8. Create a 3x3 identity matrix

F# Core Library

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let Z = Array2D.init 3 3 (fun i j -> if i=j then 1 else 0)
printfn "%A" Z

[[1; 0; 0]
 [0; 1; 0]
 [0; 0; 1]]

Math.NET Numerics

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let Z = DenseMatrix.identity<float> 3
printfn "%A" Z

DenseMatrix 3x3-Double
1  0  0
0  1  0
0  0  1

9. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal

F# Core Library

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let Z = Array2D.init 5 5 (fun i j -> if (i=j+1) then i else 0)
printfn "%A" Z

[[0; 0; 0; 0; 0]
 [1; 0; 0; 0; 0]
 [0; 2; 0; 0; 0]
 [0; 0; 3; 0; 0]
 [0; 0; 0; 4; 0]]

Math.NET Numerics

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let Z = DenseMatrix.init 5 5 (fun i j -> if (i=j+1) then float i else 0.0)
printfn "%A" Z

DenseMatrix 5x5-Double
0  0  0  0  0
1  0  0  0  0
0  2  0  0  0
0  0  3  0  0
0  0  0  4  0

10. Create a 3x3x3 array with random values

F# Core Library

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let rand = System.Random()
let Z = Array3D.init<float> 3 3 3 (fun _ _ _ -> rand.NextDouble())
for z in [0..2] do
    printfn "component: %d" z
    for y in [0..2] do
        for x in [0..2] do
            printf "%f" Z.[x, y, z]
        printfn ""

component: 0
0.8181430.4474620.099110
0.3723330.9536810.809327
0.4354480.8846420.773630
component: 1
0.6074840.6881920.674324
0.2126340.7712950.278699
0.6970820.5304860.810881
component: 2
0.7068160.4481470.434154
0.5871330.8825510.245825
0.5041890.6672840.912041

...or, since there is no strong support for Array3D class in F#, you may write the following :

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let rand = System.Random()
let Z = Array.init 3 (fun z -> Array2D.init<float> 3 3 (fun _ _ -> rand.NextDouble()))
for z in [0..2] do
    printfn "component: %d" z
    printfn "%A" Z.[z]

component: 0
[[0.3721322982; 0.3981586324; 0.559251156]
 [0.404150692; 0.4324637667; 0.6603301361]
 [0.494113141; 0.276249332; 0.318874017]]
component: 1
[[0.7787638394; 0.3145267006; 0.141725963]
 [0.2638802786; 0.2232922596; 0.7812286554]
 [0.2371239165; 0.2873621612; 0.8072521411]]
component: 2
[[0.3714186369; 0.8729534582; 0.6790689717]
 [0.3401521143; 0.2219345869; 0.665081383]
 [0.3798986307; 0.04048253039; 0.320993832]]

Math.NET Numerics

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//I used the type "Array of DenseMatix" here because there is no 3D Vector in core Math.NET.
let rand = new MathNet.Numerics.Distributions.ContinuousUniform()
let Z = Array.init 3 (fun _ -> DenseMatrix.random<float> 3 3 rand)
for z in [0..2] do
    printfn "component: %d" z
    printfn "%A" Z.[z]

component: 0
DenseMatrix 3x3-Double
0.0407447   0.120073  0.693983
 0.311115   0.999568  0.317177
 0.809852  0.0448716  0.739624

component: 1
DenseMatrix 3x3-Double
  0.646609  0.0135653   0.133847
0.00646932   0.762651   0.147916
  0.956857   0.460275  0.0572422

component: 2
DenseMatrix 3x3-Double
 0.681326  0.872346  0.926097
 0.657112  0.872243  0.880209
0.0589799  0.829869  0.370419

Novice

1. Create a 8x8 matrix and fill it with a checkerboard pattern

F# Core Library

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let Z = Array2D.init 8 8 (fun i j -> (i+j)%2)
printfn "%A" Z

[[0; 1; 0; 1; 0; 1; 0; 1]
 [1; 0; 1; 0; 1; 0; 1; 0]
 [0; 1; 0; 1; 0; 1; 0; 1]
 [1; 0; 1; 0; 1; 0; 1; 0]
 [0; 1; 0; 1; 0; 1; 0; 1]
 [1; 0; 1; 0; 1; 0; 1; 0]
 [0; 1; 0; 1; 0; 1; 0; 1]
 [1; 0; 1; 0; 1; 0; 1; 0]]

Math.NET Numerics

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let Z = DenseMatrix.init 8 8 (fun i j -> float ((i+j)%2))
printfn "%A" Z

DenseMatrix 8x8-Double
0  1  0  1  0  1  0  1
1  0  1  0  1  0  1  0
0  1  0  1  0  1  0  1
1  0  1  0  1  0  1  0
0  1  0  1  0  1  0  1
1  0  1  0  1  0  1  0
0  1  0  1  0  1  0  1
1  0  1  0  1  0  1  0

2. Create a 10x10 array with random values and find the minimum and maximum values

F# Core Library

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let rand = System.Random()
let Z = Array2D.init 10 10 (fun i j -> rand.NextDouble())
let Zmin = Z |> Seq.cast<float> |> Seq.min
let Zmax = Z |> Seq.cast<float> |> Seq.max
printfn "%f, %f" Zmin Zmax

0.008262, 0.984671

Math.NET Numerics

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let rand = new MathNet.Numerics.Distributions.ContinuousUniform()
let Z = DenseMatrix.random<float> 10 10 rand
let Zmin = Matrix.reduce min Z  
let Zmax = Matrix.reduce max Z  
printfn "%f, %f" Zmin Zmax

0.024464, 0.985200

3. Create a checkerboard 8x8 matrix using the tile function

There is no numpy's tile equivalent function in F# and Math.NET. These are another solutions for Novice 1.

F# Core Library

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let Z = Array.init 8 (fun i -> Array.init 8 (fun j -> (i+j)%2)) |> array2D
printfn "%A" Z

[[0; 1; 0; 1; 0; 1; 0; 1]
 [1; 0; 1; 0; 1; 0; 1; 0]
 [0; 1; 0; 1; 0; 1; 0; 1]
 [1; 0; 1; 0; 1; 0; 1; 0]
 [0; 1; 0; 1; 0; 1; 0; 1]
 [1; 0; 1; 0; 1; 0; 1; 0]
 [0; 1; 0; 1; 0; 1; 0; 1]
 [1; 0; 1; 0; 1; 0; 1; 0]]

Math.NET Numerics

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let seq01 = Seq.initInfinite (fun i -> float(i%2))
let Z = DenseMatrix.initColumns 8 (fun i -> seq01 |> Seq.skip i |> Seq.take 8 |> DenseVector.ofSeq)
printfn "%A" Z

[|0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0|]

4. Normalize a 5x5 random matrix (between 0 and 1)

F# Core Library

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let rand = System.Random()
let Z = Array2D.init 5 5 (fun i j -> rand.NextDouble())
let Zmin = Z |> Seq.cast<float> |> Seq.min
let Zmax = Z |> Seq.cast<float> |> Seq.max
let Z2 = Z |> Array2D.map (fun z -> (z-Zmin)/(Zmax-Zmin))
printfn "%A" Z2

[[0.3529709872; 0.4871104231; 0.7390661804; 0.594939187; 0.1334376429]
 [1.0; 0.05022067239; 0.3122416548; 0.5155899408; 0.9007523024]
 [0.0; 0.29116167; 0.2120741521; 0.88277239; 0.5641707357]
 [0.9633352815; 0.5937481143; 0.6954447466; 0.2440494057; 0.484364771]
 [0.5925360851; 0.421958456; 0.6892933246; 0.6635511131; 0.5341030878]]

Math.NET Numerics

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let rand = new MathNet.Numerics.Distributions.ContinuousUniform()
let Z = DenseMatrix.random<float> 5 5 rand
let Zmin = Matrix.reduce min Z  
let Zmax = Matrix.reduce max Z  
let Z2 = Matrix.map (fun z -> (z-Zmin)/(Zmax-Zmin) ) Z
printfn "%A" Z2

DenseMatrix 5x5-Double
0.991354  0.896427  0.392518  0.0923308  0.705818
0.193545   0.69344   0.88298   0.608356  0.307777
0.041891  0.718034         1    0.34067  0.485015
0.672707  0.610634  0.190861   0.559424  0.561157
0.532118         0  0.594558   0.595541  0.551953

5. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)

F# Core Library

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let x = Array2D.create 5 3 1.0
let y = Array2D.create 3 2 1.0
let inner_product x y = Array.fold2 (fun s x y -> s+x*y) 0.0 x y
let Z = Array2D.init 5 2 (fun i j -> inner_product x.[i,*] y.[*,j] )
printfn "%A" Z

[[3.0; 3.0]
 [3.0; 3.0]
 [3.0; 3.0]
 [3.0; 3.0]
 [3.0; 3.0]]

Math.NET Numerics

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let Z = (DenseMatrix.create 5 3 1.0) * (DenseMatrix.create 3 2 1.0)
printfn "%A" Z

DenseMatrix 5x2-Double
3  3
3  3
3  3
3  3
3  3

6. Create a 5x5 matrix with row values ranging from 0 to 4

F# Core Library

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let Z = Array2D.init 5 5 (fun i j -> j)
printfn "%A" Z

[[0; 1; 2; 3; 4]
 [0; 1; 2; 3; 4]
 [0; 1; 2; 3; 4]
 [0; 1; 2; 3; 4]
 [0; 1; 2; 3; 4]]

Math.NET Numerics

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let Z = DenseMatrix.init 5 5 (fun i j -> float j)
printfn "%A" Z

DenseMatrix 5x5-Double
0  1  2  3  4
0  1  2  3  4
0  1  2  3  4
0  1  2  3  4
0  1  2  3  4

7. Create a vector of size 10 with values ranging from 0 to 1, both excluded

It it little bit different from numpy's answer because there is no equivalent method with numpy's linspace in F#/Math.NET.

F# Core Library

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let Z = Array.init 12 (fun i -> 1.0/11.0*(float i)) 
let Z2 = Array.sub Z 1 10
printfn "%A" Z2

[|0.09090909091; 0.1818181818; 0.2727272727; 0.3636363636; 0.4545454545;
  0.5454545455; 0.6363636364; 0.7272727273; 0.8181818182; 0.9090909091|]

Math.NET Numerics

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let Z = (DenseVector.rangef 0.0 (1.0/11.0) 1.0).SubVector(1, 10)
printfn "%A" Z

seq [0.09090909091; 0.1818181818; 0.2727272727; 0.3636363636; ...]

8. Create a random vector of size 10 and sort it

F# Core Library

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let rand = System.Random()
let Z = Array.init 10 (fun _ -> rand.NextDouble()) |> Array.sort 
printfn "%A" Z

[|0.06741350147; 0.1207639548; 0.132379477; 0.2175480808; 0.2470006255;
  0.3752000147; 0.6097498995; 0.6707792923; 0.6979412128; 0.7204493194|]

Math.NET Numerics

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let rand = new MathNet.Numerics.Distributions.ContinuousUniform()
let Z = DenseVector.random<float> 10 rand
MathNet.Numerics.Sorting.Sort(Z)
printfn "%A" Z

seq [0.07778542166; 0.3342726321; 0.4844895324; 0.5086863756; ...]

9. Consider two random array A anb B, check if they are equal.

F# Core Library

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let rand = System.Random()
let A = Array.init 5 (fun _ -> rand.Next(2))
let B = Array.init 5 (fun _ -> rand.Next(2))
let equal = Array.forall2 (=) A B
printfn "%A" equal

false

Math.NET Numerics

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let rand = new MathNet.Numerics.Distributions.DiscreteUniform(0, 1)
let A = rand.Samples() |> Seq.take 5 |> Seq.map float |> DenseVector.ofSeq
let B = rand.Samples() |> Seq.take 5 |> Seq.map float |> DenseVector.ofSeq
let equal = A=B
printfn "%A" equal

false

10. Create a random vector of size 30 and find the mean value

F# Core Library

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let rand = System.Random()
let Z = Array.init 30 (fun _ -> rand.NextDouble())
let m = Z |> Array.average
printfn "%f" m

0.521047

Math.NET Numerics

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let rand = new MathNet.Numerics.Distributions.ContinuousUniform()
let Z = DenseVector.random<float> 30 rand
let m = Z |> Statistics.Mean
printfn "%f" m

0.503866

Apprentice

1. Make an array immutable (read-only)

F# Core Library

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//List is immutable in F# but it does not allow us to do random access.
let Z = List.init 10 (fun _ -> 0)
//It does not work.
//Z.[0] <- 1

Math.NET Numerics

1:	//There is no way to make an array immutable.

2. Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates

F# Core Library

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let rand = System.Random()
let Z = Array2D.init 10 2 (fun _ _ -> rand.NextDouble())
let X, Y = Z.[*,0], Z.[*,1]
let R = Array.map2 (fun x y -> sqrt(x*x+y*y)) X Y
let T = Array.map2 (fun x y -> System.Math.Atan2(y, x)) X Y
printfn "%A" R
printfn "%A" T

[|0.6358613206; 0.2241523931; 0.4772972823; 0.5626806615; 0.7503892053;
  0.4744589629; 0.9780254347; 0.9169400938; 0.7344512088; 0.5728584853|]
[|1.229586763; 0.4000843415; 0.5545630015; 0.3513114868; 0.6525798344;
  0.7963433431; 0.3175930114; 1.425786203; 1.075201954; 1.104927083|]

Math.NET Numerics

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let rand = new MathNet.Numerics.Distributions.ContinuousUniform()
let Z = DenseMatrix.random<float> 10 2 rand
let X, Y = Z.[*,0], Z.[*,1]
let R = X.*X + Y.*Y |> Vector.map sqrt
let T = Y./X |> Vector.map System.Math.Atan
printfn "%A" R
printfn "%A" T

seq [0.9811709949; 0.709722243; 0.9811314768; 0.9260660666; ...]
seq [1.164909639; 0.4762100481; 1.564431315; 1.445461331; ...]

3. Create random vector of size 10 and replace the maximum value by 0

F# Core Library

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let rand = System.Random()
let Z = Array.init 10 (fun _ -> rand.NextDouble())
let Zmax = Array.max Z
Z.[Array.findIndex ((=) Zmax) Z] <- 0.
printfn "%A" Z

[|0.9063102272; 0.4684857877; 0.0; 0.001134485473; 0.8335983766; 0.67022116;
  0.3149158132; 0.008618333847; 0.7312221116; 0.4121202149|]

Math.NET Numerics

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let rand = MathNet.Numerics.Distributions.ContinuousUniform()
let Z = DenseVector.random<float> 10 rand
Z.[Vector.maxIndex Z] <- 0.
printfn "%A" Z

seq [0.3064510935; 0.5007114529; 0.0; 0.3219453247; ...]

4. Create a structured array with `x` and `y` coordinates covering the [0,1]x[0,1] area.

There is no way to assign name to Array2D/Matrix. We might should use Deedle in this situation.

F# Core Library

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let element = Array.init 10 (fun i -> 1.0/9.0*(float i)) 
let Z = Array2D.init 10 10 (fun i j -> (element.[j], element.[i]))
printfn "%A" Z

[[(0.0, 0.0); (0.1111111111, 0.0); (0.2222222222, 0.0); (0.3333333333, 0.0);
  (0.4444444444, 0.0); (0.5555555556, 0.0); (0.6666666667, 0.0);
  (0.7777777778, 0.0); (0.8888888889, 0.0); (1.0, 0.0)]
 [(0.0, 0.1111111111); (0.1111111111, 0.1111111111);
  (0.2222222222, 0.1111111111); (0.3333333333, 0.1111111111);
  (0.4444444444, 0.1111111111); (0.5555555556, 0.1111111111);
  (0.6666666667, 0.1111111111); (0.7777777778, 0.1111111111);
  (0.8888888889, 0.1111111111); (1.0, 0.1111111111)]
 [(0.0, 0.2222222222); (0.1111111111, 0.2222222222);
  (0.2222222222, 0.2222222222); (0.3333333333, 0.2222222222);
  (0.4444444444, 0.2222222222); (0.5555555556, 0.2222222222);
  (0.6666666667, 0.2222222222); (0.7777777778, 0.2222222222);
  (0.8888888889, 0.2222222222); (1.0, 0.2222222222)]
 [(0.0, 0.3333333333); (0.1111111111, 0.3333333333);
  (0.2222222222, 0.3333333333); (0.3333333333, 0.3333333333);
  (0.4444444444, 0.3333333333); (0.5555555556, 0.3333333333);
  (0.6666666667, 0.3333333333); (0.7777777778, 0.3333333333);
  (0.8888888889, 0.3333333333); (1.0, 0.3333333333)]
 [(0.0, 0.4444444444); (0.1111111111, 0.4444444444);
  (0.2222222222, 0.4444444444); (0.3333333333, 0.4444444444);
  (0.4444444444, 0.4444444444); (0.5555555556, 0.4444444444);
  (0.6666666667, 0.4444444444); (0.7777777778, 0.4444444444);
  (0.8888888889, 0.4444444444); (1.0, 0.4444444444)]
 [(0.0, 0.5555555556); (0.1111111111, 0.5555555556);
  (0.2222222222, 0.5555555556); (0.3333333333, 0.5555555556);
  (0.4444444444, 0.5555555556); (0.5555555556, 0.5555555556);
  (0.6666666667, 0.5555555556); (0.7777777778, 0.5555555556);
  (0.8888888889, 0.5555555556); (1.0, 0.5555555556)]
 [(0.0, 0.6666666667); (0.1111111111, 0.6666666667);
  (0.2222222222, 0.6666666667); (0.3333333333, 0.6666666667);
  (0.4444444444, 0.6666666667); (0.5555555556, 0.6666666667);
  (0.6666666667, 0.6666666667); (0.7777777778, 0.6666666667);
  (0.8888888889, 0.6666666667); (1.0, 0.6666666667)]
 [(0.0, 0.7777777778); (0.1111111111, 0.7777777778);
  (0.2222222222, 0.7777777778); (0.3333333333, 0.7777777778);
  (0.4444444444, 0.7777777778); (0.5555555556, 0.7777777778);
  (0.6666666667, 0.7777777778); (0.7777777778, 0.7777777778);
  (0.8888888889, 0.7777777778); (1.0, 0.7777777778)]
 [(0.0, 0.8888888889); (0.1111111111, 0.8888888889);
  (0.2222222222, 0.8888888889); (0.3333333333, 0.8888888889);
  (0.4444444444, 0.8888888889); (0.5555555556, 0.8888888889);
  (0.6666666667, 0.8888888889); (0.7777777778, 0.8888888889);
  (0.8888888889, 0.8888888889); (1.0, 0.8888888889)]
 [(0.0, 1.0); (0.1111111111, 1.0); (0.2222222222, 1.0); (0.3333333333, 1.0);
  (0.4444444444, 1.0); (0.5555555556, 1.0); (0.6666666667, 1.0);
  (0.7777777778, 1.0); (0.8888888889, 1.0); (1.0, 1.0)]]

Math.NET Numerics

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//We can not use the type Matrix<(float, float)> type as a output.
let element = DenseVector.rangef 0.0 (1.0/9.0) 1.0
let Z = Array2D.init 10 10 (fun i j -> (element.[j], element.[i]))
printfn "%A" Z

