refactor: Huge simplifications from ExprSocket

TODO.md

@@ -527,9 +527,17 @@ Reported:
 - (SOLVED) <https://projects.blender.org/blender/blender/issues/119664>
 
 Unreported:
+- Units are unruly, and are entirely useless when it comes to going small like this.
 - The `__mp_main__` bug.
 - Animated properties within custom node trees don't update with the frame. See: <https://projects.blender.org/blender/blender/issues/66392>
-- Can't update `items` using `id_propertie_ui` of `EnumProperty`
+- Can't update `items` using `id_properties_ui` of `EnumProperty`. Maybe less a bug than an annoyance.
+- **Matrix Display Bug**: The data given to matrix properties is entirely ignored in the UI; the data is flattened, then left-to-right, up-to-down, the data is inserted. It's neither row-major nor column-major - it's completely flat.
+	- Though, if one wanted row-major (**as is consistent with `mathutils.Matrix`**), one would be disappointed - the UI prints the matrix property column-major
+	- Trying to set the matrix property with a `mathutils.Matrix` is even stranger - firstly, the size of the `mathutils.Matrix` must be transposed with respect to the property size (again the col/row major mismatch). But secondly, even when accounting for the col/row major mismatch, the values of a ex. 2x3 (row-major) matrix (written to with a 3x2 matrix with same flattened sequence) is written in a very strange order:
+	- Write `mathutils.Matrix` `[[0,1], [2,3], [4,10]]`: Results in (UI displayed row-major) `[[0,3], [4,1], [3,5]]`
+	- **Workaround (write)**: Simply flatten the 2D array, re-shape by `[cols,rows]`. The UI will display as the original array. `myarray.flatten().reshape([cols,rows])`.
+	- **Workaround (read)**: `np.array([[el1 for el1 in el0] for el0 in BLENDER_OBJ.matrix_prop]).flatten().reshape([rows,cols])`. Simply flatten the property read 2D array and re-shape by `[rows,cols]`. Mind that data type out is equal to data type in.
+	- Also, for bool matrices, `toggle=True` has no effect. `alignment='CENTER'` also doesn't align the checkboxes in their cells.
 
 ## Tidy3D bugs
 Unreported:

doc/_quarto.yml

@@ -118,11 +118,9 @@ quartodoc:
     - subtitle: "`bl_maxwell.utils`"
       desc: Utilities wo/shared global state.
       contents:
-        - utils.analyze_geonodes
         - utils.blender_type_enum
         - utils.extra_sympy_units
         - utils.logger
-        - utils.pydantic_sympy
 
     - subtitle: "`bl_maxwell.services`"
       desc: Utilities w/shared global state.
@@ -172,7 +170,6 @@ quartodoc:
         - socket_colors
         - bl_socket_types
         - bl_socket_desc_map
-        - socket_units
 
         - unit_systems
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/bl_socket_map.py

@@ -5,11 +5,9 @@ Attributes:
 	BL_SOCKET_4D_TYPE_PREFIXES: Blender socket prefixes which indicate that the Blender socket has four values.
 """
 
-import functools
 import typing as typ
 
 import bpy
-import sympy as sp
 
 from blender_maxwell.utils import extra_sympy_units as spux
 from blender_maxwell.utils import logger as _logger
@@ -19,238 +17,54 @@ from . import sockets
 
 log = _logger.get(__name__)
 
-BLSocketType: typ.TypeAlias = str  ## A Blender-Defined Socket Type
-BLSocketValue: typ.TypeAlias = typ.Any  ## A Blender Socket Value
-BLSocketSize: typ.TypeAlias = int
-DescType: typ.TypeAlias = str
-Unit: typ.TypeAlias = typ.Any  ## Type of a valid unit
-## TODO: Move this kind of thing to contracts
-
 
 ####################
-# - BL Socket Size Parser
+# - Blender -> Socket Def(s)
 ####################
-BL_SOCKET_3D_TYPE_PREFIXES = {
+def socket_def_from_bl_isocket(
-	'NodeSocketVector',
+	bl_isocket: bpy.types.NodeTreeInterfaceSocket,
-	'NodeSocketRotation',
+) -> sockets.base.SocketDef | None:
+	"""Deduces and constructs an appropriate SocketDef to match the given `bl_interface_socket`."""
+	blsck_info = ct.BLSocketType.info_from_bl_isocket(bl_isocket)
+	if blsck_info.has_support and not blsck_info.is_preview:
+		# Map Expr Socket
+		## -> Accounts for any combo of shape/MathType/PhysicalType.
+		if blsck_info.socket_type == ct.SocketType.Expr:
+			return sockets.ExprSocketDef(
+				shape=blsck_info.size.shape,
+				mathtype=blsck_info.mathtype,
+				physical_type=blsck_info.physical_type,
+				default_unit=ct.UNITS_BLENDER[blsck_info.physical_type],
+				default_value=blsck_info.default_value,
+			)
+
+		## TODO: Explicitly map default to other supported SocketDef constructors
+
+		return sockets.SOCKET_DEFS[blsck_info.socket_type]()
+	return None
+
+
+def sockets_from_geonodes(
+	geonodes: bpy.types.GeometryNodeTree,
+) -> dict[ct.SocketName, sockets.base.SocketDef]:
+	"""Deduces and constructs appropriate SocketDefs to match all input sockets to the given GeoNodes tree."""
+	raw_socket_defs = {
+		socket_name: socket_def_from_bl_isocket(bl_isocket)
+		for socket_name, bl_isocket in geonodes.interface.items_tree.items()
 	}
-BL_SOCKET_4D_TYPE_PREFIXES = {
+	return {
-	'NodeSocketColor',
+		socket_name: socket_def
+		for socket_name, socket_def in raw_socket_defs.items()
+		if socket_def is not None
 	}
 
 
-@functools.lru_cache(maxsize=4096)
+## TODO: Make it fast, it's in a hot loop...
-def _size_from_bl_socket(
+def info_from_geonodes(
-	description: str,
+	geonodes: bpy.types.GeometryNodeTree,
-	bl_socket_type: BLSocketType,
+) -> dict[ct.SocketName, ct.BLSocketInfo]:
-):
+	"""Deduces and constructs appropriate SocketDefs to match all input sockets to the given GeoNodes tree."""
-	"""Parses the number of elements contained in a Blender interface socket.
+	return {
-
+		socket_name: ct.BLSocketType.info_from_bl_isocket(bl_isocket)
-	Since there are no 2D sockets in Blender, the user can specify "2D" in the Blender socket's description to "promise" that only the first two values will be used.
+		for socket_name, bl_isocket in geonodes.interface.items_tree.items()
-	When this is done, the third value is just never altered by the addon.
+	}
-
-	A hard-coded set of NodeSocket<Type> prefixes are used to determine which interface sockets are, in fact, 3D.
-	- For 3D sockets, a hard-coded list of Blender node socket types is used.
-	- Else, it is a 1D socket type.
-	"""
-	if description.startswith('2D'):
-		return 2
-	if any(
-		bl_socket_type.startswith(bl_socket_3d_type_prefix)
-		for bl_socket_3d_type_prefix in BL_SOCKET_3D_TYPE_PREFIXES
-	):
-		return 3
-	if any(
-		bl_socket_type.startswith(bl_socket_4d_type_prefix)
-		for bl_socket_4d_type_prefix in BL_SOCKET_4D_TYPE_PREFIXES
-	):
-		return 4
-
-	return 1
-
-
-####################
-# - BL Socket Type / Unit Parser
-####################
-@functools.lru_cache(maxsize=4096)
-def _socket_type_from_bl_socket(
-	description: str,
-	bl_socket_type: BLSocketType,
-) -> ct.SocketType:
-	"""Parse a Blender socket for a matching BLMaxwell socket type, relying on both the Blender socket type and user-generated hints in the description.
-
-	Arguments:
-		description: The description from Blender socket, aka. `bl_socket.description`.
-		bl_socket_type: The Blender socket type, aka. `bl_socket.socket_type`.
-
-	Returns:
-		The type of a MaxwellSimSocket that corresponds to the Blender socket.
-	"""
-	size = _size_from_bl_socket(description, bl_socket_type)
-
-	# Determine Socket Type Directly
-	## The naive mapping from BL socket -> Maxwell socket may be good enough.
-	if (
-		direct_socket_type := ct.BL_SOCKET_DIRECT_TYPE_MAP.get((bl_socket_type, size))
-	) is None:
-		msg = "Blender interface socket has no mapping among 'MaxwellSimSocket's."
-		raise ValueError(msg)
-
-	# (No Description) Return Direct Socket Type
-	if ct.BL_SOCKET_DESCR_ANNOT_STRING not in description:
-		return direct_socket_type
-
-	# Parse Description for Socket Type
-	## The "2D" token is special; don't include it if it's there.
-	descr_params = description.split(ct.BL_SOCKET_DESCR_ANNOT_STRING)[0]
-	directive = (
-		_tokens[0] if (_tokens := descr_params.split(' '))[0] != '2D' else _tokens[1]
-	)
-	if directive == 'Preview':
-		return direct_socket_type  ## TODO: Preview element handling
-
-	if (
-		socket_type := ct.BL_SOCKET_DESCR_TYPE_MAP.get(
-			(directive, bl_socket_type, size)
-		)
-	) is None:
-		msg = f'Socket description "{(directive, bl_socket_type, size)}" doesn\'t map to a socket type + unit'
-		raise ValueError(msg)
-
-	return socket_type
-
-
-####################
-# - BL Socket Interface Definition
-####################
-@functools.lru_cache(maxsize=4096)
-def _socket_def_from_bl_socket(
-	description: str,
-	bl_socket_type: BLSocketType,
-) -> ct.SocketType:
-	return sockets.SOCKET_DEFS[_socket_type_from_bl_socket(description, bl_socket_type)]
-
-
-def socket_def_from_bl_socket(
-	bl_interface_socket: bpy.types.NodeTreeInterfaceSocket,
-) -> sockets.base.SocketDef:
-	"""Computes an appropriate (no-arg) SocketDef from the given `bl_interface_socket`, by parsing it."""
-	return _socket_def_from_bl_socket(
-		bl_interface_socket.description, bl_interface_socket.bl_socket_idname
-	)
-
-
-####################
-# - Extract Default Interface Socket Value
-####################
-def _read_bl_socket_default_value(
-	description: str,
-	bl_socket_type: BLSocketType,
-	bl_socket_value: BLSocketValue,
-	unit_system: dict | None = None,
-	allow_unit_not_in_unit_system: bool = False,
-) -> typ.Any:
-	# Parse the BL Socket Type and Value
-	## The 'lambda' delays construction until size is determined.
-	socket_type = _socket_type_from_bl_socket(description, bl_socket_type)
-	parsed_socket_value = {
-		1: lambda: bl_socket_value,
-		2: lambda: sp.Matrix(tuple(bl_socket_value)[:2]),
-		3: lambda: sp.Matrix(tuple(bl_socket_value)),
-		4: lambda: sp.Matrix(tuple(bl_socket_value)),
-	}[_size_from_bl_socket(description, bl_socket_type)]()
-
-	# Add Unit-System Unit to Parsed
-	## Use the matching socket type to lookup the unit in the unit system.
-	if unit_system is not None:
-		if (unit := unit_system.get(socket_type)) is None:
-			if allow_unit_not_in_unit_system:
-				return parsed_socket_value
-
-			msg = f'Unit system does not provide a unit for {socket_type}'
-			raise RuntimeError(msg)
-
-		return parsed_socket_value * unit
-	return parsed_socket_value
-
-
-def read_bl_socket_default_value(
-	bl_interface_socket: bpy.types.NodeTreeInterfaceSocket,
-	unit_system: dict | None = None,
-	allow_unit_not_in_unit_system: bool = False,
-) -> typ.Any:
-	"""Reads the `default_value` of a Blender socket, guaranteeing a well-formed value consistent with the passed unit system.
-
-	Arguments:
-		bl_interface_socket: The Blender interface socket to analyze for description, socket type, and default value.
-		unit_system: The mapping from BLMaxwell SocketType to corresponding unit, used to apply the appropriate unit to the output.
-
-	Returns:
-		The parsed, well-formed version of `bl_socket.default_value`, of the appropriate form and unit.
-
-	"""
-	return _read_bl_socket_default_value(
-		bl_interface_socket.description,
-		bl_interface_socket.bl_socket_idname,
-		bl_interface_socket.default_value,
-		unit_system=unit_system,
-		allow_unit_not_in_unit_system=allow_unit_not_in_unit_system,
-	)
-
-
-def _writable_bl_socket_value(
-	description: str,
-	bl_socket_type: BLSocketType,
-	value: typ.Any,
-	unit_system: dict | None = None,
-	allow_unit_not_in_unit_system: bool = False,
-) -> typ.Any:
-	socket_type = _socket_type_from_bl_socket(description, bl_socket_type)
-
-	# Retrieve Unit-System Unit
-	if unit_system is not None:
-		if (unit := unit_system.get(socket_type)) is None:
-			if allow_unit_not_in_unit_system:
-				_bl_socket_value = value
-			else:
-				msg = f'Unit system does not provide a unit for {socket_type}'
-				raise RuntimeError(msg)
-		else:
-			_bl_socket_value = spux.scale_to_unit(value, unit)
-	else:
-		_bl_socket_value = value
-
-	# Compute Blender Socket Value
-	if isinstance(_bl_socket_value, sp.Basic | sp.MatrixBase):
-		bl_socket_value = spux.sympy_to_python(_bl_socket_value)
-	else:
-		bl_socket_value = _bl_socket_value
-
-	if _size_from_bl_socket(description, bl_socket_type) == 2:  # noqa: PLR2004
-		bl_socket_value = bl_socket_value[:2]
-	return bl_socket_value
-
-
-def writable_bl_socket_value(
-	bl_interface_socket: bpy.types.NodeTreeInterfaceSocket,
-	value: typ.Any,
-	unit_system: dict | None = None,
-	allow_unit_not_in_unit_system: bool = False,
-) -> typ.Any:
-	"""Processes a value to be ready-to-write to a Blender socket.
-
-	Arguments:
-		bl_interface_socket: The Blender interface socket to analyze
-		value: The value to prepare for writing to the given Blender socket.
-		unit_system: The mapping from BLMaxwell SocketType to corresponding unit, used to scale the value to the the appropriate unit.
-
-	Returns:
-		A value corresponding to the input, which is guaranteed to be compatible with the Blender socket (incl. via a GeoNodes modifier), as well as correctly scaled with respect to the given unit system.
-	"""
-	return _writable_bl_socket_value(
-		bl_interface_socket.description,
-		bl_interface_socket.bl_socket_idname,
-		value,
-		unit_system=unit_system,
-		allow_unit_not_in_unit_system=allow_unit_not_in_unit_system,
-	)

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/__init__.py

@@ -22,8 +22,7 @@ from blender_maxwell.contracts import (
 	addon,
 )
 
-from .bl_socket_desc_map import BL_SOCKET_DESCR_ANNOT_STRING, BL_SOCKET_DESCR_TYPE_MAP
+from .bl_socket_types import BLSocketInfo, BLSocketType
-from .bl_socket_types import BL_SOCKET_DIRECT_TYPE_MAP
 from .category_labels import NODE_CAT_LABELS
 from .category_types import NodeCategory
 from .flow_events import FlowEvent
@@ -43,7 +42,6 @@ from .mobj_types import ManagedObjType
 from .node_types import NodeType
 from .socket_colors import SOCKET_COLORS
 from .socket_types import SocketType
-from .socket_units import SOCKET_UNITS, unit_to_socket_type
 from .tree_types import TreeType
 from .unit_systems import UNITS_BLENDER, UNITS_TIDY3D
 
@@ -72,15 +70,12 @@ __all__ = [
 	'Icon',
 	'TreeType',
 	'SocketType',
-	'SOCKET_UNITS',
-	'unit_to_socket_type',
 	'SOCKET_COLORS',
 	'SOCKET_SHAPES',
 	'UNITS_BLENDER',
 	'UNITS_TIDY3D',
-	'BL_SOCKET_DESCR_TYPE_MAP',
+	'BLSocketInfo',
-	'BL_SOCKET_DIRECT_TYPE_MAP',
+	'BLSocketType',
-	'BL_SOCKET_DESCR_ANNOT_STRING',
 	'NodeType',
 	'NodeCategory',
 	'NODE_CAT_LABELS',

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/bl_socket_desc_map.py

@@ -1,62 +0,0 @@
-from .socket_types import SocketType as ST
-
-BL_SOCKET_DESCR_ANNOT_STRING = ':: '
-BL_SOCKET_DESCR_TYPE_MAP = {
-	('Time', 'NodeSocketFloat', 1): ST.PhysicalTime,
-	('Angle', 'NodeSocketFloat', 1): ST.PhysicalAngle,
-	('SolidAngle', 'NodeSocketFloat', 1): ST.PhysicalSolidAngle,
-	('Rotation', 'NodeSocketVector', 2): ST.PhysicalRot2D,
-	('Rotation', 'NodeSocketVector', 3): ST.PhysicalRot3D,
-	('Freq', 'NodeSocketFloat', 1): ST.PhysicalFreq,
-	('AngFreq', 'NodeSocketFloat', 1): ST.PhysicalAngFreq,
-	## Cartesian
-	('Length', 'NodeSocketFloat', 1): ST.PhysicalLength,
-	('Area', 'NodeSocketFloat', 1): ST.PhysicalArea,
-	('Volume', 'NodeSocketFloat', 1): ST.PhysicalVolume,
-	('Disp', 'NodeSocketVector', 2): ST.PhysicalDisp2D,
-	('Disp', 'NodeSocketVector', 3): ST.PhysicalDisp3D,
-	('Point', 'NodeSocketFloat', 1): ST.PhysicalPoint1D,
-	('Point', 'NodeSocketVector', 2): ST.PhysicalPoint2D,
-	('Point', 'NodeSocketVector', 3): ST.PhysicalPoint3D,
-	('Size', 'NodeSocketVector', 2): ST.PhysicalSize2D,
-	('Size', 'NodeSocketVector', 3): ST.PhysicalSize3D,
-	## Mechanical
-	('Mass', 'NodeSocketFloat', 1): ST.PhysicalMass,
-	('Speed', 'NodeSocketFloat', 1): ST.PhysicalSpeed,
-	('Vel', 'NodeSocketVector', 2): ST.PhysicalVel2D,
-	('Vel', 'NodeSocketVector', 3): ST.PhysicalVel3D,
-	('Accel', 'NodeSocketFloat', 1): ST.PhysicalAccelScalar,
-	('Accel', 'NodeSocketVector', 2): ST.PhysicalAccel2D,
-	('Accel', 'NodeSocketVector', 3): ST.PhysicalAccel3D,
-	('Force', 'NodeSocketFloat', 1): ST.PhysicalForceScalar,
-	('Force', 'NodeSocketVector', 2): ST.PhysicalForce2D,
-	('Force', 'NodeSocketVector', 3): ST.PhysicalForce3D,
-	('Pressure', 'NodeSocketFloat', 1): ST.PhysicalPressure,
-	## Energetic
-	('Energy', 'NodeSocketFloat', 1): ST.PhysicalEnergy,
-	('Power', 'NodeSocketFloat', 1): ST.PhysicalPower,
-	('Temp', 'NodeSocketFloat', 1): ST.PhysicalTemp,
-	## ELectrodynamical
-	('Curr', 'NodeSocketFloat', 1): ST.PhysicalCurr,
-	('CurrDens', 'NodeSocketVector', 2): ST.PhysicalCurrDens2D,
-	('CurrDens', 'NodeSocketVector', 3): ST.PhysicalCurrDens3D,
-	('Charge', 'NodeSocketFloat', 1): ST.PhysicalCharge,
-	('Voltage', 'NodeSocketFloat', 1): ST.PhysicalVoltage,
-	('Capacitance', 'NodeSocketFloat', 1): ST.PhysicalCapacitance,
-	('Resistance', 'NodeSocketFloat', 1): ST.PhysicalResistance,
-	('Conductance', 'NodeSocketFloat', 1): ST.PhysicalConductance,
-	('MagFlux', 'NodeSocketFloat', 1): ST.PhysicalMagFlux,
-	('MagFluxDens', 'NodeSocketFloat', 1): ST.PhysicalMagFluxDens,
-	('Inductance', 'NodeSocketFloat', 1): ST.PhysicalInductance,
-	('EField', 'NodeSocketFloat', 2): ST.PhysicalEField3D,
-	('EField', 'NodeSocketFloat', 3): ST.PhysicalEField2D,
-	('HField', 'NodeSocketFloat', 2): ST.PhysicalHField3D,
-	('HField', 'NodeSocketFloat', 3): ST.PhysicalHField2D,
-	## Luminal
-	('LumIntensity', 'NodeSocketFloat', 1): ST.PhysicalLumIntensity,
-	('LumFlux', 'NodeSocketFloat', 1): ST.PhysicalLumFlux,
-	('Illuminance', 'NodeSocketFloat', 1): ST.PhysicalIlluminance,
-	## Optical
-	('PolJones', 'NodeSocketFloat', 2): ST.PhysicalPolJones,
-	('Pol', 'NodeSocketFloat', 4): ST.PhysicalPol,
-}

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/bl_socket_types.py

@@ -1,39 +1,312 @@
-from .socket_types import SocketType as ST
+import dataclasses
+import enum
+import typing as typ
 
