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## Numpy Dot Product

To compute dot product of numpy nd arrays, you can use numpy.dot() function.

numpy.dot() functions accepts two numpy arrays as arguments, computes their dot product and returns the result.

### Syntax – numpy.dot()

The syntax of numpy.dot() function is

`numpy.dot(a, b, out=None)`

Parameter | Description |
---|---|

a | [mandatory] First argument for dot product operation. |

b | [mandatory] Second argument for dot product operation. |

out | [optional] This argument is used for performance. This has to be a C-contiguous array, and the dtype must be the dtype that would be returned for dot(a,b). |

### Behavior of numpy.dot() based on Input Array Dimensions

The following table specifies the type of operation done based on the dimensions of input arrays: a and b.

Dimension of ‘a’ and ‘b’ | Output |
---|---|

Zero-Dimension (Scalar) | Multiplication of two scalars, a and b. |

One-Dimensional Arrays (Vector) | Inner product of vectors. |

Two-Dimensional Arrays (Matrix) | Matrix Multiplication. |

a: N-Dimensional Array b: 1-D Array | Sum product over the last axis of a and b. |

a: N-Dimensional Array b: M-Dimensional Array (M>=2) | Sum product over the last axis of a and second-to-last axis of b. |

### Example 1: Numpy Dot Product of Scalars

In this example, we take two scalars and calculate their dot product using numpy.dot() function. Dot product using numpy.dot() with two scalars as arguments return multiplication of the two scalars.

**Python Program**

```
import numpy as np
a = 3
b = 4
output = np.dot(a,b)
print(output)
```

Run **Output**

`12`

**Explanation**

```
output = a * b
= 3 * 4
= 12
```

### Example 2: Numpy Dot Product of 1D Arrays (Vectors)

In this example, we take two numpy one-dimensional arrays and calculate their dot product using numpy.dot() function. We already know that, if input arguments to dot() method are one-dimensional, then the output would be inner product of these two vectors (since these are 1D arrays).

**Python Program**

```
import numpy as np
#initialize arrays
A = np.array([2, 1, 5, 4])
B = np.array([3, 4, 7, 8])
#dot product
output = np.dot(A, B)
print(output)
```

Run **Output**

`77`

**Dot Product**

```
output = [2, 1, 5, 4].[3, 4, 7, 8]
= 2*3 + 1*4 + 5*7 + 4*8
= 77
```

### Example 3: Numpy Dot Product of 2-D Arrays (Matrix)

In this example, we take two two-dimensional numpy arrays and calculate their dot product. Dot product of two 2-D arrays returns matrix multiplication of the two input arrays.

**Python Program**

```
import numpy as np
#initialize arrays
A = np.array([[2, 1], [5, 4]])
B = np.array([[3, 4], [7, 8]])
#dot product
output = np.dot(A, B)
print(output)
```

Run **Output**

```
[[13 16]
[43 52]]
```

**Dot Product**

```
output = [[2, 1], [5, 4]].[[3, 4], [7, 8]]
= [[2*3+1*7, 2*4+1*8], [5*3+4*7, 5*4+4*8]]
= [[13, 16], [43, 52]]
```

### Summary

In this tutorial of Python Examples, we learned how to calculate the dot product of numpy arrays, with the help of well detailed example programs.