如何生成0-3区间靠近3处更密集的非均匀NumPy采样序列？

Great question! To create a sequence from 0 to 3 where points are sparser at the start (0) and denser near the end (3), we need a transformation that produces larger steps early on and smaller steps as we approach 3. Here are a few robust, mathematically clear ways to achieve this:

Method 1: Inverted Logarithmic Transformation #

Your initial logarithmic approach created density near 0 because logarithmic functions grow slowly at low values. To flip this, we can generate a log-dense sequence near 0, then invert it to shift the density to 3:

import numpy as np

# Generate a log-dense sequence from 0 to 3 (dense at 0)
log_dense_at_0 = 3 * (np.logspace(np.log10(1), np.log10(1001), 100) - 1) / 1000
# Invert and reverse to get dense at 3, ordered from 0 to 3
log_dense_at_3 = np.flip(3 - log_dense_at_0)

• How it works: np.logspace creates points from 1 to 1001 (logarithmically spaced, so dense near 1). Subtract 1 to shift to 0–1000, scale to 0–3. Subtract from 3 to flip the density to the upper end, then reverse to get the sequence in 0→3 order.

Method 2: Power Function (Fractional Exponent) #

Using a fractional exponent (between 0 and 1) on a linear sequence will make values grow quickly at first, then slow down near 3—exactly the density pattern we want:

# Linear base sequence from 0 to 1
lin_base = np.linspace(0, 1, 100)
# Apply fractional exponent and scale to 0–3
power_dense_at_3 = 3 * (lin_base ** 0.5)  # sqrt(t) works; use 0.3 for even denser points near 3

• Adjusting density: Use a smaller exponent (like 0.3) to make the density near 3 more pronounced, or a larger exponent (like 0.8) for a milder effect.

Method 3: Inverted Exponential Transformation #

An inverted exponential function grows quickly at the start and asymptotes towards 3, creating smaller steps near the upper bound:

# Linear base sequence from 0 to 5 (adjust upper limit to control approach to 3)
lin_base = np.linspace(0, 5, 100)
# Inverted exponential to get dense at 3
exp_dense_at_3 = 3 * (1 - np.exp(-0.7 * lin_base))

• Tuning: Increase the multiplier (0.7) to make the sequence approach 3 faster, or decrease it to stretch out the approach.

Addressing Your Proposed Solution #

Your code s = -1*(3*10**(-np.linspace(0,4,25))-1) simplifies to 1 - 3*10**(-t) where t ranges from 0 to 4. This produces values from -2 to ~0.9997, which doesn’t cover the full 0–3 range—likely a small typo. If you adjust it to target the 0–3 range, you’d end up with density near 0 (since exponential growth speeds up). The methods above are more direct for achieving density near 3.

内容的提问来源于stack exchange，提问作者Alejandro