-BL_SOCKET_DIRECT_TYPE_MAP = {
+import bpy
+import sympy as sp
+
+from blender_maxwell.utils import blender_type_enum
+from blender_maxwell.utils import extra_sympy_units as spux
+
+from .socket_types import SocketType
+
+BL_SOCKET_DESCR_ANNOT_STRING = ':: '
+
+
+@dataclasses.dataclass(kw_only=True, frozen=True)
+class BLSocketInfo:
+	has_support: bool
+	is_preview: bool
+	socket_type: SocketType | None
+	size: spux.NumberSize1D | None
+	physical_type: spux.PhysicalType | None
+	default_value: spux.ScalarUnitlessRealExpr
+
+	bl_isocket_identifier: spux.ScalarUnitlessRealExpr
+
+
+@blender_type_enum.prefix_values_with('NodeSocket')
+class BLSocketType(enum.StrEnum):
+	Virtual = 'Virtual'
 	# Blender
-	('NodeSocketCollection', 1): ST.BlenderCollection,
+	Image = 'Image'
-	('NodeSocketImage', 1): ST.BlenderImage,
+	Shader = 'Shader'
-	('NodeSocketObject', 1): ST.BlenderObject,
+	Material = 'Material'
-	('NodeSocketMaterial', 1): ST.BlenderMaterial,
+	Geometry = 'Material'
+	Object = 'Object'
+	Collection = 'Collection'
 	# Basic
-	('NodeSocketString', 1): ST.String,
+	Bool = 'Bool'
-	('NodeSocketBool', 1): ST.Bool,
+	String = 'String'
+	Menu = 'Menu'
 	# Float
-	('NodeSocketFloat', 1): ST.RealNumber,
+	Float = 'Float'
-	# ("NodeSocketFloatAngle", 1): ST.PhysicalAngle,
+	FloatUnsigned = 'FloatUnsigned'
-	# ("NodeSocketFloatDistance", 1): ST.PhysicalLength,
+	FloatAngle = 'FloatAngle'
-	('NodeSocketFloatFactor', 1): ST.RealNumber,
+	FloatDistance = 'FloatDistance'
-	('NodeSocketFloatPercentage', 1): ST.RealNumber,
+	FloatFactor = 'FloatFactor'
-	# ("NodeSocketFloatTime", 1): ST.PhysicalTime,
+	FloatPercentage = 'FloatPercentage'
-	# ("NodeSocketFloatTimeAbsolute", 1): ST.PhysicalTime,
+	FloatTime = 'FloatTime'
+	FloatTimeAbsolute = 'FloatTimeAbsolute'
 	# Int
-	('NodeSocketInt', 1): ST.IntegerNumber,
+	Int = 'Int'
-	('NodeSocketIntFactor', 1): ST.IntegerNumber,
+	IntFactor = 'IntFactor'
-	('NodeSocketIntPercentage', 1): ST.IntegerNumber,
+	IntPercentage = 'IntPercentage'
-	('NodeSocketIntUnsigned', 1): ST.IntegerNumber,
+	IntUnsigned = 'IntUnsigned'
+	# Vector
+	Color = 'Color'
+	Rotation = 'Rotation'
+	Vector = 'Vector'
+	VectorAcceleration = 'Acceleration'
+	VectorDirection = 'Direction'
+	VectorEuler = 'Euler'
+	VectorTranslation = 'Translation'
+	VectorVelocity = 'Velocity'
+	VectorXYZ = 'XYZ'
+
+	@staticmethod
+	def from_bl_isocket(
+		bl_isocket: bpy.types.NodeTreeInterfaceSocket,
+	) -> typ.Self:
+		return BLSocketType[bl_isocket.bl_socket_idname]
+
+	@staticmethod
+	def info_from_bl_isocket(
+		bl_isocket: bpy.types.NodeTreeInterfaceSocket,
+	) -> typ.Self:
+		return BLSocketType.from_bl_isocket(bl_isocket).parse(
+			bl_isocket.default_value, bl_isocket.description, bl_isocket.identifier
+		)
+
+	####################
+	# - Direct Properties
+	####################
+	@property
+	def has_support(self) -> bool:
+		BLST = BLSocketType
+		return {
+			BLST.Virtual: False,
+			BLST.Geometry: False,
+			BLST.Shader: False,
+			BLST.FloatUnsigned: False,
+			BLST.IntUnsigned: False,
+		}.get(self, True)
+
+	@property
+	def socket_type(self) -> SocketType | None:
+		"""Deduce `SocketType` corresponding to the Blender socket type.
+
+		**The socket type alone is not enough** to actually create the socket.
+		To declare a socket in the addon, an appropriate `socket.SocketDef` must be constructed in a manner that respects contextual information.
+
+		Returns:
+			The corresponding socket type, if the addon has support for mapping this Blender socket.
+			For sockets with support, the fallback is always `SocketType.Expr`.
+
+			Support is determined using `self.has_support`
+		"""
+		if not self.has_support:
+			return None
+
+		BLST = BLSocketType
+		ST = SocketType
+		return {
+			# Blender
+			# Basic
+			BLST.Bool: ST.String,
+			# Float
 			# Array-Like
-	('NodeSocketColor', 3): ST.Color,
+			BLST.Color: ST.Color,
-	('NodeSocketRotation', 2): ST.PhysicalRot2D,
+		}.get(self, ST.Expr)
-	('NodeSocketVector', 2): ST.Real2DVector,
+
-	('NodeSocketVector', 3): ST.Real3DVector,
+	@property
-	# ("NodeSocketVectorAcceleration", 2): ST.PhysicalAccel2D,
+	def mathtype(self) -> spux.MathType | None:
-	# ("NodeSocketVectorAcceleration", 3): ST.PhysicalAccel3D,
+		"""Deduce `spux.MathType` corresponding to the Blender socket type.
-	# ("NodeSocketVectorDirection", 2): ST.Real2DVectorDir,
+
-	# ("NodeSocketVectorDirection", 3): ST.Real3DVectorDir,
+		**The socket type alone is not enough** to actually create the socket.
-	('NodeSocketVectorEuler', 2): ST.PhysicalRot2D,
+		To declare a socket in the addon, an appropriate `socket.SocketDef` must be constructed in a manner that respects contextual information.
-	('NodeSocketVectorEuler', 3): ST.PhysicalRot3D,
+
-	# ("NodeSocketVectorTranslation", 3): ST.PhysicalDisp3D,
+		Returns:
-	# ("NodeSocketVectorVelocity", 3): ST.PhysicalVel3D,
+			The corresponding socket type, if the addon has support for mapping this Blender socket.
-	# ("NodeSocketVectorXYZ", 3): ST.PhysicalPoint3D,
+			For sockets with support, the fallback is always `SocketType.Expr`.
-}
+
+			Support is determined using `self.has_support`
+		"""
+		if not self.has_support:
+			return None
+
+		BLST = BLSocketType
+		MT = spux.MathType
+		return {
+			# Blender
+			# Basic
+			BLST.Bool: MT.Bool,
+			# Float
+			BLST.Float: MT.Real,
+			BLST.FloatAngle: MT.Real,
+			BLST.FloatDistance: MT.Real,
+			BLST.FloatFactor: MT.Real,
+			BLST.FloatPercentage: MT.Real,
+			BLST.FloatTime: MT.Real,
+			BLST.FloatTimeAbsolute: MT.Real,
+			# Int
+			BLST.Int: MT.Integer,
+			BLST.IntFactor: MT.Integer,
+			BLST.IntPercentage: MT.Integer,
+			# Vector
+			BLST.Color: MT.Real,
+			BLST.Rotation: MT.Real,
+			BLST.Vector: MT.Real,
+			BLST.VectorAcceleration: MT.Real,
+			BLST.VectorDirection: MT.Real,
+			BLST.VectorEuler: MT.Real,
+			BLST.VectorTranslation: MT.Real,
+			BLST.VectorVelocity: MT.Real,
+			BLST.VectorXYZ: MT.Real,
+		}.get(self)
+
+	@property
+	def size(
+		self,
+	) -> (
+		typ.Literal[
+			spux.NumberSize1D.Scalar, spux.NumberSize1D.Vec3, spux.NumberSize1D.Vec4
+		]
+		| None
+	):
+		"""Deduce the internal size of the Blender socket's data.
+
+		Returns:
+			A `spux.NumberSize1D` reflecting the internal data representation.
+			Always falls back to `{spux.NumberSize1D.Scalar}`.
+		"""
+		if not self.has_support:
+			return None
+
+		S = spux.NumberSize1D
+		BLST = BLSocketType
+		return {
+			BLST.Color: S.Vec4,
+			BLST.Rotation: S.Vec3,
+			BLST.VectorAcceleration: S.Vec3,
+			BLST.VectorDirection: S.Vec3,
+			BLST.VectorEuler: S.Vec3,
+			BLST.VectorTranslation: S.Vec3,
+			BLST.VectorVelocity: S.Vec3,
+			BLST.VectorXYZ: S.Vec3,
+		}.get(self, {S.Scalar})
+
+	@property
+	def unambiguous_physical_type(self) -> spux.PhysicalType | None:
+		"""Deduce an **unambiguous** physical type from the Blender socket, if any.
+
+		Blender does have its own unit systems, which leads to some Blender socket subtypes having an obvious choice of physical unit dimension (ex. `BLSocketType.FloatTime`).
+		In such cases, the `spux.PhysicalType` that matches the Blender socket can be uniquely determined.
+
+		When a phsyical type cannot be immediately determined in this way, other mechanisms must be used to deduce what to do.
+
+		Returns:
+			A physical type corresponding to the Blender socket, **if exactly one** can be determined with no ambiguity - else `None`.
+
+			If more than one physical type might apply,  `None`.
+		"""
+		if not self.has_support:
+			return None
+
+		P = spux.PhysicalType
+		BLST = BLSocketType
+		{
+			BLST.FloatAngle: P.Angle,
+			BLST.FloatDistance: P.Length,
+			BLST.FloatTime: P.Time,
+			BLST.FloatTimeAbsolute: P.Time,  ## What's the difference?
+			BLST.VectorAcceleration: P.Accel,
+			## BLST.VectorDirection: Directions are unitless (within cartesian)
+			BLST.VectorEuler: P.Angle,
+			BLST.VectorTranslation: P.Length,
+			BLST.VectorVelocity: P.Vel,
+			BLST.VectorXYZ: P.Length,
+		}.get(self)
+
+	@property
+	def valid_sizes(self) -> set[spux.NumberSize1D] | None:
+		"""Deduce which sizes it would be valid to interpret a Blender socket as having.
+
+		This property's purpose is merely to present a set of options that _are valid_.
+		Whether an a size _is truly usable_, can only be determined with contextual information, wherein certain decisions can be made:
+
+		- **2D vs. 3D**:  In general, Blender's vector socket types are **only** 3D, and we cannot ever _really_ have a 2D vector.
+			If one chooses interpret ex. `BLSocketType.Vector` as 2D, one might do so by pretending the third coordinate doesn't exist.
+			But **this is a subjective decision**, which always has to align with the logic on the other side of the Blender socket.
+		- **Colors**: Generally, `BLSocketType.Color` is always 4D, representing `RGBA` (with alpha channel).
+			However, we often don't care about alpha; therefore, we might choose to "just" push a 3D `RGB` vector.
+			Again, **this is a subjective decision** which requires one to make a decision about alpha, for example "alpha is always 1".
+		- **Scalars**: We can generally always interpret a scalar as a vector, using well-defined "broadcasting".
+
+		Returns:
+			The set of `spux.NumberSize1D`s, which it would be safe to interpret the Blender socket as having.
+
+			Always falls back to `{spux.NumberSize1D.Scalar}`.
+		"""
+		if not self.has_support:
+			return None
+
+		S = spux.NumberSize1D
+		BLST = BLSocketType
+		return {
+			BLST.Color: {S.Scalar, S.Vec3, S.Vec4},
+			BLST.Rotation: {S.Vec2, S.Vec3},
+			BLST.VectorAcceleration: {S.Scalar, S.Vec2, S.Vec3},
+			BLST.VectorDirection: {S.Scalar, S.Vec2, S.Vec3},
+			BLST.VectorEuler: {S.Vec2, S.Vec3},
+			BLST.VectorTranslation: {S.Scalar, S.Vec2, S.Vec3},
+			BLST.VectorVelocity: {S.Scalar, S.Vec2, S.Vec3},
+			BLST.VectorXYZ: {S.Scalar, S.Vec2, S.Vec3},
+		}.get(self, {S.Scalar})
+
+	####################
+	# - Parsed Properties
+	####################
+	def parse(
+		self, bl_default_value: typ.Any, description: str, bl_isocket_identifier: str
+	) -> BLSocketInfo:
+		# Parse the Description
+		## TODO: Some kind of error on invalid parse if there is also no unambiguous physical type
+		descr_params = description.split(BL_SOCKET_DESCR_ANNOT_STRING)[0]
+		directive = (
+			_tokens[0]
+			if (_tokens := descr_params.split(' '))[0] != '2D'
+			else _tokens[1]
+		)
+
+		## Interpret the Description Parse
+		parsed_physical_type = getattr(spux.PhysicalType, directive, None)
+		physical_type = (
+			self.unambiguous_physical_type
+			if self.unambiguous_physical_type is not None
+			else parsed_physical_type
+		)
+
+		# Parse the Default Value
+		if self.mathtype is not None:
+			if self.size == spux.NumberSize1D.Scalar:
+				default_value = self.mathtype.pytype(bl_default_value)
+			elif description.startswith('2D'):
+				default_value = sp.Matrix(tuple(bl_default_value)[:2])
+			else:
+				default_value = sp.Matrix(tuple(bl_default_value))
+		else:
+			default_value = bl_default_value
+
+		# Return Parsed Socket Information
+		## -> Combining directly known and parsed knowledge.
+		## -> Should contain everything needed to match the Blender socket.
+		return BLSocketInfo(
+			has_support=self.has_support,
+			is_preview=(directive == 'Preview'),
+			socket_type=self.socket_type,
+			size=self.size,
+			physical_type=physical_type,
+			default_value=default_value,
+			bl_isocket_identifier=bl_isocket_identifier,
+		)

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds.py

@@ -316,8 +316,12 @@ class LazyValueFuncFlow:
 	"""
 
 	func: LazyFunction
-	func_args: list[type] = dataclasses.field(default_factory=list)
+	func_args: list[spux.MathType | spux.PhysicalType] = dataclasses.field(
-	func_kwargs: dict[str, type] = dataclasses.field(default_factory=dict)
+		default_factory=list
+	)
+	func_kwargs: dict[str, spux.MathType | spux.PhysicalType] = dataclasses.field(
+		default_factory=dict
+	)
 	supports_jax: bool = False
 	supports_numba: bool = False
 
@@ -432,9 +436,7 @@ class LazyArrayRangeFlow:
 
 		unit: The unit of the generated array values
 
-		int_symbols: Set of integer-valued variables from which `start` and/or `stop` are determined.
+		symbols: Set of variables from which `start` and/or `stop` are determined.
-		real_symbols: Set of real-valued variables from which `start` and/or `stop` are determined.
-		complex_symbols: Set of complex-valued variables from which `start` and/or `stop` are determined.
 	"""
 
 	start: spux.ScalarUnitlessComplexExpr
@@ -444,12 +446,10 @@ class LazyArrayRangeFlow:
 
 	unit: spux.Unit | None = None
 
-	int_symbols: set[spux.IntSymbol] = frozenset()
+	symbols: frozenset[spux.IntSymbol] = frozenset()
-	real_symbols: set[spux.RealSymbol] = frozenset()
-	complex_symbols: set[spux.ComplexSymbol] = frozenset()
 
 	@functools.cached_property
-	def symbols(self) -> list[sp.Symbol]:
+	def sorted_symbols(self) -> list[sp.Symbol]:
 		"""Retrieves all symbols by concatenating int, real, and complex symbols, and sorting them by name.
 
 		The order is guaranteed to be **deterministic**.
@@ -457,10 +457,7 @@ class LazyArrayRangeFlow:
 		Returns:
 			All symbols valid for use in the expression.
 		"""
-		return sorted(
+		return sorted(self.symbols, key=lambda sym: sym.name)
-			self.int_symbols | self.real_symbols | self.complex_symbols,
-			key=lambda sym: sym.name,
-		)
 
 	@functools.cached_property
 	def mathtype(self) -> spux.MathType:
@@ -508,9 +505,7 @@ class LazyArrayRangeFlow:
 				steps=self.steps,
 				scaling=self.scaling,
 				unit=corrected_unit,
-				int_symbols=self.int_symbols,
+				symbols=self.symbols,
-				real_symbols=self.real_symbols,
-				complex_symbols=self.complex_symbols,
 			)
 
 		msg = f'Tried to correct unit of unitless LazyDataValueRange "{corrected_unit}"'
@@ -530,15 +525,12 @@ class LazyArrayRangeFlow:
 		"""
 		if self.unit is not None:
 			return LazyArrayRangeFlow(
-				start=spu.convert_to(self.start, unit),
+				start=spu.scale_to_unit(self.start * self.unit, unit),
-				stop=spu.convert_to(self.stop, unit),
+				stop=spu.scale_to_unit(self.stop * self.unit, unit),
 				steps=self.steps,
 				scaling=self.scaling,
 				unit=unit,
 				symbols=self.symbols,
-				int_symbols=self.int_symbols,
-				real_symbols=self.real_symbols,
-				complex_symbols=self.complex_symbols,
 			)
 
 		msg = f'Tried to rescale unitless LazyDataValueRange to unit {unit}'
@@ -549,7 +541,7 @@ class LazyArrayRangeFlow:
 	####################
 	def rescale_bounds(
 		self,
-		scaler: typ.Callable[
+		rescale_func: typ.Callable[
 			[spux.ScalarUnitlessComplexExpr], spux.ScalarUnitlessComplexExpr
 		],
 		reverse: bool = False,
@@ -570,18 +562,12 @@ class LazyArrayRangeFlow:
 			A rescaled `LazyArrayRangeFlow`.
 		"""
 		return LazyArrayRangeFlow(
-			start=spu.convert_to(
+			start=rescale_func(self.start if not reverse else self.stop),
-				scaler(self.start if not reverse else self.stop), self.unit
+			stop=rescale_func(self.stop if not reverse else self.start),
-			),
-			stop=spu.convert_to(
-				scaler(self.stop if not reverse else self.start), self.unit
-			),
 			steps=self.steps,
 			scaling=self.scaling,
 			unit=self.unit,
-			int_symbols=self.int_symbols,
+			symbols=self.symbols,
-			real_symbols=self.real_symbols,
-			complex_symbols=self.complex_symbols,
 		)
 
 	####################
@@ -650,9 +636,7 @@ class LazyArrayRangeFlow:
 		"""
 		return LazyValueFuncFlow(
 			func=self.as_func,
-			func_args=[
+			func_args=[(spux.MathType.from_expr(sym)) for sym in self.symbols],
-				(sym.name, spux.sympy_to_python_type(sym)) for sym in self.symbols
-			],
 			supports_jax=True,
 		)
 
@@ -709,13 +693,38 @@ class LazyArrayRangeFlow:
 ####################
 @dataclasses.dataclass(frozen=True, kw_only=True)
 class ParamsFlow:
-	func_args: list[typ.Any] = dataclasses.field(default_factory=list)
+	func_args: list[spux.SympyExpr] = dataclasses.field(default_factory=list)
-	func_kwargs: dict[str, typ.Any] = dataclasses.field(default_factory=dict)
+	func_kwargs: dict[str, spux.SympyExpr] = dataclasses.field(default_factory=dict)
 
+	####################
+	# - Scaled Func Args
+	####################
+	def scaled_func_args(self, unit_system: spux.UnitSystem):
+		"""Return the function arguments, scaled to the unit system, stripped of units, and cast to jax-compatible arguments."""
+		return [
+			spux.convert_to_unit_system(func_arg, unit_system, use_jax_array=True)
+			for func_arg in self.func_args
+		]
+
+	def scaled_func_kwargs(self, unit_system: spux.UnitSystem):
+		"""Return the function arguments, scaled to the unit system, stripped of units, and cast to jax-compatible arguments."""
+		return {
+			arg_name: spux.convert_to_unit_system(arg, unit_system, use_jax_array=True)
+			for arg_name, arg in self.func_args
+		}
+
+	####################
+	# - Operations
+	####################
 	def __or__(
 		self,
 		other: typ.Self,
 	):
+		"""Combine two function parameter lists, such that the LHS will be concatenated with the RHS.
+
+		Just like its neighbor in `LazyValueFunc`, this effectively combines two functions with unique parameters.
+		The next composed function will receive a tuple of two arrays, instead of just one, allowing binary operations to occur.
+		"""
 		return ParamsFlow(
 			func_args=self.func_args + other.func_args,
 			func_kwargs=self.func_kwargs | other.func_kwargs,
@@ -723,10 +732,8 @@ class ParamsFlow:
 
 	def compose_within(
 		self,
-		enclosing_func_args: list[tuple[type]] = (),
+		enclosing_func_args: list[spux.SympyExpr] = (),
-		enclosing_func_kwargs: dict[str, type] = MappingProxyType({}),
+		enclosing_func_kwargs: dict[str, spux.SympyExpr] = MappingProxyType({}),
-		enclosing_func_arg_units: dict[str, type] = MappingProxyType({}),
-		enclosing_func_kwarg_units: dict[str, type] = MappingProxyType({}),
 	) -> typ.Self:
 		return ParamsFlow(
 			func_args=self.func_args + list(enclosing_func_args),
@@ -745,6 +752,8 @@ class InfoFlow:
 		default_factory=dict
 	)  ## TODO: Rename to dim_idxs
 
+	## TODO: Add PhysicalType
+
 	@functools.cached_property
 	def dim_lens(self) -> dict[str, int]:
 		return {dim_name: len(dim_idx) for dim_name, dim_idx in self.dim_idx.items()}
@@ -769,12 +778,14 @@ class InfoFlow:
 		]
 
 	# Output Information
+	## TODO: Add PhysicalType
 	output_name: str = dataclasses.field(default_factory=list)
 	output_shape: tuple[int, ...] | None = dataclasses.field(default=None)
 	output_mathtype: spux.MathType = dataclasses.field()
 	output_unit: spux.Unit | None = dataclasses.field()
 
 	# Pinned Dimension Information
+	## TODO: Add PhysicalType
 	pinned_dim_names: list[str] = dataclasses.field(default_factory=list)
 	pinned_dim_values: dict[str, float | complex] = dataclasses.field(
 		default_factory=dict

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/socket_colors.py

@@ -4,42 +4,13 @@ from .socket_types import SocketType as ST
 SOCKET_COLORS = {
 	# Basic
 	ST.Any: (0.9, 0.9, 0.9, 1.0),  # Light Grey
-	ST.Data: (0.8, 0.8, 0.8, 1.0),  # Light Grey
 	ST.Bool: (0.7, 0.7, 0.7, 1.0),  # Medium Light Grey
 	ST.String: (0.7, 0.7, 0.7, 1.0),  # Medium Light Grey
 	ST.FilePath: (0.6, 0.6, 0.6, 1.0),  # Medium Grey
 	ST.Expr: (0.5, 0.5, 0.5, 1.0),  # Medium Grey
-	# Number
-	ST.IntegerNumber: (0.5, 0.5, 1.0, 1.0),  # Light Blue
-	ST.RationalNumber: (0.4, 0.4, 0.9, 1.0),  # Medium Light Blue
-	ST.RealNumber: (0.3, 0.3, 0.8, 1.0),  # Medium Blue
-	ST.ComplexNumber: (0.2, 0.2, 0.7, 1.0),  # Dark Blue
-	# Vector
-	ST.Integer2DVector: (0.5, 1.0, 0.5, 1.0),  # Light Green
-	ST.Real2DVector: (0.5, 1.0, 0.5, 1.0),  # Light Green
-	ST.Complex2DVector: (0.4, 0.9, 0.4, 1.0),  # Medium Light Green
-	ST.Integer3DVector: (0.3, 0.8, 0.3, 1.0),  # Medium Green
-	ST.Real3DVector: (0.3, 0.8, 0.3, 1.0),  # Medium Green
-	ST.Complex3DVector: (0.2, 0.7, 0.2, 1.0),  # Dark Green
 	# Physical
 	ST.PhysicalUnitSystem: (1.0, 0.5, 0.5, 1.0),  # Light Red
-	ST.PhysicalTime: (1.0, 0.5, 0.5, 1.0),  # Light Red
-	ST.PhysicalAngle: (0.9, 0.45, 0.45, 1.0),  # Medium Light Red
-	ST.PhysicalLength: (0.8, 0.4, 0.4, 1.0),  # Medium Red
-	ST.PhysicalArea: (0.7, 0.35, 0.35, 1.0),  # Medium Dark Red
-	ST.PhysicalVolume: (0.6, 0.3, 0.3, 1.0),  # Dark Red
-	ST.PhysicalPoint2D: (0.7, 0.35, 0.35, 1.0),  # Medium Dark Red
-	ST.PhysicalPoint3D: (0.6, 0.3, 0.3, 1.0),  # Dark Red
-	ST.PhysicalSize2D: (0.7, 0.35, 0.35, 1.0),  # Medium Dark Red
-	ST.PhysicalSize3D: (0.6, 0.3, 0.3, 1.0),  # Dark Red
-	ST.PhysicalMass: (0.9, 0.6, 0.4, 1.0),  # Light Orange
-	ST.PhysicalSpeed: (0.8, 0.55, 0.35, 1.0),  # Medium Light Orange
-	ST.PhysicalAccelScalar: (0.7, 0.5, 0.3, 1.0),  # Medium Orange
-	ST.PhysicalForceScalar: (0.6, 0.45, 0.25, 1.0),  # Medium Dark Orange
-	ST.PhysicalAccel3D: (0.7, 0.5, 0.3, 1.0),  # Medium Orange
-	ST.PhysicalForce3D: (0.6, 0.45, 0.25, 1.0),  # Medium Dark Orange
 	ST.PhysicalPol: (0.5, 0.4, 0.2, 1.0),  # Dark Orange
-	ST.PhysicalFreq: (1.0, 0.7, 0.5, 1.0),  # Light Peach
 	# Blender
 	ST.BlenderMaterial: (0.8, 0.6, 1.0, 1.0),  # Lighter Purple
 	ST.BlenderObject: (0.7, 0.5, 1.0, 1.0),  # Light Purple
@@ -56,6 +27,7 @@ SOCKET_COLORS = {
 	ST.MaxwellBoundConds: (0.9, 0.8, 0.5, 1.0),  # Light Gold
 	ST.MaxwellBoundCond: (0.8, 0.7, 0.45, 1.0),  # Medium Light Gold
 	ST.MaxwellMonitor: (0.7, 0.6, 0.4, 1.0),  # Medium Gold
+	ST.MaxwellMonitorData: (0.7, 0.6, 0.4, 1.0),  # Medium Gold
 	ST.MaxwellFDTDSim: (0.6, 0.5, 0.35, 1.0),  # Medium Dark Gold
 	ST.MaxwellFDTDSimData: (0.6, 0.5, 0.35, 1.0),  # Medium Dark Gold
 	ST.MaxwellSimGrid: (0.5, 0.4, 0.3, 1.0),  # Dark Gold

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/socket_types.py

@@ -5,31 +5,14 @@ from blender_maxwell.utils import blender_type_enum
 
 @blender_type_enum.append_cls_name_to_values
 class SocketType(blender_type_enum.BlenderTypeEnum):
+	Expr = enum.auto()
+
 	# Base
 	Any = enum.auto()
-	Data = enum.auto()
 	Bool = enum.auto()
 	String = enum.auto()
 	FilePath = enum.auto()
 	Color = enum.auto()
-	Expr = enum.auto()
-
-	# Number
-	IntegerNumber = enum.auto()
-	RationalNumber = enum.auto()
-	RealNumber = enum.auto()
-	ComplexNumber = enum.auto()
-
-	# Vector
-	Integer2DVector = enum.auto()
-	Real2DVector = enum.auto()
-	Real2DVectorDir = enum.auto()
-	Complex2DVector = enum.auto()
-
-	Integer3DVector = enum.auto()
-	Real3DVector = enum.auto()
-	Real3DVectorDir = enum.auto()
-	Complex3DVector = enum.auto()
 
 	# Blender
 	BlenderMaterial = enum.auto()
@@ -53,6 +36,7 @@ class SocketType(blender_type_enum.BlenderTypeEnum):
 
 	MaxwellStructure = enum.auto()
 	MaxwellMonitor = enum.auto()
+	MaxwellMonitorData = enum.auto()
 
 	MaxwellFDTDSim = enum.auto()
 	MaxwellFDTDSimData = enum.auto()
@@ -66,76 +50,5 @@ class SocketType(blender_type_enum.BlenderTypeEnum):
 	# Physical
 	PhysicalUnitSystem = enum.auto()
 
-	PhysicalTime = enum.auto()
-
-	PhysicalAngle = enum.auto()
-	PhysicalSolidAngle = enum.auto()
-
-	PhysicalRot2D = enum.auto()
-	PhysicalRot3D = enum.auto()
-
-	PhysicalFreq = enum.auto()
-	PhysicalAngFreq = enum.auto()
-
-	## Cartesian
-	PhysicalLength = enum.auto()
-	PhysicalArea = enum.auto()
-	PhysicalVolume = enum.auto()
-
-	PhysicalDisp2D = enum.auto()
-	PhysicalDisp3D = enum.auto()
-
-	PhysicalPoint1D = enum.auto()
-	PhysicalPoint2D = enum.auto()
-	PhysicalPoint3D = enum.auto()
-
-	PhysicalSize2D = enum.auto()
-	PhysicalSize3D = enum.auto()
-
-	## Mechanical
-	PhysicalMass = enum.auto()
-
-	PhysicalSpeed = enum.auto()
-	PhysicalVel2D = enum.auto()
-	PhysicalVel3D = enum.auto()
-	PhysicalAccelScalar = enum.auto()
-	PhysicalAccel2D = enum.auto()
-	PhysicalAccel3D = enum.auto()
-	PhysicalForceScalar = enum.auto()
-	PhysicalForce2D = enum.auto()
-	PhysicalForce3D = enum.auto()
-	PhysicalPressure = enum.auto()
-
-	## Energetic
-	PhysicalEnergy = enum.auto()
-	PhysicalPower = enum.auto()
-	PhysicalTemp = enum.auto()
-
-	## Electrodynamical
-	PhysicalCurr = enum.auto()
-	PhysicalCurrDens2D = enum.auto()
-	PhysicalCurrDens3D = enum.auto()
-
-	PhysicalCharge = enum.auto()
-	PhysicalVoltage = enum.auto()
-	PhysicalCapacitance = enum.auto()
-	PhysicalResistance = enum.auto()
-	PhysicalConductance = enum.auto()
-
-	PhysicalMagFlux = enum.auto()
-	PhysicalMagFluxDens = enum.auto()
-	PhysicalInductance = enum.auto()
-
-	PhysicalEField2D = enum.auto()
-	PhysicalEField3D = enum.auto()
-	PhysicalHField2D = enum.auto()
-	PhysicalHField3D = enum.auto()
-
-	## Luminal
-	PhysicalLumIntensity = enum.auto()
-	PhysicalLumFlux = enum.auto()
-	PhysicalIlluminance = enum.auto()
-
 	## Optical
-	PhysicalPolJones = enum.auto()
 	PhysicalPol = enum.auto()

