File:Integration path in complex plane crossing saddle-point.png
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[edit]DescriptionIntegration path in complex plane crossing saddle-point.png |
English: A modular surface (blue) with an integration path (red and green) which crosses a saddle-point. The modular surface describes . The red part of the integration path is the part which crosses the saddle-point. The green part is the "tail". |
Date | |
Source | Own work |
Author | Dom walden |
PNG development InfoField | This plot was created with Matplotlib. |
Source code InfoField | Python codeimport matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np
# Make data
X = np.arange(-4, 4, 0.25)
Y = np.arange(-4, 4, 0.25)
X, Y = np.meshgrid(X, Y)
Z = abs(np.exp(X+Y*1j) / (1 - (X+Y*1j)))
# Plot the surface
fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
ax.plot_wireframe(X, Y, Z, alpha=0.5)
ax.set(xticklabels=[],
yticklabels=[],
zticklabels=[])
# Prepare arrays x, y, z
theta = np.linspace(-np.pi/4, np.pi/4, 1000)
r = 2
z = abs(np.exp(r * np.exp(1j*theta)) / (1 - r * np.exp(1j*theta)))
x = r * np.sin(theta + np.pi/2)
y = r * np.cos(theta + np.pi/2)
# Plot through saddle-point
ax.plot(x, y, z, 'red')
theta = np.linspace(np.pi - np.pi*3/4, np.pi + np.pi*3/4, 1000)
r = 2
z = abs(np.exp(r * np.exp(1j*theta)) / (1 - r * np.exp(1j*theta)))
x = r * np.sin(theta + np.pi/2)
y = r * np.cos(theta + np.pi/2)
# Plot the "tail"
ax.plot(x, y, z, 'green')
ax.legend()
plt.show()
|
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[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 07:18, 28 May 2023 | 834 × 660 (315 KB) | Dom walden (talk | contribs) | Uploaded own work with UploadWizard |
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Unique ID of original document | xmp.did:8576c97c-2f59-478a-bf62-0206e40bf461 |
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Software used | GIMP 2.10 |
Horizontal resolution | 39.37 dpc |
Vertical resolution | 39.37 dpc |
File change date and time | 06:42, 28 May 2023 |