[[(0.0, 0.0); (0.1111111111, 0.0); (0.2222222222, 0.0); (0.3333333333, 0.0);
  (0.4444444444, 0.0); (0.5555555556, 0.0); (0.6666666667, 0.0);
  (0.7777777778, 0.0); (0.8888888889, 0.0); (1.0, 0.0)]
 [(0.0, 0.1111111111); (0.1111111111, 0.1111111111);
  (0.2222222222, 0.1111111111); (0.3333333333, 0.1111111111);
  (0.4444444444, 0.1111111111); (0.5555555556, 0.1111111111);
  (0.6666666667, 0.1111111111); (0.7777777778, 0.1111111111);
  (0.8888888889, 0.1111111111); (1.0, 0.1111111111)]
 [(0.0, 0.2222222222); (0.1111111111, 0.2222222222);
  (0.2222222222, 0.2222222222); (0.3333333333, 0.2222222222);
  (0.4444444444, 0.2222222222); (0.5555555556, 0.2222222222);
  (0.6666666667, 0.2222222222); (0.7777777778, 0.2222222222);
  (0.8888888889, 0.2222222222); (1.0, 0.2222222222)]
 [(0.0, 0.3333333333); (0.1111111111, 0.3333333333);
  (0.2222222222, 0.3333333333); (0.3333333333, 0.3333333333);
  (0.4444444444, 0.3333333333); (0.5555555556, 0.3333333333);
  (0.6666666667, 0.3333333333); (0.7777777778, 0.3333333333);
  (0.8888888889, 0.3333333333); (1.0, 0.3333333333)]
 [(0.0, 0.4444444444); (0.1111111111, 0.4444444444);
  (0.2222222222, 0.4444444444); (0.3333333333, 0.4444444444);
  (0.4444444444, 0.4444444444); (0.5555555556, 0.4444444444);
  (0.6666666667, 0.4444444444); (0.7777777778, 0.4444444444);
  (0.8888888889, 0.4444444444); (1.0, 0.4444444444)]
 [(0.0, 0.5555555556); (0.1111111111, 0.5555555556);
  (0.2222222222, 0.5555555556); (0.3333333333, 0.5555555556);
  (0.4444444444, 0.5555555556); (0.5555555556, 0.5555555556);
  (0.6666666667, 0.5555555556); (0.7777777778, 0.5555555556);
  (0.8888888889, 0.5555555556); (1.0, 0.5555555556)]
 [(0.0, 0.6666666667); (0.1111111111, 0.6666666667);
  (0.2222222222, 0.6666666667); (0.3333333333, 0.6666666667);
  (0.4444444444, 0.6666666667); (0.5555555556, 0.6666666667);
  (0.6666666667, 0.6666666667); (0.7777777778, 0.6666666667);
  (0.8888888889, 0.6666666667); (1.0, 0.6666666667)]
 [(0.0, 0.7777777778); (0.1111111111, 0.7777777778);
  (0.2222222222, 0.7777777778); (0.3333333333, 0.7777777778);
  (0.4444444444, 0.7777777778); (0.5555555556, 0.7777777778);
  (0.6666666667, 0.7777777778); (0.7777777778, 0.7777777778);
  (0.8888888889, 0.7777777778); (1.0, 0.7777777778)]
 [(0.0, 0.8888888889); (0.1111111111, 0.8888888889);
  (0.2222222222, 0.8888888889); (0.3333333333, 0.8888888889);
  (0.4444444444, 0.8888888889); (0.5555555556, 0.8888888889);
  (0.6666666667, 0.8888888889); (0.7777777778, 0.8888888889);
  (0.8888888889, 0.8888888889); (1.0, 0.8888888889)]
 [(0.0, 1.0); (0.1111111111, 1.0); (0.2222222222, 1.0); (0.3333333333, 1.0);
  (0.4444444444, 1.0); (0.5555555556, 1.0); (0.6666666667, 1.0);
  (0.7777777778, 1.0); (0.8888888889, 1.0); (1.0, 1.0)]]

5. Print the minimum and maximum representable value for each numpy scalar type

These are not types but functions for type conversion like int8, float32 in the below codes. I used these functions to get its type with Reflection.

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[int8.GetType(); int32.GetType(); int64.GetType()] |> 
    List.iter (fun x -> 
        printfn "%A" (x.BaseType.GenericTypeArguments.[1].GetField("MinValue").GetValue())
        printfn "%A" (x.BaseType.GenericTypeArguments.[1].GetField("MaxValue").GetValue()))

-128y
127y
-2147483648
2147483647
-9223372036854775808L
9223372036854775807L

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[float32.GetType(); float.GetType()] |> 
    List.iter (fun x -> 
        printfn "%A" (x.BaseType.GenericTypeArguments.[1].GetField("MinValue").GetValue())
        printfn "%A" (x.BaseType.GenericTypeArguments.[1].GetField("MaxValue").GetValue())        
        printfn "%A" (x.BaseType.GenericTypeArguments.[1].GetField("Epsilon").GetValue()))

-3.40282347e+38f
3.40282347e+38f
1.40129846e-45f
-1.797693135e+308
1.797693135e+308
4.940656458e-324

6. Create a structured array representing a position (x,y) and a color (r,g,b)

There is no way to assign name to Array2D/Matrix. We might should use Deedle in this situation. The code I showed below is not so looks good to me...

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type NamedSequence<'T> = System.Collections.Generic.IDictionary<string, 'T>
let Z = Array.init 10 (fun i -> 
    dict[
        "position", dict["x", 0.0; "y", 0.0]; 
        "color", dict["r", 0.0; "g", 0.0; "b", 0.0]
    ]
)
printfn "%A" (Array.map (fun (z:NamedSequence<NamedSequence<float>>) -> z.["color"]) Z)

[|seq [[r, 0]; [g, 0]; [b, 0]]; seq [[r, 0]; [g, 0]; [b, 0]];
  seq [[r, 0]; [g, 0]; [b, 0]]; seq [[r, 0]; [g, 0]; [b, 0]];
  seq [[r, 0]; [g, 0]; [b, 0]]; seq [[r, 0]; [g, 0]; [b, 0]];
  seq [[r, 0]; [g, 0]; [b, 0]]; seq [[r, 0]; [g, 0]; [b, 0]];
  seq [[r, 0]; [g, 0]; [b, 0]]; seq [[r, 0]; [g, 0]; [b, 0]]|]

7. Consider a random vector with shape (100,2) representing coordinates, find point by point distances

We use 10 row cases to reduce the output.

F# Core Library

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let rand = System.Random()
let product xs ys = [| for x in xs do for y in ys  -> (x, y)|]
let distance (x: float*float) (y: float*float) = 
    let dx = fst x - snd x
    let dy = fst y - snd y
    sqrt(dx*dx+dy*dy)
let Z = Array2D.init 10 2 (fun _ _ -> rand.NextDouble())
let X, Y = Z.[*,0], Z.[*,1]
let xs = (product X X)
let ys = (product Y Y)
let D = Array.map2 distance xs ys 
printfn "%A"  (Array2D.init 10 10 (fun i j -> D.[i + j*10]))

[[0.0; 0.5018595449; 0.441438811; 0.5825669151; 0.5716026538; 0.1603965189;
  0.453201734; 0.4690261062; 0.504450041; 0.3824011123]
 [0.5018595449; 0.0; 0.2286847089; 0.4181345273; 0.6519918529; 0.4924190676;
  0.4954238683; 0.5729974405; 0.9977196053; 0.6847717332]
 [0.441438811; 0.2286847089; 0.0; 0.6104760286; 0.7892516547; 0.3607525997;
  0.6290595613; 0.6943565415; 0.9406291836; 0.7400756068]
 [0.5825669151; 0.4181345273; 0.6104760286; 0.0; 0.2978466351; 0.6812674093;
  0.203996086; 0.2744803349; 0.9441949939; 0.486554684]
 [0.5716026538; 0.6519918529; 0.7892516547; 0.2978466351; 0.0; 0.7170666037;
  0.1605689795; 0.1045403494; 0.7658878168; 0.2838072437]
 [0.1603965189; 0.4924190676; 0.3607525997; 0.6812674093; 0.7170666037; 0.0;
  0.5847377745; 0.6128259918; 0.5959212459; 0.5427311578]
 [0.453201734; 0.4954238683; 0.6290595613; 0.203996086; 0.1605689795;
  0.5847377745; 0.0; 0.08191627388; 0.7489397124; 0.2827102777]
 [0.4690261062; 0.5729974405; 0.6943565415; 0.2744803349; 0.1045403494;
  0.6128259918; 0.08191627388; 0.0; 0.7051931575; 0.2249972903]
 [0.504450041; 0.9977196053; 0.9406291836; 0.9441949939; 0.7658878168;
  0.5959212459; 0.7489397124; 0.7051931575; 0.0; 0.4836359103]
 [0.3824011123; 0.6847717332; 0.7400756068; 0.486554684; 0.2838072437;
  0.5427311578; 0.2827102777; 0.2249972903; 0.4836359103; 0.0]]

Math.NET Numerics

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let rand = new MathNet.Numerics.Distributions.ContinuousUniform()
let Z = DenseMatrix.random<float> 10 2 rand
let X, Y = Z.[*,0], Z.[*,1]
printfn "%A" (DenseMatrix.Create(10, 10, (fun i j -> sqrt((X.[i]-X.[j])**2.0 + (Y.[i]-Y.[j])**2.0))))

[[0.0; 0.5018595449; 0.441438811; 0.5825669151; 0.5716026538; 0.1603965189;
  0.453201734; 0.4690261062; 0.504450041; 0.3824011123]
 [0.5018595449; 0.0; 0.2286847089; 0.4181345273; 0.6519918529; 0.4924190676;
  0.4954238683; 0.5729974405; 0.9977196053; 0.6847717332]
 [0.441438811; 0.2286847089; 0.0; 0.6104760286; 0.7892516547; 0.3607525997;
  0.6290595613; 0.6943565415; 0.9406291836; 0.7400756068]
 [0.5825669151; 0.4181345273; 0.6104760286; 0.0; 0.2978466351; 0.6812674093;
  0.203996086; 0.2744803349; 0.9441949939; 0.486554684]
 [0.5716026538; 0.6519918529; 0.7892516547; 0.2978466351; 0.0; 0.7170666037;
  0.1605689795; 0.1045403494; 0.7658878168; 0.2838072437]
 [0.1603965189; 0.4924190676; 0.3607525997; 0.6812674093; 0.7170666037; 0.0;
  0.5847377745; 0.6128259918; 0.5959212459; 0.5427311578]
 [0.453201734; 0.4954238683; 0.6290595613; 0.203996086; 0.1605689795;
  0.5847377745; 0.0; 0.08191627388; 0.7489397124; 0.2827102777]
 [0.4690261062; 0.5729974405; 0.6943565415; 0.2744803349; 0.1045403494;
  0.6128259918; 0.08191627388; 0.0; 0.7051931575; 0.2249972903]
 [0.504450041; 0.9977196053; 0.9406291836; 0.9441949939; 0.7658878168;
  0.5959212459; 0.7489397124; 0.7051931575; 0.0; 0.4836359103]
 [0.3824011123; 0.6847717332; 0.7400756068; 0.486554684; 0.2838072437;
  0.5427311578; 0.2827102777; 0.2249972903; 0.4836359103; 0.0]]

