> ## Documentation Index
> Fetch the complete documentation index at: https://docs.flatkey.ai/llms.txt
> Use this file to discover all available pages before exploring further.

# 嵌入 — POST /v1/embeddings

> 使用 POST /v1/embeddings 为文本生成向量嵌入。支持批量输入和多种嵌入模型，可用于语义搜索、聚类和 RAG。

`/v1/embeddings` 端点为文本输入生成向量嵌入。嵌入以高维浮点数组表示文本的语义，可用于相似度搜索、聚类和检索增强生成（RAG）。此端点兼容 OpenAI Embeddings API。

## 端点

```
POST https://router.flatkey.ai/v1/embeddings
```

## 支持的嵌入模型

| 模型                       | 维度   | 供应商    |
| ------------------------ | ---- | ------ |
| `gemini-embedding-001`   | 3072 | Google |
| `text-embedding-3-small` | 1536 | OpenAI |
| `text-embedding-3-large` | 3072 | OpenAI |

当前可用情况和价格请参阅[模型目录](/zh/reference/model-list)。

## 请求

### 请求头

| 请求头             | 值                         |
| --------------- | ------------------------- |
| `Authorization` | `Bearer $FLATKEY_API_KEY` |
| `Content-Type`  | `application/json`        |

### 请求体参数

<ParamField body="model" type="string" required>
  嵌入模型 ID。例如：`"gemini-embedding-001"`、`"text-embedding-3-small"`。
</ParamField>

<ParamField body="input" type="string | array" required>
  要进行嵌入的文本。可以是单个字符串，也可以是用于批量嵌入的字符串数组。
</ParamField>

<ParamField body="encoding_format" type="string">
  `"float"`（默认）返回浮点数组；`"base64"` 返回 Base64 编码的字符串。
</ParamField>

<ParamField body="dimensions" type="integer">
  输出嵌入的维度数。并非所有模型都支持此参数。
</ParamField>

## 请求示例

<CodeGroup>
  ```python python theme={null}
  import os
  from openai import OpenAI

  client = OpenAI(
      api_key=os.environ["FLATKEY_API_KEY"],
      base_url="https://router.flatkey.ai/v1",
  )

  # Single text
  response = client.embeddings.create(
      model="gemini-embedding-001",
      input="The quick brown fox jumps over the lazy dog",
  )

  embedding = response.data[0].embedding
  print(f"Embedding dimensions: {len(embedding)}")
  print(f"First 5 values: {embedding[:5]}")
  ```

  ```python python batch theme={null}
  import os
  from openai import OpenAI

  client = OpenAI(
      api_key=os.environ["FLATKEY_API_KEY"],
      base_url="https://router.flatkey.ai/v1",
  )

  # Batch embedding
  texts = [
      "What is machine learning?",
      "How does neural network training work?",
      "Explain gradient descent",
  ]

  response = client.embeddings.create(
      model="gemini-embedding-001",
      input=texts,
  )

  for i, item in enumerate(response.data):
      print(f"{texts[i]}: {len(item.embedding)} dimensions")
  ```

  ```bash curl theme={null}
  curl https://router.flatkey.ai/v1/embeddings \
    -H "Authorization: Bearer $FLATKEY_API_KEY" \
    -H "Content-Type: application/json" \
    -d '{
      "model": "gemini-embedding-001",
      "input": "The quick brown fox jumps over the lazy dog"
    }'
  ```
</CodeGroup>

## 响应

```json theme={null}
{
  "object": "list",
  "data": [
    {
      "object": "embedding",
      "index": 0,
      "embedding": [0.0023064255, -0.009327292, ...]
    }
  ],
  "model": "gemini-embedding-001",
  "usage": {
    "prompt_tokens": 9,
    "total_tokens": 9
  }
}
```

### 响应字段

<ResponseField name="data" type="array">
  嵌入对象数组，每个输入字符串对应一个对象。

  <Expandable title="嵌入对象">
    <ResponseField name="index" type="integer">在输入数组中的位置。</ResponseField>
    <ResponseField name="embedding" type="array">嵌入向量的浮点数组。</ResponseField>
  </Expandable>
</ResponseField>

<ResponseField name="usage.prompt_tokens" type="integer">
  已处理的 token 数量。
</ResponseField>

## 余弦相似度示例

```python python theme={null}
import os
import numpy as np
from openai import OpenAI

client = OpenAI(
    api_key=os.environ["FLATKEY_API_KEY"],
    base_url="https://router.flatkey.ai/v1",
)

def embed(text):
    return client.embeddings.create(
        model="gemini-embedding-001",
        input=text,
    ).data[0].embedding

def cosine_similarity(a, b):
    a, b = np.array(a), np.array(b)
    return np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))

q = embed("capital city of France")
doc1 = embed("Paris is the capital and most populous city of France.")
doc2 = embed("The Eiffel Tower is a famous landmark.")

print(cosine_similarity(q, doc1))  # higher — more relevant
print(cosine_similarity(q, doc2))  # lower
```