From 2e34a26e0c34c3175276a12f70b2e0289e5c192b Mon Sep 17 00:00:00 2001
From: Bryan Lozano <b.lozano.havoc@gmail.com>
Date: Thu, 21 Mar 2024 14:44:41 -0700
Subject: [PATCH 1/3] Update README.md

Correcting matrix multiplication expected result.
---
 examples/simple/README.md | 31 ++++++++++++++++++++++++++++---
 1 file changed, 28 insertions(+), 3 deletions(-)

diff --git a/examples/simple/README.md b/examples/simple/README.md
index ba3a4fd1a..37db48249 100644
--- a/examples/simple/README.md
+++ b/examples/simple/README.md
@@ -2,6 +2,19 @@
 
 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.
 
+Normally in matrix multiplication...
+
+$$
+A * B = C
+$$
+
+In `ggml` the weight matrix is already transposed.
+
+So your inputs are: $$A \text{ and } B^T$$  
+And the output is: $$C^T$$
+
+Let's look at a traditional matrix multiplication:
+
 $$
 \begin{bmatrix}
 2 & 8 \\
@@ -16,9 +29,21 @@ $$
 \end{bmatrix}
 \=
 \begin{bmatrix}
-60 & 110 & 54 & 29 \\
-55 & 90 & 126 & 28 \\
-50 & 54 & 42 & 64 \\
+60 & 90 & 42 \\
+55 & 54 & 29 \\
+50 &  54 & 28 \\
+110 & 126 & 64 \\
+\end{bmatrix}
+$$
+
+In `ggml` the second matrix above will be stored transposed in memory, and the output will also be transposed in memory.  
+So `ggml` will yield:
+
+$$
+\begin{bmatrix}
+60 & 55 & 50 & 110 \\
+90 & 54 & 54 & 126 \\
+42 & 29 & 28 & 64 \\
 \end{bmatrix}
 $$
 

From 084da3422b3bbc02e632f819390dc07f0d4eaa62 Mon Sep 17 00:00:00 2001
From: Bryan Lozano <b.lozano.havoc@gmail.com>
Date: Thu, 21 Mar 2024 14:54:47 -0700
Subject: [PATCH 2/3] Update simple-ctx.cpp

Fix incorrect striding through output.
---
 examples/simple/simple-ctx.cpp | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/examples/simple/simple-ctx.cpp b/examples/simple/simple-ctx.cpp
index d331a4c1f..b2d4e4ba5 100644
--- a/examples/simple/simple-ctx.cpp
+++ b/examples/simple/simple-ctx.cpp
@@ -104,9 +104,9 @@ int main(void) {
     memcpy(out_data.data(), result->data, ggml_nbytes(result));
 
     // expected result:
-    // [ 60.00 110.00 54.00 29.00
-    //  55.00 90.00 126.00 28.00
-    //  50.00 54.00 42.00 64.00 ]
+    // [ 60.00 55.00 50.00 110.00
+    //   90.00 54.00 54.00 126.00
+    //   42.00 29.00 28.00 64.00 ]
 
     printf("mul mat (%d x %d) (transposed result):\n[", (int) result->ne[0], (int) result->ne[1]);
     for (int j = 0; j < result->ne[1] /* rows */; j++) {
@@ -115,7 +115,7 @@ int main(void) {
         }
 
         for (int i = 0; i < result->ne[0] /* cols */; i++) {
-            printf(" %.2f", out_data[i * result->ne[1] + j]);
+            printf(" %.2f", out_data[j * result->ne[0] + i]);
         }
     }
     printf(" ]\n");

From 858945dffbf5a712c31e72ff57a5fa4c396781b2 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Fri, 22 Mar 2024 09:16:32 +0200
Subject: [PATCH 3/3] simple : update readme

---
 examples/simple/README.md | 33 ++++++++++++++++++++++-----------
 1 file changed, 22 insertions(+), 11 deletions(-)

diff --git a/examples/simple/README.md b/examples/simple/README.md
index 37db48249..28c549fc9 100644
--- a/examples/simple/README.md
+++ b/examples/simple/README.md
@@ -2,19 +2,12 @@
 
 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.
 
-Normally in matrix multiplication...
+Traditional matrix multiplication goes like this (multiply row-by-column):
 
 $$
-A * B = C
+A \times B = C
 $$
 
-In `ggml` the weight matrix is already transposed.
-
-So your inputs are: $$A \text{ and } B^T$$  
-And the output is: $$C^T$$
-
-Let's look at a traditional matrix multiplication:
-
 $$
 \begin{bmatrix}
 2 & 8 \\
@@ -36,10 +29,28 @@ $$
 \end{bmatrix}
 $$
 
-In `ggml` the second matrix above will be stored transposed in memory, and the output will also be transposed in memory.  
-So `ggml` will yield:
+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 \\