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#!/usr/bin/env python3
"""
Visualization of the transpose operation from PYTHON/transpose.py
This script creates a figure explaining what the code:
for i in range(order):
for j in range(order):
B[i][j] += A[j][i]
A[j][i] += 1.0
is doing - it shows how matrix elements are being accessed and modified.
"""
import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def create_transpose_code_visualization():
"""Create a visualization showing what the transpose code is doing."""
plt.style.use('seaborn-v0_8-whitegrid')
fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(20, 7))
fig.subplots_adjust(left=0.05, right=0.95, top=0.85, bottom=0.15, wspace=0.25)
# Matrix size for visualization
n = 5
# Create sample matrices
A = np.arange(n*n).reshape(n, n).astype(float)
B = np.zeros((n, n))
# Colors for visualization
colors = {
'A_read': '#FFE6E6', # Light red for A[j][i] (read)
'A_write': '#FF9999', # Darker red for A[j][i] (write)
'B_write': '#E6F3FF', # Light blue for B[i][j] (write)
'arrow': '#FF4444', # Red for arrows
'grid': '#CCCCCC' # Gray for grid
}
# === Matrix A (Source) ===
ax1.set_title('Matrix A (Source)\nReading A[j][i]', fontsize=14, fontweight='bold')
# Draw matrix A with grid
im1 = ax1.imshow(A, cmap='Blues', alpha=0.3, origin='upper')
# Add grid
for i in range(n + 1):
ax1.axhline(i - 0.5, color=colors['grid'], linewidth=1)
ax1.axvline(i - 0.5, color=colors['grid'], linewidth=1)
# Add matrix values
for i in range(n):
for j in range(n):
ax1.text(j, i, f'{A[i,j]:.0f}', ha='center', va='center',
fontsize=10, fontweight='bold')
# Highlight transpose access pattern (j,i instead of i,j)
example_i, example_j = 1, 3
rect1 = patches.Rectangle((example_i - 0.4, example_j - 0.4), 0.8, 0.8,
linewidth=3, edgecolor=colors['arrow'],
facecolor=colors['A_read'], alpha=0.7)
ax1.add_patch(rect1)
ax1.annotate(f'A[{example_j}][{example_i}]\n(transpose access)',
xy=(example_i, example_j), xytext=(example_i + 1.5, example_j - 1.5),
arrowprops=dict(arrowstyle='->', color=colors['arrow'], lw=2),
fontsize=11, fontweight='bold', ha='center',
bbox=dict(boxstyle="round,pad=0.3", facecolor='white', alpha=0.8))
ax1.set_xlim(-0.5, n - 0.5)
ax1.set_ylim(-0.5, n - 0.5)
ax1.set_xticks(range(n))
ax1.set_yticks(range(n))
ax1.set_xlabel('j (column index)', fontsize=12, fontweight='bold')
ax1.set_ylabel('i (row index)', fontsize=12, fontweight='bold')
ax1.invert_yaxis()
# === Arrow showing the operation ===
ax2.axis('off')
ax2.set_xlim(0, 1)
ax2.set_ylim(0, 1)
# Large arrow
arrow = patches.FancyArrowPatch((0.1, 0.5), (0.9, 0.5),
arrowstyle='->', mutation_scale=30,
color=colors['arrow'], linewidth=4)
ax2.add_patch(arrow)
# Code explanation
code_text = """Code Operation:
for i in range(order):
for j in range(order):
B[i][j] += A[j][i]
A[j][i] += 1.0
• Read from A[j][i] (transpose)
• Add to B[i][j] (normal order)
• Increment A[j][i] by 1.0"""
ax2.text(0.5, 0.5, code_text, ha='center', va='center', fontsize=12,
bbox=dict(boxstyle="round,pad=0.5", facecolor='lightyellow', alpha=0.8),
family='monospace')
# === Matrix B (Destination) ===
ax3.set_title('Matrix B (Destination)\nWriting B[i][j]', fontsize=14, fontweight='bold')
# Simulate the operation result
B_result = np.zeros((n, n))
for i in range(n):
for j in range(n):
B_result[i, j] = A[j, i] # This is what B[i][j] += A[j][i] does (first iteration)
# Draw matrix B
im3 = ax3.imshow(B_result, cmap='Oranges', alpha=0.3, origin='upper')
# Add grid
for i in range(n + 1):
ax3.axhline(i - 0.5, color=colors['grid'], linewidth=1)
ax3.axvline(i - 0.5, color=colors['grid'], linewidth=1)
# Add matrix values
for i in range(n):
for j in range(n):
ax3.text(j, i, f'{B_result[i,j]:.0f}', ha='center', va='center',
fontsize=10, fontweight='bold')
# Highlight corresponding write position
rect3 = patches.Rectangle((example_j - 0.4, example_i - 0.4), 0.8, 0.8,
linewidth=3, edgecolor=colors['arrow'],
facecolor=colors['B_write'], alpha=0.7)
ax3.add_patch(rect3)
ax3.annotate(f'B[{example_i}][{example_j}]\n(normal access)',
xy=(example_j, example_i), xytext=(example_j - 1.5, example_i + 1.5),
arrowprops=dict(arrowstyle='->', color=colors['arrow'], lw=2),
fontsize=11, fontweight='bold', ha='center',
bbox=dict(boxstyle="round,pad=0.3", facecolor='white', alpha=0.8))
ax3.set_xlim(-0.5, n - 0.5)
ax3.set_ylim(-0.5, n - 0.5)
ax3.set_xticks(range(n))
ax3.set_yticks(range(n))
ax3.set_xlabel('j (column index)', fontsize=12, fontweight='bold')
ax3.set_ylabel('i (row index)', fontsize=12, fontweight='bold')
ax3.invert_yaxis()
# Main title
fig.suptitle('Matrix Transpose Operation: B[i][j] += A[j][i]; A[j][i] += 1.0',
fontsize=16, fontweight='bold')
# Add explanation text
explanation = (
"The code performs a transpose operation where:\n"
"• Elements are read from A using transposed indices A[j][i]\n"
"• These values are accumulated into B using normal indices B[i][j]\n"
"• Matrix A is modified by incrementing each accessed element by 1.0\n"
"• This effectively computes B = Aᵀ while updating A"
)
plt.figtext(0.02, 0.02, explanation, fontsize=11, va='bottom',
bbox=dict(boxstyle="round,pad=0.5", facecolor='lightgray', alpha=0.8))
plt.tight_layout()
return fig
def create_access_pattern_animation():
"""Create an animation showing the access pattern step by step."""
