Numpy is a Python package that allows you to create an array that makes mathematical calculations very easy. There are many functions for creating an numpy array in Python and numpy.linspace() is one of them. In this tutorial, you will learn how to use numpy linspace function in Python.

## What is linspace in Numpy?

The numpy.linspace is a function in the NumPy library that allows you to create an array of evenly spaced values over a specified range. The syntax for numpy.linspace is as follows

```
numpy.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0)
```

Below is the explanation of the numpy linspace syntax.

**start:** The starting value of the sequence.**stop:** The end value of the sequence.**num: **The number of evenly spaced values to generate. The default is 50.**endpoint: **If True, stop is the last value in the range. If False, the range does not include a stop. Default is True.**retstep:** If True, return the step size between the values. The default is False.**dtype:** The data type of the output array. If not specified, the data type is inferred from the input values.

axis: The axis in the result along which the linspace samples are stored. The default is 0.

## Create a sample numpy linspace

```
import numpy as np
# Generate an array of 10 evenly spaced values between 0 and 1 (inclusive)
arr = np.linspace(0, 20, num=10)
print(arr)
```

**Output**

```
[ 0. 2.22222222 4.44444444 6.66666667 8.88888889 11.11111111
13.33333333 15.55555556 17.77777778 20.]
```

Note: The step size between the values is calculated based on the specified number of points (num) and the range (start to stop). If retstep is set to True, the function will return both the array and the step size.

## Plot a Graph of numpy linspace using matplotlib

The numpy and matplotlib packages are often used together in scientific computing and data visualization. You can use the numpy.linspace for creating data for plotting. On the other hand, matplotlib is a popular plotting library in Python.

Below is an example of using numpy.linspace along with matplotlib to create a simple plot.

```
import numpy as np
import matplotlib.pyplot as plt
# Generate 100 evenly spaced values between 0 and 2π (inclusive)
x = np.linspace(0, 2 * np.pi, 100)
# Calculate the corresponding y values using a function, e.g., sin(x)
y = np.sin(x)
# Create a plot
plt.plot(x, y, label='sin(x)')
# Add labels and a legend
plt.xlabel('x')
plt.ylabel('y')
plt.title('Plot of sin(x)')
plt.legend()
# Display the plot
plt.show()
```

**Output**

## Application of the Numpy linspace function

The numpy.linspace has various applications across different domains, as it can generate evenly spaced values within a specified range. Here are some common applications:

### Data Visualization with Matplotlib

- numpy.linspace is often used to generate x-values for creating smooth plots and curves.
- It allows you to create more data points for a function to make the resulting plot look smoother.

```
import numpy as np
import matplotlib.pyplot as plt
# Generate x values
x = np.linspace(0, 10, 100)
# Example function: quadratic equation
y = x**2
# Plotting
plt.plot(x, y)
plt.show()
```

**Output**

### Signal Processing

- In signal processing, generating evenly spaced values is useful for creating time vectors.
- The linspace is often used in the analysis and visualization of signals.

```
import numpy as np
# Generate time vector for signal processing
time_vector = np.linspace(0, 1, 1000) # 1000 points from 0 to 1
print(time_vector )
```

### Machine Learning

In machine learning, when splitting data into training and testing sets, numpy.linspace can be used to create indices for random sampling or to divide data into specific ranges.

```
import numpy as np
# Generating indices for train-test split
total_samples = 1000
train_indices = np.linspace(0, total_samples-1, 800, dtype=int)
test_indices = np.setdiff1d(np.arange(total_samples), train_indices)
```

### Physics and Engineering Simulations

In simulations, particularly in physics and engineering, numpy.linspace is used to define a range of values for parameters or time steps.

```
import numpy as np
# Define time steps for a simulation
time_steps = np.linspace(0, 10, 1000)
```

### Numerical Analysis

In numerical analysis, when solving differential equations or integrating functions, numpy.linspace helps in defining a range of values over which the computation is performed.

```
import numpy as np
from scipy.integrate import odeint
# Define time points for solving ODEs
time_points = np.linspace(0, 10, 100)
```

## Conclusion

In this tutorial, you have learned the syntax of the numpy.linspace() function. You have also to know how to use the numpy.linspace() function using simple example and at last learned what are its applications in real life.

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