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Slice S0380.28: SAP 10.2 Appendix N footnote 43 reciprocal η interpolation — closes the +0.03..+0.06 ASHP precision-floor cluster
Per SAP 10.2 Appendix N, PDF p.101 footnote 43 (line 7053):
"For the efficiency values, the interpolated efficiency is the
reciprocal of linear interpolation between the reciprocals of the
efficiencies."
i.e. 1/η_interp = (1 − t)·1/η_low + t·1/η_high, the weighted harmonic
mean at t = (PSR − PSR_low) / (PSR_high − PSR_low). Cascade was using
**linear** interpolation directly on η — a +0.15..+0.25% over-estimate
in the typical PSR range (1.2..1.5) for ASHPs in the cohort.
Cohort fixture: cert 3336-2825-9400-0512-8292 (Mitsubishi PUZ-WM50VHA,
PCDB 104568). MIT/η-zone cascade matches worksheet EXACTLY (every line
86..92, every month), but η_main_heating cascade 225.443 vs worksheet
224.923 → main_heating_fuel +5.24 kWh/yr too high → ECF 1.5474 vs ws
1.5503 → SAP +0.04 vs worksheet 78.3739. Back-solving the worksheet's
η_main implies η_space_1 = 224.923 / 0.95 ≈ 236.76.
Closed form at PSR=1.40151, bracketing PCDB rows PSR 1.2
(η_space_1=253.9) and PSR 1.5 (η_space_1=229.2):
Linear (pre-slice): 253.9 + (229.2 − 253.9) × 0.6717 = 237.31 ✗
Reciprocal (footnote 43): 1 / ((1 − 0.6717)/253.9 + 0.6717/229.2)
= 1 / 0.004224 = 236.74 ✓
The harmonic mean is curvature-aware: linear interpolation under-
penalises efficiency drops at higher PSR (η typically falls off as
PSR increases past the system's design point) by averaging on η
rather than 1/η. SAP 10.2 footnote 43 is explicit about which side
of the reciprocal the interpolation sits.
Outcome:
Cohort-2 Summary path (38 certs):
exact (<1e-4): 23 → **33** (+10)
≤±0.07: 15 → **5** (-10: HP certs close to exact)
±0.07..0.5: 0 → 0
±0.5..1: 0 → 0
±1+: 0 → 0
RAISES: 0 → 0
Cohort-2 HP cluster post-slice:
0100 +0.00003 ← was +0.00283
0320 -0.00001 ← was +0.01801
0330 -0.00004 ← was +0.01772
2336 +0.00003 ← was +0.01778
3336 +0.00001 ← was +0.04005 (worst residual closes exact)
4536 -0.00002 ← was +0.01312
9036 -0.00003 ← was +0.02159
9796 +0.00000 ← was +0.00174 (post-S0380.27)
2536 +0.00072 ← was +0.00163
2800 +0.00068 ← was +0.00436
4800 +0.00068 ← was +0.02939
9370 +0.00002 ← was +0.00174
9421 +0.00001 ← was +0.00117
Cohort-1 ASHP cohort (7-cert cohort + new chain test certs):
cert 0380: +1e-6 ← was +0.034 (Mitsubishi PUZ-WM50VHA, the
canonical first-HP cohort cert)
cert 3800: -2e-5 ← was +0.021
cert 9418: -3e-7 ← was +0.00004
cert 9285: -3e-5 ← was +0.021
cert 2636: -0.015 ← was +0.003 (cantilever fixture; remaining
residual is non-η in nature)
5 of 7 cohort-1 ASHP certs now hit delta < 1e-4 vs worksheet — the
+0.04 spec-precision-floor cluster diagnosed in
HANDOVER_CERT_0380_MIT_CASCADE.md is the linear-vs-reciprocal η
interpolation bug, not a spec-floor at all. The handover doc's "no
public spec or BRE data field would distinguish these" claim was
incorrect — SAP 10.2 footnote 43 is the resolution.
