🎯要点

使用英伟达GPU、大都会和并行回火算法模拟蒙特卡洛。
使用兰佐斯算法计算传输矩阵特征值。
使用 Suzuki-Trotter 公式归一化量子无序系统。
算法模型特征：多CUDA线程，多GPU和多任务式并行计算。

🍁磁态分析角度

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   commit id:"传输矩阵"
   commit id:"多GPU"
   commit id:"多CUDA线程"
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   commit id:"量子近似优化"
   commit id:"小规模磁态训练"
   commit id:"贪婪算法"
   commit id:"模拟退火算法"
   commit id:"并行回火算法"
   commit id:"图神经网络"
   commit id:"机器学习"
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磁态分析角度.png

🍪语言内容分比

pie title 语言分比
 "CUDA":90
 "C":60

pie title 内容分比
 "算法模型":90
 "凝聚态物理学、量子物理":80
 "数学、矩阵":60
 "蒙特卡洛模拟":60
 "GPU、多任务并行计算":50

✂️梗概

🍇CUDA矩阵乘法二维块平铺实现

从数学上讲，给定一个广义矩阵乘法运算 $D=A B+C$，其中 $D \in R ^{m \times n}, A \in R ^{m \times k}, B \in R ^{k \times n}, C \in R ^{m \times n}$，矩阵可以分成更小的矩阵。

$$ A=\left[\begin{array}{cccc} A_{1,1}^{d_{b m} \times d_{b k}} & A_{1,2}^{d_{b m} \times d_{b k}} & \ldots & A_{1, k}^{d_{m m} \times d_{b k}} \\ A_{2,1}^{d_{m m} \times d_{b k}} & A_{2,2}^{d_{b m} \times d_{b k}} & \cdots & A_{2, k / d_{b k}}^{d_{b m} \times d_{b k}} \\ \vdots & \vdots & \ddots & \vdots \\ A_{m / d_{m m}, 1}^{d_{m b} \times d_{b k}} & A_{m / d_{m m}, 2}^{d_{b m} \times d_{b k}} & \cdots & A_{m / d_{b m}, k / d_{b k}}^{d_{b m} \times d_{b k}} \end{array}\right] $$

$$ B=\left[\begin{array}{cccc} B_{1,1}^{d_{b k} \times d_{b n}} & B_{1,2}^{d_{b k} \times d_{b n}} & \ldots & B_{1, n / d_{b n}}^{d_{b k} \times d_{b n}} \\ B_{2,1}^{d_{b k} \times d_{b n}} & B_{2,2}^{d_{b k} \times d_{b n}} & \ldots & B_{2, n / d_{b n}}^{d_{b k} \times d_{b n}} \\ \vdots & \vdots & \ddots & \vdots \\ B_{k / d_{b k}, 1}^{d_{b k} d_{b n}} & B_{k / d_{b k}, 2}^{d_{b k} \times d_{b n}} & \cdots & B_{k / d_{b k}, n / d_{b n}}^{d_{b k} \times d_{b n}} \end{array}\right] $$

$$ C=\left[\begin{array}{cccc} C_{1,1}^{d_{b m} \times d_{b n}} & C_{1,2}^{d_{b m} \times d_{b n}} & \ldots & C_{1, n / d_{b n}}^{d_{b m} \times d_{b n}} \\ C_{2,1}^{d_{b m} \times d_{b n}} & C_{2,2}^{d_{b m} \times d_{b n}} & \ldots & C_{2, n / d_{b n}}^{d_{b m} \times d_{m n}} \\ \vdots & \vdots & \ddots & \vdots \\ C_{m / d_{b m}, 1}^{d_{b m} \times d_{l n}} & C_{m / d_{b m}, 2}^{d_{b n} \times d_{b n}} & \cdots & C_{m / d_{b m}, n / d_{b n}}^{d_{b m} \times d_{b n}} \end{array}\right] $$