完成求解器雅可比矩阵首轮优化，增加更新目录，整理了文档文件夹，增加了服务启动脚本

app/simulation/components/amesim/media/mediums.py

@@ -1,7 +1,8 @@
 from __future__ import annotations
 
-from collections.abc import Callable
+from collections.abc import Callable, Sequence
 from dataclasses import dataclass
+from math import isfinite
 from typing import ClassVar
 
 from app.simulation.core.errors import RecoverableTrialStateError
@@ -9,6 +10,8 @@ from app.simulation.core.medium import (
     GasMedium,
     IdealGasMedium,
     ThermodynamicProperties,
+    ThermodynamicPropertiesLinearization,
+    ThermodynamicPropertyTangents,
 )
 from app.simulation.core.peng_robinson import HELIUM_PR, PengRobinsonFluid
 from app.simulation.performance import profile_property, record_property_iterations
@@ -309,6 +312,153 @@ class AmesimHeliumPengRobinsonMedium(IdealGasMedium):
             ),
         )
 
+    def linearize_properties_from_mU(
+        self,
+        m: float,
+        U: float,
+        V: float,
+        dm: Sequence[float],
+        dU: Sequence[float],
+        dV: Sequence[float],
+        *,
+        properties: ThermodynamicProperties | None = None,
+    ) -> ThermodynamicPropertiesLinearization:
+        """Implicitly differentiate the Peng-Robinson m/U/V recovery."""
+
+        dm_values = tuple(float(value) for value in dm)
+        dU_values = tuple(float(value) for value in dU)
+        dV_values = tuple(float(value) for value in dV)
+        if not (len(dm_values) == len(dU_values) == len(dV_values)):
+            raise ValueError("Thermodynamic tangent vectors must have equal lengths.")
+        props = properties or self.properties_from_mU(m, U, V)
+        width = len(dm_values)
+
+        def invalid(reason: str) -> ThermodynamicPropertiesLinearization:
+            return ThermodynamicPropertiesLinearization(
+                properties=props,
+                tangents=ThermodynamicPropertyTangents.zeros(width),
+                valid=False,
+                reason=reason,
+            )
+
+        expected_density = m / V
+        expected_internal_energy = U / m
+        if (
+            abs(props.rho - expected_density)
+            > 1.0e-12 * max(abs(expected_density), 1.0)
+            or abs(props.u - expected_internal_energy)
+            > 1.0e-12 * max(abs(expected_internal_energy), 1.0)
+        ):
+            return invalid("properties_primal_mismatch")
+        if not all(
+            isfinite(value)
+            for values in (dm_values, dU_values, dV_values)
+            for value in values
+        ):
+            return invalid("non_finite_tangent_input")
+        if props.T <= 2.2 * (1.0 + 1.0e-10):
+            return invalid("temperature_floor_boundary")
+
+        pressure_temperature_derivative = (
+            self.fluid.pressure_temperature_derivative_at_density(
+                props.T,
+                props.rho,
+            )
+        )
+        pressure_density_derivative = (
+            self.fluid.pressure_density_derivative_at_temperature(
+                props.T,
+                props.rho,
+            )
+        )
+        cv = (
+            self.cv_at_temperature(props.T)
+            + self.fluid.residual_isochoric_heat_capacity_at_density(
+                props.T,
+                props.rho,
+            )
+        )
+        recovered_internal_energy = (
+            self.specific_internal_energy(props.T)
+            + self.fluid.residual_specific_internal_energy_at_density(
+                props.T,
+                props.rho,
+            )
+        )
+        recovery_scale = max(
+            abs(props.u),
+            abs(cv * props.T) if isfinite(cv) else 0.0,
+            1.0,
+        )
+        if (
+            not all(
+                isfinite(value)
+                for value in (
+                    pressure_temperature_derivative,
+                    pressure_density_derivative,
+                    cv,
+                    recovered_internal_energy,
+                )
+            )
+            or cv <= 0.0
+        ):
+            return invalid("invalid_peng_robinson_derivative")
+        if abs(recovered_internal_energy - props.u) > 1.0e-8 * recovery_scale:
+            return invalid("properties_recovery_not_converged")
+
+        internal_energy_density_derivative = (
+            props.p - props.T * pressure_temperature_derivative
+        ) / (props.rho * props.rho)
+        drho: list[float] = []
+        du: list[float] = []
+        dT: list[float] = []
+        dp: list[float] = []
+        dh: list[float] = []
+        for mass_tangent, energy_tangent, volume_tangent in zip(
+            dm_values,
+            dU_values,
+            dV_values,
+            strict=True,
+        ):
+            density_tangent = (
+                mass_tangent / V - m * volume_tangent / (V * V)
+            )
+            internal_energy_tangent = (
+                energy_tangent / m - U * mass_tangent / (m * m)
+            )
+            temperature_tangent = (
+                internal_energy_tangent
+                - internal_energy_density_derivative * density_tangent
+            ) / cv
+            pressure_tangent = (
+                pressure_temperature_derivative * temperature_tangent
+                + pressure_density_derivative * density_tangent
+            )
+            enthalpy_tangent = (
+                internal_energy_tangent
+                + pressure_tangent / props.rho
+                - props.p * density_tangent / (props.rho * props.rho)
+            )
+            drho.append(density_tangent)
+            du.append(internal_energy_tangent)
+            dT.append(temperature_tangent)
+            dp.append(pressure_tangent)
+            dh.append(enthalpy_tangent)
+
+        tangent_values = (*drho, *du, *dT, *dp, *dh)
+        if not all(isfinite(value) for value in tangent_values):
+            return invalid("non_finite_property_tangent")
+        return ThermodynamicPropertiesLinearization(
+            properties=props,
+            tangents=ThermodynamicPropertyTangents(
+                p=tuple(dp),
+                T=tuple(dT),
+                rho=tuple(drho),
+                u=tuple(du),
+                h=tuple(dh),
+            ),
+        )
+
 
 @dataclass(frozen=True)
 class AmesimGasPropertyModelSpec: