Analysis Modes

FastSPA supports two complementary analysis modes for different research questions.

Sector-Specific Analysis (A-Matrix Mode)

Traces direct supplier relationships through the technical coefficients matrix.

# Default mode: sector-specific
spa = SPA(A_matrix, direct_intensities, mode="sector_specific")
paths = spa.analyze(sector=42, depth=8)

Characteristics:

• Uses the A-matrix (technical coefficients) directly
• Traces direct supplier relationships only
• More efficient computation
• Coverage typically ~90-95%
• Clear pathway attribution

Use when:

• Analyzing direct supplier relationships
• Need efficient computation for many sectors
• Want clear pathway attribution
• Focus on sector-specific supply chains

System-Wide Analysis (Leontief Mode)

Traces total requirements (direct + indirect) through the Leontief inverse matrix.

# System-wide mode: uses Leontief inverse
spa = SPA(A_matrix, direct_intensities, mode="system_wide")
paths = spa.analyze(sector=42, depth=8)

Characteristics:

• Uses L = (I - A)^(-1) (Leontief inverse)
• Captures circular flows and feedback loops
• More comprehensive pathway discovery
• Coverage can exceed 100% (expected due to circular flows)
• Economy-wide perspective

Use when:

• Analyzing total supply chain requirements
• Need comprehensive pathway discovery
• Want to capture circular flows
• Studying economy-wide scenarios

Comparison

Aspect	Sector-Specific (A-Matrix)	System-Wide (Leontief)
Input Matrix	A (technical coefficients)	L (Leontief inverse)
Pathways	Fewer (~1,300 typical)	More (~12,000 typical)
Coverage	~93%	Can exceed 100%
Circular Flows	Not captured	Captured
Computation	Faster	Slower
Use Case	Sector analysis	Economy-wide scenarios

Example: Comparing Modes

from fastspa import SPA

# Same data, different modes
spa_sector = SPA(A, emissions, mode="sector_specific")
spa_system = SPA(A, emissions, mode="system_wide")

# Analyze the same sector
paths_sector = spa_sector.analyze(sector=42, depth=8)
paths_system = spa_system.analyze(sector=42, depth=8)

print(f"Sector-specific: {len(paths_sector)} paths, {paths_sector.coverage:.1%} coverage")
print(f"System-wide: {len(paths_system)} paths, {paths_system.coverage:.1%} coverage")

Pre-computed Leontief Inverse

If you already have a Leontief inverse computed, use the from_leontief factory function:

from fastspa import from_leontief

# Skip L computation - defaults to system_wide mode
spa = from_leontief(L_matrix, intensities, sectors)