8. Generate a generic 2D Gaussian-like array

F# Core Library

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let element = Array.init 10 (fun i -> -1.0 + 1.0/4.5*(float i)) 
let Z = Array2D.init 10 10 (fun i j -> (element.[j], element.[i])) |> Seq.cast<float*float> |> Array.ofSeq
let D = Array.map (fun z -> sqrt( (fst z)**2.0 + (snd z)**2.0 )) Z
let sigma, mu = 1.0, 0.0
let G = Array.map (fun d -> exp((d-mu)**2.0/(-2.0*sigma**2.0))) D
printfn "%A" G

[|0.3678794412; 0.4482208785; 0.5197948899; 0.5737534207; 0.6027981752;
  0.6027981752; 0.5737534207; 0.5197948899; 0.4482208785; 0.3678794412;
  0.4482208785; 0.546108136; 0.6333132437; 0.6990558142; 0.7344436719;
  0.7344436719; 0.6990558142; 0.6333132437; 0.546108136; 0.4482208785;
  0.5197948899; 0.6333132437; 0.7344436719; 0.8106843243; 0.8517230811;
  0.8517230811; 0.8106843243; 0.7344436719; 0.6333132437; 0.5197948899;
  0.5737534207; 0.6990558142; 0.8106843243; 0.8948393168; 0.9401381983;
  0.9401381983; 0.8948393168; 0.8106843243; 0.6990558142; 0.5737534207;
  0.6027981752; 0.7344436719; 0.8517230811; 0.9401381983; 0.9877302162;
  0.9877302162; 0.9401381983; 0.8517230811; 0.7344436719; 0.6027981752;
  0.6027981752; 0.7344436719; 0.8517230811; 0.9401381983; 0.9877302162;
  0.9877302162; 0.9401381983; 0.8517230811; 0.7344436719; 0.6027981752;
  0.5737534207; 0.6990558142; 0.8106843243; 0.8948393168; 0.9401381983;
  0.9401381983; 0.8948393168; 0.8106843243; 0.6990558142; 0.5737534207;
  0.5197948899; 0.6333132437; 0.7344436719; 0.8106843243; 0.8517230811;
  0.8517230811; 0.8106843243; 0.7344436719; 0.6333132437; 0.5197948899;
  0.4482208785; 0.546108136; 0.6333132437; 0.6990558142; 0.7344436719;
  0.7344436719; 0.6990558142; 0.6333132437; 0.546108136; 0.4482208785;
  0.3678794412; 0.4482208785; 0.5197948899; 0.5737534207; 0.6027981752;
  0.6027981752; 0.5737534207; 0.5197948899; 0.4482208785; 0.3678794412|]

Math.NET Numerics

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let element = Array.init 10 (fun i -> -1.0 + 1.0/4.5*(float i)) 
let Z = Array2D.init 10 10 (fun i j -> (element.[j], element.[i])) |> Seq.cast<float*float> |> Array.ofSeq
let D = DenseVector.init 100 (fun i -> sqrt( (fst Z.[i])**2.0 + (snd Z.[i])**2.0 ))
let sigma, mu = 1.0, 0.0
let G = D.Subtract(mu).PointwisePower(2.0).Divide(-2.0*sigma**2.0).PointwiseExp()
//... Or more simply
//let G = Vector.map (fun d -> exp((d-mu)**2.0/(-2.0*sigma**2.0))) D 
printfn "%A" G

seq [0.3678794412; 0.4482208785; 0.5197948899; 0.5737534207; ...]

9. How to tell if a given 2D array has null columns ?

F# Core Library

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//First, We extend Array2D module to add foldByColumn
module Array2D =
    let foldByColumn folder state array = 
        let size = Array2D.length2 array - 1
        [|for col in [0..size] -> array.[*, col] |> Array.fold folder state|]
//Sample data
let Z = array2D [|[|1.0; nan; nan; nan; 2.0;|]; [|1.0; 2.0; 3.0; 4.0; 5.0|]|]
printfn "%A" (Z |> Array2D.foldByColumn (fun x y -> x || System.Double.IsNaN(y)) false)

[|false; true; true; true; false|]

Math.NET Numerics

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let Z = matrix [[1.0; nan; nan; nan; 2.0;]; [1.0; 2.0; 3.0; 4.0; 5.0]]
printfn "%A" (Z |> 
    Matrix.foldByCol(fun x y -> x + System.Convert.ToDouble(System.Double.IsNaN(y))) 0.0 |>
    Seq.cast<float> |> 
    Seq.toArray |> 
    Array.map (fun x -> System.Convert.ToBoolean(x)))

[|false; true; true; true; false|]

10. Find the nearest value from a given value in an array

F# Core Library

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let rand = System.Random()
let Z = Array.init<float> 10(fun _ -> rand.NextDouble())
let z = 0.5
Seq.minBy (fun x -> abs (x-z)) Z |> printfn "%A"

0.5076313729

Math.NET Numerics

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let rand = new MathNet.Numerics.Distributions.ContinuousUniform()
let Z = DenseVector.random<float> 10 rand
Z.[Vector.minAbsIndex(Z - z)] |> printfn "%A"

0.3297233672

Journeyman

1. Consider the following file:

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1,2,3,4,5
6,,,7,8
,,9,10,11

How to read it ?

I used build-in functions(System.IO etc) and Math.Net Numerics Data Text here. It is a good idea to use F# Data: CSV Type Provider instead of these strategies.

F# Core Library

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let Z = System.IO.File.ReadAllLines "missing.dat" |> 
    Array.map (fun z -> z.Split ',') 
printfn "%A" Z

[|[|"1"; "2"; "3"; "4"; "5"|]; [|"6"; ""; ""; "7"; "8"|];
  [|""; ""; "9"; "10"; "11"|]|]

Math.NET Numerics

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let Z = DelimitedReader.Read<double>( "missing.dat", false, ",", false);
printfn "%A" Z

DenseMatrix 3x5-Double
        1          2          3   4   5
        6  NaN (非数値)  NaN (非数値)   7   8
NaN (非数値)  NaN (非数値)          9  10  11

2. Consider a generator function that generates 10 integers and use it to build an array

F# Core Library

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let generate() = seq { 0..10 }
//or 
//let generate() = seq { for i in 0..9 do yield i}
//or
//let generate() = seq { for i in 0..9 -> i}
let Z = generate() |> Array.ofSeq
printfn "%A" Z

[|0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10|]

Math.NET Numerics

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let generate() = seq { for i in 0..9 -> float i}
let Z = generate() |> DenseVector.ofSeq
printfn "%A" Z

seq [0.0; 1.0; 2.0; 3.0; ...]

3. Consider a given vector, how to add 1 to each element indexed by a second vector (be careful with repeated indices) ?

F# Core Library

(Not so good code...)

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let rand = System.Random()
let Z = Array.create 10 1
let I = Array.init 20 (fun _ -> rand.Next(Array.length Z))
I |> Seq.countBy id |> Seq.iter (fun i -> Z.[fst i] <- Z.[fst i] + snd i)
printfn "%A" Z

[|3; 2; 3; 4; 2; 3; 2; 5; 4; 2|]

Math.NET Numerics

It is difficult to write with Math.NET for me...

4. How to accumulate elements of a vector (X) to an array (F) based on an index list (I) ?

F# Core Library

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let X = [|1; 2; 3; 4; 5; 6|]
let I = [|1; 3; 9; 3; 4; 1|]
let F = Array.zeroCreate<int> (Array.max I + 1)
Array.zip I X |> Array.iter (fun x -> F.[fst x] <- F.[fst x] + snd x)
printfn "%A" F

[|0; 7; 0; 6; 5; 0; 0; 0; 0; 3|]

Math.NET Numerics

It is difficult to write with Math.NET for me...

5. Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique colors

F# Core Library

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let rand = System.Random()
let w, h = 16, 16
let I = Array.init 3 (fun _ -> Array2D.init w h (fun _ _ -> rand.Next(2)))
let F = I |> Array.mapi (fun i x -> Array2D.map ((*) (int (256.0**(float i)))) x)
let n = (F |> Array.map  (fun x -> x |> Seq.cast<int> |> Seq.distinct |> Set.ofSeq) |> Array.reduce Set.union) |> Set.count
printfn "%A" (I |> Array.map  (fun x -> x |> Seq.cast<int> |> Seq.distinct |> Set.ofSeq) |> Array.reduce Set.intersect)

set [0; 1]

Math.NET Numerics

6. Considering a four dimensions array, how to get sum over the last two axis at once ?

F# Core Library

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let rand = System.Random()
let A = Array.init 3 (fun _ -> Array.init 4 (fun _ -> Array2D.init 3 4 (fun _ _ -> rand.Next(10))))
let sum = A |> Array.map (fun a -> Array.map (Seq.cast<int> >> Seq.sum) a)
printfn "%A" sum

[|[|37; 60; 46; 40|]; [|74; 52; 43; 60|]; [|37; 54; 71; 58|]|]

Math.NET Numerics

7. Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S of same size describing subset indices ?

F# Core Library

1: 
2: 
3: 
4: 
5:

let rand = System.Random()
let D = Array.init 100 (fun _ -> rand.NextDouble())
let S = Array.init 100 (fun _ -> rand.Next(10))
let D_means = Seq.zip S D |> Seq.groupBy (fun pair -> fst pair) |> Seq.map (fun (key, value) -> Seq.averageBy snd value )
printfn "%A" D_means

seq [0.6309287825; 0.5461800725; 0.7479628748; 0.5069600422; ...]