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/socket_units.py

@@ -1,287 +0,0 @@
-import sympy.physics.units as spu
-
-from blender_maxwell.utils import extra_sympy_units as spux
-
-from .socket_types import SocketType as ST  # noqa: N817
-
-SOCKET_UNITS = {
-	ST.PhysicalTime: {
-		'default': 'PS',
-		'values': {
-			'FS': spux.femtosecond,
-			'PS': spu.picosecond,
-			'NS': spu.nanosecond,
-			'MS': spu.microsecond,
-			'MLSEC': spu.millisecond,
-			'SEC': spu.second,
-			'MIN': spu.minute,
-			'HOUR': spu.hour,
-			'DAY': spu.day,
-		},
-	},
-	ST.PhysicalAngle: {
-		'default': 'RADIAN',
-		'values': {
-			'RADIAN': spu.radian,
-			'DEGREE': spu.degree,
-			'STERAD': spu.steradian,
-			'ANGMIL': spu.angular_mil,
-		},
-	},
-	ST.PhysicalLength: {
-		'default': 'UM',
-		'values': {
-			'PM': spu.picometer,
-			'A': spu.angstrom,
-			'NM': spu.nanometer,
-			'UM': spu.micrometer,
-			'MM': spu.millimeter,
-			'CM': spu.centimeter,
-			'M': spu.meter,
-			'INCH': spu.inch,
-			'FOOT': spu.foot,
-			'YARD': spu.yard,
-			'MILE': spu.mile,
-		},
-	},
-	ST.PhysicalArea: {
-		'default': 'UM_SQ',
-		'values': {
-			'PM_SQ': spu.picometer**2,
-			'A_SQ': spu.angstrom**2,
-			'NM_SQ': spu.nanometer**2,
-			'UM_SQ': spu.micrometer**2,
-			'MM_SQ': spu.millimeter**2,
-			'CM_SQ': spu.centimeter**2,
-			'M_SQ': spu.meter**2,
-			'INCH_SQ': spu.inch**2,
-			'FOOT_SQ': spu.foot**2,
-			'YARD_SQ': spu.yard**2,
-			'MILE_SQ': spu.mile**2,
-		},
-	},
-	ST.PhysicalVolume: {
-		'default': 'UM_CB',
-		'values': {
-			'PM_CB': spu.picometer**3,
-			'A_CB': spu.angstrom**3,
-			'NM_CB': spu.nanometer**3,
-			'UM_CB': spu.micrometer**3,
-			'MM_CB': spu.millimeter**3,
-			'CM_CB': spu.centimeter**3,
-			'M_CB': spu.meter**3,
-			'ML': spu.milliliter,
-			'L': spu.liter,
-			'INCH_CB': spu.inch**3,
-			'FOOT_CB': spu.foot**3,
-			'YARD_CB': spu.yard**3,
-			'MILE_CB': spu.mile**3,
-		},
-	},
-	ST.PhysicalPoint2D: {
-		'default': 'UM',
-		'values': {
-			'PM': spu.picometer,
-			'A': spu.angstrom,
-			'NM': spu.nanometer,
-			'UM': spu.micrometer,
-			'MM': spu.millimeter,
-			'CM': spu.centimeter,
-			'M': spu.meter,
-			'INCH': spu.inch,
-			'FOOT': spu.foot,
-			'YARD': spu.yard,
-			'MILE': spu.mile,
-		},
-	},
-	ST.PhysicalPoint3D: {
-		'default': 'UM',
-		'values': {
-			'PM': spu.picometer,
-			'A': spu.angstrom,
-			'NM': spu.nanometer,
-			'UM': spu.micrometer,
-			'MM': spu.millimeter,
-			'CM': spu.centimeter,
-			'M': spu.meter,
-			'INCH': spu.inch,
-			'FOOT': spu.foot,
-			'YARD': spu.yard,
-			'MILE': spu.mile,
-		},
-	},
-	ST.PhysicalSize2D: {
-		'default': 'UM',
-		'values': {
-			'PM': spu.picometer,
-			'A': spu.angstrom,
-			'NM': spu.nanometer,
-			'UM': spu.micrometer,
-			'MM': spu.millimeter,
-			'CM': spu.centimeter,
-			'M': spu.meter,
-			'INCH': spu.inch,
-			'FOOT': spu.foot,
-			'YARD': spu.yard,
-			'MILE': spu.mile,
-		},
-	},
-	ST.PhysicalSize3D: {
-		'default': 'UM',
-		'values': {
-			'PM': spu.picometer,
-			'A': spu.angstrom,
-			'NM': spu.nanometer,
-			'UM': spu.micrometer,
-			'MM': spu.millimeter,
-			'CM': spu.centimeter,
-			'M': spu.meter,
-			'INCH': spu.inch,
-			'FOOT': spu.foot,
-			'YARD': spu.yard,
-			'MILE': spu.mile,
-		},
-	},
-	ST.PhysicalMass: {
-		'default': 'UG',
-		'values': {
-			'E_REST': spu.electron_rest_mass,
-			'DAL': spu.dalton,
-			'UG': spu.microgram,
-			'MG': spu.milligram,
-			'G': spu.gram,
-			'KG': spu.kilogram,
-			'TON': spu.metric_ton,
-		},
-	},
-	ST.PhysicalSpeed: {
-		'default': 'UM_S',
-		'values': {
-			'PM_S': spu.picometer / spu.second,
-			'NM_S': spu.nanometer / spu.second,
-			'UM_S': spu.micrometer / spu.second,
-			'MM_S': spu.millimeter / spu.second,
-			'M_S': spu.meter / spu.second,
-			'KM_S': spu.kilometer / spu.second,
-			'KM_H': spu.kilometer / spu.hour,
-			'FT_S': spu.feet / spu.second,
-			'MI_H': spu.mile / spu.hour,
-		},
-	},
-	ST.PhysicalAccelScalar: {
-		'default': 'UM_S_SQ',
-		'values': {
-			'PM_S_SQ': spu.picometer / spu.second**2,
-			'NM_S_SQ': spu.nanometer / spu.second**2,
-			'UM_S_SQ': spu.micrometer / spu.second**2,
-			'MM_S_SQ': spu.millimeter / spu.second**2,
-			'M_S_SQ': spu.meter / spu.second**2,
-			'KM_S_SQ': spu.kilometer / spu.second**2,
-			'FT_S_SQ': spu.feet / spu.second**2,
-		},
-	},
-	ST.PhysicalForceScalar: {
-		'default': 'UNEWT',
-		'values': {
-			'KG_M_S_SQ': spu.kg * spu.m / spu.second**2,
-			'NNEWT': spux.nanonewton,
-			'UNEWT': spux.micronewton,
-			'MNEWT': spux.millinewton,
-			'NEWT': spu.newton,
-		},
-	},
-	ST.PhysicalAccel3D: {
-		'default': 'UM_S_SQ',
-		'values': {
-			'PM_S_SQ': spu.picometer / spu.second**2,
-			'NM_S_SQ': spu.nanometer / spu.second**2,
-			'UM_S_SQ': spu.micrometer / spu.second**2,
-			'MM_S_SQ': spu.millimeter / spu.second**2,
-			'M_S_SQ': spu.meter / spu.second**2,
-			'KM_S_SQ': spu.kilometer / spu.second**2,
-			'FT_S_SQ': spu.feet / spu.second**2,
-		},
-	},
-	ST.PhysicalForce3D: {
-		'default': 'UNEWT',
-		'values': {
-			'KG_M_S_SQ': spu.kg * spu.m / spu.second**2,
-			'NNEWT': spux.nanonewton,
-			'UNEWT': spux.micronewton,
-			'MNEWT': spux.millinewton,
-			'NEWT': spu.newton,
-		},
-	},
-	ST.PhysicalFreq: {
-		'default': 'THZ',
-		'values': {
-			'HZ': spu.hertz,
-			'KHZ': spux.kilohertz,
-			'MHZ': spux.megahertz,
-			'GHZ': spux.gigahertz,
-			'THZ': spux.terahertz,
-			'PHZ': spux.petahertz,
-			'EHZ': spux.exahertz,
-		},
-	},
-	ST.PhysicalPol: {
-		'default': 'RADIAN',
-		'values': {
-			'RADIAN': spu.radian,
-			'DEGREE': spu.degree,
-			'STERAD': spu.steradian,
-			'ANGMIL': spu.angular_mil,
-		},
-	},
-	ST.MaxwellMedium: {
-		'default': 'NM',
-		'values': {
-			'PM': spu.picometer,  ## c(vac) = wl*freq
-			'A': spu.angstrom,
-			'NM': spu.nanometer,
-			'UM': spu.micrometer,
-			'MM': spu.millimeter,
-			'CM': spu.centimeter,
-			'M': spu.meter,
-		},
-	},
-	ST.MaxwellMonitor: {
-		'default': 'NM',
-		'values': {
-			'PM': spu.picometer,  ## c(vac) = wl*freq
-			'A': spu.angstrom,
-			'NM': spu.nanometer,
-			'UM': spu.micrometer,
-			'MM': spu.millimeter,
-			'CM': spu.centimeter,
-			'M': spu.meter,
-		},
-	},
-}
-
-
-def unit_to_socket_type(
-	unit: spux.Unit | None, fallback_mathtype: spux.MathType | None = None
-) -> ST:
-	"""Returns a SocketType that accepts the given unit.
-
-	Only the unit-compatibility is taken into account; in the case of overlap, several the ordering of `SOCKET_UNITS` determines which is returned.
-	This isn't super clean, but it's good enough for our needs right now.
-
-	Returns:
-		**The first `SocketType` in `SOCKET_UNITS`, which contains the given unit as a valid possibility.
-	"""
-	if unit is None and fallback_mathtype is not None:
-		return {
-			spux.MathType.Integer: ST.IntegerNumber,
-			spux.MathType.Rational: ST.RationalNumber,
-			spux.MathType.Real: ST.RealNumber,
-			spux.MathType.Complex: ST.ComplexNumber,
-		}[fallback_mathtype]
-
-	for socket_type, _units in SOCKET_UNITS.items():
-		if unit in _units['values'].values():
-			return socket_type
-
-	msg = f"Unit {unit} doesn't have an obvious SocketType."
-	raise ValueError(msg)

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/unit_systems.py

@@ -1,59 +1,69 @@
+"""Specifies unit systems for use in the node tree.
+
+Attributes:
+	UNITS_BLENDER: A unit system that serves as a reasonable default for the a 3D workspace that interprets the results of electromagnetic simulations.
+		**NOTE**: The addon _specifically_ neglects to respect Blender's builtin units.
+		In testing, Blender's system was found to be extremely brittle when "going small" like this; in particular, `picosecond`-order time units were impossible to specify functionally.
+	UNITS_TIDY3D: A unit system that aligns with Tidy3D's simulator.
+		See <https://docs.flexcompute.com/projects/tidy3d/en/latest/faq/docs/faq/What-are-the-units-used-in-the-simulation.html>
+"""
+
 import typing as typ
 
 import sympy.physics.units as spu
 
 from blender_maxwell.utils import extra_sympy_units as spux
-from blender_maxwell.utils.pydantic_sympy import SympyExpr
 
-from .socket_types import SocketType as ST  # noqa: N817
-from .socket_units import SOCKET_UNITS
-
-
-def _socket_units(socket_type):
-	return SOCKET_UNITS[socket_type]['values']
-
-
-UnitSystem: typ.TypeAlias = dict[ST, SympyExpr]
 ####################
 # - Unit Systems
 ####################
-UNITS_BLENDER: UnitSystem = {
+_PT: typ.TypeAlias = spux.PhysicalType
-	ST.PhysicalTime: spu.picosecond,
+UNITS_BLENDER: spux.UnitSystem = spux.UNITS_SI | {
-	ST.PhysicalAngle: spu.radian,
+	# Global
-	ST.PhysicalLength: spu.micrometer,
+	_PT.Time: spu.picosecond,
-	ST.PhysicalArea: spu.micrometer**2,
+	_PT.Freq: spux.terahertz,
-	ST.PhysicalVolume: spu.micrometer**3,
+	_PT.AngFreq: spu.radian * spux.terahertz,
-	ST.PhysicalPoint2D: spu.micrometer,
+	# Cartesian
-	ST.PhysicalPoint3D: spu.micrometer,
+	_PT.Length: spu.micrometer,
-	ST.PhysicalSize2D: spu.micrometer,
+	_PT.Area: spu.micrometer**2,
-	ST.PhysicalSize3D: spu.micrometer,
+	_PT.Volume: spu.micrometer**3,
-	ST.PhysicalMass: spu.microgram,
+	# Energy
-	ST.PhysicalSpeed: spu.um / spu.second,
+	_PT.PowerFlux: spu.watt / spu.um**2,
-	ST.PhysicalAccelScalar: spu.um / spu.second**2,
+	# Electrodynamics
-	ST.PhysicalForceScalar: spux.micronewton,
+	_PT.CurrentDensity: spu.ampere / spu.um**2,
-	ST.PhysicalAccel3D: spu.um / spu.second**2,
+	_PT.Conductivity: spu.siemens / spu.um,
-	ST.PhysicalForce3D: spux.micronewton,
+	_PT.PoyntingVector: spu.watt / spu.um**2,
-	ST.PhysicalFreq: spux.terahertz,
+	_PT.EField: spu.volt / spu.um,
-	ST.PhysicalPol: spu.radian,
+	_PT.HField: spu.ampere / spu.um,
+	# Mechanical
+	_PT.Vel: spu.um / spu.second,
+	_PT.Accel: spu.um / spu.second,
+	_PT.Mass: spu.microgram,
+	_PT.Force: spux.micronewton,
+	# Luminal
+	# Optics
+	_PT.PoyntingVector: spu.watt / spu.um**2,
 }  ## TODO: Load (dynamically?) from addon preferences
 
-UNITS_TIDY3D: UnitSystem = {
+UNITS_TIDY3D: spux.UnitSystem = spux.UNITS_SI | {
-	## https://docs.flexcompute.com/projects/tidy3d/en/latest/faq/docs/faq/What-are-the-units-used-in-the-simulation.html
+	# Global
-	ST.PhysicalTime: spu.second,
+	# Cartesian
-	ST.PhysicalAngle: spu.radian,
+	_PT.Length: spu.um,
-	ST.PhysicalLength: spu.micrometer,
+	_PT.Area: spu.um**2,
-	ST.PhysicalArea: spu.micrometer**2,
+	_PT.Volume: spu.um**3,
-	ST.PhysicalVolume: spu.micrometer**3,
+	# Mechanical
-	ST.PhysicalPoint2D: spu.micrometer,
+	_PT.Vel: spu.um / spu.second,
-	ST.PhysicalPoint3D: spu.micrometer,
+	_PT.Accel: spu.um / spu.second,
-	ST.PhysicalSize2D: spu.micrometer,
+	# Energy
-	ST.PhysicalSize3D: spu.micrometer,
+	_PT.PowerFlux: spu.watt / spu.um**2,
-	ST.PhysicalMass: spu.microgram,
+	# Electrodynamics
-	ST.PhysicalSpeed: spu.um / spu.second,
+	_PT.CurrentDensity: spu.ampere / spu.um**2,
-	ST.PhysicalAccelScalar: spu.um / spu.second**2,
+	_PT.Conductivity: spu.siemens / spu.um,
-	ST.PhysicalForceScalar: spux.micronewton,
+	_PT.PoyntingVector: spu.watt / spu.um**2,
-	ST.PhysicalAccel3D: spu.um / spu.second**2,
+	_PT.EField: spu.volt / spu.um,
-	ST.PhysicalForce3D: spux.micronewton,
+	_PT.HField: spu.ampere / spu.um,
-	ST.PhysicalFreq: spu.hertz,
+	# Luminal
-	ST.PhysicalPol: spu.radian,
+	# Optics
+	_PT.PoyntingVector: spu.watt / spu.um**2,
+	## NOTE: w/o source normalization, EField/HField/Modal amps are * 1/Hz
 }

src/blender_maxwell/node_trees/maxwell_sim_nodes/managed_objs/managed_bl_mesh.py

@@ -101,6 +101,10 @@ class ManagedBLMesh(base.ManagedObj):
 	####################
 	# - Methods
 	####################
+	@property
+	def exists(self) -> bool:
+		return bpy.data.objects.get(self.name) is not None
+
 	def show_preview(self) -> None:
 		"""Moves the managed Blender object to the preview collection.
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/managed_objs/managed_bl_modifier.py

@@ -4,7 +4,8 @@ import typing as typ
 
 import bpy
 
-from blender_maxwell.utils import analyze_geonodes, logger
+from blender_maxwell.utils import extra_sympy_units as spux
+from blender_maxwell.utils import logger
 
 from .. import bl_socket_map
 from .. import contracts as ct
@@ -25,13 +26,12 @@ class ModifierAttrsNODES(typ.TypedDict):
 		node_group: The GeoNodes group to use in the modifier.
 		unit_system: The unit system used by the GeoNodes output.
 			Generally, `ct.UNITS_BLENDER` is a good choice.
-		inputs: Values to associate with each GeoNodes interface socket.
+		inputs: Values to associate with each GeoNodes interface socket name.
-			Use `analyze_geonodes.interface(..., direc='INPUT')` to determine acceptable values.
 	"""
 
 	node_group: bpy.types.GeometryNodeTree
 	unit_system: UnitSystem
-	inputs: dict[ct.BLNodeTreeInterfaceID, typ.Any]
+	inputs: dict[ct.SocketName, typ.Any]
 
 
 class ModifierAttrsARRAY(typ.TypedDict):
@@ -47,7 +47,7 @@ MODIFIER_NAMES = {
 
 
 ####################
-# - Read Modifier Information
+# - Read Modifier
 ####################
 def read_modifier(bl_modifier: bpy.types.Modifier) -> ModifierAttrs:
 	if bl_modifier.type == 'NODES':
@@ -62,7 +62,7 @@ def read_modifier(bl_modifier: bpy.types.Modifier) -> ModifierAttrs:
 
 
 ####################
-# - Write Modifier Information
+# - Write Modifier: GeoNodes
 ####################
 def write_modifier_geonodes(
 	bl_modifier: bpy.types.NodesModifier,
@@ -78,6 +78,7 @@ def write_modifier_geonodes(
 		True if the modifier was altered.
 	"""
 	modifier_altered = False
+
 	# Alter GeoNodes Group
 	if bl_modifier.node_group != modifier_attrs['node_group']:
 		log.info(
@@ -89,53 +90,22 @@ def write_modifier_geonodes(
 		modifier_altered = True
 
 	# Alter GeoNodes Modifier Inputs
-	## First we retrieve the interface items by-Socket Name
+	socket_infos = bl_socket_map.info_from_geonodes(bl_modifier.node_group)
-	geonodes_interface = analyze_geonodes.interface(
+
-		bl_modifier.node_group, direc='INPUT'
+	for socket_name in modifier_attrs['inputs']:
+		iface_id = socket_infos[socket_name].bl_isocket_identifier
+		bl_modifier[iface_id] = spux.scale_to_unit_system(
+			modifier_attrs['inputs'][socket_name], modifier_attrs['unit_system']
 		)
-	for (
-		socket_name,
-		value,
-	) in modifier_attrs['inputs'].items():
-		# Compute Writable BL Socket Value
-		## Analyzes the socket and unitsys to prep a ready-to-write value.
-		## Write directly to the modifier dict.
-		bl_socket_value = bl_socket_map.writable_bl_socket_value(
-			geonodes_interface[socket_name],
-			value,
-			unit_system=modifier_attrs['unit_system'],
-			allow_unit_not_in_unit_system=True,
-		)
-
-		# Compute Interface ID from Socket Name
-		## We can't index the modifier by socket name; only by Interface ID.
-		## Still, we require that socket names are unique.
-		iface_id = geonodes_interface[socket_name].identifier
-
-		# IF List-Like: Alter Differing Elements
-		if isinstance(bl_socket_value, tuple):
-			for i, bl_socket_subvalue in enumerate(bl_socket_value):
-				if bl_modifier[iface_id][i] != bl_socket_subvalue:
-					bl_modifier[iface_id][i] = bl_socket_subvalue
 	modifier_altered = True
+	## TODO: More fine-grained alterations
 
-		# IF int/float Mismatch: Assign Float-Cast of Integer
+	return modifier_altered  # noqa: RET504
-		## Blender is strict; only floats can set float vals.
-		## We are less strict; if the user passes an int, that's okay.
-		elif isinstance(bl_socket_value, int) and isinstance(
-			bl_modifier[iface_id],
-			float,
-		):
-			bl_modifier[iface_id] = float(bl_socket_value)
-			modifier_altered = True
-		else:
-			## TODO: Whitelist what can be here. I'm done with the TypeErrors.
-			bl_modifier[iface_id] = bl_socket_value
-			modifier_altered = True
-
-	return modifier_altered
 
 
+####################
+# - Write Modifier
+####################
 def write_modifier(
 	bl_modifier: bpy.types.Modifier,
 	modifier_attrs: ModifierAttrs,
@@ -184,8 +154,11 @@ class ManagedBLModifier(base.ManagedObj):
 	def __init__(self, name: str):
 		self.name = name
 
-	def bl_select(self) -> None: pass
+	def bl_select(self) -> None:
-	def hide_preview(self) -> None: pass
+		pass
+
+	def hide_preview(self) -> None:
+		pass
 
 	####################
 	# - Deallocation
@@ -255,7 +228,8 @@ class ManagedBLModifier(base.ManagedObj):
 				type=modifier_type,
 			)
 
-		if modifier_altered := write_modifier(bl_modifier, modifier_attrs):
+		modifier_altered = write_modifier(bl_modifier, modifier_attrs)
+		if modifier_altered:
 			bl_object.data.update()
 
 		return bl_modifier

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/extract_data.py

@@ -41,18 +41,17 @@ class ExtractDataNode(base.MaxwellSimNode):
 
 	input_socket_sets: typ.ClassVar = {
 		'Sim Data': {'Sim Data': sockets.MaxwellFDTDSimDataSocketDef()},
-		'Monitor Data': {'Monitor Data': sockets.DataSocketDef(format='monitor_data')},
+		'Monitor Data': {'Monitor Data': sockets.MaxwellMonitorDataSocketDef()},
 	}
 	output_socket_sets: typ.ClassVar = {
-		'Sim Data': {'Monitor Data': sockets.DataSocketDef(format='monitor_data')},
+		'Sim Data': {'Monitor Data': sockets.MaxwellMonitorDataSocketDef()},
-		'Monitor Data': {'Data': sockets.DataSocketDef(format='jax')},
+		'Monitor Data': {'Expr': sockets.ExprSocketDef()},
 	}
 
 	####################
 	# - Properties
 	####################
 	extract_filter: enum.Enum = bl_cache.BLField(
-		None,
 		prop_ui=True,
 		enum_cb=lambda self, _: self.search_extract_filters(),
 	)
@@ -62,7 +61,7 @@ class ExtractDataNode(base.MaxwellSimNode):
 	####################
 	@property
 	def sim_data(self) -> td.SimulationData | None:
-		"""Computes the (cached) simulation data from the input socket.
+		"""Extracts the simulation data from the input socket.
 
 		Return:
 			Either the simulation data, if available, or None.
@@ -70,14 +69,15 @@ class ExtractDataNode(base.MaxwellSimNode):
 		sim_data = self._compute_input(
 			'Sim Data', kind=ct.FlowKind.Value, optional=True
 		)
-		if not ct.FlowSignal.check(sim_data):
+		has_sim_data = not ct.FlowSignal.check(sim_data)
+		if has_sim_data:
 			return sim_data
 
 		return None
 
 	@bl_cache.cached_bl_property()
 	def sim_data_monitor_nametype(self) -> dict[str, str] | None:
-		"""For simulation data, computes and and caches a map from name to "type".
+		"""For simulation data, deduces a map from the monitor name to the monitor "type".
 
 		Return:
 			The name to type of monitors in the simulation data.
@@ -95,7 +95,7 @@ class ExtractDataNode(base.MaxwellSimNode):
 	####################
 	@property
 	def monitor_data(self) -> TDMonitorData | None:
-		"""Computes the (cached) monitor data from the input socket.
+		"""Extracts the monitor data from the input socket.
 
 		Return:
 			Either the monitor data, if available, or None.
@@ -103,17 +103,26 @@ class ExtractDataNode(base.MaxwellSimNode):
 		monitor_data = self._compute_input(
 			'Monitor Data', kind=ct.FlowKind.Value, optional=True
 		)
-		if not ct.FlowSignal.check(monitor_data):
+		has_monitor_data = not ct.FlowSignal.check(monitor_data)
+		if has_monitor_data:
 			return monitor_data
 
 		return None
 
 	@bl_cache.cached_bl_property()
 	def monitor_data_type(self) -> str | None:
-		"""For monitor data, computes and caches the monitor "type".
+		r"""For monitor data, deduces the monitor "type".
+
+		- **Field(Time)**: A monitor storing values/pixels/voxels with electromagnetic field values, on the time or frequency domain.
+		- **Permittivity**: A monitor storing values/pixels/voxels containing the diagonal of the relative permittivity tensor.
+		- **Flux(Time)**: A monitor storing the directional flux on the time or frequency domain.
+			For planes, an explicit direction is defined.
+			For volumes, the the integral of all outgoing energy is stored.
+		- **FieldProjection(...)**: A monitor storing the spherical-coordinate electromagnetic field components of a near-to-far-field projection.
+		- **Diffraction**: A monitor storing a near-to-far-field projection by diffraction order.
 
 		Notes:
-			Should be invalidated with (before) `self.monitor_data_components`.
+			Should be invalidated with (before) `self.monitor_data_attrs`.
 
 		Return:
 			The "type" of the monitor, if available, else None.
@@ -124,10 +133,10 @@ class ExtractDataNode(base.MaxwellSimNode):
 		return None
 
 	@bl_cache.cached_bl_property()
-	def monitor_data_components(self) -> list[str] | None:
+	def monitor_data_attrs(self) -> list[str] | None:
-		r"""For monitor data, computes and caches the component sof the monitor.
+		r"""For monitor data, deduces the valid data-containing attributes.
 
-		The output depends entirely on the output of `self.monitor_data`.
+		The output depends entirely on the output of `self.monitor_data_type`, since the valid attributes of each monitor type is well-defined without needing to perform dynamic lookups.
 
 		- **Field(Time)**: Whichever `[E|H][x|y|z]` are not `None` on the monitor.
 		- **Permittivity**: Specifically `['xx', 'yy', 'zz']`.
@@ -183,7 +192,7 @@ class ExtractDataNode(base.MaxwellSimNode):
 		"""Compute valid values for `self.extract_filter`, for a dynamic `EnumProperty`.
 
 		Notes:
-			Should be reset (via `self.extract_filter`) with (after) `self.sim_data_monitor_nametype`, `self.monitor_data_components`, and (implicitly) `self.monitor_type`.
+			Should be reset (via `self.extract_filter`) with (after) `self.sim_data_monitor_nametype`, `self.monitor_data_attrs`, and (implicitly) `self.monitor_type`.
 
 			See `bl_cache.BLField` for more on dynamic `EnumProperty`.
 
@@ -198,16 +207,56 @@ class ExtractDataNode(base.MaxwellSimNode):
 				)
 			]
 
-		if self.monitor_data_components is not None:
+		if self.monitor_data_attrs is not None:
+			# Field/FieldTime
+			if self.monitor_data_type in ['Field', 'FieldTime']:
 				return [
 					(
-					component_name,
+						monitor_attr,
-					component_name,
+						monitor_attr,
-					f'ℂ {component_name[1]}-polarization of the {"electric" if component_name[0] == "E" else "magnetic"} field',
+						f'ℂ {monitor_attr[1]}-polarization of the {"electric" if monitor_attr[0] == "E" else "magnetic"} field',
 						'',
 						i,
 					)
-				for i, component_name in enumerate(self.monitor_data_components)
+					for i, monitor_attr in enumerate(self.monitor_data_attrs)
+				]
+
+			# Permittivity
+			if self.monitor_data_type == 'Permittivity':
+				return [
+					(monitor_attr, monitor_attr, f'ℂ ε_{monitor_attr}', '', i)
+					for i, monitor_attr in enumerate(self.monitor_data_attrs)
+				]
+
+			# Flux/FluxTime
+			if self.monitor_data_type in ['Flux', 'FluxTime']:
+				return [
+					(
+						monitor_attr,
+						monitor_attr,
+						'Power flux integral through the plane / out of the volume',
+						'',
+						i,
+					)
+					for i, monitor_attr in enumerate(self.monitor_data_attrs)
+				]
+
+			# FieldProjection(Angle/Cartesian/KSpace)/Diffraction
+			if self.monitor_data_type in [
+				'FieldProjectionAngle',
+				'FieldProjectionCartesian',
+				'FieldProjectionKSpace',
+				'Diffraction',
+			]:
+				return [
+					(
+						monitor_attr,
+						monitor_attr,
+						f'ℂ {monitor_attr[1]}-component of the spherical {"electric" if monitor_attr[0] == "E" else "magnetic"} field',
+						'',
+						i,
+					)
+					for i, monitor_attr in enumerate(self.monitor_data_attrs)
 				]
 
 		return []
@@ -215,9 +264,14 @@ class ExtractDataNode(base.MaxwellSimNode):
 	####################
 	# - UI
 	####################
-	def draw_label(self):
+	def draw_label(self) -> None:
+		"""Show the extracted data (if any) in the node's header label.
+
+		Notes:
+			Called by Blender to determine the text to place in the node's header.
+		"""
 		has_sim_data = self.sim_data_monitor_nametype is not None
-		has_monitor_data = self.monitor_data_components is not None
+		has_monitor_data = self.monitor_data_attrs is not None
 
 		if has_sim_data or has_monitor_data:
 			return f'Extract: {self.extract_filter}'
@@ -245,11 +299,11 @@ class ExtractDataNode(base.MaxwellSimNode):
 		"""Invalidate the cached properties for sim data / monitor data, and reset the extraction filter."""
 		self.sim_data_monitor_nametype = bl_cache.Signal.InvalidateCache
 		self.monitor_data_type = bl_cache.Signal.InvalidateCache
-		self.monitor_data_components = bl_cache.Signal.InvalidateCache
+		self.monitor_data_attrs = bl_cache.Signal.InvalidateCache
 		self.extract_filter = bl_cache.Signal.ResetEnumItems
 
 	####################
-	# - Output: Sim Data -> Monitor Data
+	# - Output (Value): Sim Data -> Monitor Data
 	####################
 	@events.computes_output_socket(
 		# Trigger
@@ -262,96 +316,84 @@ class ExtractDataNode(base.MaxwellSimNode):
 	def compute_monitor_data(
 		self, props: dict, input_sockets: dict
 	) -> TDMonitorData | ct.FlowSignal:
-		"""Compute `Monitor Data` by querying an attribute of `Sim Data`.
+		"""Compute `Monitor Data` by querying the attribute of `Sim Data` referenced by the property `self.extract_filter`.
-
-		Notes:
-			The attribute to query is read directly from `self.extract_filter`.
-			This is also the mechanism that protects from trying to reference an invalid attribute.
 
