Example of diagrams, math and source highlighting

Posted on October 1, 2023

Enable mermaid rendering

reference https://jackgruber.github.io/2021-05-09-Embed-Mermaid-in-Jekyll-without-plugin/

With mermaid: true you can now enable the rendering of mermaid diagrams in your post or page. This has the advantage that the relatively large mermaid.min.js is only loaded when it is needed.

Writing a mermaid diagram

https://mermaid.js.org/syntax/examples.html

You can now write a mermaid diagram like this in your site or posts.

```mermaid
graph TD;
    A-->B;
    A-->C;
    B-->D;
    C-->D;
```

Which are rendered automatically

graph TD;
    A-->B;
    A-->C;
    B-->D;
    C-->D;

Entity relationship diagram

```mermaid
erDiagram
    CUSTOMER ||--o{ ORDER : places
    ORDER ||--|{ LINE-ITEM : contains
    CUSTOMER }|..|{ DELIVERY-ADDRESS : uses
```  

erDiagram
    CUSTOMER ||--o{ ORDER : places
    ORDER ||--|{ LINE-ITEM : contains
    CUSTOMER }|..|{ DELIVERY-ADDRESS : uses

Neural network

graph LR
subgraph Input Layer
I1((I1))
I2((I2))
I3((I3))
end
subgraph Hidden Layer 1
H11((H11))
H12((H12))
H13((H13))
H14((H14))
H15((H15))
H16((H16))
end
subgraph Hidden Layer 2
H21((H21))
H22((H22))
H23((H23))
H24((H24))
H25((H25))
H26((H26))
H27((H27))
end
subgraph Output Layer
O1((O1))
O2((O2))
O3((O3))
O4((O4))
end
I1 -->|w11| H11
I1 -->|w12| H12
I1 -->|w13| H13
I1 -->|w14| H14
I1 -->|w15| H15
I1 -->|w16| H16
I2 -->|w21| H11
I2 -->|w22| H12
I2 -->|w23| H13
I2 -->|w24| H14
I2 -->|w25| H15
I2 -->|w26| H16
I3 -->|w31| H11
I3 -->|w32| H12
I3 -->|w33| H13
I3 -->|w34| H14
I3 -->|w35| H15
I3 -->|w36| H16
H11 -->|v11| H21
H11 -->|v12| H22
H11 -->|v13| H23
H11 -->|v14| H24
H11 -->|v15| H25
H11 -->|v16| H26
H11 -->|v17| H27
H12 -->|v21| H21

smaller neural network

graph LR
    subgraph Input_Layer
        I1(Input 1)
        I2(Input 2)
        I3(Input 3)
    end

    subgraph Hidden_Layer_1
        H1(Hidden 1)
        H2(Hidden 2)
        H3(Hidden 3)
        H4(Hidden 4)
    end

    subgraph Hidden_Layer_2
        H5(Hidden 5)
        H6(Hidden 6)
        H7(Hidden 7)
    end

    subgraph Output_Layer
        O1(Output 1)
        O2(Output 2)
    end

    I1 --> H1
    I1 --> H2
    I1 --> H3
    I1 --> H4
    I2 --> H1
    I2 --> H2
    I2 --> H3
    I2 --> H4
    I3 --> H1
    I3 --> H2
    I3 --> H3
    I3 --> H4

    H1 --> H5
    H1 --> H6
    H1 --> H7
    H2 --> H5
    H2 --> H6
    H2 --> H7
    H3 --> H5
    H3 --> H6
    H3 --> H7
    H4 --> H5
    H4 --> H6
    H4 --> H7

    H5 --> O1
    H5 --> O2
    H6 --> O1
    H6 --> O2
    H7 --> O1
    H7 --> O2

Large fully connected neural network

graph TD
    subgraph Input_Layer
        style Input_Layer fill:#D3D3D3,stroke:#333,stroke-width:2px,stroke-dasharray:5,5
        I1((Input 1))
        I2((Input 2))
        I3((Input 3))
    end

    subgraph Hidden_Layer_1
        style Hidden_Layer_1 fill:#D3D3D3,stroke:#333,stroke-width:2px,stroke-dasharray:5,5
        H1((Hidden 1))
        H2((Hidden 2))
        H3((Hidden 3))
        H4((Hidden 4))
        H5((Hidden 5))
        H6((Hidden 6))
    end

    subgraph Hidden_Layer_2
        style Hidden_Layer_2 fill:#D3D3D3,stroke:#333,stroke-width:2px,stroke-dasharray:5,5
        H7((Hidden 7))
        H8((Hidden 8))
        H9((Hidden 9))
        H10((Hidden 10))
        H11((Hidden 11))
        H12((Hidden 12))
        H13((Hidden 13))
    end

    subgraph Output_Layer
        style Output_Layer fill:#D3D3D3,stroke:#333,stroke-width:2px,stroke-dasharray:5,5
        O1((Output 1))
        O2((Output 2))
        O3((Output 3))
        O4((Output 4))
    end

    I1 --> H1
    I1 --> H2
    I1 --> H3
    I1 --> H4
    I1 --> H5
    I1 --> H6
    I2 --> H1
    I2 --> H2
    I2 --> H3
    I2 --> H4
    I2 --> H5
    I2 --> H6
    I3 --> H1
    I3 --> H2
    I3 --> H3
    I3 --> H4
    I3 --> H5
    I3 --> H6