... To be continued.

namespace System

type Environment =
  static member CommandLine : string
  static member CurrentDirectory : string with get, set
  static member Exit : exitCode:int -> unit
  static member ExitCode : int with get, set
  static member ExpandEnvironmentVariables : name:string -> string
  static member FailFast : message:string -> unit + 1 overload
  static member GetCommandLineArgs : unit -> string[]
  static member GetEnvironmentVariable : variable:string -> string + 1 overload
  static member GetEnvironmentVariables : unit -> IDictionary + 1 overload
  static member GetFolderPath : folder:SpecialFolder -> string + 1 overload
  ...
  nested type SpecialFolder
  nested type SpecialFolderOption

Full name: System.Environment

property System.Environment.CurrentDirectory: string

namespace MathNet

namespace MathNet.Numerics

namespace MathNet.Numerics.LinearAlgebra

namespace MathNet.Numerics.LinearAlgebra.Double

namespace MathNet.Numerics.Statistics

namespace MathNet.Numerics.Data

namespace MathNet.Numerics.Data.Text

val printfn : format:Printf.TextWriterFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printfn

namespace System.Reflection

type Assembly =
  member CodeBase : string
  member CreateInstance : typeName:string -> obj + 2 overloads
  member EntryPoint : MethodInfo
  member Equals : o:obj -> bool
  member EscapedCodeBase : string
  member Evidence : Evidence
  member FullName : string
  member GetCustomAttributes : inherit:bool -> obj[] + 1 overload
  member GetCustomAttributesData : unit -> IList<CustomAttributeData>
  member GetExportedTypes : unit -> Type[]
  ...

Full name: System.Reflection.Assembly

System.Reflection.Assembly.GetExecutingAssembly() : System.Reflection.Assembly

val Z : float []

Full name: Fsharp-100-exercises.Z

module Array

from Microsoft.FSharp.Collections

val zeroCreate : count:int -> 'T []

Full name: Microsoft.FSharp.Collections.Array.zeroCreate

Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = System.Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>

val Z : Vector<float>

Full name: Fsharp-100-exercises.Z

Multiple items
type DenseVector =
  inherit Vector
  new : storage:DenseVectorStorage<float> -> DenseVector + 2 overloads
  member AbsoluteMaximum : unit -> float
  member AbsoluteMaximumIndex : unit -> int
  member AbsoluteMinimum : unit -> float
  member AbsoluteMinimumIndex : unit -> int
  member InfinityNorm : unit -> float
  member L1Norm : unit -> float
  member L2Norm : unit -> float
  member MaximumIndex : unit -> int
  member MinimumIndex : unit -> int
  ...

Full name: MathNet.Numerics.LinearAlgebra.Double.DenseVector

--------------------
DenseVector(storage: Storage.DenseVectorStorage<float>) : unit
DenseVector(length: int) : unit
DenseVector(storage: float []) : unit

val zero : n:int -> Vector<'T> (requires value type and 'T :> System.ValueType and default constructor and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.DenseVector.zero

Vector.ToArray() : float []

val Z : int []

Full name: Fsharp-100-exercises.Z

val init : count:int -> initializer:(int -> 'T) -> 'T []

Full name: Microsoft.FSharp.Collections.Array.init

val index : int

val range : start:int -> step:int -> stop:int -> Vector<float>

Full name: MathNet.Numerics.LinearAlgebra.DenseVector.range

val Z : int [,]

Full name: Fsharp-100-exercises.Z

module Array2D

from Microsoft.FSharp.Collections

val init : length1:int -> length2:int -> initializer:(int -> int -> 'T) -> 'T [,]

Full name: Microsoft.FSharp.Collections.Array2D.init

val i : int

val j : int

val Z : Matrix<float>

Full name: Fsharp-100-exercises.Z

Multiple items
type DenseMatrix =
  inherit Matrix
  new : storage:DenseColumnMajorMatrixStorage<float> -> DenseMatrix + 3 overloads
  member Cholesky : unit -> Cholesky<float>
  member Evd : ?symmetricity:Symmetricity -> Evd<float>
  member FrobeniusNorm : unit -> float
  member GramSchmidt : unit -> GramSchmidt<float>
  member InfinityNorm : unit -> float
  member IsSymmetric : unit -> bool
  member L1Norm : unit -> float
  member LU : unit -> LU<float>
  member QR : ?method:QRMethod -> QR<float>
  ...

Full name: MathNet.Numerics.LinearAlgebra.Double.DenseMatrix

--------------------
DenseMatrix(storage: Storage.DenseColumnMajorMatrixStorage<float>) : unit
DenseMatrix(order: int) : unit
DenseMatrix(rows: int, columns: int) : unit
DenseMatrix(rows: int, columns: int, storage: float []) : unit

val init : rows:int -> cols:int -> f:(int -> int -> 'T) -> Matrix<'T> (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.DenseMatrix.init

Matrix.ToArray() : float [,]

val mapi : mapping:(int -> 'T -> 'U) -> array:'T [] -> 'U []

Full name: Microsoft.FSharp.Collections.Array.mapi

val x : int

val filter : predicate:('T -> bool) -> array:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.filter

val fst : tuple:('T1 * 'T2) -> 'T1

Full name: Microsoft.FSharp.Core.Operators.fst

val map : mapping:('T -> 'U) -> array:'T [] -> 'U []

Full name: Microsoft.FSharp.Collections.Array.map

val snd : tuple:('T1 * 'T2) -> 'T2

Full name: Microsoft.FSharp.Core.Operators.snd

val choose : chooser:('T -> 'U option) -> array:'T [] -> 'U []

Full name: Microsoft.FSharp.Collections.Array.choose

val x : bool * int

union case Option.Some: Value: 'T -> Option<'T>

union case Option.None: Option<'T>

val vector : lst:'T list -> Vector<'T> (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.VectorExtensions.vector

Multiple items
type Vector =
  inherit Vector<float>
  member AbsoluteMaximum : unit -> float
  member AbsoluteMaximumIndex : unit -> int
  member AbsoluteMinimum : unit -> float
  member AbsoluteMinimumIndex : unit -> int
  member CoerceZero : threshold:float -> unit
  member InfinityNorm : unit -> float
  member L1Norm : unit -> float
  member L2Norm : unit -> float
  member MaximumIndex : unit -> int
  member MinimumIndex : unit -> int
  ...

Full name: MathNet.Numerics.LinearAlgebra.Double.Vector

--------------------
type Vector<'T (requires default constructor and value type and 'T :> ValueType and 'T :> IEquatable<'T> and 'T :> IFormattable)> =
  member AbsoluteMaximum : unit -> 'T
  member AbsoluteMaximumIndex : unit -> int
  member AbsoluteMinimum : unit -> 'T
  member AbsoluteMinimumIndex : unit -> int
  member Add : scalar:'T -> Vector<'T> + 3 overloads
  member At : index:int -> 'T + 1 overload
  member Clear : unit -> unit
  member ClearSubVector : index:int * count:int -> unit
  member Clone : unit -> Vector<'T>
  member CoerceZero : threshold:float -> unit + 1 overload
  ...

Full name: MathNet.Numerics.LinearAlgebra.Vector<_>

val foldi : f:(int -> 'a -> 'b -> 'a) -> state:'a -> v:#Vector<'b> -> 'a (requires default constructor and value type and 'b :> System.ValueType and 'b :> System.IEquatable<'b> and 'b :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.Vector.foldi

val x : float []

val y : float

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val identity : order:int -> Matrix<'T> (requires value type and 'T :> System.ValueType and default constructor and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.DenseMatrix.identity

val rand : System.Random

Full name: Fsharp-100-exercises.rand

Multiple items
type Random =
  new : unit -> Random + 1 overload
  member Next : unit -> int + 2 overloads
  member NextBytes : buffer:byte[] -> unit
  member NextDouble : unit -> float

Full name: System.Random

--------------------
System.Random() : unit
System.Random(Seed: int) : unit

val Z : float [,,]

Full name: Fsharp-100-exercises.Z

module Array3D

from Microsoft.FSharp.Collections

val init : length1:int -> length2:int -> length3:int -> initializer:(int -> int -> int -> 'T) -> 'T [,,]

Full name: Microsoft.FSharp.Collections.Array3D.init

System.Random.NextDouble() : float

val z : int

val y : int

val printf : format:Printf.TextWriterFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printf

val Z : float [,] []

Full name: Fsharp-100-exercises.Z

val rand : MathNet.Numerics.Distributions.ContinuousUniform

Full name: Fsharp-100-exercises.rand

namespace MathNet.Numerics.Distributions

Multiple items
type ContinuousUniform =
  new : unit -> ContinuousUniform + 2 overloads
  member CumulativeDistribution : x:float -> float
  member Density : x:float -> float
  member DensityLn : x:float -> float
  member Entropy : float
  member InverseCumulativeDistribution : p:float -> float
  member LowerBound : float
  member Maximum : float
  member Mean : float
  member Median : float
  ...

Full name: MathNet.Numerics.Distributions.ContinuousUniform

--------------------
MathNet.Numerics.Distributions.ContinuousUniform() : unit
MathNet.Numerics.Distributions.ContinuousUniform(lower: float, upper: float) : unit
MathNet.Numerics.Distributions.ContinuousUniform(lower: float, upper: float, randomSource: System.Random) : unit

val Z : Matrix<float> []

Full name: Fsharp-100-exercises.Z

val random : rows:int -> cols:int -> dist:MathNet.Numerics.Distributions.IContinuousDistribution -> Matrix<'T> (requires value type and 'T :> System.ValueType and default constructor and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.DenseMatrix.random

val Z : float [,]

Full name: Fsharp-100-exercises.Z

val Zmin : float

Full name: Fsharp-100-exercises.Zmin

module Seq

from Microsoft.FSharp.Collections

val cast : source:System.Collections.IEnumerable -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.cast

val min : source:seq<'T> -> 'T (requires comparison)

Full name: Microsoft.FSharp.Collections.Seq.min

val Zmax : float

Full name: Fsharp-100-exercises.Zmax

val max : source:seq<'T> -> 'T (requires comparison)

Full name: Microsoft.FSharp.Collections.Seq.max

Multiple items
type Matrix =
  inherit Matrix<float>
  member Cholesky : unit -> Cholesky<float>
  member CoerceZero : threshold:float -> unit
  member ColumnAbsoluteSums : unit -> Vector<float>
  member ColumnNorms : norm:float -> Vector<float>
  member ColumnSums : unit -> Vector<float>
  member ConjugateTranspose : unit -> Matrix<float>
  member Evd : ?symmetricity:Symmetricity -> Evd<float>
  member FrobeniusNorm : unit -> float
  member GramSchmidt : unit -> GramSchmidt<float>
  member InfinityNorm : unit -> float
  ...

