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tmigot merged 1 commit into from
Feb 11, 2026
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Updates from JSOTutorials #217

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69 changes: 34 additions & 35 deletions tutorials/introduction-to-linear-operators/index.md
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Original file line number Diff line number Diff line change
Expand Up @@ -6,9 +6,9 @@


![JSON 0.21.4](https://img.shields.io/badge/JSON-0.21.4-000?style=flat-square&labelColor=999)
[![LinearOperators 2.5.2](https://img.shields.io/badge/LinearOperators-2.5.2-4b0082?style=flat-square&labelColor=9558b2)](https://jso.dev/LinearOperators.jl/stable/)
[![Krylov 0.9.4](https://img.shields.io/badge/Krylov-0.9.4-4b0082?style=flat-square&labelColor=9558b2)](https://jso.dev/Krylov.jl/stable/)
![FFTW 1.7.1](https://img.shields.io/badge/FFTW-1.7.1-000?style=flat-square&labelColor=999)
[![LinearOperators 2.11.0](https://img.shields.io/badge/LinearOperators-2.11.0-4b0082?style=flat-square&labelColor=9558b2)](https://jso.dev/LinearOperators.jl/stable/)
[![Krylov 0.9.10](https://img.shields.io/badge/Krylov-0.9.10-4b0082?style=flat-square&labelColor=9558b2)](https://jso.dev/Krylov.jl/stable/)
![FFTW 1.10.0](https://img.shields.io/badge/FFTW-1.10.0-000?style=flat-square&labelColor=999)



Expand Down Expand Up @@ -38,8 +38,8 @@ y = op * x
```plaintext
5-element Vector{Float64}:
0.24766385713448147
0.34471427066907173
0.6399025892338569
0.3447142706690718
0.6399025892338568
0.246664873173519
0.5258420478788777
```
Expand All @@ -62,7 +62,7 @@ norm(A \ v - op * v) / norm(v)
```

```plaintext
1.148733996146629e-13
3.3842227055482783e-15
```


Expand Down Expand Up @@ -138,7 +138,7 @@ norm(dft' * y - x) # DFT is a unitary operator
```

```plaintext
3.3612925285989963e-16
1.1320399892723098e-16
```


Expand All @@ -149,16 +149,16 @@ transpose(dft) * y

```plaintext
10-element Vector{ComplexF64}:
0.7113168325963566 - 0.0im
0.2148297961020408 - 0.0im
0.9453427110792467 - 0.0im
0.7309321298104021 - 0.0im
0.23194328498409336 - 0.0im
0.9501874396162999 - 0.0im
0.5123847829172379 - 0.0im
0.9037088931078092 - 0.0im
0.005729552514365821 + 0.0im
0.2588088046728426 - 0.0im
0.003820639240554513 - 0.0im
0.8695984692566511 - 0.0im
0.6447374729383316 - 0.0im
0.8365781167218365 - 0.0im
0.7119679627204016 - 0.0im
0.4093590753517967 - 0.0im
0.8669244192719149 - 0.0im
0.4754090095137926 - 0.0im
0.5455204733218788 + 0.0im
0.042978926103728554 - 0.0im
```


Expand Down Expand Up @@ -280,7 +280,7 @@ end
```

```plaintext
ex = InexactError(:Float64, Float64, 0.47507530806279163 - 0.3832301880068187im)
ex = InexactError(:Float64, (Float64, 0.5164858914848688 + 0.24488071994631527im))
```


Expand All @@ -296,7 +296,7 @@ end
```

```plaintext
ex = InexactError(:Float64, Float64, 0.8090169943749475 - 0.5877852522924731im)
ex = InexactError(:Float64, (Float64, 0.8090169943749475 - 0.5877852522924731im))
```


Expand All @@ -317,7 +317,7 @@ norm(b - opAAT * x)
```

```plaintext
2.3624810325472306e-13
1.9772018739020697e-13
```


Expand All @@ -344,7 +344,7 @@ r
```

```plaintext
3.919077465054229e-13
3.815809259303818e-13
```


Expand All @@ -355,7 +355,6 @@ There is also a Limited-Memory SR1 operator for which only the forward form is i
Note that the SR1 operator can be indefinite; therefore, its inverse form is less relevant than for the BFGS approximation.
For this reason, the inverse form is not implemented for the SR1 operator.


## Restriction, extension and slices

The restriction operator restricts a vector to a set of indices.
Expand Down Expand Up @@ -425,9 +424,9 @@ A[I,J] * ones(3)

```plaintext
3-element Vector{Float64}:
1.043315409692812
1.126646200633167
1.2315932943898407
1.855452693501958
1.2659861763815514
1.5303428526550302
```


Expand All @@ -438,9 +437,9 @@ opRestriction(I, 5) * opA * opExtension(J, 5) * ones(3)

```plaintext
3-element Vector{Float64}:
1.043315409692812
1.126646200633167
1.2315932943898407
1.8554526935019582
1.2659861763815514
1.5303428526550302
```


Expand All @@ -455,7 +454,7 @@ opA[1,:] * ones(5)

```plaintext
1-element Vector{Float64}:
1.9634567072673046
2.9159013209470097
```


Expand All @@ -466,11 +465,11 @@ opA[:,1] * ones(1)

```plaintext
5-element Vector{Float64}:
0.02203447865143171
0.18781833339603016
0.1692361439290926
0.20276666600590854
0.24969824326802326
0.7011787151612684
0.4203121328637791
0.19620605317757256
0.6722900514676972
0.7640075887373438
```


Expand All @@ -481,6 +480,6 @@ opA[1,1] * ones(1)

```plaintext
1-element Vector{Float64}:
0.02203447865143171
0.7011787151612684
```

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