Add DotProduct Method and README Example for Embedding Similarity Search (#492)

* Add DotProduct Method and README Example for Embedding Similarity Search

- Implement a DotProduct() method for the Embedding struct to calculate the dot product between two embeddings.
- Add a custom error type for vector length mismatch.
- Update README.md with a complete example demonstrating how to perform an embedding similarity search for user queries.
- Add unit tests to validate the new DotProduct() method and error handling.

* Update README to focus on Embedding Semantic Similarity

Author: ealvar3z

README.md

@@ -483,6 +483,62 @@ func main() {
 ```
 </details>
 
+<detail>
+<summary>Embedding Semantic Similarity</summary>
+
+```go
+package main
+
+import (
+	"context"
+	"log"
+	openai "github.com/sashabaranov/go-openai"
+
+)
+
+func main() {
+	client := openai.NewClient("your-token")
+
+	// Create an EmbeddingRequest for the user query
+	queryReq := openai.EmbeddingRequest{
+		Input: []string{"How many chucks would a woodchuck chuck"},
+		Model: openai.AdaEmbeddingv2,
+	}
+
+	// Create an embedding for the user query
+	queryResponse, err := client.CreateEmbeddings(context.Background(), queryReq)
+	if err != nil {
+		log.Fatal("Error creating query embedding:", err)
+	}
+
+	// Create an EmbeddingRequest for the target text
+	targetReq := openai.EmbeddingRequest{
+		Input: []string{"How many chucks would a woodchuck chuck if the woodchuck could chuck wood"},
+		Model: openai.AdaEmbeddingv2,
+	}
+
+	// Create an embedding for the target text
+	targetResponse, err := client.CreateEmbeddings(context.Background(), targetReq)
+	if err != nil {
+		log.Fatal("Error creating target embedding:", err)
+	}
+
+	// Now that we have the embeddings for the user query and the target text, we
+	// can calculate their similarity.
+	queryEmbedding := queryResponse.Data[0]
+	targetEmbedding := targetResponse.Data[0]
+
+	similarity, err := queryEmbedding.DotProduct(&targetEmbedding)
+	if err != nil {
+		log.Fatal("Error calculating dot product:", err)
+	}
+
+	log.Printf("The similarity score between the query and the target is %f", similarity)
+}
+
+```
+</detail>
+
 <details>
 <summary>Azure OpenAI Embeddings</summary>
 

embeddings.go

@@ -4,10 +4,13 @@ import (
 	"context"
 	"encoding/base64"
 	"encoding/binary"
+	"errors"
 	"math"
 	"net/http"
 )
 
+var ErrVectorLengthMismatch = errors.New("vector length mismatch")
+
 // EmbeddingModel enumerates the models which can be used
 // to generate Embedding vectors.
 type EmbeddingModel int
@@ -124,6 +127,23 @@ type Embedding struct {
 	Index     int       `json:"index"`
 }
 
+// DotProduct calculates the dot product of the embedding vector with another
+// embedding vector. Both vectors must have the same length; otherwise, an
+// ErrVectorLengthMismatch is returned. The method returns the calculated dot
+// product as a float32 value.
+func (e *Embedding) DotProduct(other *Embedding) (float32, error) {
+	if len(e.Embedding) != len(other.Embedding) {
+		return 0, ErrVectorLengthMismatch
+	}
+
+	var dotProduct float32
+	for i := range e.Embedding {
+		dotProduct += e.Embedding[i] * other.Embedding[i]
+	}
+
+	return dotProduct, nil
+}
+
 // EmbeddingResponse is the response from a Create embeddings request.
 type EmbeddingResponse struct {
 	Object string         `json:"object"`

embeddings_test.go

@@ -4,7 +4,9 @@ import (
 	"bytes"
 	"context"
 	"encoding/json"
+	"errors"
 	"fmt"
+	"math"
 	"net/http"
 	"reflect"
 	"testing"
@@ -233,3 +235,39 @@ func TestEmbeddingResponseBase64_ToEmbeddingResponse(t *testing.T) {
 		})
 	}
 }
+
+func TestDotProduct(t *testing.T) {
+	v1 := &Embedding{Embedding: []float32{1, 2, 3}}
+	v2 := &Embedding{Embedding: []float32{2, 4, 6}}
+	expected := float32(28.0)
+
+	result, err := v1.DotProduct(v2)
+	if err != nil {
+		t.Errorf("Unexpected error: %v", err)
+	}
+
+	if math.Abs(float64(result-expected)) > 1e-12 {
+		t.Errorf("Unexpected result. Expected: %v, but got %v", expected, result)
+	}
+
+	v1 = &Embedding{Embedding: []float32{1, 0, 0}}
+	v2 = &Embedding{Embedding: []float32{0, 1, 0}}
+	expected = float32(0.0)
+
+	result, err = v1.DotProduct(v2)
+	if err != nil {
+		t.Errorf("Unexpected error: %v", err)
+	}
+
+	if math.Abs(float64(result-expected)) > 1e-12 {
+		t.Errorf("Unexpected result. Expected: %v, but got %v", expected, result)
+	}
+
+	// Test for VectorLengthMismatchError
+	v1 = &Embedding{Embedding: []float32{1, 0, 0}}
+	v2 = &Embedding{Embedding: []float32{0, 1}}
+	_, err = v1.DotProduct(v2)
+	if !errors.Is(err, ErrVectorLengthMismatch) {
+		t.Errorf("Expected Vector Length Mismatch Error, but got: %v", err)
+	}
+}