 		Returns:
 			Monitor data, if available, else `ct.FlowSignal.FlowPending`.
 		"""
+		extract_filter = props['extract_filter']
 		sim_data = input_sockets['Sim Data']
 		has_sim_data = not ct.FlowSignal.check(sim_data)
 
-		if has_sim_data and props['extract_filter'] != 'NONE':
+		if has_sim_data and extract_filter is not None:
-			return input_sockets['Sim Data'].monitor_data[props['extract_filter']]
+			return sim_data.monitor_data[extract_filter]
-
-		# Propagate NoFlow
-		if ct.FlowSignal.check_single(sim_data, ct.FlowSignal.NoFlow):
-			return ct.FlowSignal.NoFlow
 
 		return ct.FlowSignal.FlowPending
 
 	####################
-	# - Output: Monitor Data -> Data
+	# - Output (Array): Monitor Data -> Expr
 	####################
 	@events.computes_output_socket(
 		# Trigger
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.Array,
 		# Loaded
 		props={'extract_filter'},
 		input_sockets={'Monitor Data'},
 		input_socket_kinds={'Monitor Data': ct.FlowKind.Value},
 	)
-	def compute_data(
+	def compute_expr(
 		self, props: dict, input_sockets: dict
 	) -> jax.Array | ct.FlowSignal:
-		"""Compute `Data:Array` by querying an array-like attribute of `Monitor Data`, then constructing an `ct.ArrayFlow`.
+		"""Compute `Expr:Array` by querying an array-like attribute of `Monitor Data`, then constructing an `ct.ArrayFlow` around it.
 
 		Uses the internal `xarray` data returned by Tidy3D.
 		By using `np.array` on the `.data` attribute of the `xarray`, instead of the usual JAX array constructor, we should save a (possibly very big) copy.
 
-		Notes:
-			The attribute to query is read directly from `self.extract_filter`.
-			This is also the mechanism that protects from trying to reference an invalid attribute.
-
-			Used as the first part of the `LazyFuncValue` chain used for further array manipulations with Math nodes.
-
 		Returns:
 			The data array, if available, else `ct.FlowSignal.FlowPending`.
 		"""
-		has_monitor_data = not ct.FlowSignal.check(input_sockets['Monitor Data'])
+		extract_filter = props['extract_filter']
+		monitor_data = input_sockets['Monitor Data']
+		has_monitor_data = not ct.FlowSignal.check(monitor_data)
 
-		if has_monitor_data and props['extract_filter'] != 'NONE':
+		if has_monitor_data and extract_filter is not None:
-			xarray_data = getattr(
+			xarray_data = getattr(monitor_data, extract_filter)
-				input_sockets['Monitor Data'], props['extract_filter']
-			)
 			return ct.ArrayFlow(values=np.array(xarray_data.data), unit=None)
 
 		return ct.FlowSignal.FlowPending
 
 	@events.computes_output_socket(
 		# Trigger
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.LazyValueFunc,
 		# Loaded
-		output_sockets={'Data'},
+		output_sockets={'Expr'},
-		output_socket_kinds={'Data': ct.FlowKind.Array},
+		output_socket_kinds={'Expr': ct.FlowKind.Array},
 	)
 	def compute_extracted_data_lazy(
 		self, output_sockets: dict
 	) -> ct.LazyValueFuncFlow | None:
-		"""Declare `Data:LazyValueFunc` by creating a simple function that directly wraps `Data:Array`.
+		"""Declare `Expr:LazyValueFunc` by creating a simple function that directly wraps `Expr:Array`.
 
 		Returns:
 			The composable function array, if available, else `ct.FlowSignal.FlowPending`.
 		"""
-		has_output_data = not ct.FlowSignal.check(output_sockets['Data'])
+		output_expr = output_sockets['Expr']
+		has_output_expr = not ct.FlowSignal.check(output_expr)
 
-		if has_output_data:
+		if has_output_expr:
 			return ct.LazyValueFuncFlow(
-				func=lambda: output_sockets['Data'].values, supports_jax=True
+				func=lambda: output_expr.values, supports_jax=True
 			)
 
 		return ct.FlowSignal.FlowPending
 
 	####################
-	# - Auxiliary: Monitor Data -> Data
+	# - Auxiliary (Params): Monitor Data -> Expr
 	####################
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.Params,
 	)
 	def compute_data_params(self) -> ct.ParamsFlow:
@@ -362,6 +404,9 @@ class ExtractDataNode(base.MaxwellSimNode):
 		"""
 		return ct.ParamsFlow()
 
+	####################
+	# - Auxiliary (Info): Monitor Data -> Expr
+	####################
 	@events.computes_output_socket(
 		# Trigger
 		'Data',
@@ -380,20 +425,21 @@ class ExtractDataNode(base.MaxwellSimNode):
 		Returns:
 			Information describing the `Data:LazyValueFunc`, if available, else `ct.FlowSignal.FlowPending`.
 		"""
-		has_monitor_data = not ct.FlowSignal.check(input_sockets['Monitor Data'])
+		monitor_data = input_sockets['Monitor Data']
+		monitor_data_type = props['monitor_data_type']
+		extract_filter = props['extract_filter']
+
+		has_monitor_data = not ct.FlowSignal.check(monitor_data)
 
 		# Retrieve XArray
-		if has_monitor_data and props['extract_filter'] != 'NONE':
+		if has_monitor_data and extract_filter is not None:
-			xarr = getattr(input_sockets['Monitor Data'], props['extract_filter'])
+			xarr = getattr(monitor_data, extract_filter)
 		else:
 			return ct.FlowSignal.FlowPending
 
-		info_output_name = props['extract_filter']
-		info_output_shape = None
-
 		# Compute InfoFlow from XArray
 		## XYZF: Field / Permittivity / FieldProjectionCartesian
-		if props['monitor_data_type'] in {
+		if monitor_data_type in {
 			'Field',
 			'Permittivity',
 			#'FieldProjectionCartesian',
@@ -413,18 +459,16 @@ class ExtractDataNode(base.MaxwellSimNode):
 						is_sorted=True,
 					),
 				},
-				output_name=props['extract_filter'],
+				output_name=extract_filter,
 				output_shape=None,
 				output_mathtype=spux.MathType.Complex,
 				output_unit=(
-					spu.volt / spu.micrometer
+					spu.volt / spu.micrometer if monitor_data_type == 'Field' else None
-					if props['monitor_data_type'] == 'Field'
-					else None
 				),
 			)
 
 		## XYZT: FieldTime
-		if props['monitor_data_type'] == 'FieldTime':
+		if monitor_data_type == 'FieldTime':
 			return ct.InfoFlow(
 				dim_names=['x', 'y', 'z', 't'],
 				dim_idx={
@@ -440,18 +484,16 @@ class ExtractDataNode(base.MaxwellSimNode):
 						is_sorted=True,
 					),
 				},
-				output_name=props['extract_filter'],
+				output_name=extract_filter,
 				output_shape=None,
 				output_mathtype=spux.MathType.Complex,
 				output_unit=(
-					spu.volt / spu.micrometer
+					spu.volt / spu.micrometer if monitor_data_type == 'Field' else None
-					if props['monitor_data_type'] == 'Field'
-					else None
 				),
 			)
 
 		## F: Flux
-		if props['monitor_data_type'] == 'Flux':
+		if monitor_data_type == 'Flux':
 			return ct.InfoFlow(
 				dim_names=['f'],
 				dim_idx={
@@ -461,14 +503,14 @@ class ExtractDataNode(base.MaxwellSimNode):
 						is_sorted=True,
 					),
 				},
-				output_name=props['extract_filter'],
+				output_name=extract_filter,
 				output_shape=None,
 				output_mathtype=spux.MathType.Real,
 				output_unit=spu.watt,
 			)
 
 		## T: FluxTime
-		if props['monitor_data_type'] == 'FluxTime':
+		if monitor_data_type == 'FluxTime':
 			return ct.InfoFlow(
 				dim_names=['t'],
 				dim_idx={
@@ -478,14 +520,14 @@ class ExtractDataNode(base.MaxwellSimNode):
 						is_sorted=True,
 					),
 				},
-				output_name=props['extract_filter'],
+				output_name=extract_filter,
 				output_shape=None,
 				output_mathtype=spux.MathType.Real,
 				output_unit=spu.watt,
 			)
 
 		## RThetaPhiF: FieldProjectionAngle
-		if props['monitor_data_type'] == 'FieldProjectionAngle':
+		if monitor_data_type == 'FieldProjectionAngle':
 			return ct.InfoFlow(
 				dim_names=['r', 'theta', 'phi', 'f'],
 				dim_idx={
@@ -508,18 +550,18 @@ class ExtractDataNode(base.MaxwellSimNode):
 						is_sorted=True,
 					),
 				},
-				output_name=props['extract_filter'],
+				output_name=extract_filter,
 				output_shape=None,
 				output_mathtype=spux.MathType.Real,
 				output_unit=(
 					spu.volt / spu.micrometer
-					if props['extract_filter'].startswith('E')
+					if extract_filter.startswith('E')
 					else spu.ampere / spu.micrometer
 				),
 			)
 
 		## UxUyRF: FieldProjectionKSpace
-		if props['monitor_data_type'] == 'FieldProjectionKSpace':
+		if monitor_data_type == 'FieldProjectionKSpace':
 			return ct.InfoFlow(
 				dim_names=['ux', 'uy', 'r', 'f'],
 				dim_idx={
@@ -540,18 +582,18 @@ class ExtractDataNode(base.MaxwellSimNode):
 						is_sorted=True,
 					),
 				},
-				output_name=props['extract_filter'],
+				output_name=extract_filter,
 				output_shape=None,
 				output_mathtype=spux.MathType.Real,
 				output_unit=(
 					spu.volt / spu.micrometer
-					if props['extract_filter'].startswith('E')
+					if extract_filter.startswith('E')
 					else spu.ampere / spu.micrometer
 				),
 			)
 
 		## OrderxOrderyF: Diffraction
-		if props['monitor_data_type'] == 'Diffraction':
+		if monitor_data_type == 'Diffraction':
 			return ct.InfoFlow(
 				dim_names=['orders_x', 'orders_y', 'f'],
 				dim_idx={
@@ -569,17 +611,17 @@ class ExtractDataNode(base.MaxwellSimNode):
 						is_sorted=True,
 					),
 				},
-				output_name=props['extract_filter'],
+				output_name=extract_filter,
 				output_shape=None,
 				output_mathtype=spux.MathType.Real,
 				output_unit=(
 					spu.volt / spu.micrometer
-					if props['extract_filter'].startswith('E')
+					if extract_filter.startswith('E')
 					else spu.ampere / spu.micrometer
 				),
 			)
 
-		msg = f'Unsupported Monitor Data Type {props["monitor_data_type"]} in "FlowKind.Info" of "{self.bl_label}"'
+		msg = f'Unsupported Monitor Data Type {monitor_data_type} in "FlowKind.Info" of "{self.bl_label}"'
 		raise RuntimeError(msg)
 
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/math/__init__.py

@@ -1,16 +1,16 @@
-from . import filter_math, map_math, operate_math, reduce_math, transform_math
+from . import filter_math, map_math, operate_math  # , #reduce_math, transform_math
 
 BL_REGISTER = [
+	*operate_math.BL_REGISTER,
 	*map_math.BL_REGISTER,
 	*filter_math.BL_REGISTER,
-	*reduce_math.BL_REGISTER,
+	# *reduce_math.BL_REGISTER,
-	*operate_math.BL_REGISTER,
+	# *transform_math.BL_REGISTER,
-	*transform_math.BL_REGISTER,
 ]
 BL_NODES = {
+	**operate_math.BL_NODES,
 	**map_math.BL_NODES,
 	**filter_math.BL_NODES,
-	**reduce_math.BL_NODES,
+	# **reduce_math.BL_NODES,
-	**operate_math.BL_NODES,
+	# **transform_math.BL_NODES,
-	**transform_math.BL_NODES,
 }

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/math/filter_math.py

@@ -4,10 +4,10 @@ import enum
 import typing as typ
 
 import bpy
-import jax
 import jax.numpy as jnp
 
 from blender_maxwell.utils import bl_cache, logger
+from blender_maxwell.utils import extra_sympy_units as spux
 
 from .... import contracts as ct
 from .... import sockets
@@ -16,6 +16,78 @@ from ... import base, events
 log = logger.get(__name__)
 
 
+class FilterOperation(enum.StrEnum):
+	"""Valid operations for the `FilterMathNode`.
+
+	Attributes:
+		DimToVec: Shift last dimension to output.
+		DimsToMat: Shift last 2 dimensions to output.
+		PinLen1: Remove a len(1) dimension.
+		Pin: Remove a len(n) dimension by selecting a particular index.
+		Swap: Swap the positions of two dimensions.
+	"""
+
+	# Dimensions
+	PinLen1 = enum.auto()
+	Pin = enum.auto()
+	Swap = enum.auto()
+
+	# Interpret
+	DimToVec = enum.auto()
+	DimsToMat = enum.auto()
+
+	@staticmethod
+	def to_name(value: typ.Self) -> str:
+		FO = FilterOperation
+		return {
+			# Dimensions
+			FO.PinLen1: 'pinₐ =1',
+			FO.Pin: 'pinₐ ≈v',
+			FO.Swap: 'a₁ ↔ a₂',
+			# Interpret
+			FO.DimToVec: '→ Vector',
+			FO.DimsToMat: '→ Matrix',
+		}[value]
+
+	@staticmethod
+	def to_icon(value: typ.Self) -> str:
+		return ''
+
+	def are_dims_valid(self, dim_0: int | None, dim_1: int | None):
+		return not (
+			(
+				dim_0 is None
+				and self
+				in [FilterOperation.PinLen1, FilterOperation.Pin, FilterOperation.Swap]
+			)
+			or (dim_1 is None and self == FilterOperation.Swap)
+		)
+
+	def jax_func(self, axis_0: int | None, axis_1: int | None):
+		return {
+			# Interpret
+			FilterOperation.DimToVec: lambda data: data,
+			FilterOperation.DimsToMat: lambda data: data,
+			# Dimensions
+			FilterOperation.PinLen1: lambda data: jnp.squeeze(data, axis_0),
+			FilterOperation.Pin: lambda data, fixed_axis_idx: jnp.take(
+				data, fixed_axis_idx, axis=axis_0
+			),
+			FilterOperation.Swap: lambda data: jnp.swapaxes(data, axis_0, axis_1),
+		}[self]
+
+	def transform_info(self, info: ct.InfoFlow, dim_0: str, dim_1: str):
+		return {
+			# Interpret
+			FilterOperation.DimToVec: lambda: info.shift_last_input,
+			FilterOperation.DimsToMat: lambda: info.shift_last_input.shift_last_input,
+			# Dimensions
+			FilterOperation.PinLen1: lambda: info.delete_dimension(dim_0),
+			FilterOperation.Pin: lambda: info.delete_dimension(dim_0),
+			FilterOperation.Swap: lambda: info.swap_dimensions(dim_0, dim_1),
+		}[self]()
+
+
 class FilterMathNode(base.MaxwellSimNode):
 	r"""Applies a function that operates on the shape of the array.
 
@@ -38,21 +110,18 @@ class FilterMathNode(base.MaxwellSimNode):
 	bl_label = 'Filter Math'
 
 	input_sockets: typ.ClassVar = {
-		'Data': sockets.DataSocketDef(format='jax'),
+		'Expr': sockets.ExprSocketDef(),
-	}
-	input_socket_sets: typ.ClassVar = {
-		'Interpret': {},
-		'Dimensions': {},
 	}
 	output_sockets: typ.ClassVar = {
-		'Data': sockets.DataSocketDef(format='jax'),
+		'Expr': sockets.ExprSocketDef(),
 	}
 
 	####################
 	# - Properties
 	####################
-	operation: enum.Enum = bl_cache.BLField(
+	operation: FilterOperation = bl_cache.BLField(
-		prop_ui=True, enum_cb=lambda self, _: self.search_operations()
+		FilterOperation.PinLen1,
+		prop_ui=True,
 	)
 
 	# Dimension Selection
@@ -68,49 +137,26 @@ class FilterMathNode(base.MaxwellSimNode):
 	####################
 	@property
 	def data_info(self) -> ct.InfoFlow | None:
-		info = self._compute_input('Data', kind=ct.FlowKind.Info)
+		info = self._compute_input('Expr', kind=ct.FlowKind.Info)
 		if not ct.FlowSignal.check(info):
 			return info
 
 		return None
 
 	####################
-	# - Operation Search
+	# - Search Dimensions
-	####################
-	def search_operations(self) -> list[tuple[str, str, str]]:
-		items = []
-		if self.active_socket_set == 'Interpret':
-			items += [
-				('DIM_TO_VEC', '→ Vector', 'Shift last dimension to output.'),
-				('DIMS_TO_MAT', '→ Matrix', 'Shift last 2 dimensions to output.'),
-			]
-		elif self.active_socket_set == 'Dimensions':
-			items += [
-				('PIN_LEN_ONE', 'pinₐ =1', 'Remove a len(1) dimension'),
-				(
-					'PIN',
-					'pinₐ ≈v',
-					'Remove a len(n) dimension by selecting an index',
-				),
-				('SWAP', 'a₁ ↔ a₂', 'Swap the position of two dimensions'),
-			]
-
-		return [(*item, '', i) for i, item in enumerate(items)]
-
-	####################
-	# - Dimensions Search
 	####################
 	def search_dims(self) -> list[ct.BLEnumElement]:
 		if self.data_info is None:
 			return []
 
-		if self.operation == 'PIN_LEN_ONE':
+		if self.operation == FilterOperation.PinLen1:
 			dims = [
 				(dim_name, dim_name, f'Dimension "{dim_name}" of length 1')
 				for dim_name in self.data_info.dim_names
 				if self.data_info.dim_lens[dim_name] == 1
 			]
-		elif self.operation in ['PIN', 'SWAP']:
+		elif self.operation in [FilterOperation.Pin, FilterOperation.Swap]:
 			dims = [
 				(dim_name, dim_name, f'Dimension "{dim_name}"')
 				for dim_name in self.data_info.dim_names
@@ -124,12 +170,13 @@ class FilterMathNode(base.MaxwellSimNode):
 	# - UI
 	####################
 	def draw_label(self):
+		FO = FilterOperation
 		labels = {
-			'PIN_LEN_ONE': lambda: f'Filter: Pin {self.dim_0} (len=1)',
+			FO.PinLen1: lambda: f'Filter: Pin {self.dim_0} (len=1)',
-			'PIN': lambda: f'Filter: Pin {self.dim_0}',
+			FO.Pin: lambda: f'Filter: Pin {self.dim_0}',
-			'SWAP': lambda: f'Filter: Swap {self.dim_0}|{self.dim_1}',
+			FO.Swap: lambda: f'Filter: Swap {self.dim_0}|{self.dim_1}',
-			'DIM_TO_VEC': lambda: 'Filter: -> Vector',
+			FO.DimToVec: lambda: 'Filter: -> Vector',
-			'DIMS_TO_MAT': lambda: 'Filter: -> Matrix',
+			FO.DimsToMat: lambda: 'Filter: -> Matrix',
 		}
 
 		if (label := labels.get(self.operation)) is not None:
@@ -141,10 +188,10 @@ class FilterMathNode(base.MaxwellSimNode):
 		layout.prop(self, self.blfields['operation'], text='')
 
 		if self.active_socket_set == 'Dimensions':
-			if self.operation in ['PIN_LEN_ONE', 'PIN']:
+			if self.operation in [FilterOperation.PinLen1, FilterOperation.Pin]:
 				layout.prop(self, self.blfields['dim_0'], text='')
 
-			if self.operation == 'SWAP':
+			if self.operation == FilterOperation.Swap:
 				row = layout.row(align=True)
 				row.prop(self, self.blfields['dim_0'], text='')
 				row.prop(self, self.blfields['dim_1'], text='')
@@ -152,215 +199,199 @@ class FilterMathNode(base.MaxwellSimNode):
 	####################
 	# - Events
 	####################
-	@events.on_value_changed(
-		prop_name='active_socket_set',
-		run_on_init=True,
-	)
-	def on_socket_set_changed(self):
-		self.operation = bl_cache.Signal.ResetEnumItems
-
 	@events.on_value_changed(
 		# Trigger
-		socket_name='Data',
+		socket_name='Expr',
-		prop_name={'active_socket_set', 'operation'},
+		prop_name={'operation'},
 		run_on_init=True,
-		# Loaded
-		props={'operation'},
 	)
-	def on_any_change(self, props: dict) -> None:
+	def on_input_changed(self) -> None:
 		self.dim_0 = bl_cache.Signal.ResetEnumItems
 		self.dim_1 = bl_cache.Signal.ResetEnumItems
 
 	@events.on_value_changed(
-		socket_name='Data',
+		# Trigger
+		socket_name='Expr',
 		prop_name={'dim_0', 'dim_1', 'operation'},
-		## run_on_init: Implicitly triggered.
+		run_on_init=True,
+		# Loaded
 		props={'operation', 'dim_0', 'dim_1'},
-		input_sockets={'Data'},
+		input_sockets={'Expr'},
-		input_socket_kinds={'Data': ct.FlowKind.Info},
+		input_socket_kinds={'Expr': ct.FlowKind.Info},
 	)
-	def on_dim_change(self, props: dict, input_sockets: dict):
+	def on_pin_changed(self, props: dict, input_sockets: dict):
-		has_data = not ct.FlowSignal.check(input_sockets['Data'])
+		info = input_sockets['Expr']
-		if not has_data:
+		has_info = not ct.FlowSignal.check(info)
+		if not has_info:
 			return
 
 		# "Dimensions"|"PIN": Add/Remove Input Socket
-		if props['operation'] == 'PIN' and props['dim_0'] != 'NONE':
+		if props['operation'] == FilterOperation.Pin and props['dim_0'] is not None:
+			pinned_unit = info.dim_units[props['dim_0']]
+			pinned_mathtype = info.dim_mathtypes[props['dim_0']]
+			pinned_physical_type = spux.PhysicalType.from_unit(pinned_unit)
+
+			wanted_mathtype = (
+				spux.MathType.Complex
+				if pinned_mathtype == spux.MathType.Complex
+				and spux.MathType.Complex in pinned_physical_type.valid_mathtypes
+				else spux.MathType.Real
+			)
+
 			# Get Current and Wanted Socket Defs
 			current_bl_socket = self.loose_input_sockets.get('Value')
-			wanted_socket_def = sockets.SOCKET_DEFS[
-				ct.unit_to_socket_type(
-					input_sockets['Data'].dim_idx[props['dim_0']].unit
-				)
-			]
 
 			# Determine Whether to Declare New Loose Input SOcket
 			if (
 				current_bl_socket is None
-				or sockets.SOCKET_DEFS[current_bl_socket.socket_type]
+				or current_bl_socket.shape is not None
-				!= wanted_socket_def
+				or current_bl_socket.physical_type != pinned_physical_type
+				or current_bl_socket.mathtype != wanted_mathtype
 			):
 				self.loose_input_sockets = {
-					'Value': wanted_socket_def(),
+					'Value': sockets.ExprSocketDef(
+						active_kind=ct.FlowKind.Value,
+						shape=None,
+						physical_type=pinned_physical_type,
+						mathtype=wanted_mathtype,
+						default_unit=pinned_unit,
+					),
 				}
 		elif self.loose_input_sockets:
 			self.loose_input_sockets = {}
 
 	####################
-	# - Compute: LazyValueFunc / Array
+	# - Output
 	####################
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.LazyValueFunc,
 		props={'operation', 'dim_0', 'dim_1'},
-		input_sockets={'Data'},
+		input_sockets={'Expr'},
-		input_socket_kinds={'Data': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Info}},
+		input_socket_kinds={'Expr': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Info}},
 	)
-	def compute_data(self, props: dict, input_sockets: dict):
+	def compute_lazy_value_func(self, props: dict, input_sockets: dict):
-		lazy_value_func = input_sockets['Data'][ct.FlowKind.LazyValueFunc]
-		info = input_sockets['Data'][ct.FlowKind.Info]
-
-		# Check Flow
-		if any(ct.FlowSignal.check(inp) for inp in [info, lazy_value_func]):
-			return ct.FlowSignal.FlowPending
-
-		# Compute Function Arguments
 		operation = props['operation']
-		if operation == 'NONE':
+		lazy_value_func = input_sockets['Expr'][ct.FlowKind.LazyValueFunc]
-			return ct.FlowSignal.FlowPending
+		info = input_sockets['Expr'][ct.FlowKind.Info]
 