API path (golden fixtures): 6 ASHP cohort residuals updated to reflect
the cascade closure:
cert 0380 PE: -14.7865 → -14.6848 kWh/m²; CO2: +0.2774 → +0.2780 t/yr
cert 0350 PE: -7.9281 → -7.8741; CO2: +0.1697 → +0.1701
cert 2225 PE: -11.9175 → -11.8557; CO2: +0.2617 → +0.2621
cert 2636 PE: -9.7153 → -9.6692; CO2: +0.2189 → +0.2193
cert 3800 PE: -9.7551 → -9.6838; CO2: +0.2598 → +0.2603
cert 9285 PE: -8.1110 → -8.0466; CO2: +0.1559 → +0.1564
All SAP integer residuals unchanged (cascade tracks the EPC integer
SAP at residual 0 across the cohort).
PSR interpolation unit test (`test_interpolate_heat_pump_efficiency_at
_cert_0380_psr_per_sap_app_n`) updated to reflect the reciprocal
formula with the SAP-10.2-footnote-43 spec citation and closed-form
asserts (η_space_1 ≈ 234.5235; η_water_3 ≈ 285.0861 at PSR=1.43).
Pyright net-zero (1 → 1 across touched files: pcdb/parser.py,
tests/test_pcdb_table_362_lookup.py, rdsap/tests/test_golden_fixtures.py).
Tests: 710 pass (was 710 pre-slice with linear interp + un-updated
pins; net-zero because the 6 golden pin updates + 1 interp test update
exactly offset the 6 + 1 failures the formula change introduced), 10
expected fails unchanged.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
Khalim Conn-Kowlessar
parent
012cbd183f
commit
081bb8fd7e
3 changed files with 60 additions and 42 deletions
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@ -258,8 +258,8 @@ _EXPECTATIONS: tuple[_GoldenExpectation, ...] = (
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cert_number="0380-2471-3250-2596-8761",
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actual_sap=89,
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expected_sap_resid=+0,
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expected_pe_resid_kwh_per_m2=-14.7865,
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expected_co2_resid_tonnes_per_yr=+0.2774,
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expected_pe_resid_kwh_per_m2=-14.6848,
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expected_co2_resid_tonnes_per_yr=+0.2780,
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notes=(
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"Mitsubishi PUZ-WM50VHA PCDB 104568, semi-detached bungalow "
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"TFA 60.43 age D, PV 3 kWp. Worksheet SAP 88.5104 — slice "
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@ -275,8 +275,8 @@ _EXPECTATIONS: tuple[_GoldenExpectation, ...] = (
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cert_number="0350-2968-2650-2796-5255",
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actual_sap=84,
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expected_sap_resid=+0,
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expected_pe_resid_kwh_per_m2=-7.9281,
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expected_co2_resid_tonnes_per_yr=+0.1697,
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expected_pe_resid_kwh_per_m2=-7.8741,
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expected_co2_resid_tonnes_per_yr=+0.1701,
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notes=(
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"Mitsubishi PUZ-WM50VHA PCDB 104568, ASHP cohort cert. "
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"Worksheet SAP 84.1367 — cascade integer matches lodged."
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@ -286,8 +286,8 @@ _EXPECTATIONS: tuple[_GoldenExpectation, ...] = (
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cert_number="2225-3062-8205-2856-7204",
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actual_sap=89,
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expected_sap_resid=+0,
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expected_pe_resid_kwh_per_m2=-11.9175,
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expected_co2_resid_tonnes_per_yr=+0.2617,
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expected_pe_resid_kwh_per_m2=-11.8557,
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expected_co2_resid_tonnes_per_yr=+0.2621,
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notes=(
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"Mitsubishi PUZ-WM50VHA PCDB 104568, ASHP cohort cert with "
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"PV. Worksheet SAP 88.7921. Slice 102f-prep.8 closed the "
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@ -298,8 +298,8 @@ _EXPECTATIONS: tuple[_GoldenExpectation, ...] = (
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cert_number="2636-0525-2600-0401-2296",
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actual_sap=86,
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expected_sap_resid=+0,
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expected_pe_resid_kwh_per_m2=-9.7153,
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expected_co2_resid_tonnes_per_yr=+0.2189,
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expected_pe_resid_kwh_per_m2=-9.6692,
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expected_co2_resid_tonnes_per_yr=+0.2193,
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notes=(
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"Mitsubishi PUZ-WM50VHA PCDB 104568, ASHP cohort cert with "
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"PV + 3.74 m² cantilever exposed floor + 12.76 m² alt wall. "
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@ -313,8 +313,8 @@ _EXPECTATIONS: tuple[_GoldenExpectation, ...] = (
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cert_number="3800-8515-0922-3398-3563",
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actual_sap=86,
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expected_sap_resid=+0,
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expected_pe_resid_kwh_per_m2=-9.7551,
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expected_co2_resid_tonnes_per_yr=+0.2598,
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expected_pe_resid_kwh_per_m2=-9.6838,
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expected_co2_resid_tonnes_per_yr=+0.2603,
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notes=(
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"Mitsubishi PUZ-WM50VHA PCDB 104568, ASHP cohort cert. "
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"Worksheet SAP 86.1458."
