PolicyEngine Vectorization Patterns

Critical patterns for vectorized operations in PolicyEngine. Scalar logic with arrays will crash the microsimulation.

The Golden Rule

PolicyEngine processes multiple households simultaneously using NumPy arrays. NEVER use if-elif-else with entity data.

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1. Critical: What Will Crash

❌ NEVER: if-elif-else with Arrays

# THIS WILL CRASH - household data is an array
def formula(household, period, parameters):
    income = household("income", period)
    if income > 1000:  # ❌ CRASH: "truth value of array is ambiguous"
        return 500
    else:
        return 100

✅ ALWAYS: Vectorized Operations

# CORRECT - works with arrays
def formula(household, period, parameters):
    income = household("income", period)
    return where(income > 1000, 500, 100)  # ✅ Vectorized

---

2. Common Vectorization Patterns

Pattern 1: Simple Conditions → where()

# Instead of if-else
❌ if age >= 65:
    amount = senior_amount
else:
    amount = regular_amount

✅ amount = where(age >= 65, senior_amount, regular_amount)

Pattern 2: Multiple Conditions → select()

# Instead of if-elif-else
❌ if age < 18:
    benefit = child_amount
elif age >= 65:
    benefit = senior_amount
else:
    benefit = adult_amount

✅ benefit = select(
    [age < 18, age >= 65],
    [child_amount, senior_amount],
    default=adult_amount
)

Pattern 2b: Enum Dispatch → List ALL Conditions

When dispatching on an Enum variable, list all values explicitly in select(). Set the default to match the Enum's default_value so unexpected values get consistent behavior.

# ❌ BAD — hides one option in default, unclear which is the fallback
provider_type = person("ri_ccap_provider_type", period)
types = provider_type.possible_values
return select(
    [
        provider_type == types.LICENSED_CENTER,
        provider_type == types.LICENSED_FAMILY,
    ],
    [center_rate, family_rate],
    default=exempt_rate,  # Why exempt as fallback?
)

# ✅ GOOD — all options listed, default matches Enum default_value
provider_type = person("ri_ccap_provider_type", period)
types = provider_type.possible_values
return select(
    [
        provider_type == types.LICENSED_CENTER,
        provider_type == types.LICENSED_FAMILY,
        provider_type == types.LICENSE_EXEMPT,
    ],
    [center_rate, family_rate, exempt_rate],
    default=center_rate,  # Matches default_value = LICENSED_CENTER
)

Pattern 3: Boolean Operations

# Combining conditions
eligible = (age >= 18) & (income < threshold)  # Use & not 'and'
eligible = (is_disabled | is_elderly)          # Use | not 'or'
eligible = ~is_excluded                        # Use ~ not 'not'

Pattern 4: Clipping Values

# Instead of if for bounds checking
❌ if amount < 0:
    amount = 0
elif amount > maximum:
    amount = maximum

✅ amount = clip(amount, 0, maximum)
# Or: amount = max_(0, min_(amount, maximum))

Pattern 5: Flooring Subtraction Results (CRITICAL)

When subtracting values and wanting to floor at zero, you must wrap the entire subtraction in max_():

# Common scenario: income after deductions/losses
❌ WRONG - Creates phantom negative values:
income = max_(income, 0) - capital_loss  # If capital_loss > income, result is negative!

✅ CORRECT - Properly floors at zero:
income = max_(income - capital_loss, 0)  # Entire subtraction floored

# Real example from MT income tax bug:
❌ WRONG - Tax on phantom negative income:
def formula(tax_unit, period, parameters):
    income = tax_unit("adjusted_gross_income", period)
    capital_gains = tax_unit("capital_gains", period)

    # BUG: If capital_gains is negative (loss), this creates negative income
    # But max_() only floors income, not the result
    regular_income = max_(income, 0) - capital_gains
    return calculate_tax(regular_income)  # Tax on negative number!