-		## Dimension(s)
+		has_lazy_value_func = not ct.FlowSignal.check(lazy_value_func)
+		has_info = not ct.FlowSignal.check(info)
+
+		# Dimension(s)
 		dim_0 = props['dim_0']
 		dim_1 = props['dim_1']
-		if operation in ['PIN_LEN_ONE', 'PIN', 'SWAP'] and dim_0 == 'NONE':
+		if (
-			return ct.FlowSignal.FlowPending
+			has_lazy_value_func
-		if operation == 'SWAP' and dim_1 == 'NONE':
+			and has_info
-			return ct.FlowSignal.FlowPending
+			and operation is not None
-
+			and operation.are_dims_valid(dim_0, dim_1)
-		## Axis/Axes
+		):
-		axis_0 = info.dim_names.index(dim_0) if dim_0 != 'NONE' else None
+			axis_0 = info.dim_names.index(dim_0) if dim_0 is not None else None
-		axis_1 = info.dim_names.index(dim_1) if dim_1 != 'NONE' else None
+			axis_1 = info.dim_names.index(dim_1) if dim_1 is not None else None
-
-		# Compose Output Function
-		filter_func = {
-			# Dimensions
-			'PIN_LEN_ONE': lambda data: jnp.squeeze(data, axis_0),
-			'PIN': lambda data, fixed_axis_idx: jnp.take(
-				data, fixed_axis_idx, axis=axis_0
-			),
-			'SWAP': lambda data: jnp.swapaxes(data, axis_0, axis_1),
-			# Interpret
-			'DIM_TO_VEC': lambda data: data,
-			'DIMS_TO_MAT': lambda data: data,
-		}[props['operation']]
 
 			return lazy_value_func.compose_within(
-			filter_func,
+				operation.jax_func(axis_0, axis_1),
 				enclosing_func_args=[int] if operation == 'PIN' else [],
 				supports_jax=True,
 			)
-
-	@events.computes_output_socket(
-		'Data',
-		kind=ct.FlowKind.Array,
-		output_sockets={'Data'},
-		output_socket_kinds={
-			'Data': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Params},
-		},
-	)
-	def compute_array(self, output_sockets: dict) -> ct.ArrayFlow:
-		lazy_value_func = output_sockets['Data'][ct.FlowKind.LazyValueFunc]
-		params = output_sockets['Data'][ct.FlowKind.Params]
-
-		# Check Flow
-		if any(ct.FlowSignal.check(inp) for inp in [lazy_value_func, params]):
 		return ct.FlowSignal.FlowPending
 
-		return ct.ArrayFlow(
+	@events.computes_output_socket(
-			values=lazy_value_func.func_jax(*params.func_args, **params.func_kwargs),
+		'Expr',
-			unit=None,
+		kind=ct.FlowKind.Array,
+		output_sockets={'Expr'},
+		output_socket_kinds={
+			'Expr': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Params},
+		},
+		unit_systems={'BlenderUnits': ct.UNITS_BLENDER},
 	)
+	def compute_array(self, output_sockets, unit_systems) -> ct.ArrayFlow:
+		lazy_value_func = output_sockets['Expr'][ct.FlowKind.LazyValueFunc]
+		params = output_sockets['Expr'][ct.FlowKind.Params]
+
+		has_lazy_value_func = not ct.FlowSignal.check(lazy_value_func)
+		has_params = not ct.FlowSignal.check(params)
+
+		if has_lazy_value_func and has_params:
+			unit_system = unit_systems['BlenderUnits']
+			return ct.ArrayFlow(
+				values=lazy_value_func.func_jax(
+					*params.scaled_func_args(unit_system),
+					**params.scaled_func_kwargs(unit_system),
+				),
+			)
+		return ct.FlowSignal.FlowPending
 
 	####################
-	# - Compute Auxiliary: Info
+	# - Auxiliary: Info
 	####################
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.Info,
 		props={'dim_0', 'dim_1', 'operation'},
-		input_sockets={'Data'},
+		input_sockets={'Expr'},
-		input_socket_kinds={'Data': ct.FlowKind.Info},
+		input_socket_kinds={'Expr': ct.FlowKind.Info},
 	)
-	def compute_data_info(self, props: dict, input_sockets: dict) -> ct.InfoFlow:
+	def compute_info(self, props: dict, input_sockets: dict) -> ct.InfoFlow:
-		info = input_sockets['Data']
+		operation = props['operation']
+		info = input_sockets['Expr']
 
-		# Check Flow
+		has_info = not ct.FlowSignal.check(info)
-		if ct.FlowSignal.check(info):
-			return ct.FlowSignal.FlowPending
 
-		# Collect Information
+		# Dimension(s)
 		dim_0 = props['dim_0']
 		dim_1 = props['dim_1']
+		if (
+			has_info
+			and operation is not None
+			and operation.are_dims_valid(dim_0, dim_1)
+		):
+			return operation.transform_info(info, dim_0, dim_1)
 
-		if props['operation'] in ['PIN_LEN_ONE', 'PIN', 'SWAP'] and dim_0 == 'NONE':
 		return ct.FlowSignal.FlowPending
-		if props['operation'] == 'SWAP' and dim_1 == 'NONE':
-			return ct.FlowSignal.FlowPending
-
-		return {
-			# Dimensions
-			'PIN_LEN_ONE': lambda: info.delete_dimension(dim_0),
-			'PIN': lambda: info.delete_dimension(dim_0),
-			'SWAP': lambda: info.swap_dimensions(dim_0, dim_1),
-			# Interpret
-			'DIM_TO_VEC': lambda: info.shift_last_input,
-			'DIMS_TO_MAT': lambda: info.shift_last_input.shift_last_input,
-		}[props['operation']]()
 
 	####################
-	# - Compute Auxiliary: Info
+	# - Auxiliary: Params
 	####################
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.Params,
 		props={'dim_0', 'dim_1', 'operation'},
-		input_sockets={'Data', 'Value'},
+		input_sockets={'Expr', 'Value'},
-		input_socket_kinds={'Data': {ct.FlowKind.Info, ct.FlowKind.Params}},
+		input_socket_kinds={'Expr': {ct.FlowKind.Info, ct.FlowKind.Params}},
 		input_sockets_optional={'Value': True},
 	)
-	def compute_composed_params(
+	def compute_params(self, props: dict, input_sockets: dict) -> ct.ParamsFlow:
-		self, props: dict, input_sockets: dict
+		operation = props['operation']
-	) -> ct.ParamsFlow:
+		info = input_sockets['Expr'][ct.FlowKind.Info]
-		info = input_sockets['Data'][ct.FlowKind.Info]
+		params = input_sockets['Expr'][ct.FlowKind.Params]
-		params = input_sockets['Data'][ct.FlowKind.Params]
 
-		# Check Flow
+		has_info = not ct.FlowSignal.check(info)
-		if any(ct.FlowSignal.check(inp) for inp in [info, params]):
+		has_params = not ct.FlowSignal.check(params)
-			return ct.FlowSignal.FlowPending
 
-		# Collect Information
+		# Dimension(s)
-		## Dimensions
 		dim_0 = props['dim_0']
 		dim_1 = props['dim_1']
-
+		if (
-		if props['operation'] in ['PIN_LEN_ONE', 'PIN', 'SWAP'] and dim_0 == 'NONE':
+			has_info
-			return ct.FlowSignal.FlowPending
+			and has_params
-		if props['operation'] == 'SWAP' and dim_1 == 'NONE':
+			and operation is not None
-			return ct.FlowSignal.FlowPending
+			and operation.are_dims_valid(dim_0, dim_1)
-
+		):
 			## Pinned Value
 			pinned_value = input_sockets['Value']
 			has_pinned_value = not ct.FlowSignal.check(pinned_value)
 
 			if props['operation'] == 'PIN' and has_pinned_value:
-			# Compute IDX Corresponding to Dimension Index
 				nearest_idx_to_value = info.dim_idx[dim_0].nearest_idx_of(
-				input_sockets['Value'], require_sorted=True
+					pinned_value, require_sorted=True
 				)
 
 				return params.compose_within(enclosing_func_args=[nearest_idx_to_value])
 
 			return params
+		return ct.FlowSignal.FlowPending
 
 
 ####################

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/math/map_math.py

@@ -20,6 +20,248 @@ log = logger.get(__name__)
 X_COMPLEX = sp.Symbol('x', complex=True)
 
 
+class MapOperation(enum.StrEnum):
+	"""Valid operations for the `MapMathNode`.
+
+	Attributes:
+		UserExpr: Use a user-provided mapping expression.
+		Real: Compute the real part of the input.
+		Imag: Compute the imaginary part of the input.
+		Abs: Compute the absolute value of the input.
+		Sq: Square the input.
+		Sqrt: Compute the (principal) square root of the input.
+		InvSqrt: Compute the inverse square root of the input.
+		Cos: Compute the cosine of the input.
+		Sin: Compute the sine of the input.
+		Tan: Compute the tangent of the input.
+		Acos: Compute the inverse cosine of the input.
+		Asin: Compute the inverse sine of the input.
+		Atan: Compute the inverse tangent of the input.
+		Norm2: Compute the 2-norm (aka. length) of the input vector.
+		Det: Compute the determinant of the input matrix.
+		Cond: Compute the condition number of the input matrix.
+		NormFro: Compute the frobenius norm of the input matrix.
+		Rank: Compute the rank of the input matrix.
+		Diag: Compute the diagonal vector of the input matrix.
+		EigVals: Compute the eigenvalues vector of the input matrix.
+		SvdVals: Compute the singular values vector of the input matrix.
+		Inv: Compute the inverse matrix of the input matrix.
+		Tra: Compute the transpose matrix of the input matrix.
+		Qr: Compute the QR-factorized matrices of the input matrix.
+		Chol: Compute the Cholesky-factorized matrices of the input matrix.
+		Svd: Compute the SVD-factorized matrices of the input matrix.
+	"""
+
+	# By User Expression
+	UserExpr = enum.auto()
+	# By Number
+	Real = enum.auto()
+	Imag = enum.auto()
+	Abs = enum.auto()
+	Sq = enum.auto()
+	Sqrt = enum.auto()
+	InvSqrt = enum.auto()
+	Cos = enum.auto()
+	Sin = enum.auto()
+	Tan = enum.auto()
+	Acos = enum.auto()
+	Asin = enum.auto()
+	Atan = enum.auto()
+	Sinc = enum.auto()
+	# By Vector
+	Norm2 = enum.auto()
+	# By Matrix
+	Det = enum.auto()
+	Cond = enum.auto()
+	NormFro = enum.auto()
+	Rank = enum.auto()
+	Diag = enum.auto()
+	EigVals = enum.auto()
+	SvdVals = enum.auto()
+	Inv = enum.auto()
+	Tra = enum.auto()
+	Qr = enum.auto()
+	Chol = enum.auto()
+	Svd = enum.auto()
+
+	@staticmethod
+	def to_name(value: typ.Self) -> str:
+		MO = MapOperation
+		return {
+			# By User Expression
+			MO.UserExpr: '*',
+			# By Number
+			MO.Real: 'ℝ(v)',
+			MO.Imag: 'Im(v)',
+			MO.Abs: '|v|',
+			MO.Sq: 'v²',
+			MO.Sqrt: '√v',
+			MO.InvSqrt: '1/√v',
+			MO.Cos: 'cos v',
+			MO.Sin: 'sin v',
+			MO.Tan: 'tan v',
+			MO.Acos: 'acos v',
+			MO.Asin: 'asin v',
+			MO.Atan: 'atan v',
+			MO.Sinc: 'sinc v',
+			# By Vector
+			MO.Norm2: '||v||₂',
+			# By Matrix
+			MO.Det: 'det V',
+			MO.Cond: 'κ(V)',
+			MO.NormFro: '||V||_F',
+			MO.Rank: 'rank V',
+			MO.Diag: 'diag V',
+			MO.EigVals: 'eigvals V',
+			MO.SvdVals: 'svdvals V',
+			MO.Inv: 'V⁻¹',
+			MO.Tra: 'Vt',
+			MO.Qr: 'qr V',
+			MO.Chol: 'chol V',
+			MO.Svd: 'svd V',
+		}[value]
+
+	@staticmethod
+	def to_icon(value: typ.Self) -> str:
+		return ''
+
+	def bl_enum_element(self, i: int) -> ct.BLEnumElement:
+		MO = MapOperation
+		return (
+			str(self),
+			MO.to_name(self),
+			MO.to_name(self),
+			MO.to_icon(self),
+			i,
+		)
+
+	@staticmethod
+	def by_element_shape(shape: tuple[int, ...] | None) -> list[typ.Self]:
+		MO = MapOperation
+		# By Number
+		if shape is None:
+			return [
+				MO.Real,
+				MO.Imag,
+				MO.Abs,
+				MO.Sq,
+				MO.Sqrt,
+				MO.InvSqrt,
+				MO.Cos,
+				MO.Sin,
+				MO.Tan,
+				MO.Acos,
+				MO.Asin,
+				MO.Atan,
+				MO.Sinc,
+			]
+
+		# By Vector
+		if len(shape) == 1:
+			return [
+				MO.Norm2,
+			]
+		# By Matrix
+		if len(shape) == 2:
+			return [
+				MO.Det,
+				MO.Cond,
+				MO.NormFro,
+				MO.Rank,
+				MO.Diag,
+				MO.EigVals,
+				MO.SvdVals,
+				MO.Inv,
+				MO.Tra,
+				MO.Qr,
+				MO.Chol,
+				MO.Svd,
+			]
+
+		return []
+
+	def jax_func(self, user_expr_func: ct.LazyValueFuncFlow | None = None):
+		MO = MapOperation
+		if self == MO.UserExpr and user_expr_func is not None:
+			return lambda data: user_expr_func.func(data)
+		return {
+			# By Number
+			MO.Real: lambda data: jnp.real(data),
+			MO.Imag: lambda data: jnp.imag(data),
+			MO.Abs: lambda data: jnp.abs(data),
+			MO.Sq: lambda data: jnp.square(data),
+			MO.Sqrt: lambda data: jnp.sqrt(data),
+			MO.InvSqrt: lambda data: 1 / jnp.sqrt(data),
+			MO.Cos: lambda data: jnp.cos(data),
+			MO.Sin: lambda data: jnp.sin(data),
+			MO.Tan: lambda data: jnp.tan(data),
+			MO.Acos: lambda data: jnp.acos(data),
+			MO.Asin: lambda data: jnp.asin(data),
+			MO.Atan: lambda data: jnp.atan(data),
+			MO.Sinc: lambda data: jnp.sinc(data),
+			# By Vector
+			# Vector -> Number
+			MO.Norm2: lambda data: jnp.linalg.norm(data, ord=2, axis=-1),
+			# By Matrix
+			# Matrix -> Number
+			MO.Det: lambda data: jnp.linalg.det(data),
+			MO.Cond: lambda data: jnp.linalg.cond(data),
+			MO.NormFro: lambda data: jnp.linalg.matrix_norm(data, ord='fro'),
+			MO.Rank: lambda data: jnp.linalg.matrix_rank(data),
+			# Matrix -> Vec
+			MO.Diag: lambda data: jnp.diagonal(data, axis1=-2, axis2=-1),
+			MO.EigVals: lambda data: jnp.linalg.eigvals(data),
+			MO.SvdVals: lambda data: jnp.linalg.svdvals(data),
+			# Matrix -> Matrix
+			MO.Inv: lambda data: jnp.linalg.inv(data),
+			MO.Tra: lambda data: jnp.matrix_transpose(data),
+			# Matrix -> Matrices
+			MO.Qr: lambda data: jnp.linalg.qr(data),
+			MO.Chol: lambda data: jnp.linalg.cholesky(data),
+			MO.Svd: lambda data: jnp.linalg.svd(data),
+		}[self]
+
+	def transform_info(self, info: ct.InfoFlow):
+		MO = MapOperation
+		return {
+			# By User Expression
+			MO.UserExpr: '*',
+			# By Number
+			MO.Real: lambda: info.set_output_mathtype(spux.MathType.Real),
+			MO.Imag: lambda: info.set_output_mathtype(spux.MathType.Real),
+			MO.Abs: lambda: info.set_output_mathtype(spux.MathType.Real),
+			# By Vector
+			MO.Norm2: lambda: info.collapse_output(
+				collapsed_name=MO.to_name(self).replace('v', info.output_name),
+				collapsed_mathtype=spux.MathType.Real,
+				collapsed_unit=info.output_unit,
+			),
+			# By Matrix
+			MO.Det: lambda: info.collapse_output(
+				collapsed_name=MO.to_name(self).replace('V', info.output_name),
+				collapsed_mathtype=info.output_mathtype,
+				collapsed_unit=info.output_unit,
+			),
+			MO.Cond: lambda: info.collapse_output(
+				collapsed_name=MO.to_name(self).replace('V', info.output_name),
+				collapsed_mathtype=spux.MathType.Real,
+				collapsed_unit=None,
+			),
+			MO.NormFro: lambda: info.collapse_output(
+				collapsed_name=MO.to_name(self).replace('V', info.output_name),
+				collapsed_mathtype=spux.MathType.Real,
+				collapsed_unit=info.output_unit,
+			),
+			MO.Rank: lambda: info.collapse_output(
+				collapsed_name=MO.to_name(self).replace('V', info.output_name),
+				collapsed_mathtype=spux.MathType.Integer,
+				collapsed_unit=None,
+			),
+			## TODO: Matrix -> Vec
+			## TODO: Matrix -> Matrices
+		}.get(self, info)
+
+
 class MapMathNode(base.MaxwellSimNode):
 	r"""Applies a function by-structure to the data.
 
@@ -104,120 +346,46 @@ class MapMathNode(base.MaxwellSimNode):
 	bl_label = 'Map Math'
 
 	input_sockets: typ.ClassVar = {
-		'Data': sockets.DataSocketDef(format='jax'),
+		'Expr': sockets.ExprSocketDef(),
-	}
-	input_socket_sets: typ.ClassVar = {
-		'By Element': {},
-		'By Vector': {},
-		'By Matrix': {},
-		'Expr': {
-			'Mapper': sockets.ExprSocketDef(
-				complex_symbols=[X_COMPLEX],
-				default_expr=X_COMPLEX,
-			),
-		},
 	}
 	output_sockets: typ.ClassVar = {
-		'Data': sockets.DataSocketDef(format='jax'),
+		'Expr': sockets.ExprSocketDef(),
 	}
 
 	####################
 	# - Properties
 	####################
-	operation: enum.Enum = bl_cache.BLField(
+	operation: MapOperation = bl_cache.BLField(
 		prop_ui=True, enum_cb=lambda self, _: self.search_operations()
 	)
 
-	def search_operations(self) -> list[ct.BLEnumElement]:
+	@property
-		if self.active_socket_set == 'By Element':
+	def expr_output_shape(self) -> ct.InfoFlow | None:
-			items = [
+		info = self._compute_input('Expr', kind=ct.FlowKind.Info)
-				# General
+		has_info = not ct.FlowSignal.check(info)
-				('REAL', 'ℝ(v)', 'real(v) (by el)'),
+		if has_info:
-				('IMAG', 'Im(v)', 'imag(v) (by el)'),
+			return info.output_shape
-				('ABS', '|v|', 'abs(v) (by el)'),
-				('SQ', 'v²', 'v^2 (by el)'),
-				('SQRT', '√v', 'sqrt(v) (by el)'),
-				('INV_SQRT', '1/√v', '1/sqrt(v) (by el)'),
-				None,
-				# Trigonometry
-				('COS', 'cos v', 'cos(v) (by el)'),
-				('SIN', 'sin v', 'sin(v) (by el)'),
-				('TAN', 'tan v', 'tan(v) (by el)'),
-				('ACOS', 'acos v', 'acos(v) (by el)'),
-				('ASIN', 'asin v', 'asin(v) (by el)'),
-				('ATAN', 'atan v', 'atan(v) (by el)'),
-			]
-		elif self.active_socket_set in 'By Vector':
-			items = [
-				# Vector -> Number
-				('NORM_2', '||v||₂', 'norm(v, 2) (by Vec)'),
-			]
-		elif self.active_socket_set == 'By Matrix':
-			items = [
-				# Matrix -> Number
-				('DET', 'det V', 'det(V) (by Mat)'),
-				('COND', 'κ(V)', 'cond(V) (by Mat)'),
-				('NORM_FRO', '||V||_F', 'norm(V, frobenius) (by Mat)'),
-				('RANK', 'rank V', 'rank(V) (by Mat)'),
-				None,
-				# Matrix -> Array
-				('DIAG', 'diag V', 'diag(V) (by Mat)'),
-				('EIG_VALS', 'eigvals V', 'eigvals(V) (by Mat)'),
-				('SVD_VALS', 'svdvals V', 'diag(svd(V)) (by Mat)'),
-				None,
-				# Matrix -> Matrix
-				('INV', 'V⁻¹', 'V^(-1) (by Mat)'),
-				('TRA', 'Vt', 'V^T (by Mat)'),
-				None,
-				# Matrix -> Matrices
-				('QR', 'qr V', 'qr(V) -> Q·R (by Mat)'),
-				('CHOL', 'chol V', 'cholesky(V) -> V·V† (by Mat)'),
-				('SVD', 'svd V', 'svd(V) -> U·Σ·V† (by Mat)'),
-			]
-		elif self.active_socket_set == 'Expr':
-			items = [('EXPR_EL', 'By Element', 'Expression-defined (by el)')]
-		else:
-			msg = f'Active socket set {self.active_socket_set} is unknown'
-			raise RuntimeError(msg)
 
+		return None
+
+	output_shape: tuple[int, ...] | None = bl_cache.BLField(None)
+
+	def search_operations(self) -> list[ct.BLEnumElement]:
+		if self.expr_output_shape is not None:
 			return [
-			(*item, '', i) if item is not None else None for i, item in enumerate(items)
+				operation.bl_enum_element(i)
+				for i, operation in enumerate(
+					MapOperation.by_element_shape(self.expr_output_shape)
+				)
 			]
+		return []
 
 	####################
 	# - UI
 	####################
 	def draw_label(self):
-		labels = {
+		if self.operation is not None:
-			'REAL': 'ℝ(v)',
+			return 'Map: ' + MapOperation.to_name(self.operation)
-			'IMAG': 'Im(v)',
-			'ABS': '|v|',
-			'SQ': 'v²',
-			'SQRT': '√v',
-			'INV_SQRT': '1/√v',
-			'COS': 'cos v',
-			'SIN': 'sin v',
-			'TAN': 'tan v',
-			'ACOS': 'acos v',
-			'ASIN': 'asin v',
-			'ATAN': 'atan v',
-			'NORM_2': '||v||₂',
-			'DET': 'det V',
-			'COND': 'κ(V)',
-			'NORM_FRO': '||V||_F',
-			'RANK': 'rank V',
-			'DIAG': 'diag V',
-			'EIG_VALS': 'eigvals V',
-			'SVD_VALS': 'svdvals V',
-			'INV': 'V⁻¹',
-			'TRA': 'Vt',
-			'QR': 'qr V',
-			'CHOL': 'chol V',
-			'SVD': 'svd V',
-		}
-
-		if (label := labels.get(self.operation)) is not None:
-			return 'Map: ' + label
 
 		return self.bl_label
 
@@ -228,106 +396,98 @@ class MapMathNode(base.MaxwellSimNode):
 	# - Events
 	####################
 	@events.on_value_changed(
-		prop_name='active_socket_set',
+		# Trigger
+		socket_name='Expr',
 		run_on_init=True,
 	)
-	def on_socket_set_changed(self):
+	def on_input_changed(self):
+		if self.operation not in MapOperation.by_element_shape(self.expr_output_shape):
 			self.operation = bl_cache.Signal.ResetEnumItems
 
+	@events.on_value_changed(
+		# Trigger
+		prop_name={'operation'},
+		run_on_init=True,
+		# Loaded
+		props={'operation'},
+	)
+	def on_operation_changed(self, props: dict) -> None:
+		operation = props['operation']
+
+		# UserExpr: Add/Remove Input Socket
+		if operation == MapOperation.UserExpr:
+			current_bl_socket = self.loose_input_sockets.get('Mapper')
+			if current_bl_socket is None:
+				self.loose_input_sockets = {
+					'Mapper': sockets.ExprSocketDef(
+						symbols={X_COMPLEX},
+						default_value=X_COMPLEX,
+						mathtype=spux.MathType.Complex,
+					),
+				}
+
+		elif self.loose_input_sockets:
+			self.loose_input_sockets = {}
+
 	####################
 	# - Compute: LazyValueFunc / Array
 	####################
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.LazyValueFunc,
-		props={'active_socket_set', 'operation'},
+		props={'operation'},
-		input_sockets={'Data', 'Mapper'},
+		input_sockets={'Expr', 'Mapper'},
 		input_socket_kinds={
-			'Data': ct.FlowKind.LazyValueFunc,
+			'Expr': ct.FlowKind.LazyValueFunc,
 			'Mapper': ct.FlowKind.LazyValueFunc,
 		},
 		input_sockets_optional={'Mapper': True},
 	)
 	def compute_data(self, props: dict, input_sockets: dict):
-		has_data = not ct.FlowSignal.check(input_sockets['Data'])
+		operation = props['operation']
-		if (
+		expr = input_sockets['Expr']
-			not has_data
+		mapper = input_sockets['Mapper']
-			or props['operation'] == 'NONE'
-			or (
-				props['active_socket_set'] == 'Expr'
-				and ct.FlowSignal.check(input_sockets['Mapper'])
-			)
-		):
-			return ct.FlowSignal.FlowPending
 
-		mapping_func: typ.Callable[[jax.Array], jax.Array] = {
+		has_expr = not ct.FlowSignal.check(expr)
-			'By Element': {
+		has_mapper = not ct.FlowSignal.check(expr)
-				'REAL': lambda data: jnp.real(data),
-				'IMAG': lambda data: jnp.imag(data),
-				'ABS': lambda data: jnp.abs(data),
-				'SQ': lambda data: jnp.square(data),
-				'SQRT': lambda data: jnp.sqrt(data),
-				'INV_SQRT': lambda data: 1 / jnp.sqrt(data),
-				'COS': lambda data: jnp.cos(data),
-				'SIN': lambda data: jnp.sin(data),
-				'TAN': lambda data: jnp.tan(data),
-				'ACOS': lambda data: jnp.acos(data),
-				'ASIN': lambda data: jnp.asin(data),
-				'ATAN': lambda data: jnp.atan(data),
-				'SINC': lambda data: jnp.sinc(data),
-			},
-			'By Vector': {
-				'NORM_2': lambda data: jnp.linalg.norm(data, ord=2, axis=-1),
-			},
-			'By Matrix': {
-				# Matrix -> Number
-				'DET': lambda data: jnp.linalg.det(data),
-				'COND': lambda data: jnp.linalg.cond(data),
-				'NORM_FRO': lambda data: jnp.linalg.matrix_norm(data, ord='fro'),
-				'RANK': lambda data: jnp.linalg.matrix_rank(data),
-				# Matrix -> Vec
-				'DIAG': lambda data: jnp.diagonal(data, axis1=-2, axis2=-1),
-				'EIG_VALS': lambda data: jnp.linalg.eigvals(data),
-				'SVD_VALS': lambda data: jnp.linalg.svdvals(data),
-				# Matrix -> Matrix
-				'INV': lambda data: jnp.linalg.inv(data),
-				'TRA': lambda data: jnp.matrix_transpose(data),
-				# Matrix -> Matrices
-				'QR': lambda data: jnp.linalg.qr(data),
-				'CHOL': lambda data: jnp.linalg.cholesky(data),
-				'SVD': lambda data: jnp.linalg.svd(data),
-			},
-			'Expr': {
-				'EXPR_EL': lambda data: input_sockets['Mapper'].func(data),
-			},
-		}[props['active_socket_set']][props['operation']]
 
-		# Compose w/Lazy Root Function Data
+		if has_expr and operation is not None:
-		return input_sockets['Data'].compose_within(
+			if not has_mapper:
-			mapping_func,
+				return expr.compose_within(
+					operation.jax_func(),
 					supports_jax=True,
 				)
+			if operation == MapOperation.UserExpr and has_mapper:
+				return expr.compose_within(
+					operation.jax_func(user_expr_func=mapper),
+					supports_jax=True,
+				)
+		return ct.FlowSignal.FlowPending
 