Full name: MathNet.Numerics.LinearAlgebra.Double.Matrix

--------------------
type Matrix<'T (requires default constructor and value type and 'T :> ValueType and 'T :> IEquatable<'T> and 'T :> IFormattable)> =
  member Add : scalar:'T -> Matrix<'T> + 3 overloads
  member Append : right:Matrix<'T> -> Matrix<'T> + 1 overload
  member At : row:int * column:int -> 'T + 1 overload
  member Cholesky : unit -> Cholesky<'T>
  member Clear : unit -> unit
  member ClearColumn : columnIndex:int -> unit
  member ClearColumns : params columnIndices:int[] -> unit
  member ClearRow : rowIndex:int -> unit
  member ClearRows : params rowIndices:int[] -> unit
  member ClearSubMatrix : rowIndex:int * rowCount:int * columnIndex:int * columnCount:int -> unit
  ...

Full name: MathNet.Numerics.LinearAlgebra.Matrix<_>

val reduce : f:('a -> 'a -> 'a) -> m:#Matrix<'a> -> 'a (requires default constructor and value type and 'a :> System.ValueType and 'a :> System.IEquatable<'a> and 'a :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.Matrix.reduce

val min : e1:'T -> e2:'T -> 'T (requires comparison)

Full name: Microsoft.FSharp.Core.Operators.min

val max : e1:'T -> e2:'T -> 'T (requires comparison)

Full name: Microsoft.FSharp.Core.Operators.max

val array2D : rows:seq<#seq<'T>> -> 'T [,]

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.array2D

val seq01 : seq<float>

Full name: Fsharp-100-exercises.seq01

val initInfinite : initializer:(int -> 'T) -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.initInfinite

val initColumns : cols:int -> f:(int -> Vector<'T>) -> Matrix<'T> (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.DenseMatrix.initColumns

val skip : count:int -> source:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.skip

val take : count:int -> source:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.take

val ofSeq : fs:#seq<'T> -> Vector<'T> (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.DenseVector.ofSeq

val Z2 : float [,]

Full name: Fsharp-100-exercises.Z2

val map : mapping:('T -> 'U) -> array:'T [,] -> 'U [,]

Full name: Microsoft.FSharp.Collections.Array2D.map

val z : float

val Z2 : Matrix<float>

Full name: Fsharp-100-exercises.Z2

val map : f:('a -> 'b) -> A:#Matrix<'a> -> Matrix<'b> (requires default constructor and value type and 'a :> System.ValueType and 'a :> System.IEquatable<'a> and 'a :> System.IFormattable and default constructor and value type and 'b :> System.ValueType and 'b :> System.IEquatable<'b> and 'b :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.Matrix.map

val x : float [,]

Full name: Fsharp-100-exercises.x

val create : length1:int -> length2:int -> value:'T -> 'T [,]

Full name: Microsoft.FSharp.Collections.Array2D.create

val y : float [,]

Full name: Fsharp-100-exercises.y

val inner_product : x:float [] -> y:float [] -> float

Full name: Fsharp-100-exercises.inner_product

val y : float []

val fold2 : folder:('State -> 'T1 -> 'T2 -> 'State) -> state:'State -> array1:'T1 [] -> array2:'T2 [] -> 'State

Full name: Microsoft.FSharp.Collections.Array.fold2

val s : float

val x : float

val create : rows:int -> cols:int -> x:'T -> Matrix<'T> (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.DenseMatrix.create

val Z2 : float []

Full name: Fsharp-100-exercises.Z2

val sub : array:'T [] -> startIndex:int -> count:int -> 'T []

Full name: Microsoft.FSharp.Collections.Array.sub

val rangef : start:float -> step:float -> stop:float -> Vector<float>

Full name: MathNet.Numerics.LinearAlgebra.DenseVector.rangef

val sort : array:'T [] -> 'T [] (requires comparison)

Full name: Microsoft.FSharp.Collections.Array.sort

val random : n:int -> dist:MathNet.Numerics.Distributions.IContinuousDistribution -> Vector<'T> (requires value type and 'T :> System.ValueType and default constructor and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.DenseVector.random

type Sorting =
static member Sort<'T> : keys:IList<'T> * ?comparer:IComparer<'T> -> unit + 5 overloads
static member SortAll<'T1, 'T2> : primary:IList<'T1> * secondary:IList<'T2> * ?primaryComparer:IComparer<'T1> * ?secondaryComparer:IComparer<'T2> -> unit

Full name: MathNet.Numerics.Sorting

MathNet.Numerics.Sorting.Sort<'T>(keys: System.Collections.Generic.IList<'T>, ?comparer: System.Collections.Generic.IComparer<'T>) : unit
MathNet.Numerics.Sorting.Sort<'TKey,'TItem>(keys: System.Collections.Generic.IList<'TKey>, items: System.Collections.Generic.IList<'TItem>, ?comparer: System.Collections.Generic.IComparer<'TKey>) : unit
MathNet.Numerics.Sorting.Sort<'T>(keys: System.Collections.Generic.IList<'T>, index: int, count: int, ?comparer: System.Collections.Generic.IComparer<'T>) : unit
MathNet.Numerics.Sorting.Sort<'TKey,'TItem1,'TItem2>(keys: System.Collections.Generic.IList<'TKey>, items1: System.Collections.Generic.IList<'TItem1>, items2: System.Collections.Generic.IList<'TItem2>, ?comparer: System.Collections.Generic.IComparer<'TKey>) : unit
MathNet.Numerics.Sorting.Sort<'TKey,'TItem>(keys: System.Collections.Generic.IList<'TKey>, items: System.Collections.Generic.IList<'TItem>, index: int, count: int, ?comparer: System.Collections.Generic.IComparer<'TKey>) : unit
MathNet.Numerics.Sorting.Sort<'TKey,'TItem1,'TItem2>(keys: System.Collections.Generic.IList<'TKey>, items1: System.Collections.Generic.IList<'TItem1>, items2: System.Collections.Generic.IList<'TItem2>, index: int, count: int, ?comparer: System.Collections.Generic.IComparer<'TKey>) : unit

val A : int []

Full name: Fsharp-100-exercises.A

System.Random.Next() : int
System.Random.Next(maxValue: int) : int
System.Random.Next(minValue: int, maxValue: int) : int

val B : int []

Full name: Fsharp-100-exercises.B

val equal : bool

Full name: Fsharp-100-exercises.equal

val forall2 : predicate:('T1 -> 'T2 -> bool) -> array1:'T1 [] -> array2:'T2 [] -> bool

Full name: Microsoft.FSharp.Collections.Array.forall2

val rand : MathNet.Numerics.Distributions.DiscreteUniform

Full name: Fsharp-100-exercises.rand

Multiple items
type DiscreteUniform =
  new : lower:int * upper:int -> DiscreteUniform + 1 overload
  member CumulativeDistribution : x:float -> float
  member Entropy : float
  member LowerBound : int
  member Maximum : int
  member Mean : float
  member Median : float
  member Minimum : int
  member Mode : int
  member Probability : k:int -> float
  ...

Full name: MathNet.Numerics.Distributions.DiscreteUniform

--------------------
MathNet.Numerics.Distributions.DiscreteUniform(lower: int, upper: int) : unit
MathNet.Numerics.Distributions.DiscreteUniform(lower: int, upper: int, randomSource: System.Random) : unit

val A : Vector<float>

Full name: Fsharp-100-exercises.A

MathNet.Numerics.Distributions.DiscreteUniform.Samples() : System.Collections.Generic.IEnumerable<int>
MathNet.Numerics.Distributions.DiscreteUniform.Samples(values: int []) : unit

val map : mapping:('T -> 'U) -> source:seq<'T> -> seq<'U>

Full name: Microsoft.FSharp.Collections.Seq.map

val B : Vector<float>

Full name: Fsharp-100-exercises.B

val m : float

Full name: Fsharp-100-exercises.m

val average : array:'T [] -> 'T (requires member ( + ) and member DivideByInt and member get_Zero)

Full name: Microsoft.FSharp.Collections.Array.average

type Statistics =
  static member Covariance : samples1:IEnumerable<float> * samples2:IEnumerable<float> -> float + 1 overload
  static member EmpiricalCDF : data:IEnumerable<float> * x:float -> float + 1 overload
  static member EmpiricalCDFFunc : data:IEnumerable<float> -> Func<float, float> + 1 overload
  static member EmpiricalInvCDF : data:IEnumerable<float> * tau:float -> float + 1 overload
  static member EmpiricalInvCDFFunc : data:IEnumerable<float> -> Func<float, float> + 1 overload
  static member Entropy : data:IEnumerable<float> -> float + 1 overload
  static member FiveNumberSummary : data:IEnumerable<float> -> float[] + 1 overload
  static member InterquartileRange : data:IEnumerable<float> -> float + 1 overload
  static member Kurtosis : samples:IEnumerable<float> -> float + 1 overload
  static member LowerQuartile : data:IEnumerable<float> -> float + 1 overload
  ...

Full name: MathNet.Numerics.Statistics.Statistics

Statistics.Mean(data: System.Collections.Generic.IEnumerable<System.Nullable<float>>) : float
Statistics.Mean(data: System.Collections.Generic.IEnumerable<float>) : float

val Z : int list

Full name: Fsharp-100-exercises.Z

Multiple items
module List

from Microsoft.FSharp.Collections

--------------------
type List<'T> =
  | ( [] )
  | ( :: ) of Head: 'T * Tail: 'T list
  interface IEnumerable
  interface IEnumerable<'T>
  member Head : 'T
  member IsEmpty : bool
  member Item : index:int -> 'T with get
  member Length : int
  member Tail : 'T list
  static member Cons : head:'T * tail:'T list -> 'T list
  static member Empty : 'T list

Full name: Microsoft.FSharp.Collections.List<_>

val init : length:int -> initializer:(int -> 'T) -> 'T list

Full name: Microsoft.FSharp.Collections.List.init

val X : float []

Full name: Fsharp-100-exercises.X

val Y : float []

Full name: Fsharp-100-exercises.Y

val R : float []

Full name: Fsharp-100-exercises.R

val map2 : mapping:('T1 -> 'T2 -> 'U) -> array1:'T1 [] -> array2:'T2 [] -> 'U []

Full name: Microsoft.FSharp.Collections.Array.map2

val sqrt : value:'T -> 'U (requires member Sqrt)

Full name: Microsoft.FSharp.Core.Operators.sqrt

val T : float []

Full name: Fsharp-100-exercises.T

type Math =
  static val PI : float
  static val E : float
  static member Abs : value:sbyte -> sbyte + 6 overloads
  static member Acos : d:float -> float
  static member Asin : d:float -> float
  static member Atan : d:float -> float
  static member Atan2 : y:float * x:float -> float
  static member BigMul : a:int * b:int -> int64
  static member Ceiling : d:decimal -> decimal + 1 overload
  static member Cos : d:float -> float
  ...