✅ CORRECT - No phantom income:
def formula(tax_unit, period, parameters):
    income = tax_unit("adjusted_gross_income", period)
    capital_gains = tax_unit("capital_gains", period)

    # Properly floors the entire result
    regular_income = max_(income - capital_gains, 0)
    return calculate_tax(regular_income)  # Never negative

Why this matters:

• If capital_gains = -3000 (loss), then income - capital_gains = income + 3000
• The wrong pattern max_(income, 0) - capital_gains allows the subtraction to make the result negative
• This creates "phantom income" where none exists, leading to incorrect tax calculations

Rule: When the formula is A - B and you want the result floored at zero, use max_(A - B, 0), NOT max_(A, 0) - B.

---

3. When if-else IS Acceptable

✅ OK: Parameter-Only Conditions

# OK - parameters are scalars, not arrays
def formula(entity, period, parameters):
    p = parameters(period).gov.program

    # This is fine - p.enabled is a scalar boolean
    if p.enabled:
        base = p.base_amount
    else:
        base = 0

    # But must vectorize when using entity data
    income = entity("income", period)
    return where(income < p.threshold, base, 0)

✅ OK: Control Flow (Not Data)

# OK - controlling which calculation to use
def formula(entity, period, parameters):
    year = period.start.year

    if year >= 2024:
        # Use new formula (still vectorized)
        return entity("new_calculation", period)
    else:
        # Use old formula (still vectorized)
        return entity("old_calculation", period)

---

4. Common Vectorization Mistakes

Mistake 1: Scalar Comparison with Array

❌ WRONG:
if household("income", period) > 1000:
    # Error: truth value of array is ambiguous

✅ CORRECT:
income = household("income", period)
high_income = income > 1000  # Boolean array
benefit = where(high_income, low_benefit, high_benefit)

Mistake 2: Using Python's and/or/not

❌ WRONG:
eligible = is_elderly or is_disabled  # Python's 'or'

✅ CORRECT:
eligible = is_elderly | is_disabled   # NumPy's '|'

Mistake 3: Nested if Statements

❌ WRONG:
if eligible:
    if income < threshold:
        return full_benefit
    else:
        return partial_benefit
else:
    return 0

✅ CORRECT:
return where(
    eligible,
    where(income < threshold, full_benefit, partial_benefit),
    0
)

---

5. CRITICAL: Avoiding Divide-by-Zero Warnings

The Problem with where() for Division

where() evaluates BOTH branches before selecting. This causes divide-by-zero warnings even when the zero case wouldn't be selected:

# ❌ WRONG - causes divide-by-zero warning
proportion = where(
    total_income > 0,
    person_income / total_income,  # Still evaluated when total_income = 0!
    0,
)

✅ CORRECT: Use np.divide with where Parameter

# ✅ CORRECT - only divides where mask is True
# The `out` parameter IS the default value - positions where mask=False keep this value
mask = total_income > 0
proportion = np.divide(
    person_income,
    total_income,
    out=np.zeros_like(person_income),  # Default to 0 where mask is False
    where=mask,
)

How out works as the default:

• out=np.zeros_like(...) → default is 0
• out=np.ones_like(...) → default is 1
• Positions where where=False keep their out value unchanged

✅ CORRECT: Alternative Mask Pattern

# ✅ CORRECT - traditional mask assignment
proportion = np.zeros_like(total_income)
mask = total_income > 0
proportion[mask] = person_income[mask] / total_income[mask]

Common Use Cases

Proportional allocation (e.g., splitting deductions between spouses):

# Allocate proportionally by income
unit_income = tax_unit.sum(person_income)
mask = unit_income > 0
share = np.divide(
    person_income,
    unit_income,
    out=np.zeros_like(person_income),
    where=mask,
)
# Default share when unit has no income
share = where(mask, share, where(is_head, 1.0, 0.0))

Calculating ratios:

# AGI ratio for credit calculations
mask = us_agi != 0
ratio = np.divide(
    state_agi,
    us_agi,
    out=np.zeros_like(us_agi),
    where=mask,
)