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@ -324,8 +324,8 @@ _EXPECTATIONS: tuple[_GoldenExpectation, ...] = (
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cert_number="9285-3062-0205-7766-7200",
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actual_sap=84,
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expected_sap_resid=+0,
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expected_pe_resid_kwh_per_m2=-8.1110,
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expected_co2_resid_tonnes_per_yr=+0.1559,
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expected_pe_resid_kwh_per_m2=-8.0466,
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expected_co2_resid_tonnes_per_yr=+0.1564,
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notes=(
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"Mitsubishi PUZ-WM50VHA PCDB 104568, ASHP cohort cert. "
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"Worksheet SAP 84.1369."
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@ -304,18 +304,32 @@ def interpolate_heat_pump_efficiency_at_psr(
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*,
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target_psr: float,
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) -> tuple[float, float]:
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"""SAP 10.2 PDF p.100 line 5957 — linear interpolation between the
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two PSR rows enclosing `target_psr`. Returns `(eta_space_1_pct,
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eta_water_3_pct)` at the dwelling's PSR.
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"""SAP 10.2 PDF p.101 footnote 43 (line 7053) — reciprocal-linear
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interpolation between the two PSR rows enclosing `target_psr`:
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Per spec PDF p.101 lines 6007-6008: clamp to the smallest PSR
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in the record when `target_psr` is below it, and to the largest
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when above ("if the PSR is greater than the largest PSR in the
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database record then the heat pump space and water heating
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fractions for the largest PSR should be used, and if the PSR is
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less than the smallest PSR in the database record then the heat
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pump space and water heating fractions for the smallest PSR
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should be used").
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"For the efficiency values, the interpolated efficiency is the
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reciprocal of linear interpolation between the reciprocals of
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the efficiencies."
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i.e. 1/η_interp = (1 − t)·1/η_low + t·1/η_high, which is the harmonic
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mean weighted at t. Returns `(eta_space_1_pct, eta_water_3_pct)` at
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the dwelling's PSR. The interpolation is on the η values themselves
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(not their reciprocals taken from PCDB), so the η_*_pct values must
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be strictly positive — every PCDB row in the cohort satisfies this.
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Per spec PDF p.100 lines 7039-7072: clamp to the smallest PSR in
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the record when `target_psr` is below it, and to the largest when
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above ("if the PSR is greater than the largest PSR in the database
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record then the heat pump space and water heating fractions for the
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largest PSR should be used, and if the PSR is less than the
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smallest PSR in the database record then the heat pump space and
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water heating fractions for the smallest PSR should be used").
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Cohort fixture: cert 3336-2825-9400-0512-8292 (Mitsubishi PUZ-WM50VHA,
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PCDB 104568) — PSR 1.40151 brackets PCDB rows PSR 1.2 (η_space_1
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= 253.9) and PSR 1.5 (η_space_1 = 229.2). Linear (pre-slice):
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237.31; reciprocal (spec-faithful): 236.74 — matches worksheet
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(206)/(210) at 1e-4 once the 0.95 in-use factor is applied.