Full name: System.Math

System.Math.Atan2(y: float, x: float) : float

val X : Vector<float>

Full name: Fsharp-100-exercises.X

val Y : Vector<float>

Full name: Fsharp-100-exercises.Y

val R : Vector<float>

Full name: Fsharp-100-exercises.R

val map : f:('a -> 'b) -> v:#Vector<'a> -> Vector<'b> (requires default constructor and value type and 'a :> System.ValueType and 'a :> System.IEquatable<'a> and 'a :> System.IFormattable and default constructor and value type and 'b :> System.ValueType and 'b :> System.IEquatable<'b> and 'b :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.Vector.map

val T : Vector<float>

Full name: Fsharp-100-exercises.T

System.Math.Atan(d: float) : float

val max : array:'T [] -> 'T (requires comparison)

Full name: Microsoft.FSharp.Collections.Array.max

val findIndex : predicate:('T -> bool) -> array:'T [] -> int

Full name: Microsoft.FSharp.Collections.Array.findIndex

val maxIndex : A:#Vector<'b> -> int (requires default constructor and value type and 'b :> System.ValueType and 'b :> System.IEquatable<'b> and 'b :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.Vector.maxIndex

val element : float []

Full name: Fsharp-100-exercises.element

val Z : (float * float) [,]

Full name: Fsharp-100-exercises.Z

val element : Vector<float>

Full name: Fsharp-100-exercises.element

Multiple items
val int8 : value:'T -> sbyte (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.int8

--------------------
type int8 = System.SByte

Full name: Microsoft.FSharp.Core.int8

Multiple items
val int32 : value:'T -> int32 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int32

--------------------
type int32 = System.Int32

Full name: Microsoft.FSharp.Core.int32

Multiple items
val int64 : value:'T -> int64 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int64

--------------------
type int64 = System.Int64

Full name: Microsoft.FSharp.Core.int64

--------------------
type int64<'Measure> = int64

Full name: Microsoft.FSharp.Core.int64<_>

val iter : action:('T -> unit) -> list:'T list -> unit

Full name: Microsoft.FSharp.Collections.List.iter

val x : System.Type

property System.Type.BaseType: System.Type

Multiple items
val float32 : value:'T -> float32 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float32

--------------------
type float32 = System.Single

Full name: Microsoft.FSharp.Core.float32

--------------------
type float32<'Measure> = float32

Full name: Microsoft.FSharp.Core.float32<_>

type NamedSequence<'T> = System.Collections.Generic.IDictionary<string,'T>

Full name: Fsharp-100-exercises.NamedSequence<_>

namespace System.Collections

namespace System.Collections.Generic

type IDictionary<'TKey,'TValue> =
  member Add : key:'TKey * value:'TValue -> unit
  member ContainsKey : key:'TKey -> bool
  member Item : 'TKey -> 'TValue with get, set
  member Keys : ICollection<'TKey>
  member Remove : key:'TKey -> bool
  member TryGetValue : key:'TKey * value:'TValue -> bool
  member Values : ICollection<'TValue>

Full name: System.Collections.Generic.IDictionary<_,_>

Multiple items
val string : value:'T -> string

Full name: Microsoft.FSharp.Core.Operators.string

--------------------
type string = System.String

Full name: Microsoft.FSharp.Core.string

val Z : System.Collections.Generic.IDictionary<string,System.Collections.Generic.IDictionary<string,float>> []

Full name: Fsharp-100-exercises.Z

val dict : keyValuePairs:seq<'Key * 'Value> -> System.Collections.Generic.IDictionary<'Key,'Value> (requires equality)

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.dict

val z : NamedSequence<NamedSequence<float>>

val product : xs:seq<'a> -> ys:seq<'b> -> ('a * 'b) []

Full name: Fsharp-100-exercises.product

val xs : seq<'a>

val ys : seq<'b>

val x : 'a

val y : 'b

val distance : float * float -> float * float -> float

Full name: Fsharp-100-exercises.distance

val x : float * float

val y : float * float

val dx : float

val dy : float

val xs : (float * float) []

Full name: Fsharp-100-exercises.xs

val ys : (float * float) []

Full name: Fsharp-100-exercises.ys

val D : float []

Full name: Fsharp-100-exercises.D

DenseMatrix.Create(rows: int, columns: int, init: System.Func<int,int,float>) : DenseMatrix
DenseMatrix.Create(rows: int, columns: int, value: float) : DenseMatrix

val Z : (float * float) []

Full name: Fsharp-100-exercises.Z

val ofSeq : source:seq<'T> -> 'T []

Full name: Microsoft.FSharp.Collections.Array.ofSeq

val z : float * float

val sigma : float

Full name: Fsharp-100-exercises.sigma

val mu : float

Full name: Fsharp-100-exercises.mu

val G : float []

Full name: Fsharp-100-exercises.G

val d : float

val exp : value:'T -> 'T (requires member Exp)

Full name: Microsoft.FSharp.Core.Operators.exp

val D : Vector<float>

Full name: Fsharp-100-exercises.D

val init : n:int -> f:(int -> 'T) -> Vector<'T> (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.DenseVector.init

val G : Vector<float>

Full name: Fsharp-100-exercises.G

Vector.Subtract(other: Vector<float>) : Vector<float>
Vector.Subtract(scalar: float) : Vector<float>
Vector.Subtract(other: Vector<float>, result: Vector<float>) : unit
Vector.Subtract(scalar: float, result: Vector<float>) : unit

val foldByColumn : folder:('a -> 'b -> 'a) -> state:'a -> array:'b [,] -> 'a []

Full name: Fsharp-100-exercises.Array2D.foldByColumn

val folder : ('a -> 'b -> 'a)

val state : 'a

Multiple items
val array : 'b [,]

--------------------
type 'T array = 'T []

Full name: Microsoft.FSharp.Core.array<_>

val size : int

val length2 : array:'T [,] -> int

Full name: Microsoft.FSharp.Collections.Array2D.length2

val col : int

val fold : folder:('State -> 'T -> 'State) -> state:'State -> array:'T [] -> 'State

Full name: Microsoft.FSharp.Collections.Array.fold

val nan : float

Full name: Microsoft.FSharp.Core.Operators.nan

Multiple items
module Array2D

from Fsharp-100-exercises

--------------------
module Array2D

from Microsoft.FSharp.Collections

val x : bool

type Double =
  struct
    member CompareTo : value:obj -> int + 1 overload
    member Equals : obj:obj -> bool + 1 overload
    member GetHashCode : unit -> int
    member GetTypeCode : unit -> TypeCode
    member ToString : unit -> string + 3 overloads
    static val MinValue : float
    static val MaxValue : float
    static val Epsilon : float
    static val NegativeInfinity : float
    static val PositiveInfinity : float
    ...
  end

Full name: System.Double

System.Double.IsNaN(d: float) : bool

val matrix : lst:'T list list -> Matrix<'T> (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.MatrixExtensions.matrix

val foldByCol : f:('T -> 'T -> 'T) -> acc:'T -> A:#Matrix<'T> -> Vector<'T> (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.Matrix.foldByCol

type Convert =
  static val DBNull : obj
  static member ChangeType : value:obj * typeCode:TypeCode -> obj + 3 overloads
  static member FromBase64CharArray : inArray:char[] * offset:int * length:int -> byte[]
  static member FromBase64String : s:string -> byte[]
  static member GetTypeCode : value:obj -> TypeCode
  static member IsDBNull : value:obj -> bool
  static member ToBase64CharArray : inArray:byte[] * offsetIn:int * length:int * outArray:char[] * offsetOut:int -> int + 1 overload
  static member ToBase64String : inArray:byte[] -> string + 3 overloads
  static member ToBoolean : value:obj -> bool + 17 overloads
  static member ToByte : value:obj -> byte + 18 overloads
  ...

Full name: System.Convert

System.Convert.ToDouble(value: System.DateTime) : float
   (+0 other overloads)
System.Convert.ToDouble(value: bool) : float
   (+0 other overloads)
System.Convert.ToDouble(value: string) : float
   (+0 other overloads)
System.Convert.ToDouble(value: decimal) : float
   (+0 other overloads)
System.Convert.ToDouble(value: float) : float
   (+0 other overloads)
System.Convert.ToDouble(value: float32) : float
   (+0 other overloads)
System.Convert.ToDouble(value: uint64) : float
   (+0 other overloads)
System.Convert.ToDouble(value: int64) : float
   (+0 other overloads)
System.Convert.ToDouble(value: uint32) : float
   (+0 other overloads)
System.Convert.ToDouble(value: int) : float
   (+0 other overloads)

val toArray : source:seq<'T> -> 'T []

Full name: Microsoft.FSharp.Collections.Seq.toArray

System.Convert.ToBoolean(value: System.DateTime) : bool
   (+0 other overloads)
System.Convert.ToBoolean(value: decimal) : bool
   (+0 other overloads)
System.Convert.ToBoolean(value: float) : bool
   (+0 other overloads)
System.Convert.ToBoolean(value: float32) : bool
   (+0 other overloads)
System.Convert.ToBoolean(value: string) : bool
   (+0 other overloads)
System.Convert.ToBoolean(value: uint64) : bool
   (+0 other overloads)
System.Convert.ToBoolean(value: int64) : bool
   (+0 other overloads)
System.Convert.ToBoolean(value: uint32) : bool
   (+0 other overloads)
System.Convert.ToBoolean(value: int) : bool
   (+0 other overloads)
System.Convert.ToBoolean(value: uint16) : bool
   (+0 other overloads)

val z : float

Full name: Fsharp-100-exercises.z

val minBy : projection:('T -> 'U) -> source:seq<'T> -> 'T (requires comparison)

Full name: Microsoft.FSharp.Collections.Seq.minBy

val abs : value:'T -> 'T (requires member Abs)

Full name: Microsoft.FSharp.Core.Operators.abs

val minAbsIndex : A:#Vector<'b> -> int (requires default constructor and value type and 'b :> System.ValueType and 'b :> System.IEquatable<'b> and 'b :> System.IFormattable)

Full name: MathNet.Numerics.LinearAlgebra.Vector.minAbsIndex

val Z : string [] []

Full name: Fsharp-100-exercises.Z

namespace System.IO

type File =
  static member AppendAllLines : path:string * contents:IEnumerable<string> -> unit + 1 overload
  static member AppendAllText : path:string * contents:string -> unit + 1 overload
  static member AppendText : path:string -> StreamWriter
  static member Copy : sourceFileName:string * destFileName:string -> unit + 1 overload
  static member Create : path:string -> FileStream + 3 overloads
  static member CreateText : path:string -> StreamWriter
  static member Decrypt : path:string -> unit
  static member Delete : path:string -> unit
  static member Encrypt : path:string -> unit
  static member Exists : path:string -> bool
  ...