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.Array,
-		output_sockets={'Data'},
+		output_sockets={'Expr'},
 		output_socket_kinds={
-			'Data': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Params},
+			'Expr': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Params},
 		},
+		unit_systems={'BlenderUnits': ct.UNITS_BLENDER},
 	)
-	def compute_array(self, output_sockets: dict) -> ct.ArrayFlow:
+	def compute_array(self, output_sockets, unit_systems) -> ct.ArrayFlow:
-		lazy_value_func = output_sockets['Data'][ct.FlowKind.LazyValueFunc]
+		lazy_value_func = output_sockets['Expr'][ct.FlowKind.LazyValueFunc]
-		params = output_sockets['Data'][ct.FlowKind.Params]
+		params = output_sockets['Expr'][ct.FlowKind.Params]
 
-		if all(not ct.FlowSignal.check(inp) for inp in [lazy_value_func, params]):
+		has_lazy_value_func = not ct.FlowSignal.check(lazy_value_func)
+		has_params = not ct.FlowSignal.check(params)
+
+		if has_lazy_value_func and has_params:
+			unit_system = unit_systems['BlenderUnits']
 			return ct.ArrayFlow(
 				values=lazy_value_func.func_jax(
-					*params.func_args, **params.func_kwargs
+					*params.scaled_func_args(unit_system),
+					**params.scaled_func_kwargs(unit_system),
 				),
-				unit=None,
 			)
-
 		return ct.FlowSignal.FlowPending
 
 	####################
@@ -341,60 +501,16 @@ class MapMathNode(base.MaxwellSimNode):
 		input_socket_kinds={'Data': ct.FlowKind.Info},
 	)
 	def compute_data_info(self, props: dict, input_sockets: dict) -> ct.InfoFlow:
-		info = input_sockets['Data']
+		operation = props['operation']
-		if ct.FlowSignal.check(info):
+		info = input_sockets['Expr']
+
+		has_info = not ct.FlowSignal.check(info)
+
+		if has_info and operation is not None:
+			return operation.transform_info(info)
+
 		return ct.FlowSignal.FlowPending
 
-		# Complex -> Real
-		if props['active_socket_set'] == 'By Element' and props['operation'] in [
-			'REAL',
-			'IMAG',
-			'ABS',
-		]:
-			return info.set_output_mathtype(spux.MathType.Real)
-
-		if props['active_socket_set'] == 'By Vector' and props['operation'] in [
-			'NORM_2'
-		]:
-			return {
-				'NORM_2': lambda: info.collapse_output(
-					collapsed_name=f'||{info.output_name}||₂',
-					collapsed_mathtype=spux.MathType.Real,
-					collapsed_unit=info.output_unit,
-				)
-			}[props['operation']]()
-
-		if props['active_socket_set'] == 'By Matrix' and props['operation'] in [
-			'DET',
-			'COND',
-			'NORM_FRO',
-			'RANK',
-		]:
-			return {
-				'DET': lambda: info.collapse_output(
-					collapsed_name=f'det {info.output_name}',
-					collapsed_mathtype=info.output_mathtype,
-					collapsed_unit=info.output_unit,
-				),
-				'COND': lambda: info.collapse_output(
-					collapsed_name=f'κ({info.output_name})',
-					collapsed_mathtype=spux.MathType.Real,
-					collapsed_unit=None,
-				),
-				'NORM_FRO': lambda: info.collapse_output(
-					collapsed_name=f'||({info.output_name}||_F',
-					collapsed_mathtype=spux.MathType.Real,
-					collapsed_unit=info.output_unit,
-				),
-				'RANK': lambda: info.collapse_output(
-					collapsed_name=f'rank {info.output_name}',
-					collapsed_mathtype=spux.MathType.Integer,
-					collapsed_unit=None,
-				),
-			}[props['operation']]()
-
-		return info
-
 	@events.computes_output_socket(
 		'Data',
 		kind=ct.FlowKind.Params,

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/math/operate_math.py

@@ -14,6 +14,29 @@ from ... import base, events
 
 log = logger.get(__name__)
 
+FUNCS = {
+	'ADD': lambda exprs: exprs[0] + exprs[1],
+	'SUB': lambda exprs: exprs[0] - exprs[1],
+	'MUL': lambda exprs: exprs[0] * exprs[1],
+	'DIV': lambda exprs: exprs[0] / exprs[1],
+	'POW': lambda exprs: exprs[0] ** exprs[1],
+}
+
+SP_FUNCS = FUNCS
+JAX_FUNCS = FUNCS | {
+	# Number | *
+	'ATAN2': lambda exprs: jnp.atan2(exprs[1], exprs[0]),
+	# Vector | Vector
+	'VEC_VEC_DOT': lambda exprs: jnp.matmul(exprs[0], exprs[1]),
+	'CROSS': lambda exprs: jnp.cross(exprs[0], exprs[1]),
+	# Matrix | Vector
+	'MAT_VEC_DOT': lambda exprs: jnp.matmul(exprs[0], exprs[1]),
+	'LIN_SOLVE': lambda exprs: jnp.linalg.solve(exprs[0], exprs[1]),
+	'LSQ_SOLVE': lambda exprs: jnp.linalg.lstsq(exprs[0], exprs[1]),
+	# Matrix | Matrix
+	'MAT_MAT_DOT': lambda exprs: jnp.matmul(exprs[0], exprs[1]),
+}
+
 
 class OperateMathNode(base.MaxwellSimNode):
 	r"""Applies a function that depends on two inputs.
@@ -28,40 +51,12 @@ class OperateMathNode(base.MaxwellSimNode):
 	node_type = ct.NodeType.OperateMath
 	bl_label = 'Operate Math'
 
-	input_socket_sets: typ.ClassVar = {
+	input_sockets: typ.ClassVar = {
-		'Expr | Expr': {
+		'Expr L': sockets.ExprSocketDef(show_info_columns=False),
-			'Expr L': sockets.ExprSocketDef(),
+		'Expr R': sockets.ExprSocketDef(show_info_columns=False),
-			'Expr R': sockets.ExprSocketDef(),
-		},
-		'Data | Data': {
-			'Data L': sockets.DataSocketDef(
-				format='jax', default_show_info_columns=False
-			),
-			'Data R': sockets.DataSocketDef(
-				format='jax', default_show_info_columns=False
-			),
-		},
-		'Expr | Data': {
-			'Expr L': sockets.ExprSocketDef(),
-			'Data R': sockets.DataSocketDef(
-				format='jax', default_show_info_columns=False
-			),
-		},
 	}
-	output_socket_sets: typ.ClassVar = {
+	output_sockets: typ.ClassVar = {
-		'Expr | Expr': {
 		'Expr': sockets.ExprSocketDef(),
-		},
-		'Data | Data': {
-			'Data': sockets.DataSocketDef(
-				format='jax', default_show_info_columns=False
-			),
-		},
-		'Expr | Data': {
-			'Data': sockets.DataSocketDef(
-				format='jax', default_show_info_columns=False
-			),
-		},
 	}
 
 	####################
@@ -77,15 +72,15 @@ class OperateMathNode(base.MaxwellSimNode):
 
 	def search_categories(self) -> list[ct.BLEnumElement]:
 		"""Deduce and return a list of valid categories for the current socket set and input data."""
-		data_l_info = self._compute_input(
+		expr_l_info = self._compute_input(
-			'Data L', kind=ct.FlowKind.Info, optional=True
+			'Expr L', kind=ct.FlowKind.Info, optional=True
 		)
-		data_r_info = self._compute_input(
+		expr_r_info = self._compute_input(
-			'Data R', kind=ct.FlowKind.Info, optional=True
+			'Expr R', kind=ct.FlowKind.Info, optional=True
 		)
 
-		has_data_l_info = not ct.FlowSignal.check(data_l_info)
+		has_expr_l_info = not ct.FlowSignal.check(expr_l_info)
-		has_data_r_info = not ct.FlowSignal.check(data_r_info)
+		has_expr_r_info = not ct.FlowSignal.check(expr_r_info)
 
 		# Categories by Socket Set
 		NUMBER_NUMBER = (
@@ -120,64 +115,45 @@ class OperateMathNode(base.MaxwellSimNode):
 		)
 		categories = []
 
-		## Expr | Expr
+		if has_expr_l_info and has_expr_r_info:
-		if self.active_socket_set == 'Expr | Expr':
-			return [NUMBER_NUMBER]
-
-		## Data | Data
-		if (
-			self.active_socket_set == 'Data | Data'
-			and has_data_l_info
-			and has_data_r_info
-		):
 			# Check Valid Broadcasting
 			## Number | Number
-			if data_l_info.output_shape is None and data_r_info.output_shape is None:
+			if expr_l_info.output_shape is None and expr_r_info.output_shape is None:
 				categories = [NUMBER_NUMBER]
 
 			## Number | Vector
 			elif (
-				data_l_info.output_shape is None and len(data_r_info.output_shape) == 1
+				expr_l_info.output_shape is None and len(expr_r_info.output_shape) == 1
 			):
 				categories = [NUMBER_VECTOR]
 
 			## Number | Matrix
 			elif (
-				data_l_info.output_shape is None and len(data_r_info.output_shape) == 2
+				expr_l_info.output_shape is None and len(expr_r_info.output_shape) == 2
-			):  # noqa: PLR2004
+			):
 				categories = [NUMBER_MATRIX]
 
 			## Vector | Vector
 			elif (
-				len(data_l_info.output_shape) == 1
+				len(expr_l_info.output_shape) == 1
-				and len(data_r_info.output_shape) == 1
+				and len(expr_r_info.output_shape) == 1
 			):
 				categories = [VECTOR_VECTOR]
 
 			## Matrix | Vector
 			elif (
-				len(data_l_info.output_shape) == 2  # noqa: PLR2004
+				len(expr_l_info.output_shape) == 2  # noqa: PLR2004
-				and len(data_r_info.output_shape) == 1
+				and len(expr_r_info.output_shape) == 1
 			):
 				categories = [MATRIX_VECTOR]
 
 			## Matrix | Matrix
 			elif (
-				len(data_l_info.output_shape) == 2  # noqa: PLR2004
+				len(expr_l_info.output_shape) == 2  # noqa: PLR2004
-				and len(data_r_info.output_shape) == 2  # noqa: PLR2004
+				and len(expr_r_info.output_shape) == 2  # noqa: PLR2004
 			):
 				categories = [MATRIX_MATRIX]
 
-		## Expr | Data
-		if self.active_socket_set == 'Expr | Data' and has_data_r_info:
-			if data_r_info.output_shape is None:
-				categories = [NUMBER_NUMBER]
-			else:
-				categories = {
-					1: [NUMBER_NUMBER, NUMBER_VECTOR],
-					2: [NUMBER_NUMBER, NUMBER_MATRIX],
-				}[len(data_r_info.output_shape)]
-
 		return [
 			(*category, '', i) if category is not None else None
 			for i, category in enumerate(categories)
@@ -248,11 +224,10 @@ class OperateMathNode(base.MaxwellSimNode):
 	####################
 	@events.on_value_changed(
 		# Trigger
-		socket_name={'Expr L', 'Expr R', 'Data L', 'Data R'},
+		socket_name={'Expr L', 'Expr R'},
-		prop_name='active_socket_set',
 		run_on_init=True,
 	)
-	def on_socket_set_changed(self) -> None:
+	def on_socket_changed(self) -> None:
 		# Recompute Valid Categories
 		self.category = bl_cache.Signal.ResetEnumItems
 		self.operation = bl_cache.Signal.ResetEnumItems
@@ -272,224 +247,135 @@ class OperateMathNode(base.MaxwellSimNode):
 		kind=ct.FlowKind.Value,
 		props={'operation'},
 		input_sockets={'Expr L', 'Expr R'},
+		input_socket_kinds={
+			'Expr L': ct.FlowKind.Value,
+			'Expr R': ct.FlowKind.Value,
+		},
 	)
-	def compute_expr(self, props: dict, input_sockets: dict):
+	def compute_value(self, props: dict, input_sockets: dict):
+		operation = props['operation']
 		expr_l = input_sockets['Expr L']
 		expr_r = input_sockets['Expr R']
 
-		return {
+		has_expr_l_value = not ct.FlowSignal.check(expr_l)
-			'ADD': lambda: expr_l + expr_r,
+		has_expr_r_value = not ct.FlowSignal.check(expr_r)
-			'SUB': lambda: expr_l - expr_r,
+
-			'MUL': lambda: expr_l * expr_r,
+		if has_expr_l_value and has_expr_r_value and operation is not None:
-			'DIV': lambda: expr_l / expr_r,
+			return SP_FUNCS[operation]([expr_l, expr_r])
-			'POW': lambda: expr_l**expr_r,
+
-			'ATAN2': lambda: sp.atan2(expr_r, expr_l),
+		return ct.Flowsignal.FlowPending
-		}[props['operation']]()
 
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.LazyValueFunc,
 		props={'operation'},
-		input_sockets={'Data L', 'Data R'},
+		input_sockets={'Expr L', 'Expr R'},
 		input_socket_kinds={
-			'Data L': ct.FlowKind.LazyValueFunc,
+			'Expr L': ct.FlowKind.LazyValueFunc,
-			'Data R': ct.FlowKind.LazyValueFunc,
+			'Expr R': ct.FlowKind.LazyValueFunc,
-		},
-		input_sockets_optional={
-			'Data L': True,
-			'Data R': True,
 		},
 	)
-	def compute_data(self, props: dict, input_sockets: dict):
+	def compose_func(self, props: dict, input_sockets: dict):
-		data_l = input_sockets['Data L']
+		operation = props['operation']
-		data_r = input_sockets['Data R']
+		if operation is None:
-		has_data_l = not ct.FlowSignal.check(data_l)
+			return ct.FlowSignal.FlowPending
 
-		mapping_func = {
+		expr_l = input_sockets['Expr L']
-			# Number | *
+		expr_r = input_sockets['Expr R']
-			'ADD': lambda datas: datas[0] + datas[1],
-			'SUB': lambda datas: datas[0] - datas[1],
-			'MUL': lambda datas: datas[0] * datas[1],
-			'DIV': lambda datas: datas[0] / datas[1],
-			'POW': lambda datas: datas[0] ** datas[1],
-			'ATAN2': lambda datas: jnp.atan2(datas[1], datas[0]),
-			# Vector | Vector
-			'VEC_VEC_DOT': lambda datas: jnp.matmul(datas[0], datas[1]),
-			'CROSS': lambda datas: jnp.cross(datas[0], datas[1]),
-			# Matrix | Vector
-			'MAT_VEC_DOT': lambda datas: jnp.matmul(datas[0], datas[1]),
-			'LIN_SOLVE': lambda datas: jnp.linalg.solve(datas[0], datas[1]),
-			'LSQ_SOLVE': lambda datas: jnp.linalg.lstsq(datas[0], datas[1]),
-			# Matrix | Matrix
-			'MAT_MAT_DOT': lambda datas: jnp.matmul(datas[0], datas[1]),
-		}[props['operation']]
 
-		# Compose by Socket Set
+		has_expr_l = not ct.FlowSignal.check(expr_l)
-		## Data | Data
+		has_expr_r = not ct.FlowSignal.check(expr_r)
-		if has_data_l:
+
-			return (data_l | data_r).compose_within(
+		if has_expr_l and has_expr_r:
-				mapping_func,
+			return (expr_l | expr_r).compose_within(
-				supports_jax=True,
+				JAX_FUNCS[operation],
-			)
-
-		## Expr | Data
-		expr_l_lazy_value_func = ct.LazyValueFuncFlow(
-			func=lambda expr_l_value: expr_l_value,
-			func_args=[typ.Any],
-			supports_jax=True,
-		)
-		return (expr_l_lazy_value_func | data_r).compose_within(
-			mapping_func,
 				supports_jax=True,
 			)
+		return ct.FlowSignal.FlowPending
 
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.Array,
-		output_sockets={'Data'},
+		output_sockets={'Expr'},
 		output_socket_kinds={
-			'Data': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Params},
+			'Expr': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Params},
 		},
+		unit_systems={'BlenderUnits': ct.UNITS_BLENDER},
 	)
-	def compute_array(self, output_sockets: dict) -> ct.ArrayFlow:
+	def compute_array(self, output_sockets, unit_systems) -> ct.ArrayFlow:
-		lazy_value_func = output_sockets['Data'][ct.FlowKind.LazyValueFunc]
+		lazy_value_func = output_sockets['Expr'][ct.FlowKind.LazyValueFunc]
-		params = output_sockets['Data'][ct.FlowKind.Params]
+		params = output_sockets['Expr'][ct.FlowKind.Params]
 
 		has_lazy_value_func = not ct.FlowSignal.check(lazy_value_func)
 		has_params = not ct.FlowSignal.check(params)
 
 		if has_lazy_value_func and has_params:
+			unit_system = unit_systems['BlenderUnits']
 			return ct.ArrayFlow(
 				values=lazy_value_func.func_jax(
-					*params.func_args, **params.func_kwargs
+					*params.scaled_func_args(unit_system),
+					**params.scaled_func_kwargs(unit_system),
 				),
 				unit=None,
 			)
 
 		return ct.FlowSignal.FlowPending
 
-	####################
-	# - Auxiliary: Params
-	####################
-	@events.computes_output_socket(
-		'Data',
-		kind=ct.FlowKind.Params,
-		props={'operation'},
-		input_sockets={'Expr L', 'Data L', 'Data R'},
-		input_socket_kinds={
-			'Expr L': ct.FlowKind.Value,
-			'Data L': {ct.FlowKind.Info, ct.FlowKind.Params},
-			'Data R': {ct.FlowKind.Info, ct.FlowKind.Params},
-		},
-		input_sockets_optional={
-			'Expr L': True,
-			'Data L': True,
-			'Data R': True,
-		},
-	)
-	def compute_data_params(
-		self, props, input_sockets
-	) -> ct.ParamsFlow | ct.FlowSignal:
-		expr_l = input_sockets['Expr L']
-		data_l_info = input_sockets['Data L'][ct.FlowKind.Info]
-		data_l_params = input_sockets['Data L'][ct.FlowKind.Params]
-		data_r_info = input_sockets['Data R'][ct.FlowKind.Info]
-		data_r_params = input_sockets['Data R'][ct.FlowKind.Params]
-
-		has_expr_l = not ct.FlowSignal.check(expr_l)
-		has_data_l_info = not ct.FlowSignal.check(data_l_info)
-		has_data_l_params = not ct.FlowSignal.check(data_l_params)
-		has_data_r_info = not ct.FlowSignal.check(data_r_info)
-		has_data_r_params = not ct.FlowSignal.check(data_r_params)
-
-		# Compose by Socket Set
-		## Data | Data
-		if (
-			has_data_l_info
-			and has_data_l_params
-			and has_data_r_info
-			and has_data_r_params
-		):
-			return data_l_params | data_r_params
-
-		## Expr | Data
-		if has_expr_l and has_data_r_info and has_data_r_params:
-			operation = props['operation']
-			data_unit = data_r_info.output_unit
-
-			# By Operation
-			## Add/Sub: Scale to Output Unit
-			if operation in ['ADD', 'SUB', 'MUL', 'DIV']:
-				if not spux.uses_units(expr_l):
-					value = spux.sympy_to_python(expr_l)
-				else:
-					value = spux.sympy_to_python(spux.scale_to_unit(expr_l, data_unit))
-
-				return data_r_params.compose_within(
-					enclosing_func_args=[value],
-				)
-
-			## Pow: Doesn't Exist (?)
-			## -> See https://math.stackexchange.com/questions/4326081/units-of-the-exponential-function
-			if operation == 'POW':
-				return ct.FlowSignal.FlowPending
-
-			## atan2(): Only Length
-			## -> Implicitly presume that Data L/R use length units.
-			if operation == 'ATAN2':
-				if not spux.uses_units(expr_l):
-					value = spux.sympy_to_python(expr_l)
-				else:
-					value = spux.sympy_to_python(spux.scale_to_unit(expr_l, data_unit))
-
-				return data_r_params.compose_within(
-					enclosing_func_args=[value],
-				)
-
-			return data_r_params.compose_within(
-				enclosing_func_args=[
-					spux.sympy_to_python(spux.scale_to_unit(expr_l, data_unit))
-				]
-			)
-
-		return ct.FlowSignal.FlowPending
-
 	####################
 	# - Auxiliary: Info
 	####################
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.Info,
-		input_sockets={'Expr L', 'Data L', 'Data R'},
+		props={'operation'},
+		input_sockets={'Expr L', 'Expr R'},
 		input_socket_kinds={
-			'Expr L': ct.FlowKind.Value,
+			'Expr L': ct.FlowKind.Info,
-			'Data L': ct.FlowKind.Info,
+			'Expr R': ct.FlowKind.Info,
-			'Data R': ct.FlowKind.Info,
-		},
-		input_sockets_optional={
-			'Expr L': True,
-			'Data L': True,
-			'Data R': True,
 		},
 	)
-	def compute_data_info(self, input_sockets: dict) -> ct.InfoFlow:
+	def compute_info(self, props, input_sockets) -> ct.InfoFlow:
-		expr_l = input_sockets['Expr L']
+		operation = props['operation']
-		data_l_info = input_sockets['Data L']
+		info_l = input_sockets['Expr L']
-		data_r_info = input_sockets['Data R']
+		info_r = input_sockets['Expr R']
 
-		has_expr_l = not ct.FlowSignal.check(expr_l)
+		has_info_l = not ct.FlowSignal.check(info_l)
-		has_data_l_info = not ct.FlowSignal.check(data_l_info)
+		has_info_r = not ct.FlowSignal.check(info_r)
-		has_data_r_info = not ct.FlowSignal.check(data_r_info)
 
-		# Info by Socket Set
+		# Return Info of RHS
-		## Data | Data
+		## -> Fundamentall, this is why 'category' only has the given options.
-		if has_data_l_info and has_data_r_info:
+		## -> Via 'category', we enforce that the operated-on structure is always RHS.
-			return data_r_info
+		## -> That makes it super duper easy to track info changes.
+		if has_info_l and has_info_r and operation is not None:
+			return info_r
 
-		## Expr | Data
+		return ct.FlowSignal.FlowPending
-		if has_expr_l and has_data_r_info:
-			return data_r_info
 
+	####################
+	# - Auxiliary: Params
+	####################
+	@events.computes_output_socket(
+		'Expr',
+		kind=ct.FlowKind.Params,
+		props={'operation'},
+		input_sockets={'Expr L', 'Expr R'},
+		input_socket_kinds={
+			'Expr L': ct.FlowKind.Params,
+			'Expr R': ct.FlowKind.Params,
+		},
+	)
+	def compute_params(
+		self, props, input_sockets
+	) -> ct.ParamsFlow | ct.FlowSignal:
+		operation = props['operation']
+		params_l = input_sockets['Expr L']
+		params_r = input_sockets['Expr R']
+
+		has_params_l = not ct.FlowSignal.check(params_l)
+		has_params_r = not ct.FlowSignal.check(params_r)
+
+		if has_params_l and has_params_r and operation is not None:
+			return params_l | params_r
 		return ct.FlowSignal.FlowPending
 
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/viz.py

@@ -147,7 +147,7 @@ class VizTarget(enum.StrEnum):
 	@staticmethod
 	def valid_targets_for(viz_mode: VizMode) -> list[typ.Self] | None:
 		return {
-			'NONE': [],
+			None: [],
 			VizMode.Hist1D: [VizTarget.Plot2D],
 			VizMode.BoxPlot1D: [VizTarget.Plot2D],
 			VizMode.Curve2D: [VizTarget.Plot2D],
@@ -192,7 +192,7 @@ class VizNode(base.MaxwellSimNode):
 	# - Sockets
 	####################
 	input_sockets: typ.ClassVar = {
-		'Data': sockets.DataSocketDef(format='jax'),
+		'Expr': sockets.ExprSocketDef(),
 	}
 	output_sockets: typ.ClassVar = {
 		'Preview': sockets.AnySocketDef(),
@@ -222,7 +222,7 @@ class VizNode(base.MaxwellSimNode):
 	#####################
 	@property
 	def data_info(self) -> ct.InfoFlow:
-		return self._compute_input('Data', kind=ct.FlowKind.Info)
+		return self._compute_input('Expr', kind=ct.FlowKind.Info)
 
 	def search_modes(self) -> list[ct.BLEnumElement]:
 		if not ct.FlowSignal.check(self.data_info):
@@ -243,7 +243,7 @@ class VizNode(base.MaxwellSimNode):
 	## - Target Searcher
 	#####################
 	def search_targets(self) -> list[ct.BLEnumElement]:
-		if self.viz_mode != 'NONE':
+		if self.viz_mode is not None:
 			return [
 				(
 					viz_target,
@@ -271,15 +271,15 @@ class VizNode(base.MaxwellSimNode):
 	# - Events
 	####################
 	@events.on_value_changed(
-		socket_name='Data',
+		socket_name='Expr',
-		input_sockets={'Data'},
+		input_sockets={'Expr'},
 		run_on_init=True,
-		input_socket_kinds={'Data': ct.FlowKind.Info},
+		input_socket_kinds={'Expr': ct.FlowKind.Info},
-		input_sockets_optional={'Data': True},
+		input_sockets_optional={'Expr': True},
 	)
 	def on_any_changed(self, input_sockets: dict):
 		if not ct.FlowSignal.check_single(
-			input_sockets['Data'], ct.FlowSignal.FlowPending
+			input_sockets['Expr'], ct.FlowSignal.FlowPending
 		):
 			self.viz_mode = bl_cache.Signal.ResetEnumItems
 			self.viz_target = bl_cache.Signal.ResetEnumItems
@@ -297,8 +297,8 @@ class VizNode(base.MaxwellSimNode):
 	@events.on_show_plot(
 		managed_objs={'plot'},
 		props={'viz_mode', 'viz_target', 'colormap'},
-		input_sockets={'Data'},
+		input_sockets={'Expr'},
-		input_socket_kinds={'Data': {ct.FlowKind.Array, ct.FlowKind.Info}},
+		input_socket_kinds={'Expr': {ct.FlowKind.Array, ct.FlowKind.Info}},
 		stop_propagation=True,
 	)
 	def on_show_plot(
@@ -308,14 +308,14 @@ class VizNode(base.MaxwellSimNode):
 		props: dict,
 	):
 		# Retrieve Inputs
-		array_flow = input_sockets['Data'][ct.FlowKind.Array]
+		array_flow = input_sockets['Expr'][ct.FlowKind.Array]
-		info = input_sockets['Data'][ct.FlowKind.Info]
+		info = input_sockets['Expr'][ct.FlowKind.Info]
 
 		# Check Flow
 		if (
 			any(ct.FlowSignal.check(inp) for inp in [array_flow, info])
-			or props['viz_mode'] == 'NONE'
+			or props['viz_mode'] is None
-			or props['viz_target'] == 'NONE'
+			or props['viz_target'] is None
 		):
 			return
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/__init__.py

@@ -1,7 +1,7 @@
 from . import (
     constants,
     file_importers,
-    unit_system,
+    #unit_system,
     wave_constant,
     web_importers,
 )
@@ -10,14 +10,14 @@ from . import (
 