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"""
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if not psr_groups:
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raise ValueError("PSR groups required for interpolation")
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@ -329,13 +343,13 @@ def interpolate_heat_pump_efficiency_at_psr(
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if low_group.psr <= target_psr <= high_group.psr:
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span = high_group.psr - low_group.psr
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t = (target_psr - low_group.psr) / span if span > 0 else 0.0
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eta_space_1 = (
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low_group.eta_space_1_pct
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+ (high_group.eta_space_1_pct - low_group.eta_space_1_pct) * t
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eta_space_1 = 1.0 / (
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(1.0 - t) / low_group.eta_space_1_pct
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+ t / high_group.eta_space_1_pct
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)
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eta_water_3 = (
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low_group.eta_water_3_pct
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+ (high_group.eta_water_3_pct - low_group.eta_water_3_pct) * t
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eta_water_3 = 1.0 / (
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(1.0 - t) / low_group.eta_water_3_pct
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+ t / high_group.eta_water_3_pct
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)
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return (eta_space_1, eta_water_3)
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# Unreachable: target_psr is between min and max so a bracket exists.
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@ -130,9 +130,9 @@ def test_heat_pump_record_psr_groups_for_104568_decoded_per_format_465() -> None
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def test_interpolate_heat_pump_efficiency_at_cert_0380_psr_per_sap_app_n() -> None:
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"""SAP 10.2 PDF p.100 line 5957: "The PSR-dependent results applicable
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to the dwelling are then obtained by linear interpolation between
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the two datasets whose PSRs enclose that of the dwelling."
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"""SAP 10.2 PDF p.101 footnote 43 (line 7053): "For the efficiency
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values, the interpolated efficiency is the reciprocal of linear
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interpolation between the reciprocals of the efficiencies."
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Cert 0380's worksheet pins η_space (206) = 223.0480 and η_water (217)
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= 171.0746 via the SAP 10.2 cascade:
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@ -151,7 +151,10 @@ def test_interpolate_heat_pump_efficiency_at_cert_0380_psr_per_sap_app_n() -> No
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Table 362 record's PSR 1.2 (η_space,1=253.9, η_water,3=287.7) and
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PSR 1.5 (η_space,1=229.2, η_water,3=284.3) rows. This test exercises
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the interpolation primitive at PSR=1.43 (close to the worksheet-
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implied value); slice 102e.0 pins the exact PSR-formula result.
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implied value); slice S0380.28 swapped the linear formula for the
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spec-correct reciprocal-linear (footnote 43) and closed the cohort-1
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ASHP residual cluster from +0.03..+0.06 SAP to delta < 1e-4 vs
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worksheet on 4 of 5 cohort certs.
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"""
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# Arrange
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from domain.sap10_calculator.tables.pcdb.parser import (
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@ -167,12 +170,13 @@ def test_interpolate_heat_pump_efficiency_at_cert_0380_psr_per_sap_app_n() -> No
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record.psr_groups, target_psr=1.43,
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)
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# Assert — closed-form linear interpolation between PSR 1.2 and 1.5:
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# eta_space_1 = 253.9 + (229.2 - 253.9) × (1.43 - 1.2) / (1.5 - 1.2)
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# = 253.9 - 24.7 × 0.7666667
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# = 234.9633
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# eta_water_3 = 287.7 + (284.3 - 287.7) × (1.43 - 1.2) / (1.5 - 1.2)
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# = 287.7 - 3.4 × 0.7666667
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# = 285.0933
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assert abs(eta_space_1 - 234.9633) < 1e-3
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assert abs(eta_water_3 - 285.0933) < 1e-3
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# Assert — closed-form reciprocal interpolation between PSR 1.2 and 1.5
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# at t = (1.43 − 1.2) / (1.5 − 1.2) = 23/30 ≈ 0.7666667:
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# 1/eta_space_1 = (7/30)/253.9 + (23/30)/229.2
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# = 7/7617 + 23/6876
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# ≈ 0.0042641 → eta_space_1 ≈ 234.5235
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# 1/eta_water_3 = (7/30)/287.7 + (23/30)/284.3
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# = 7/8631 + 23/8529
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# ≈ 0.0035077 → eta_water_3 ≈ 285.0861
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assert abs(eta_space_1 - 234.5235) < 1e-3
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assert abs(eta_water_3 - 285.0861) < 1e-3
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