Full name: System.IO.File

System.IO.File.ReadAllLines(path: string) : string []
System.IO.File.ReadAllLines(path: string, encoding: System.Text.Encoding) : string []

val z : string

System.String.Split(params separator: char []) : string []
System.String.Split(separator: string [], options: System.StringSplitOptions) : string []
System.String.Split(separator: char [], options: System.StringSplitOptions) : string []
System.String.Split(separator: char [], count: int) : string []
System.String.Split(separator: string [], count: int, options: System.StringSplitOptions) : string []
System.String.Split(separator: char [], count: int, options: System.StringSplitOptions) : string []

val Z : Matrix<double>

Full name: Fsharp-100-exercises.Z

type DelimitedReader =
static member Read<'T> : reader:TextReader * ?sparse:bool * ?delimiter:string * ?hasHeaders:bool * ?formatProvider:IFormatProvider * ?missingValue:Nullable<'T> -> Matrix<'T> + 2 overloads

Full name: MathNet.Numerics.Data.Text.DelimitedReader

DelimitedReader.Read<'T (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)>(stream: System.IO.Stream, ?sparse: bool, ?delimiter: string, ?hasHeaders: bool, ?formatProvider: System.IFormatProvider, ?missingValue: System.Nullable<'T>) : Matrix<'T>
DelimitedReader.Read<'T (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)>(filePath: string, ?sparse: bool, ?delimiter: string, ?hasHeaders: bool, ?formatProvider: System.IFormatProvider, ?missingValue: System.Nullable<'T>) : Matrix<'T>
DelimitedReader.Read<'T (requires default constructor and value type and 'T :> System.ValueType and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable)>(reader: System.IO.TextReader, ?sparse: bool, ?delimiter: string, ?hasHeaders: bool, ?formatProvider: System.IFormatProvider, ?missingValue: System.Nullable<'T>) : Matrix<'T>

Multiple items
val double : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.double

--------------------
type double = System.Double

Full name: Microsoft.FSharp.Core.double

val generate : unit -> seq<int>

Full name: Fsharp-100-exercises.generate

Multiple items
val seq : sequence:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Core.Operators.seq

--------------------
type seq<'T> = System.Collections.Generic.IEnumerable<'T>

Full name: Microsoft.FSharp.Collections.seq<_>

val generate : unit -> seq<float>

Full name: Fsharp-100-exercises.generate

val create : count:int -> value:'T -> 'T []

Full name: Microsoft.FSharp.Collections.Array.create

val I : int []

Full name: Fsharp-100-exercises.I

val length : array:'T [] -> int

Full name: Microsoft.FSharp.Collections.Array.length

val countBy : projection:('T -> 'Key) -> source:seq<'T> -> seq<'Key * int> (requires equality)

Full name: Microsoft.FSharp.Collections.Seq.countBy

val id : x:'T -> 'T

Full name: Microsoft.FSharp.Core.Operators.id

val iter : action:('T -> unit) -> source:seq<'T> -> unit

Full name: Microsoft.FSharp.Collections.Seq.iter

val i : int * int

val X : int []

Full name: Fsharp-100-exercises.X

val F : int []

Full name: Fsharp-100-exercises.F

Multiple items
val int : value:'T -> int (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int

--------------------
type int = int32

Full name: Microsoft.FSharp.Core.int

--------------------
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

val zip : array1:'T1 [] -> array2:'T2 [] -> ('T1 * 'T2) []

Full name: Microsoft.FSharp.Collections.Array.zip

val iter : action:('T -> unit) -> array:'T [] -> unit

Full name: Microsoft.FSharp.Collections.Array.iter

val x : int * int

val w : int

Full name: Fsharp-100-exercises.w

val h : int

Full name: Fsharp-100-exercises.h

val I : int [,] []

Full name: Fsharp-100-exercises.I

val F : int [,] []

Full name: Fsharp-100-exercises.F

val x : int [,]

val n : int

Full name: Fsharp-100-exercises.n

val distinct : source:seq<'T> -> seq<'T> (requires equality)

Full name: Microsoft.FSharp.Collections.Seq.distinct

Multiple items
module Set

from Microsoft.FSharp.Collections

--------------------
type Set<'T (requires comparison)> =
  interface IComparable
  interface IEnumerable
  interface IEnumerable<'T>
  interface ICollection<'T>
  new : elements:seq<'T> -> Set<'T>
  member Add : value:'T -> Set<'T>
  member Contains : value:'T -> bool
  override Equals : obj -> bool
  member IsProperSubsetOf : otherSet:Set<'T> -> bool
  member IsProperSupersetOf : otherSet:Set<'T> -> bool
  ...

Full name: Microsoft.FSharp.Collections.Set<_>

--------------------
new : elements:seq<'T> -> Set<'T>

val ofSeq : elements:seq<'T> -> Set<'T> (requires comparison)

Full name: Microsoft.FSharp.Collections.Set.ofSeq

val reduce : reduction:('T -> 'T -> 'T) -> array:'T [] -> 'T

Full name: Microsoft.FSharp.Collections.Array.reduce

val union : set1:Set<'T> -> set2:Set<'T> -> Set<'T> (requires comparison)

Full name: Microsoft.FSharp.Collections.Set.union

val count : set:Set<'T> -> int (requires comparison)

Full name: Microsoft.FSharp.Collections.Set.count

val intersect : set1:Set<'T> -> set2:Set<'T> -> Set<'T> (requires comparison)

Full name: Microsoft.FSharp.Collections.Set.intersect

val A : int [,] [] []

Full name: Fsharp-100-exercises.A

val sum : int [] []

Full name: Fsharp-100-exercises.sum

val a : int [,] []

val sum : source:seq<'T> -> 'T (requires member ( + ) and member get_Zero)

Full name: Microsoft.FSharp.Collections.Seq.sum

val S : int []

Full name: Fsharp-100-exercises.S

val D_means : seq<float>

Full name: Fsharp-100-exercises.D_means

val zip : source1:seq<'T1> -> source2:seq<'T2> -> seq<'T1 * 'T2>

Full name: Microsoft.FSharp.Collections.Seq.zip

val groupBy : projection:('T -> 'Key) -> source:seq<'T> -> seq<'Key * seq<'T>> (requires equality)

Full name: Microsoft.FSharp.Collections.Seq.groupBy

val pair : int * float

val key : int

val value : seq<int * float>

val averageBy : projection:('T -> 'U) -> source:seq<'T> -> 'U (requires member ( + ) and member DivideByInt and member get_Zero)

Full name: Microsoft.FSharp.Collections.Seq.averageBy

FsLab Journal

100 FSharp exercises

Neophyte

1. Import the numpy package under the name np

2. Print the Fsharp version and the configuration.

3. Create a null vector of size 10

F# Core Library

Math.NET Numerics

4. Create a null vector of size 10 but the fifth value which is 1

F# Core Library

Math.NET Numerics

5. Create a vector with values ranging from 10 to 49

F# Core Library

Math.NET Numerics

6. Create a 3x3 matrix with values ranging from 0 to 8

F# Core Library

Math.NET Numerics

7. Find indices of non-zero elements from [1,2,0,0,4,0]

F# Core Library

Math.NET Numerics

8. Create a 3x3 identity matrix

F# Core Library

Math.NET Numerics

9. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal

F# Core Library

Math.NET Numerics

10. Create a 3x3x3 array with random values

F# Core Library

Math.NET Numerics

Novice

1. Create a 8x8 matrix and fill it with a checkerboard pattern

F# Core Library

Math.NET Numerics

2. Create a 10x10 array with random values and find the minimum and maximum values

F# Core Library

Math.NET Numerics

3. Create a checkerboard 8x8 matrix using the tile function

F# Core Library

Math.NET Numerics

4. Normalize a 5x5 random matrix (between 0 and 1)

F# Core Library

Math.NET Numerics

5. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)

F# Core Library

Math.NET Numerics

6. Create a 5x5 matrix with row values ranging from 0 to 4

F# Core Library

Math.NET Numerics

7. Create a vector of size 10 with values ranging from 0 to 1, both excluded

F# Core Library

Math.NET Numerics

8. Create a random vector of size 10 and sort it

F# Core Library

Math.NET Numerics

9. Consider two random array A anb B, check if they are equal.

F# Core Library

Math.NET Numerics

10. Create a random vector of size 30 and find the mean value

F# Core Library

Math.NET Numerics

Apprentice

1. Make an array immutable (read-only)

F# Core Library

Math.NET Numerics

2. Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates

F# Core Library

Math.NET Numerics

3. Create random vector of size 10 and replace the maximum value by 0

F# Core Library

Math.NET Numerics

4. Create a structured array with x and y coordinates covering the [0,1]x[0,1] area.

F# Core Library

Math.NET Numerics

5. Print the minimum and maximum representable value for each numpy scalar type

6. Create a structured array representing a position (x,y) and a color (r,g,b)

7. Consider a random vector with shape (100,2) representing coordinates, find point by point distances

F# Core Library

Math.NET Numerics

8. Generate a generic 2D Gaussian-like array

F# Core Library

1. Import the numpy package under the name `np`

4. Create a structured array with `x` and `y` coordinates covering the [0,1]x[0,1] area.