Real Examples in Codebase

See these files for reference implementations:

• taxable_social_security.py - person share of unit benefits
• mo_taxable_income.py - AGI share allocation
• md_two_income_subtraction.py - head's share of couple income
• ok_child_care_child_tax_credit.py - AGI ratio

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6. More Advanced Patterns

Pattern: Vectorized Lookup Tables

# Instead of if-elif for ranges
❌ if size == 1:
    amount = 100
elif size == 2:
    amount = 150
elif size == 3:
    amount = 190

✅ # Using parameter brackets
amount = p.benefit_schedule.calc(size)

✅ # Or using select
amounts = [100, 150, 190, 220, 250]
amount = select(
    [size == i for i in range(1, 6)],
    amounts[:5],
    default=amounts[-1]  # 5+ people
)

Pattern: Accumulating Conditions

# Building complex eligibility
income_eligible = income < p.income_threshold
resource_eligible = resources < p.resource_limit
demographic_eligible = (age < 18) | is_pregnant

# Combine with & (not 'and')
eligible = income_eligible & resource_eligible & demographic_eligible

Pattern: Conditional Accumulation

# Sum only for eligible members
person = household.members
is_eligible = person("is_eligible", period)
person_income = person("income", period)

# Only count income of eligible members
eligible_income = where(is_eligible, person_income, 0)
total = household.sum(eligible_income)

---

7. Testing for Vectorization Issues

Signs Your Code Isn't Vectorized

Error messages:

• "The truth value of an array is ambiguous"
• "ValueError: The truth value of an array with more than one element"

Performance:

• Tests run slowly
• Microsimulation times out

How to Test

# Your formula should work with arrays
def test_vectorization():
    # Create array inputs
    incomes = np.array([500, 1500, 3000])

    # Should return array output
    benefits = formula_with_arrays(incomes)
    assert len(benefits) == 3

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Quick Reference Card

Operation	Scalar (WRONG)	Vectorized (CORRECT)
Simple condition	if x > 5:	where(x > 5, ...)
Multiple conditions	if-elif-else	select([...], [...])
Boolean AND	and	&
Boolean OR	or	|
Boolean NOT	not	~
Bounds checking	if x < 0: x = 0	max_(0, x)
Floor subtraction	max_(x, 0) - y ❌	max_(x - y, 0) ✅
Complex logic	Nested if	Nested where/select

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8. Debugging Phantom Values in Tax Calculations

Problem: Non-Zero Tax Despite Zero Taxable Income

When state tax calculations produce small non-zero values (e.g., $277) even though taxable income is zero, the root cause is usually phantom intermediate values in calculation chains.

Phantom Intermediate Values in Calculation Chains

When taxable income is zero but tax is non-zero, trace the calculation chain:

# Tax calculation chain (Montana example)
taxable_income: 0          # ✓ Correct
rate: 0.0475              # Used despite zero income
brackets: [15_600]        # Used despite zero income
tax_before_credits: 277.41 # ❌ PHANTOM VALUE

# The bug: Brackets calculated regular tax even when taxable income was zero
# due to missing zero-check in bracket calculation

Debugging Pattern

When you see phantom tax values:

1. Check the calculation chain - Run test with verbose output to see intermediate values:

   pytest tests/file.py -vv
   

2. Verify zero-income handling - Look for formulas that don't short-circuit on zero income:

   ✅ GOOD:
   def formula(entity, period, parameters):
       taxable_income = entity("taxable_income", period)
       # Short-circuit when income is zero
       return where(taxable_income == 0, 0, calculate_tax(...))
   
   ❌ BAD:
   def formula(entity, period, parameters):
       # Always calculates, even when income is zero
       return calculate_brackets(taxable_income, rates, brackets)
   

3. Check type consistency - Ensure operations preserve NumPy array dtypes:

   ✅ Use: max_(value, 0) or clip(value, 0, None)
   ❌ Avoid: max(value, 0) - Python's max can cause type issues