Optimizing radiotherapy plans for cancer treatment with Tensor Networks 公式推导解读

资料链接:http://tesi.cab.unipd.it/63583/1/Tesi_LM_P_Cavinato_Samuele.pdf

公式推导

1.列出基本等式,并将原式平方展开

Optimizing radiotherapy plans for cancer treatment with Tensor Networks 公式推导解读

2.对 H 1 H_{1} H1​进行处理, H 1 H_{1} H1​也分为两部分,分别为 H 1 A H_{1}^{A} H1A​, H 1 B H_{1}^{B} H1B​

Optimizing radiotherapy plans for cancer treatment with Tensor Networks 公式推导解读

3.简化 H 1 A H_{1}^{A} H1A​,并得到 H 1 B H_{1}^{B} H1B​

Optimizing radiotherapy plans for cancer treatment with Tensor Networks 公式推导解读

4.简化 H 1 B H_{1}^{B} H1B​

Optimizing radiotherapy plans for cancer treatment with Tensor Networks 公式推导解读

5.对 H 2 H_{2} H2​进行处理,简化并引入常数项

Optimizing radiotherapy plans for cancer treatment with Tensor Networks 公式推导解读

6.对 H H H进行汇总

Optimizing radiotherapy plans for cancer treatment with Tensor Networks 公式推导解读

7.将 H H H重新排列为伊辛形式

Optimizing radiotherapy plans for cancer treatment with Tensor Networks 公式推导解读

Optimizing radiotherapy plans for cancer treatment with Tensor Networks 公式推导解读

8.伊辛形式是由等式相加整合得到

Optimizing radiotherapy plans for cancer treatment with Tensor Networks 公式推导解读

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