    H1 --> H7
    H1 --> H8
    H1 --> H9
    H1 --> H10
    H1 --> H11
    H1 --> H12
    H1 --> H13
    H2 --> H7
    H2 --> H8
    H2 --> H9
    H2 --> H10
    H2 --> H11
    H2 --> H12
    H2 --> H13
    H3 --> H7
    H3 --> H8
    H3 --> H9
    H3 --> H10
    H3 --> H11
    H3 --> H12
    H3 --> H13
    H4 --> H7
    H4 --> H8
    H4 --> H9
    H4 --> H10
    H4 --> H11
    H4 --> H12
    H4 --> H13
    H5 --> H7
    H5 --> H8
    H5 --> H9
    H5 --> H10
    H5 --> H11
    H5 --> H12
    H5 --> H13
    H6 --> H7
    H6 --> H8
    H6 --> H9
    H6 --> H10
    H6 --> H11
    H6 --> H12
    H6 --> H13

    H7 --> O1
    H7 --> O2
    H7 --> O3
    H7 --> O4
    H8 --> O1
    H8 --> O2
    H8 --> O3
    H8 --> O4
    H9 --> O1
    H9 --> O2
    H9 --> O3
    H9 --> O4
    H10 --> O1
    H10 --> O2
    H10 --> O3
    H10 --> O4
    H11 --> O1
    H11 --> O2
    H11 --> O3
    H11 --> O4
    H12 --> O1
    H12 --> O2
    H12 --> O3
    H12 --> O4
    H13 --> O1
    H13 --> O2
    H13 --> O3
    H13 --> O4

definition of finite automata A

graph TD
    q0 -->|a| q0
    q0 -->|b| q1
    q1 -->|a| q2
    q1 -->|b| q2
    q2 -->|a| q2
    q2 -->|b| q2
    q0[(>q0)]
    q1[(q1)]
    q2[(q2)]

B

graph TD
    q0 -->|a| q1
    q0 -->|b| q2
    q1 -->|a| q3
    q1 -->|b| q0
    q2 -->|a| q0
    q2 -->|b| q2
    q3 -->|a| q3
    q3 -->|b| q3
    q0[(>q0)]
    q1[(q1)]
    q2[(q2)]
    q3[(q3)]

Math Symbols with MathJax

reference https://jojozhuang.github.io/tutorial/jekyll-math-symbols-with-mathjax/

Showing Math Symbols on Web Page

The support of displaying math symbols with html tags is limited. Though you can use UTF-8 to display some special characters, it is hard to remember them and it is inconvenient to use.

Title Formula HTML Tag
Square n2 n<sup>2</sup>
Square Root √, √ &radic;, or &#8730;
Summary ∑, ∑ &sum;, or &#8721;

MathJax

MathJax is a cross-browser JavaScript library that displays mathematical notation in web browsers.

With mathjax: true you can now enable the rendering of mathjax expressions in your post or page.

1) Example One: Construct the formula with following markdown.

$a^2 + b^2 = c^2$

Then you will get the formula as follows.

$a^2 + b^2 = c^2$

2) Example Two: Construct the formula with following markdown.

$ x = {-b \pm \sqrt{b^2-4ac} \over 2a} $

Then you will get the formula as follows.

$ x = {-b \pm \sqrt{b^2-4ac} \over 2a} $

3) Example Three: Construct the formula with following markdown.

$$\begin{eqnarray}
x' &=& &x \sin\phi &+& z \cos\phi \\
z' &=& - &x \cos\phi &+& z \sin\phi \\
\end{eqnarray}$$

Then you will get the formula as follows.

\[\begin{eqnarray} x' &=& &x \sin\phi &+& z \cos\phi \\ z' &=& - &x \cos\phi &+& z \sin\phi \\ \end{eqnarray}\]

Here are some notes about the above example:

  • The inline formula is between $ ... $.
  • The display formula is between $$ ... $$.
  • You can use the math envrionment directly, for example, \begin{equation}...\end{equation} or \begin{align}...\end{align}.
  • Whenever in the inline math or display math, the star character * must be escaped.
  • In the multi-lines display math, the line break symbol double-backslash \\ should be escaped, i.e., use four backslash \\\\.
  • If you found error while typesetting math formula, try to escape some special characters.

Source code highlighting

some of the supported language identifiers : java, javascript, html, c, cpp, ruby, xml, yaml, json, clojure, smalltalk

```java
    // A method that sorts an array of integers using bubble sort algorithm
    public static void bubbleSort(int[] array) {
        // Get the length of the array
        int n = array.length;
        // Loop through the array from the first element to the second last element
        for (int i = 0; i < n - 1; i++) {
            // Loop through the array from the first element to the last element that is not sorted yet
            for (int j = 0; j < n - i - 1; j++) {
                // Compare the current element with the next element
                if (array[j] > array[j + 1]) {
                    // Swap them if the current element is larger than the next element
                    int temp = array[j];
                    array[j] = array[j + 1];
                    array[j + 1] = temp;
                }
            }
        }
    }
```

    // A method that sorts an array of integers using bubble sort algorithm
    public static void bubbleSort(int[] array) {
        // Get the length of the array
        int n = array.length;
        // Loop through the array from the first element to the second last element
        for (int i = 0; i < n - 1; i++) {
            // Loop through the array from the first element to the last element that is not sorted yet
            for (int j = 0; j < n - i - 1; j++) {
                // Compare the current element with the next element
                if (array[j] > array[j + 1]) {
                    // Swap them if the current element is larger than the next element
                    int temp = array[j];
                    array[j] = array[j + 1];
                    array[j + 1] = temp;
                }
            }
        }
    }

Displaying line numbers for highlighted code

{% highlight java linenos %}
    public class HelloWorld {
        public static void main(String[] args) {
            System.out.println("Hello World!");
        }
    }
{% endhighlight %}

1
2
3
4
5

    public class HelloWorld {
        public static void main(String[] args) {
            System.out.println("Hello World!");
        }
    }
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