creating numerical arrays with logic

 

**Title: Navigating Numerical Spaces with NumPy: arange vs linspace vs logspace**

When it comes to generating numerical sequences in Python, NumPy offers a plethora of options, each tailored to specific needs. Among these, `arange`, `linspace`, and `logspace` stand out as versatile tools for crafting arrays. Let’s embark on a journey through these functions, exploring their nuances and applications! 🚀

### The Basics: arange

NumPy’s `arange` function is akin to Python’s built-in `range`, but with the added capability of generating arrays with non-integer steps. It’s your go-to tool for creating sequences with regular spacing.

```python

import numpy as np

# Syntax: np.arange(start, stop, step)

arr = np.arange(0, 10, 2)

print(arr) # Output: [0 2 4 6 8]

```

think of it as points in an closed/open interval

[a,b) with step s between each point 

🧩 **Use Case**: When you need control over the step size and want a compact syntax.

### The Uniform Choice: linspace

`linspace` divides a specified range into a given number of equally spaced points. It’s perfect for scenarios requiring uniform sampling, such as plotting functions or interpolating data.

```python

# Syntax: np.linspace(start, stop, num)

arr = np.linspace(0, 10, 5)

print(arr) # Output: [ 0. 2.5 5. 7.5 10. ]

```

📏 **Use Case**: Visualizations, interpolation, and scenarios demanding evenly spaced points.

### Scaling Up: logspace

Need points spaced evenly on a logarithmic scale? Enter `logspace`. This function generates numbers spaced evenly on a logarithmic scale, making it indispensable for tasks involving orders of magnitude.

```python

# Syntax: np.logspace(start, stop, num, base)

arr = np.logspace(1, 3, 4, base=10)

print(arr) # Output: [ 10. 100. 1000. 10000.]

```

🔢 **Use Case**: Logarithmic scales, such as frequency bands in signal processing or plotting exponential growth.

### The Verdict

Choosing the right tool depends on your specific needs:

- 🧩 `arange`: For fine-grained control over step size.

- 📏 `linspace`: When uniform spacing is paramount.

- 🔢 `logspace`: When working with logarithmic scales or exponential growth.

### Conclusion

NumPy’s `arange`, `linspace`, and `logspace` functions are indispensable companions in the world of numerical computing. By understanding their differences and applications, you can navigate numerical spaces with confidence, unlocking new possibilities in your Python projects. So, whether you’re traversing linear grids or exploring logarithmic realms, NumPy has you covered! 🌟

### beyond 

create your own logic with a formation law

n=100

arr=np.zeros(n)

for i in range(n):

  arr[i] = f (arr, i,n) # any function that can depend on the previous values in arr, on the counter i and the size n

or

lis=[]

i=0

while True:

  item = f(lis,i)

  if condition_accept (item,i):

    lis.append( item )

    i+=1

elif condition_skip:

  continue 

else: #stop

  break

# finally

n=len(lis)

arr=np.array(lis)

interactive example:

(coming soon)