 BL_REGISTER = [
 	*wave_constant.BL_REGISTER,
-	*unit_system.BL_REGISTER,
+	#*unit_system.BL_REGISTER,
 	*constants.BL_REGISTER,
 	*web_importers.BL_REGISTER,
 	*file_importers.BL_REGISTER,
 ]
 BL_NODES = {
 	**wave_constant.BL_NODES,
-	**unit_system.BL_NODES,
+	#**unit_system.BL_NODES,
 	**constants.BL_NODES,
 	**web_importers.BL_NODES,
 	**file_importers.BL_NODES,

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/constants/number_constant.py

@@ -1,32 +1,65 @@
+import enum
 import typing as typ
 
+import bpy
+
+from blender_maxwell.utils import bl_cache
+from blender_maxwell.utils import extra_sympy_units as spux
+
 from .... import contracts as ct
 from .... import sockets
 from ... import base, events
 
 
 class NumberConstantNode(base.MaxwellSimNode):
+	"""A unitless number of configurable math type ex. integer, real, etc. .
+
+	Attributes:
+		mathtype: The math type to specify the number as.
+	"""
+
 	node_type = ct.NodeType.NumberConstant
 	bl_label = 'Numerical Constant'
 
-	input_socket_sets: typ.ClassVar = {
+	input_sockets: typ.ClassVar = {
-		'Integer': {
+		'Value': sockets.ExprSocketDef(),
-			'Value': sockets.IntegerNumberSocketDef(),
+	}
-		},
+	output_sockets: typ.ClassVar = {
-		'Rational': {
+		'Value': sockets.ExprSocketDef(),
-			'Value': sockets.RationalNumberSocketDef(),
-		},
-		'Real': {
-			'Value': sockets.RealNumberSocketDef(),
-		},
-		'Complex': {
-			'Value': sockets.ComplexNumberSocketDef(),
-		},
 	}
-	output_socket_sets = input_socket_sets
 
 	####################
-	# - Callbacks
+	# - Properties
+	####################
+	mathtype: spux.MathType = bl_cache.BLField(
+		spux.MathType.Integer,
+		prop_ui=True,
+	)
+
+	size: spux.NumberSize1D = bl_cache.BLField(
+		spux.NumberSize1D.Scalar,
+		prop_ui=True,
+	)
+
+	####################
+	# - UI
+	####################
+	def draw_value(self, col: bpy.types.UILayout) -> None:
+		row = col.row(align=True)
+		row.prop(self, self.blfields['mathtype'], text='')
+		row.prop(self, self.blfields['size'], text='')
+
+	####################
+	# - Events
+	####################
+	@events.on_value_changed(prop_name={'mathtype', 'size'}, props={'mathtype', 'size'})
+	def on_mathtype_size_changed(self, props) -> None:
+		"""Change the input/output expression sockets to match the mathtype declared in the node."""
+		self.inputs['Value'].mathtype = props['mathtype']
+		self.inputs['Value'].shape = props['mathtype'].shape
+
+	####################
+	# - FlowKind
 	####################
 	@events.computes_output_socket('Value', input_sockets={'Value'})
 	def compute_value(self, input_sockets) -> typ.Any:

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/constants/physical_constant.py

@@ -1,54 +1,91 @@
+import enum
 import typing as typ
 
 import sympy as sp
 
+from blender_maxwell.utils import bl_cache
+from blender_maxwell.utils import extra_sympy_units as spux
+
 from .... import contracts, sockets
 from ... import base, events
 
 
 class PhysicalConstantNode(base.MaxwellSimTreeNode):
+	"""A number of configurable unit dimension, ex. time, length, etc. .
+
+	Attributes:
+		physical_type: The physical type to specify.
+		size: The size of the physical type, if it can be a vector.
+	"""
+
 	node_type = contracts.NodeType.PhysicalConstant
 	bl_label = 'Physical Constant'
 
-	input_socket_sets: typ.ClassVar = {
+	input_sockets: typ.ClassVar = {
-		'time': {
+		'Value': sockets.ExprSocketDef(),
-			'value': sockets.PhysicalTimeSocketDef(
-				label='Time',
-			),
-		},
-		'angle': {
-			'value': sockets.PhysicalAngleSocketDef(
-				label='Angle',
-			),
-		},
-		'length': {
-			'value': sockets.PhysicalLengthSocketDef(
-				label='Length',
-			),
-		},
-		'area': {
-			'value': sockets.PhysicalAreaSocketDef(
-				label='Area',
-			),
-		},
-		'volume': {
-			'value': sockets.PhysicalVolumeSocketDef(
-				label='Volume',
-			),
-		},
-		'point_3d': {
-			'value': sockets.PhysicalPoint3DSocketDef(
-				label='3D Point',
-			),
-		},
-		'size_3d': {
-			'value': sockets.PhysicalSize3DSocketDef(
-				label='3D Size',
-			),
-		},
-		## I got bored so maybe the rest later
 	}
-	output_socket_sets: typ.ClassVar = input_socket_sets
+	output_sockets: typ.ClassVar = {
+		'Value': sockets.ExprSocketDef(),
+	}
+
+	####################
+	# - Properties
+	####################
+	physical_type: spux.PhysicalType = bl_cache.BLField(
+		spux.PhysicalType.Time,
+		prop_ui=True,
+	)
+
+	mathtype: enum.Enum = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_mathtypes(),
+		prop_ui=True,
+	)
+
+	size: enum.Enum = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_sizes(),
+		prop_ui=True,
+	)
+
+	####################
+	# - Searchers
+	####################
+	def search_mathtypes(self):
+		return [
+			mathtype.bl_enum_element(i)
+			for i, mathtype in enumerate(self.physical_type.valid_mathtypes)
+		]
+
+	def search_sizes(self):
+		return [
+			spux.NumberSize1D.from_shape(shape).bl_enum_element(i)
+			for i, shape in enumerate(self.physical_type.valid_shapes)
+			if spux.NumberSize1D.supports_shape(shape)
+		]
+
+	####################
+	# - Events
+	####################
+	@events.on_value_changed(
+		prop_name={'physical_type', 'mathtype', 'size'},
+		props={'physical_type', 'mathtype', 'size'},
+	)
+	def on_mathtype_or_size_changed(self, props) -> None:
+		"""Change the input/output expression sockets to match the mathtype and size declared in the node."""
+		shape = spux.NumberSize1D(props['size']).shape
+
+		# Set Input Socket Physical Type
+		if self.inputs['Value'].physical_type != props['physical_type']:
+			self.inputs['Value'].physical_type = props['physical_type']
+			self.search_mathtypes = bl_cache.Signal.ResetEnumItems
+			self.search_sizes = bl_cache.Signal.ResetEnumItems
+
+		# Set Input Socket Math Type
+		if self.inputs['Value'].mathtype != props['mathtype']:
+			self.inputs['Value'].mathtype = props['mathtype']
+
+		# Set Input Socket Shape
+		if self.inputs['Value'].shape != shape:
+			self.inputs['Value'].shape = shape
 
 	####################
 	# - Callbacks

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/wave_constant.py

@@ -33,8 +33,7 @@ class WaveConstantNode(base.MaxwellSimNode):
 	input_socket_sets: typ.ClassVar = {
 		'Wavelength': {
 			'WL': sockets.ExprSocketDef(
-				active_kind=ct.FlowKind.Value,
+				physical_type=spux.PhysicalType.Length,
-				unit_dimension=spux.unit_dims.length,
 				# Defaults
 				default_unit=spu.nm,
 				default_value=500,
@@ -46,7 +45,7 @@ class WaveConstantNode(base.MaxwellSimNode):
 		'Frequency': {
 			'Freq': sockets.ExprSocketDef(
 				active_kind=ct.FlowKind.Value,
-				unit_dimension=spux.unit_dims.frequency,
+				physical_type=spux.PhysicalType.Freq,
 				# Defaults
 				default_unit=spux.THz,
 				default_value=1,
@@ -59,11 +58,11 @@ class WaveConstantNode(base.MaxwellSimNode):
 	output_sockets: typ.ClassVar = {
 		'WL': sockets.ExprSocketDef(
 			active_kind=ct.FlowKind.Value,
-			unit_dimension=spux.unit_dims.length,
+			unit_dimension=spux.Dims.length,
 		),
 		'Freq': sockets.ExprSocketDef(
 			active_kind=ct.FlowKind.Value,
-			unit_dimension=spux.unit_dims.frequency,
+			unit_dimension=spux.Dims.frequency,
 		),
 	}
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/monitors/eh_field_monitor.py

@@ -1,6 +1,7 @@
 import typing as typ
 
 import sympy as sp
+import sympy.physics.units as spu
 import tidy3d as td
 
 from blender_maxwell.assets.geonodes import GeoNodes, import_geonodes
@@ -25,22 +26,44 @@ class EHFieldMonitorNode(base.MaxwellSimNode):
 	# - Sockets
 	####################
 	input_sockets: typ.ClassVar = {
-		'Center': sockets.PhysicalPoint3DSocketDef(),
+		'Center': sockets.ExprSocketDef(
-		'Size': sockets.PhysicalSize3DSocketDef(),
+			shape=(3,),
-		'Samples/Space': sockets.Integer3DVectorSocketDef(
+			physical_type=spux.PhysicalType.Length,
-			default_value=sp.Matrix([10, 10, 10])
 		),
+		'Size': sockets.ExprSocketDef(
+			shape=(3,),
+			physical_type=spux.PhysicalType.Length,
+		),
+		'Spatial Subdivs': sockets.ExprSocketDef(
+			shape=(3,),
+			mathtype=spux.MathType.Integer,
+			default_value=sp.Matrix([10, 10, 10]),
+		),
+		## TODO: Pass a grid instead of size and resolution
+		## TODO: 1D (line), 2D (plane), 3D modes
 	}
 	input_socket_sets: typ.ClassVar = {
 		'Freq Domain': {
-			'Freqs': sockets.PhysicalFreqSocketDef(
+			'Freqs': sockets.ExprSocketDef(
-				is_array=True,
+				active_kind=ct.FlowKind.LazyArrayRange,
+				physical_type=spux.PhysicalType.Freq,
+				default_unit=spux.THz,
+				default_min=374.7406,  ## 800nm
+				default_max=1498.962,  ## 200nm
+				default_steps=100,
 			),
 		},
 		'Time Domain': {
-			'Rec Start': sockets.PhysicalTimeSocketDef(),
+			'Time Range': sockets.ExprSocketDef(
-			'Rec Stop': sockets.PhysicalTimeSocketDef(default_value=200 * spux.fs),
+				active_kind=ct.FlowKind.LazyArrayRange,
-			'Samples/Time': sockets.IntegerNumberSocketDef(
+				physical_type=spux.PhysicalType.Time,
+				default_unit=spu.picosecond,
+				default_min=0,
+				default_max=10,
+				default_steps=2,
+			),
+			'Temporal Subdivs': sockets.ExprSocketDef(
+				mathtype=spux.MathType.Integer,
 				default_value=100,
 			),
 		},
@@ -56,7 +79,7 @@ class EHFieldMonitorNode(base.MaxwellSimNode):
 	}
 
 	####################
-	# - Output Sockets
+	# - Output
 	####################
 	@events.computes_output_socket(
 		'Freq Monitor',
@@ -64,7 +87,7 @@ class EHFieldMonitorNode(base.MaxwellSimNode):
 		input_sockets={
 			'Center',
 			'Size',
-			'Samples/Space',
+			'Spatial Subdivs',
 			'Freqs',
 		},
 		input_socket_kinds={
@@ -93,12 +116,12 @@ class EHFieldMonitorNode(base.MaxwellSimNode):
 			center=input_sockets['Center'],
 			size=input_sockets['Size'],
 			name=props['sim_node_name'],
-			interval_space=tuple(input_sockets['Samples/Space']),
+			interval_space=tuple(input_sockets['Spatial Subdivs']),
 			freqs=input_sockets['Freqs'].realize().values,
 		)
 
 	####################
-	# - Preview - Changes to Input Sockets
+	# - Preview
 	####################
 	@events.on_value_changed(
 		socket_name={'Center', 'Size'},

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/monitors/field_power_flux_monitor.py

@@ -1,6 +1,7 @@
 import typing as typ
 
 import sympy as sp
+import sympy.physics.units as spu
 import tidy3d as td
 
 from blender_maxwell.assets.geonodes import GeoNodes, import_geonodes
@@ -23,23 +24,43 @@ class PowerFluxMonitorNode(base.MaxwellSimNode):
 	# - Sockets
 	####################
 	input_sockets: typ.ClassVar = {
-		'Center': sockets.PhysicalPoint3DSocketDef(),
+		'Center': sockets.ExprSocketDef(
-		'Size': sockets.PhysicalSize3DSocketDef(),
+			shape=(3,),
-		'Samples/Space': sockets.Integer3DVectorSocketDef(
+			physical_type=spux.PhysicalType.Length,
-			default_value=sp.Matrix([10, 10, 10])
+		),
+		'Size': sockets.ExprSocketDef(
+			shape=(3,),
+			physical_type=spux.PhysicalType.Length,
+		),
+		'Samples/Space': sockets.ExprSocketDef(
+			shape=(3,),
+			mathtype=spux.MathType.Integer,
+			default_value=sp.Matrix([10, 10, 10]),
 		),
 		'Direction': sockets.BoolSocketDef(),
 	}
 	input_socket_sets: typ.ClassVar = {
 		'Freq Domain': {
-			'Freqs': sockets.PhysicalFreqSocketDef(
+			'Freqs': sockets.ExprSocketDef(
-				is_array=True,
+				active_kind=ct.FlowKind.LazyArrayRange,
+				physical_type=spux.PhysicalType.Freq,
+				default_unit=spux.THz,
+				default_min=374.7406,  ## 800nm
+				default_max=1498.962,  ## 200nm
+				default_steps=100,
 			),
 		},
 		'Time Domain': {
-			'Rec Start': sockets.PhysicalTimeSocketDef(),
+			'Time Range': sockets.ExprSocketDef(
-			'Rec Stop': sockets.PhysicalTimeSocketDef(default_value=200 * spux.fs),
+				active_kind=ct.FlowKind.LazyArrayRange,
-			'Samples/Time': sockets.IntegerNumberSocketDef(
+				physical_type=spux.PhysicalType.Time,
+				default_unit=spu.picosecond,
+				default_min=0,
+				default_max=10,
+				default_steps=2,
+			),
+			'Samples/Time': sockets.ExprSocketDef(
+				mathtype=spux.MathType.Integer,
 				default_value=100,
 			),
 		},

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/structures/geonodes_structure.py

@@ -2,7 +2,7 @@ import typing as typ
 
 import tidy3d as td
 
-from blender_maxwell.utils import analyze_geonodes, logger
+from blender_maxwell.utils import bl_cache, logger
 
 from ... import bl_socket_map, managed_objs, sockets
 from ... import contracts as ct
@@ -20,9 +20,9 @@ class GeoNodesStructureNode(base.MaxwellSimNode):
 	# - Sockets
 	####################
 	input_sockets: typ.ClassVar = {
+		'GeoNodes': sockets.BlenderGeoNodesSocketDef(),
 		'Medium': sockets.MaxwellMediumSocketDef(),
 		'Center': sockets.PhysicalPoint3DSocketDef(),
-		'GeoNodes': sockets.BlenderGeoNodesSocketDef(),
 	}
 	output_sockets: typ.ClassVar = {
 		'Structure': sockets.MaxwellStructureSocketDef(),
@@ -34,7 +34,7 @@ class GeoNodesStructureNode(base.MaxwellSimNode):
 	}
 
 	####################
-	# - Event Methods
+	# - Output
 	####################
 	@events.computes_output_socket(
 		'Structure',
@@ -46,9 +46,10 @@ class GeoNodesStructureNode(base.MaxwellSimNode):
 		input_sockets: dict,
 		managed_objs: dict,
 	) -> td.Structure:
+		"""Computes a triangle-mesh based Tidy3D structure, by manually copying mesh data from Blender to a `td.TriangleMesh`."""
 		# Simulate Input Value Change
 		## This ensures that the mesh has been re-computed.
-		self.on_input_changed()
+		self.on_input_socket_changed()
 
 		## TODO: mesh_as_arrays might not take the Center into account.
 		## - Alternatively, Tidy3D might have a way to transform?
@@ -62,96 +63,109 @@ class GeoNodesStructureNode(base.MaxwellSimNode):
 		)
 
 	####################
-	# - Event Methods
+	# - Events: Preview Active Changed
 	####################
 	@events.on_value_changed(
-		socket_name={'GeoNodes', 'Center'},
 		prop_name='preview_active',
-		any_loose_input_socket=True,
-		run_on_init=True,
-		# Pass Data
 		props={'preview_active'},
+		input_sockets={'Center'},
+		managed_objs={'mesh'},
+	)
+	def on_preview_changed(self, props, input_sockets) -> None:
+		"""Enables/disables previewing of the GeoNodes-driven mesh, regardless of whether a particular GeoNodes tree is chosen."""
+		mesh = managed_objs['mesh']
+
+		# No Mesh: Create Empty Object
+		## Ensures that when there is mesh data, it'll be correctly previewed.
+		## Bit of a workaround - the idea is usually to make the MObj as needed.
+		if not mesh.exists:
+			center = input_sockets['Center']
+			_ = mesh.bl_object(location=center)
+
+		# Push Preview State to Managed Mesh
+		if props['preview_active']:
+			mesh.show_preview()
+		else:
+			mesh.hide_preview()
+
+	####################
+	# - Events: GN Input Changed
+	####################
+	@events.on_value_changed(
+		socket_name={'Center'},
+		any_loose_input_socket=True,
+		# Pass Data
 		managed_objs={'mesh', 'modifier'},
 		input_sockets={'Center', 'GeoNodes'},
 		all_loose_input_sockets=True,
 		unit_systems={'BlenderUnits': ct.UNITS_BLENDER},
 		scale_input_sockets={'Center': 'BlenderUnits'},
 	)
+	def on_input_socket_changed(
+		self, input_sockets, loose_input_sockets, unit_systems
+	) -> None:
+		"""Pushes any change in GeoNodes-bound input sockets to the GeoNodes modifier.
+
+		Also pushes the `Center:Value` socket to govern the object's center in 3D space.
+		"""
+		geonodes = input_sockets['GeoNodes']
+		has_geonodes = not ct.FlowSignal.check(geonodes)
+
+		if has_geonodes:
+			mesh = managed_objs['mesh']
+			modifier = managed_objs['modifier']
+			center = input_sockets['Center']
+			unit_system = unit_systems['BlenderUnits']
+
+			# Push Loose Input Values to GeoNodes Modifier
+			modifier.bl_modifier(
+				mesh.bl_object(location=center),
+				'NODES',
+				{
+					'node_group': geonodes,
+					'inputs': loose_input_sockets,
+					'unit_system': unit_system,
+				},
+			)
+
+	####################
+	# - Events: GN Tree Changed
+	####################
+	@events.on_value_changed(
+		socket_name={'GeoNodes'},
+		# Pass Data
+		managed_objs={'mesh', 'modifier'},
+		input_sockets={'GeoNodes', 'Center'},
+	)
 	def on_input_changed(
 		self,
-		props: dict,
 		managed_objs: dict,
 		input_sockets: dict,
-		loose_input_sockets: dict,
-		unit_systems: dict,
 	) -> None:
-		# No GeoNodes: Remove Modifier (if any)
+		"""Declares new loose input sockets in response to a new GeoNodes tree (if any)."""
-		if (geonodes := input_sockets['GeoNodes']) is None:
+		geonodes = input_sockets['GeoNodes']
-			if (
+		has_geonodes = not ct.FlowSignal.check(geonodes)
-				managed_objs['modifier'].name
-				in managed_objs['mesh'].bl_object().modifiers.keys().copy()
-			):
-				managed_objs['modifier'].free_from_bl_object(
-					managed_objs['mesh'].bl_object()
-				)
 
-				# Reset Loose Input Sockets
+		if has_geonodes:
-				self.loose_input_sockets = {}
+			mesh = managed_objs['mesh']
-			return
+			modifier = managed_objs['modifier']
-
-		# No Loose Input Sockets: Create from GeoNodes Interface
-		## TODO: Other reasons to trigger re-filling loose_input_sockets.
-		if not loose_input_sockets:
-			# Retrieve the GeoNodes Interface
-			geonodes_interface = analyze_geonodes.interface(
-				input_sockets['GeoNodes'], direc='INPUT'
-			)
 
 			# Fill the Loose Input Sockets
+			## -> The SocketDefs contain the default values from the interface.
 			log.info(
 				'Initializing GeoNodes Structure Node "%s" from GeoNodes Group "%s"',
 				self.bl_label,
 				str(geonodes),
 			)
-			self.loose_input_sockets = {
+			self.loose_input_sockets = bl_socket_map.sockets_from_geonodes(geonodes)
-				socket_name: bl_socket_map.socket_def_from_bl_socket(iface_socket)()
-				for socket_name, iface_socket in geonodes_interface.items()
-			}
 
-			# Set Loose Input Sockets to Interface (Default) Values
+			## -> The loose socket creation triggers 'on_input_socket_changed'
-			## Changing socket.value invokes recursion of this function.
+
-			## The else: below ensures that only one push occurs.
+		elif self.loose_input_sockets:
-			## (well, one push per .value set, which simplifies to one push)
+			self.loose_input_sockets = {}
-			log.info(
+
-				'Setting Loose Input Sockets of "%s" to GeoNodes Defaults',
+			if modifier.name in mesh.bl_object().modifiers.keys().copy():
-				self.bl_label,
+				modifier.free_from_bl_object(mesh.bl_object())
-			)
-			for socket_name in self.loose_input_sockets:
-				socket = self.inputs[socket_name]
-				socket.value = bl_socket_map.read_bl_socket_default_value(
-					geonodes_interface[socket_name],
-					unit_systems['BlenderUnits'],
-					allow_unit_not_in_unit_system=True,
-				)
-			log.info(
-				'Set Loose Input Sockets of "%s" to: %s',
-				self.bl_label,
-				str(self.loose_input_sockets),
-			)
-		else:
-			# Push Loose Input Values to GeoNodes Modifier
-			managed_objs['modifier'].bl_modifier(
-				managed_objs['mesh'].bl_object(location=input_sockets['Center']),
-				'NODES',
-				{
-					'node_group': input_sockets['GeoNodes'],
-					'unit_system': unit_systems['BlenderUnits'],
-					'inputs': loose_input_sockets,
-				},
-			)
-			# Push Preview State
-			if props['preview_active']:
-				managed_objs['mesh'].show_preview()
 
 
 ####################

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/__init__.py

@@ -1,11 +1,11 @@
 from blender_maxwell.utils import logger
 
 from .. import contracts as ct
-from . import basic, blender, maxwell, physical, tidy3d
+from . import basic, blender, expr, maxwell, physical, tidy3d
 from .scan_socket_defs import scan_for_socket_defs
 
 log = logger.get(__name__)
-sockets_modules = [basic, physical, blender, maxwell, tidy3d]
+sockets_modules = [basic, blender, expr, maxwell, physical, tidy3d]
 
 ####################
 # - Scan for SocketDefs
@@ -28,21 +28,24 @@ for socket_type in ct.SocketType:
 	):
 		log.warning('Missing SocketDef for %s', socket_type.value)
 
+
 ####################
 # - Exports
 ####################
 BL_REGISTER = [
 	*basic.BL_REGISTER,
-	*physical.BL_REGISTER,
 	*blender.BL_REGISTER,
+	*expr.BL_REGISTER,
 	*maxwell.BL_REGISTER,
+	*physical.BL_REGISTER,
 	*tidy3d.BL_REGISTER,
 ]
 
 __all__ = [
 	'basic',
-	'physical',
 	'blender',
+	'expr',
 	'maxwell',
+	'physical',
 	'tidy3d',
 ] + [socket_def_type.__name__ for socket_def_type in SOCKET_DEFS.values()]

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/base.py

@@ -5,10 +5,8 @@ from types import MappingProxyType
 
 import bpy
 import pydantic as pyd
-import sympy as sp
 
 from blender_maxwell.utils import bl_cache, logger, serialize
-from blender_maxwell.utils import extra_sympy_units as spux
 
 from .. import contracts as ct
 
@@ -126,7 +124,6 @@ class MaxwellSimSocket(bpy.types.NodeSocket):
 	socket_color: tuple
 
 	# Options
-	use_units: bool = False
 	use_prelock: bool = False
 	use_info_draw: bool = False
 
@@ -210,35 +207,6 @@ class MaxwellSimSocket(bpy.types.NodeSocket):
 			'active_kind', bpy.props.StringProperty, default=str(ct.FlowKind.Value)
 		)
 
-		# Configure Use of Units
-		if cls.use_units:
-			if not (socket_units := ct.SOCKET_UNITS.get(cls.socket_type)):
-				msg = f'{cls.socket_type}: Tried to define "use_units", but there is no unit for {cls.socket_type} defined in "contracts.SOCKET_UNITS"'
-				raise RuntimeError(msg)
-
-			cls.set_prop(
-				'active_unit',
-				bpy.props.EnumProperty,
-				name='Unit',
-				items=[
-					(unit_name, spux.sp_to_str(unit_value), sp.srepr(unit_value))
-					for unit_name, unit_value in socket_units['values'].items()
-				],
-				default=socket_units['default'],
-			)
-			cls.set_prop(
-				'prev_active_unit',
-				bpy.props.StringProperty,
-				default=socket_units['default'],
-			)
-
-	####################
-	# - Units
-	####################
-	@property
-	def prev_unit(self) -> sp.Expr:
-		return self.possible_units[self.prev_active_unit]
-
 	####################
 	# - Property Event: On Update
 	####################
@@ -250,36 +218,47 @@ class MaxwellSimSocket(bpy.types.NodeSocket):
 		"""
 		self.display_shape = (
 			'SQUARE' if self.active_kind == ct.FlowKind.LazyValueRange else 'CIRCLE'
-		) + ('_DOT' if self.use_units else '')
+		)  # + ('_DOT' if self.use_units else '')
 		## TODO: Valid Active Kinds should be a subset/subenum(?) of FlowKind
 
+	def on_socket_prop_changed(self, prop_name: str) -> None:
+		"""Called when a property has been updated.
+
+		Notes:
+			Can be overridden if a socket needs to respond to a property change.
+
+			**Always prefer using node events when possible**.
+			Think very carefully before using this, and use it with the greatest of care.
+
+		Attributes:
+			prop_name: The name of the property that was changed.
+		"""
+
 	def on_prop_changed(self, prop_name: str, _: bpy.types.Context) -> None:
 		"""Called when a property has been updated.
 
 		Contrary to `node.on_prop_changed()`, socket-specific callbacks are baked into this function:
 
 		- **Active Kind** (`self.active_kind`): Sets the socket shape to reflect the active `FlowKind`.
-		- **Unit** (`self.unit`): Corrects the internal `FlowKind` representation to match the new unit.
 
