initial release

ggml/examples/simple/README.md

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+## Simple
+
+This example simply performs a matrix multiplication, solely for the purpose of demonstrating a basic usage of ggml and backend handling. The code is commented to help understand what each part does.
+
+Traditional matrix multiplication goes like this (multiply row-by-column):
+
+$$
+A \times B = C
+$$
+
+$$
+\begin{bmatrix}
+2 & 8 \\
+5 & 1 \\
+4 & 2 \\
+8 & 6 \\
+\end{bmatrix}
+\times
+\begin{bmatrix}
+10 & 9 & 5 \\
+5 & 9 & 4 \\
+\end{bmatrix}
+\=
+\begin{bmatrix}
+60 & 90 & 42 \\
+55 & 54 & 29 \\
+50 &  54 & 28 \\
+110 & 126 & 64 \\
+\end{bmatrix}
+$$
+
+In `ggml`, we pass the matrix $B$ in transposed form and multiply row-by-row. The result $C$ is also transposed:
+
+$$
+ggml\\_mul\\_mat(A, B^T) = C^T
+$$
+
+$$
+ggml\\_mul\\_mat(
+\begin{bmatrix}
+2 & 8 \\
+5 & 1 \\
+4 & 2 \\
+8 & 6 \\
+\end{bmatrix}
+,
+\begin{bmatrix}
+10 & 5 \\
+9 & 9 \\
+5 & 4 \\
+\end{bmatrix}
+)
+\=
+\begin{bmatrix}
+60 & 55 & 50 & 110 \\
+90 & 54 & 54 & 126 \\
+42 & 29 & 28 & 64 \\
+\end{bmatrix}
+$$
+
+The `simple-ctx` doesn't support gpu acceleration. `simple-backend` demonstrates how to use other backends like CUDA and Metal.