arange and linspace¶

NumPy provides two primary functions for generating sequences of numbers: np.arange for integer steps and np.linspace for evenly spaced floats.

np.arange Function¶

Generates values within a half-open interval [start, stop) with a given step.

1. Single Argument¶

```python import numpy as np

def main(): a = np.arange(9) print("np.arange(9)") print(a)

if name == "main": main() ```

Output:

np.arange(9) [0 1 2 3 4 5 6 7 8]

2. Two Arguments¶

```python import numpy as np

def main(): a = np.arange(1, 9) print("np.arange(1, 9)") print(a)

if name == "main": main() ```

Output:

np.arange(1, 9) [1 2 3 4 5 6 7 8]

3. Three Arguments¶

```python import numpy as np

def main(): a = np.arange(1, 9, 2) print("np.arange(1, 9, 2)") print(a)

if name == "main": main() ```

Output:

np.arange(1, 9, 2) [1 3 5 7]

np.linspace Function¶

Generates evenly spaced numbers over a closed interval [start, stop].

1. Default Samples¶

```python import numpy as np

def main(): a = np.linspace(-1, 2) print("np.linspace(-1, 2)") print(a)

if name == "main": main() ```

Default is 50 evenly spaced samples.

2. Custom Samples¶

```python import numpy as np

def main(): a = np.linspace(-1, 2, 4) print("np.linspace(-1, 2, 4)") print(a)

if name == "main": main() ```

Output:

np.linspace(-1, 2, 4) [-1. 0. 1. 2.]

Key Differences¶

Understanding when to use each function is essential.

1. Endpoint Inclusion¶

np.arange excludes the endpoint; np.linspace includes it by default.

2. Parameter Meaning¶

np.arange specifies step size; np.linspace specifies number of samples.

3. Typical Use Cases¶

Use np.arange for integer sequences and np.linspace for continuous intervals.

Floating Point Caution¶

Using np.arange with floats can produce unexpected results.

1. Rounding Issues¶

```python import numpy as np

a = np.arange(0, 1, 0.1) print(len(a)) # May vary due to floating-point precision ```

2. Recommendation¶

For floating-point sequences, prefer np.linspace to guarantee exact sample count.

Scientific Computing¶

Both functions are essential for numerical computations.

1. Plotting Curves¶

```python import numpy as np

x = np.linspace(0, 2 * np.pi, 100) y = np.sin(x) ```

2. Index Arrays¶

```python import numpy as np

indices = np.arange(len(data)) ```

3. Grid Generation¶

np.linspace combined with np.meshgrid creates 2D coordinate grids.

Exercises¶

Exercise 1. Create an array of all odd numbers from 1 to 99 (inclusive) using np.arange. Verify the result has exactly 50 elements and the last element is 99.

import numpy as np

odds = np.arange(1, 100, 2)
print(f"Length: {len(odds)}")     # 50
print(f"Last element: {odds[-1]}") # 99

Exercise 2. Using np.linspace, create an array of 5 evenly spaced values from 0 to 1 (inclusive). Then create the same array using np.arange with an appropriate step size. Print both arrays and verify they are equal with np.allclose.

import numpy as np

a_linspace = np.linspace(0, 1, 5)
a_arange = np.arange(0, 1.25, 0.25)

print(f"linspace: {a_linspace}")
print(f"arange:   {a_arange}")
print(f"Equal: {np.allclose(a_linspace, a_arange)}")

Exercise 3. Demonstrate the floating-point issue with np.arange(0, 1, 0.3). Print the resulting array and its length. Then produce an equivalent result using np.linspace that guarantees exactly 4 evenly spaced values from 0 to 0.9 (inclusive).

import numpy as np

# arange with float step — unpredictable length
a = np.arange(0, 1, 0.3)
print(f"arange result: {a}")
print(f"Length: {len(a)}")  # may be 3 or 4

# linspace guarantees exact count
b = np.linspace(0, 0.9, 4)
print(f"linspace result: {b}")
print(f"Length: {len(b)}")  # always 4