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tags: Meeting
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# **Appetite Transition Analysis**

## Outline
[TOC]

## **Markov Chain Setup**

### **How many steps I need to consider?**
> 當我拿到Transition Probability Matrix(以下簡稱TPM)時，我可以先初估到底要走幾步會達到stable state，提早知道後才不會浪費電腦運算過多或是過少的steps。
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- 由上圖可知，這三個狀態在走了三步後都到達了stable state

### **Time information encoding in TPM**
> 接下來就是要進行Markov Chain的部分了，也就是要讓此Matrix同時含有過去的+現在的information，也就是matrix ** steps 的概念，如下圖。
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> 知道怎麼算後，我們就能看看我們自己算出的TPM長甚麼樣子(用Heat map展示)
- **Baseline**:
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- **Inhibition**:
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- **Control**:
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### **The correlation between different TPMs**
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## Markov Chain Analysis (Random Walk)
:::warning
In this chapter, I will show two different types of Markov Chain
:::

### Random output Sample

nstate = 5
ntest = 5000 # test的數量
nstep = 4 # 走4步
state_0 =  np.zeros((1, ntest, nstate))
lis = [0,1,2,3,4]
# initialized
i = 0
while i < ntest:
    avoid = np.random.choice(lis, 50, True) # in order to avoid [0, 0, 0, ...]
    for j in range(0, len(avoid)):
        state_0[0][i][avoid[j]] += 1
    state_0[0][i] /= len(avoid)
    i += 1

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### Markov Result
#### Mine(keep matrix)

def Result(mat: np.ndarray, nstate ,ntest: int, nstep: int, state_0: np.ndarray):
    #Get TPM
    TPM = np.ndarray((nstep, nstate, nstate))
    for step in range(0, nstep ): 
        TPM[step] = get_TPM(mat, step + 1) #加一是因為step從1開始
    
    #print(TPM)
    Result_Mat = np.ndarray((ntest, nstep, nstate))
    
    for i in range(0, ntest):
        for j in range(0, nstep):
            Result_Mat[i, j, : ] = markove_choose(TPM[j], state_0[0][i])
    return Result_Mat

#### Mark(get state every step)

def Result_Mark(mat: np.ndarray, nstate, ntest: int, nstep: int, state_0: np.ndarray):
        
    Result_Mat = np.ndarray((ntest, nstep, nstate))
    current = state_0
    
    for i in range(0, ntest):
        for j in range(0, nstep):
            #print(current[0][i])
            current[0][i] = markove_Mark(mat, current[0][i])
            Result_Mat[i, j, : ] = current[0][i]
            
    return Result_Mat

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