朴素矩阵乘法内核
二维索引基线及其局限
朴素矩阵乘法内核 是 CoddyKit 上的免费 CUDA Academy 课时。 这是第 1 节课，共 4 节。 你可以在下方免费阅读本课时的完整内容 — 然后在浏览器中使用内置代码编辑器和全天候 AI 导师进行实践。 这是 CUDA Academy 学习路径的一部分，你的进度在网页和 CoddyKit 应用中同步。 CUDA Academy 课程共包含 4 节课。
本课时的部分内容尚未翻译，以英文显示。
Matrix Multiply, GPU Style
Matrix multiplication is the heart of graphics and AI. Today you build a naive GPU version first, then learn why it leaves speed on the table.
The Math in One Line
Each output cell C[row][col] is a dot product: multiply a full row of A by a full column of B and sum the results. 🧮
C[row][col] = sum over k of A[row][k] * B[k][col]One Thread per Output
The simplest plan gives each thread one output element of C. Thousands of cells get computed at the same time across the GPU.
A 2D Grid of Threads
Since C is a 2D grid, you launch threads in two dimensions. The x index maps to a column and the y index maps to a row.
dim3 threads(16, 16);
dim3 blocks((N+15)/16, (N+15)/16);Finding This Thread's Cell
Inside the kernel, each thread computes its own row and col from its block and thread indices, just like 1D indexing but on both axes.
int row = blockIdx.y*blockDim.y + threadIdx.y;
int col = blockIdx.x*blockDim.x + threadIdx.x;The Bounds Check
Grids round up, so some threads fall outside the matrix. Guard with if (row < N && col < N) before you touch memory.
if (row < N && col < N) {
// safe to compute
}The Inner Loop
Each thread runs a loop over k, accumulating products into a local sum. That local variable lives in a fast register.
float sum = 0.0f;
for (int k = 0; k < N; ++k)
sum += A[row*N+k] * B[k*N+col];Writing the Result
After the loop finishes, the thread stores its accumulated sum into C exactly once. One thread, one clean write.
C[row*N + col] = sum;Row-Major Flattening
The matrix is a flat 1D array, so you index it as row*N + col. Getting this layout right is half the battle in matmul.
Why It Works, But Slowly
This kernel is correct and easy to read, but every thread reads its row and column straight from global memory, the slowest space.
The Hidden Cost
Neighboring threads re-read the same A rows and B columns over and over. That wasted memory traffic is exactly what tiling will fix next.
Quick Check
Think about how the naive kernel maps work to threads.
Recap
You mapped one thread to one output cell, looped over k from global memory, and saw the redundant reads. Next you cut that traffic with tiling. 🚀
常见问题解答
「朴素矩阵乘法内核」课时是免费的吗？
是的 — 「朴素矩阵乘法内核」的完整文本可在网页上免费阅读。要进行交互式练习（内置代码编辑器和全天候 AI 导师）并解锁 CUDA Academy 课程的其余内容，请升级到 CoddyKit PRO。 CUDA Academy 课程共包含 4 节课。
「朴素矩阵乘法内核」这节课中我会学到什么？
二维索引基线及其局限 你通过在浏览器中直接运行的动手代码来练习 CUDA Academy，全天候 AI 导师会在你学习这节课的过程中回答你的问题。
学习 CUDA Academy 需要有经验吗？
无需任何先前经验。CoddyKit 上的 CUDA Academy 课程适合初学者到高级学习者，你可以从这里开始或从头开始，按照自己的节奏学习。 这是第 1 节课，共 4 节。
「朴素矩阵乘法内核」课时需要多长时间？
大多数 CoddyKit 课程大约需要 5–10 分钟。每节课都很精短且互动，所以你能稳步进步，并在网页和应用中从离开的地方继续。
我能在这节 CUDA Academy 课中编写并运行代码吗？
能。每节 CUDA Academy 课都包含内置代码编辑器，你可以在浏览器中直接编写并运行真实代码，并获得即时 AI 反馈 — 无需本地设置。