from matplotlib.animation import FuncAnimation
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 8))
fig.subplots_adjust(left=0.05, right=0.95, top=0.85, bottom=0.15, wspace=0.3)
n = 5 # Matrix size for animation
A = np.arange(n*n).reshape(n, n).astype(float)
B = np.zeros((n, n))
def animate_frame(frame):
ax1.clear()
ax2.clear()
# Calculate current i, j from frame
total_ops = n * n
if frame >= total_ops:
frame = total_ops - 1
current_i = frame // n
current_j = frame % n
# Matrix A
ax1.set_title(f'Matrix A - Reading A[{current_j}][{current_i}]',
fontsize=14, fontweight='bold')
ax1.imshow(A, cmap='Blues', alpha=0.3, origin='upper')
# Add grid and values
for i in range(n + 1):
ax1.axhline(i - 0.5, color='gray', linewidth=1)
ax1.axvline(i - 0.5, color='gray', linewidth=1)
for i in range(n):
for j in range(n):
color = 'red' if (i == current_j and j == current_i) else 'black'
weight = 'bold' if (i == current_j and j == current_i) else 'normal'
ax1.text(j, i, f'{A[i,j]:.0f}', ha='center', va='center',
fontsize=12, color=color, fontweight=weight)
# Highlight current read position
rect1 = patches.Rectangle((current_i - 0.4, current_j - 0.4), 0.8, 0.8,
linewidth=3, edgecolor='red', facecolor='pink', alpha=0.7)
ax1.add_patch(rect1)
ax1.set_xlim(-0.5, n - 0.5)
ax1.set_ylim(-0.5, n - 0.5)
ax1.set_xticks(range(n))
ax1.set_yticks(range(n))
ax1.invert_yaxis()
# Matrix B
ax2.set_title(f'Matrix B - Writing B[{current_i}][{current_j}]',
fontsize=14, fontweight='bold')
# Update B matrix up to current frame
B_current = np.zeros((n, n))
for f in range(frame + 1):
fi = f // n
fj = f % n
B_current[fi, fj] += A[fj, fi]
ax2.imshow(B_current, cmap='Oranges', alpha=0.3, origin='upper')
# Add grid and values
for i in range(n + 1):
ax2.axhline(i - 0.5, color='gray', linewidth=1)
ax2.axvline(i - 0.5, color='gray', linewidth=1)
for i in range(n):
for j in range(n):
color = 'blue' if (i == current_i and j == current_j) else 'black'
weight = 'bold' if (i == current_i and j == current_j) else 'normal'
ax2.text(j, i, f'{B_current[i,j]:.0f}', ha='center', va='center',
fontsize=12, color=color, fontweight=weight)
# Highlight current write position
rect2 = patches.Rectangle((current_j - 0.4, current_i - 0.4), 0.8, 0.8,
linewidth=3, edgecolor='blue', facecolor='lightblue', alpha=0.7)
ax2.add_patch(rect2)
ax2.set_xlim(-0.5, n - 0.5)
ax2.set_ylim(-0.5, n - 0.5)
ax2.set_xticks(range(n))
ax2.set_yticks(range(n))
ax2.invert_yaxis()
# Main title with current operation
fig.suptitle(f'Step {frame + 1}/{total_ops}: B[{current_i}][{current_j}] += A[{current_j}][{current_i}] '
f'(Value: {A[current_j, current_i]:.0f})',
fontsize=16, fontweight='bold')
anim = FuncAnimation(fig, animate_frame, frames=n*n + 5, interval=800, repeat=True)
return fig, anim
if __name__ == "__main__":
# Create the static explanation
print("Creating transpose code explanation...")
fig1 = create_transpose_code_visualization()
fig1.savefig('transpose_code_explanation.png', dpi=300, bbox_inches='tight')
fig1.savefig('transpose_code_explanation.pdf', bbox_inches='tight')
# Create the animated version
print("Creating access pattern animation...")
fig2, anim = create_access_pattern_animation()
anim.save('transpose_access_pattern.gif', writer='pillow', fps=1.2)
# Show the plots
plt.show()
print("Visualizations saved as:")
print("- transpose_code_explanation.png (static explanation)")
print("- transpose_code_explanation.pdf (static explanation)")
print("- transpose_access_pattern.gif (animated access pattern)")