 		Attributes:
 			prop_name: The name of the property that was changed.
 		"""
-		# Property: Active Kind
+		if hasattr(self, prop_name):
-		if prop_name == 'active_kind':
-			self._on_active_kind_changed()
-		elif prop_name == 'unit':
-			self._on_unit_changed()
-
-		# Valid Properties
-		elif hasattr(self, prop_name):
 			# Invalidate UI BLField Caches
 			if prop_name in self.ui_blfields:
 				setattr(self, prop_name, bl_cache.Signal.InvalidateCache)
 
+			# Property Callbacks: Active Kind
+			if prop_name == 'active_kind':
+				self._on_active_kind_changed()
+
+			# Property Callbacks: Per-Socket
+			self.on_socket_prop_changed(prop_name)
+
 			# Trigger Event
 			self.trigger_event(ct.FlowEvent.DataChanged)
 
-		# Undefined Properties
 		else:
 			msg = f'Property {prop_name} not defined on socket {self.bl_label} ({self.socket_type})'
 			raise RuntimeError(msg)
@@ -760,7 +739,6 @@ class MaxwellSimSocket(bpy.types.NodeSocket):
 
 		- **Locked** (`self.locked`): The UI will be unusable.
 		- **Linked** (`self.is_linked`): Only the socket label will display.
-		- **Use Units** (`self.use_units`): The currently active unit will display as a dropdown menu.
 		- **Use Prelock** (`self.use_prelock`): The "prelock" UI drawn with `self.draw_prelock()`, which shows **regardless of `self.locked`**.
 		- **FlowKind**: The `FlowKind`-specific UI corresponding to the current `self.active_kind`.
 
@@ -786,16 +764,6 @@ class MaxwellSimSocket(bpy.types.NodeSocket):
 		## Link Check
 		if self.is_linked:
 			self.draw_input_label_row(row, text)
-		else:
-			# User Label Row (incl. Units)
-			if self.use_units:
-				split = row.split(factor=0.6, align=True)
-
-				_row = split.row(align=True)
-				self.draw_label_row(_row, text)
-
-				_col = split.column(align=True)
-				_col.prop(self, 'active_unit', text='')
 		else:
 			self.draw_label_row(row, text)
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/basic/__init__.py

@@ -1,20 +1,16 @@
 from . import any as any_socket
 from . import bool as bool_socket
-from . import expr, file_path, string, data
+from . import file_path, string
 
 AnySocketDef = any_socket.AnySocketDef
-DataSocketDef = data.DataSocketDef
 BoolSocketDef = bool_socket.BoolSocketDef
 StringSocketDef = string.StringSocketDef
 FilePathSocketDef = file_path.FilePathSocketDef
-ExprSocketDef = expr.ExprSocketDef
 
 
 BL_REGISTER = [
 	*any_socket.BL_REGISTER,
-	*data.BL_REGISTER,
 	*bool_socket.BL_REGISTER,
 	*string.BL_REGISTER,
 	*file_path.BL_REGISTER,
-	*expr.BL_REGISTER,
 ]

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/blender/geonodes.py

@@ -70,8 +70,8 @@ class BlenderGeoNodesBLSocket(base.MaxwellSimSocket):
 	# - Default Value
 	####################
 	@property
-	def value(self) -> bpy.types.NodeTree | None:
+	def value(self) -> bpy.types.NodeTree | ct.FlowSignal:
-		return self.raw_value
+		return self.raw_value if self.raw_value is not None else ct.FlowSignal.NoFlow
 
 	@value.setter
 	def value(self, value: bpy.types.NodeTree) -> None:

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/expr.py

@@ -7,16 +7,14 @@ import sympy as sp
 from blender_maxwell.utils import bl_cache, logger
 from blender_maxwell.utils import extra_sympy_units as spux
 
-from ... import contracts as ct
+from .. import contracts as ct
-from .. import base
+from . import base
 
 ## TODO: This is a big node, and there's a lot to get right.
-## - Dynamically adjust the value when the user changes the unit in the UI.
 ## - Dynamically adjust socket color in response to, especially, the unit dimension.
 ## - Iron out the meaning of display shapes.
 ## - Generally pay attention to validity checking; it's make or break.
-## - For array generation, it may pay to have both a symbolic expression (producing output according to `size` as usual) denoting how to actually make values, and how many. Enables ex. easy symbolic
+## - For array generation, it may pay to have both a symbolic expression (producing output according to `shape` as usual) denoting how to actually make values, and how many. Enables ex. easy symbolic plots.
-## - For array generation, it may pay to have both a symbolic expression (producing output according to `size` as usual)
 
 log = logger.get(__name__)
 
@@ -69,24 +67,15 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Properties
 	####################
-	size: typ.Literal[None, 2, 3] = bl_cache.BLField(None, prop_ui=True)
+	shape: tuple[int, ...] | None = bl_cache.BLField(None)
 	mathtype: spux.MathType = bl_cache.BLField(spux.MathType.Real, prop_ui=True)
+	physical_type: spux.PhysicalType | None = bl_cache.BLField(None)
 	symbols: frozenset[spux.Symbol] = bl_cache.BLField(frozenset())
 
-	## Units
-	unit_dim: spux.UnitDimension | None = bl_cache.BLField(None)
 	active_unit: enum.Enum = bl_cache.BLField(
 		None, enum_cb=lambda self, _: self.search_units(), prop_ui=True
 	)
 
-	## Info Display
-	show_info_columns: bool = bl_cache.BLField(False, prop_ui=True)
-	info_columns: InfoDisplayCol = bl_cache.BLField(
-		{InfoDisplayCol.MathType, InfoDisplayCol.Unit},
-		prop_ui=True,
-		enum_many=True,
-	)
-
 	# UI: Value
 	## Expression
 	raw_value_spstr: str = bl_cache.BLField('', prop_ui=True)
@@ -94,7 +83,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	raw_value_int: int = bl_cache.BLField(0, prop_ui=True)
 	raw_value_rat: Int2 = bl_cache.BLField((0, 1), prop_ui=True)
 	raw_value_float: float = bl_cache.BLField(0.0, float_prec=4, prop_ui=True)
-	raw_value_complex: Float2 = bl_cache.BLField((0, 1), float_prec=4, prop_ui=True)
+	raw_value_complex: Float2 = bl_cache.BLField((0.0, 0.0), float_prec=4, prop_ui=True)
 	## 2D
 	raw_value_int2: Int2 = bl_cache.BLField((0, 0), prop_ui=True)
 	raw_value_rat2: Int22 = bl_cache.BLField(((0, 1), (0, 1)), prop_ui=True)
@@ -105,7 +94,9 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	## 3D
 	raw_value_int3: Int3 = bl_cache.BLField((0, 0, 0), prop_ui=True)
 	raw_value_rat3: Int32 = bl_cache.BLField(((0, 1), (0, 1), (0, 1)), prop_ui=True)
-	raw_value_float3: Float3 = bl_cache.BLField((0.0, 0.0), float_prec=4, prop_ui=True)
+	raw_value_float3: Float3 = bl_cache.BLField(
+		(0.0, 0.0, 0.0), float_prec=4, prop_ui=True
+	)
 	raw_value_complex3: Float32 = bl_cache.BLField(
 		((0.0, 0.0), (0.0, 0.0), (0.0, 0.0)), float_prec=4, prop_ui=True
 	)
@@ -123,6 +114,14 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		((0.0, 0.0), (1.0, 1.0)), float_prec=4, prop_ui=True
 	)
 
+	# UI: Info
+	show_info_columns: bool = bl_cache.BLField(False, prop_ui=True)
+	info_columns: InfoDisplayCol = bl_cache.BLField(
+		{InfoDisplayCol.MathType, InfoDisplayCol.Unit},
+		prop_ui=True,
+		enum_many=True,
+	)
+
 	####################
 	# - Computed: Raw Expressions
 	####################
@@ -142,35 +141,63 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	# - Computed: Units
 	####################
 	def search_units(self, _: bpy.types.Context) -> list[ct.BLEnumElement]:
-		if self.unit_dim is not None:
+		if self.physical_type is not None:
 			return [
 				(sp.sstr(unit), spux.sp_to_str(unit), sp.sstr(unit), '', i)
-				for i, unit in enumerate(spux.unit_dim_units(self.unit_dim))
+				for i, unit in enumerate(self.physical_type.valid_units)
 			]
 		return []
 
-	@property
+	@bl_cache.cached_bl_property()
 	def unit(self) -> spux.Unit | None:
-		if self.active_unit != 'NONE':
+		"""Gets the current active unit.
+
+		Returns:
+			The current active `sympy` unit.
+
+			If the socket expression is unitless, this returns `None`.
+		"""
+		if self.active_unit is not None:
 			return spux.unit_str_to_unit(self.active_unit)
 
 		return None
 
 	@unit.setter
 	def unit(self, unit: spux.Unit) -> None:
-		valid_units = spux.unit_dim_units(self.unit_dim)
+		"""Set the unit, without touching the `raw_*` UI properties.
-		if unit in valid_units:
+
+		Notes:
+			To set a new unit, **and** convert the `raw_*` UI properties to the new unit, use `self.convert_unit()` instead.
+		"""
+		if unit in self.physical_type.valid_units:
 			self.active_unit = sp.sstr(unit)
 
-		msg = f'Tried to set invalid unit {unit} (unit dim "{self.unit_dim}" only supports "{valid_units}")'
+		msg = f'Tried to set invalid unit {unit} (physical type "{self.physical_type}" only supports "{self.physical_type.valid_units}")'
 		raise ValueError(msg)
 
+	def convert_unit(self, unit_to: spux.Unit) -> None:
+		if self.active_kind == ct.FlowKind.Value:
+			current_value = self.value
+			self.unit = unit_to
+			self.value = current_value
+		elif self.active_kind == ct.FlowKind.LazyArrayRange:
+			current_lazy_array_range = self.lazy_array_range
+			self.unit = unit_to
+			self.lazy_array_range = current_lazy_array_range
+
+	####################
+	# - Property Callback
+	####################
+	def on_socket_prop_changed(self, prop_name: str) -> None:
+		if prop_name == 'unit' and self.active_unit is not None:
+			self.convert_unit(spux.unit_str_to_unit(self.active_unit))
+
 	####################
 	# - Methods
 	####################
 	def _parse_expr_info(
 		self, expr: spux.SympyExpr
-	) -> tuple[spux.MathType, typ.Literal[None, 2, 3], spux.UnitDimension]:
+	) -> tuple[spux.MathType, tuple[int, ...] | None, spux.UnitDimension]:
 		# Parse MathType
 		mathtype = spux.MathType.from_expr(expr)
 		if self.mathtype != mathtype:
@@ -188,18 +215,12 @@ class ExprBLSocket(base.MaxwellSimSocket):
 				raise ValueError(msg)
 
 		# Parse Dimensions
-		size = spux.parse_size(expr)
+		shape = spux.parse_shape(expr)
-		if size != self.size:
+		if shape != self.shape:
-			msg = f'Expr {expr} has {size} dimensions, which is incompatible with the expr socket ({self.size} dimensions)'
+			msg = f'Expr {expr} has shape {shape}, which is incompatible with the expr socket (shape {self.shape})'
 			raise ValueError(msg)
 
-		# Parse Unit Dimension
+		return mathtype, shape
-		unit_dim = spux.parse_unit_dim(expr)
-		if unit_dim != self.unit_dim:
-			msg = f'Expr {expr} has unit dimension {unit_dim}, which is incompatible with socket unit dimension {self.unit_dim}'
-			raise ValueError(msg)
-
-		return mathtype, size, unit_dim
 
 	def _to_raw_value(self, expr: spux.SympyExpr):
 		if self.unit is not None:
@@ -212,7 +233,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			locals={sym.name: sym for sym in self.symbols},
 			strict=False,
 			convert_xor=True,
-		).subs(spux.ALL_UNIT_SYMBOLS) * (self.unit if self.unit is not None else 1)
+		).subs(spux.UNIT_BY_SYMBOL) * (self.unit if self.unit is not None else 1)
 
 		# Try Parsing and Returning the Expression
 		try:
@@ -245,7 +266,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		Return:
 			The expression defined by the socket, in the socket's unit.
 		"""
-		if self.symbols:
+		if self.symbols or self.shape not in [None, (2,), (3,)]:
 			expr = self.raw_value_sp
 			if expr is None:
 				return ct.FlowSignal.FlowPending
@@ -266,7 +287,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 					self.raw_value_complex[0] + sp.I * self.raw_value_complex[1]
 				),
 			},
-			2: {
+			(2,): {
 				MT_Z: lambda: sp.Matrix([Z(i) for i in self.raw_value_int2]),
 				MT_Q: lambda: sp.Matrix([Q(q[0], q[1]) for q in self.raw_value_rat2]),
 				MT_R: lambda: sp.Matrix([R(r) for r in self.raw_value_float2]),
@@ -274,7 +295,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 					[c[0] + sp.I * c[1] for c in self.raw_value_complex2]
 				),
 			},
-			3: {
+			(3,): {
 				MT_Z: lambda: sp.Matrix([Z(i) for i in self.raw_value_int3]),
 				MT_Q: lambda: sp.Matrix([Q(q[0], q[1]) for q in self.raw_value_rat3]),
 				MT_R: lambda: sp.Matrix([R(r) for r in self.raw_value_float3]),
@@ -282,7 +303,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 					[c[0] + sp.I * c[1] for c in self.raw_value_complex3]
 				),
 			},
-		}[self.size][self.mathtype]() * (self.unit if self.unit is not None else 1)
+		}[self.shape][self.mathtype]() * (self.unit if self.unit is not None else 1)
 
 	@value.setter
 	def value(self, expr: spux.SympyExpr) -> None:
@@ -291,8 +312,8 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		Notes:
 			Called to set the internal `FlowKind.Value` of this socket.
 		"""
-		mathtype, size, unit_dim = self._parse_expr_info(expr)
+		mathtype, shape = self._parse_expr_info(expr)
-		if self.symbols:
+		if self.symbols or self.shape not in [None, (2,), (3,)]:
 			self.raw_value_spstr = sp.sstr(expr)
 
 		else:
@@ -300,7 +321,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			MT_Q = spux.MathType.Rational
 			MT_R = spux.MathType.Real
 			MT_C = spux.MathType.Complex
-			if size is None:
+			if shape is None:
 				if mathtype == MT_Z:
 					self.raw_value_int = self._to_raw_value(expr)
 				elif mathtype == MT_Q:
@@ -309,7 +330,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 					self.raw_value_float = self._to_raw_value(expr)
 				elif mathtype == MT_C:
 					self.raw_value_complex = self._to_raw_value(expr)
-			elif size == 2:
+			elif shape == (2,):
 				if mathtype == MT_Z:
 					self.raw_value_int2 = self._to_raw_value(expr)
 				elif mathtype == MT_Q:
@@ -318,7 +339,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 					self.raw_value_float2 = self._to_raw_value(expr)
 				elif mathtype == MT_C:
 					self.raw_value_complex2 = self._to_raw_value(expr)
-			elif size == 3:
+			elif shape == (3,):
 				if mathtype == MT_Z:
 					self.raw_value_int3 = self._to_raw_value(expr)
 				elif mathtype == MT_Q:
@@ -341,9 +362,35 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		Return:
 			The range of lengths, which uses no symbols.
 		"""
+		if self.symbols:
 			return ct.LazyArrayRangeFlow(
-			start=sp.S(self.min_value) * self.unit,
+				start=self.raw_min_sp,
-			stop=sp.S(self.max_value) * self.unit,
+				stop=self.raw_max_sp,
+				steps=self.steps,
+				scaling='lin',
+				unit=self.unit,
+				symbols=self.symbols,
+			)
+
+		MT_Z = spux.MathType.Integer
+		MT_Q = spux.MathType.Rational
+		MT_R = spux.MathType.Real
+		MT_C = spux.MathType.Complex
+		Z = sp.Integer
+		Q = sp.Rational
+		R = sp.RealNumber
+		min_bound, max_bound = {
+			MT_Z: lambda: [Z(bound) for bound in self.raw_range_int],
+			MT_Q: lambda: [Q(bound[0], bound[1]) for bound in self.raw_range_rat],
+			MT_R: lambda: [R(bound) for bound in self.raw_range_float],
+			MT_C: lambda: [
+				bound[0] + sp.I * bound[1] for bound in self.raw_range_complex
+			],
+		}[self.mathtype]()
+
+		return ct.LazyArrayRangeFlow(
+			start=min_bound,
+			stop=max_bound,
 			steps=self.steps,
 			scaling='lin',
 			unit=self.unit,
@@ -356,25 +403,74 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		Notes:
 			Called to compute the internal `FlowKind.LazyArrayRange` of this socket.
 		"""
-		self.min_value = spux.sympy_to_python(
-			spux.scale_to_unit(value.start * value.unit, self.unit)
-		)
-		self.max_value = spux.sympy_to_python(
-			spux.scale_to_unit(value.stop * value.unit, self.unit)
-		)
 		self.steps = value.steps
+		self.unit = value.unit
+
+		if self.symbols:
+			self.raw_min_spstr = sp.sstr(value.start)
+			self.raw_max_spstr = sp.sstr(value.stop)
+
+		else:
+			MT_Z = spux.MathType.Integer
+			MT_Q = spux.MathType.Rational
+			MT_R = spux.MathType.Real
+			MT_C = spux.MathType.Complex
+
+			if value.mathtype == MT_Z:
+				self.raw_range_int = [
+					self._to_raw_value(bound) for bound in [value.start, value.stop]
+				]
+			elif value.mathtype == MT_Q:
+				self.raw_range_rat = [
+					self._to_raw_value(bound) for bound in [value.start, value.stop]
+				]
+			elif value.mathtype == MT_R:
+				self.raw_range_float = [
+					self._to_raw_value(bound) for bound in [value.start, value.stop]
+				]
+			elif value.mathtype == MT_C:
+				self.raw_range_complex = [
+					self._to_raw_value(bound) for bound in [value.start, value.stop]
+				]
 
 	####################
-	# - FlowKind: LazyValueFunc
+	# - FlowKind: LazyValueFunc (w/Params if Constant)
 	####################
 	@property
 	def lazy_value_func(self) -> ct.LazyValueFuncFlow:
+		# Lazy Value: Arbitrary Expression
+		if self.symbols or self.shape not in [None, (2,), (3,)]:
 			return ct.LazyValueFuncFlow(
 				func=sp.lambdify(self.symbols, self.value, 'jax'),
-			func_args=[spux.sympy_to_python_type(sym) for sym in self.symbols],
+				func_args=[spux.MathType.from_expr(sym) for sym in self.symbols],
 				supports_jax=True,
 			)
 
+		# Lazy Value: Constant
+		## -> A very simple function, which takes a single argument.
+		## -> What will be passed is a unit-scaled/stripped, pytype-converted Expr:Value.
+		## -> Until then, the user can utilize this LVF in a function composition chain.
+		return ct.LazyValueFuncFlow(
+			func=lambda v: v,
+			func_args=[
+				self.physical_type if self.physical_type is not None else self.mathtype
+			],
+			supports_jax=True,
+		)
+
+	@property
+	def params(self) -> ct.ParamsFlow:
+		# Params Value: Symbolic
+		## -> The Expr socket does not declare actual values for the symbols.
+		## -> Those values must come from elsewhere.
+		## -> If someone tries to load them anyway, tell them 'NoFlow'.
+		if self.symbols or self.shape not in [None, (2,), (3,)]:
+			return ct.FlowSignal.NoFlow
+
+		# Params Value: Constant
+		## -> Simply pass the Expr:Value as parameter.
+		return ct.ParamsFlow(func_args=[self.value])
+
 	####################
 	# - FlowKind: Array
 	####################
@@ -396,7 +492,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	def info(self) -> ct.ArrayFlow:
 		return ct.InfoFlow(
 			output_name='_',  ## TODO: Something else
-			output_shape=(self.size,) if self.size is not None else None,
+			output_shape=self.shape,
 			output_mathtype=self.mathtype,
 			output_unit=self.unit,
 		)
@@ -416,6 +512,16 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	####################
 	# - UI
 	####################
+	def draw_label_row(self, row: bpy.types.UILayout, text) -> None:
+		if self.active_unit is not None:
+			split = row.split(factor=0.6, align=True)
+
+			_row = split.row(align=True)
+			_row.label(text=text)
+
+			_col = split.column(align=True)
+			_col.prop(self, 'active_unit', text='')
+
 	def draw_value(self, col: bpy.types.UILayout) -> None:
 		# Property Interface
 		if self.symbols:
@@ -426,7 +532,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			MT_Q = spux.MathType.Rational
 			MT_R = spux.MathType.Real
 			MT_C = spux.MathType.Complex
-			if self.size is None:
+			if self.shape is None:
 				if self.mathtype == MT_Z:
 					col.prop(self, self.blfields['raw_value_int'], text='')
 				elif self.mathtype == MT_Q:
@@ -435,7 +541,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 					col.prop(self, self.blfields['raw_value_float'], text='')
 				elif self.mathtype == MT_C:
 					col.prop(self, self.blfields['raw_value_complex'], text='')
-			elif self.size == 2:
+			elif self.shape == (2,):
 				if self.mathtype == MT_Z:
 					col.prop(self, self.blfields['raw_value_int2'], text='')
 				elif self.mathtype == MT_Q:
@@ -444,7 +550,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 					col.prop(self, self.blfields['raw_value_float2'], text='')
 				elif self.mathtype == MT_C:
 					col.prop(self, self.blfields['raw_value_complex2'], text='')
-			elif self.size == 3:
+			elif self.shape == (3,):
 				if self.mathtype == MT_Z:
 					col.prop(self, self.blfields['raw_value_int3'], text='')
 				elif self.mathtype == MT_Q:
@@ -579,34 +685,57 @@ class ExprSocketDef(base.SocketDef):
 		ct.FlowKind.Value
 	)
 
-	# Properties
+	# Socket Interface
-	size: typ.Literal[None, 2, 3] = None
+	## TODO: __hash__ like socket method based on these?
+	shape: tuple[int, ...] | None = None
 	mathtype: spux.MathType = spux.MathType.Real
+	physical_type: spux.PhysicalType | None = None
 	symbols: frozenset[spux.Symbol] = frozenset()
-	## Units
+
-	unit_dim: spux.UnitDimension | None = None
+	# Socket Units
-	## Info Display
+	default_unit: spux.Unit | None = None
-	show_info_columns: bool = False
+
+	# FlowKind: Value
+	default_value: spux.SympyExpr = sp.S(0)
+
+	# FlowKind: LazyArrayRange
+	default_min: spux.SympyExpr = sp.S(0)
+	default_max: spux.SympyExpr = sp.S(1)
+	default_steps: int = 2
+	## TODO: Configure lin/log/... scaling (w/enumprop in UI)
 
 	## TODO: Buncha validation :)
 
-	# Defaults
+	# UI
-	default_unit: spux.Unit | None = None
+	show_info_columns: bool = False
-	default_value: spux.SympyExpr = sp.S(1)
-	default_min: spux.SympyExpr = sp.S(0)
-	default_max: spux.SympyExpr = sp.S(1)
-	default_steps: spux.SympyExpr = sp.S(2)
 
 	def init(self, bl_socket: ExprBLSocket) -> None:
 		bl_socket.active_kind = self.active_kind
-		bl_socket.size = self.size
-		bl_socket.mathtype = self.size
-		bl_socket.symbols = self.symbols
-		bl_socket.unit_dim = self.size
-		bl_socket.unit = self.symbols
-		bl_socket.show_info_columns = self.show_info_columns
 
-		bl_socket.value = self.default
+		# Socket Interface
+		bl_socket.shape = self.shape
+		bl_socket.mathtype = self.mathtype
+		bl_socket.physical_type = self.physical_type
+		bl_socket.symbols = self.symbols
+
+		# Socket Units
+		if self.default_unit is not None:
+			bl_socket.unit = self.default_unit
+
+		# FlowKind: Value
+		bl_socket.value = self.default_value
+
+		# FlowKind: LazyArrayRange
+		bl_socket.lazy_array_range = ct.LazyArrayRangeFlow(
+			start=self.default_min,
+			stop=self.default_max,
+			steps=self.default_steps,
+			scaling='lin',
+			unit=self.default_unit,
+		)
+
+		# UI
+		bl_socket.show_info_columns = self.show_info_columns
 
 
 ####################

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/maxwell/__init__.py

@@ -1,49 +1,51 @@
-from . import bound_cond, bound_conds
+from . import (
+	bound_cond,
+	bound_conds,
+	fdtd_sim,
+	fdtd_sim_data,
+	medium,
+	medium_non_linearity,
+	monitor,
+	monitor_data,
+	sim_domain,
+	sim_grid,
+	sim_grid_axis,
+	source,
+	structure,
+	temporal_shape,
+)
 
 MaxwellBoundCondSocketDef = bound_cond.MaxwellBoundCondSocketDef
 MaxwellBoundCondsSocketDef = bound_conds.MaxwellBoundCondsSocketDef
-
+MaxwellFDTDSimSocketDef = fdtd_sim.MaxwellFDTDSimSocketDef
-from . import medium, medium_non_linearity
+MaxwellFDTDSimDataSocketDef = fdtd_sim_data.MaxwellFDTDSimDataSocketDef
-
 MaxwellMediumSocketDef = medium.MaxwellMediumSocketDef
 MaxwellMediumNonLinearitySocketDef = (
 	medium_non_linearity.MaxwellMediumNonLinearitySocketDef
 )
-
-from . import source, temporal_shape
-
-MaxwellSourceSocketDef = source.MaxwellSourceSocketDef
-MaxwellTemporalShapeSocketDef = temporal_shape.MaxwellTemporalShapeSocketDef
-
-from . import structure
-
-MaxwellStructureSocketDef = structure.MaxwellStructureSocketDef
-
-from . import monitor
-
 MaxwellMonitorSocketDef = monitor.MaxwellMonitorSocketDef
-
+MaxwellMonitorDataSocketDef = monitor_data.MaxwellMonitorDataSocketDef
-from . import fdtd_sim, fdtd_sim_data, sim_domain, sim_grid, sim_grid_axis
+MaxwellSimDomainSocketDef = sim_domain.MaxwellSimDomainSocketDef
-
-MaxwellFDTDSimSocketDef = fdtd_sim.MaxwellFDTDSimSocketDef
-MaxwellFDTDSimDataSocketDef = fdtd_sim_data.MaxwellFDTDSimDataSocketDef
 MaxwellSimGridSocketDef = sim_grid.MaxwellSimGridSocketDef
 MaxwellSimGridAxisSocketDef = sim_grid_axis.MaxwellSimGridAxisSocketDef
-MaxwellSimDomainSocketDef = sim_domain.MaxwellSimDomainSocketDef
+MaxwellSourceSocketDef = source.MaxwellSourceSocketDef
+MaxwellStructureSocketDef = structure.MaxwellStructureSocketDef
+MaxwellTemporalShapeSocketDef = temporal_shape.MaxwellTemporalShapeSocketDef
 
 
 BL_REGISTER = [
 	*bound_cond.BL_REGISTER,
 	*bound_conds.BL_REGISTER,
-	*medium.BL_REGISTER,
-	*medium_non_linearity.BL_REGISTER,
-	*source.BL_REGISTER,
-	*temporal_shape.BL_REGISTER,
-	*structure.BL_REGISTER,
-	*monitor.BL_REGISTER,
 	*fdtd_sim.BL_REGISTER,
 	*fdtd_sim_data.BL_REGISTER,
+	*medium.BL_REGISTER,
+	*medium_non_linearity.BL_REGISTER,
+	*monitor.BL_REGISTER,
+	*monitor_data.BL_REGISTER,
+	*sim_domain.BL_REGISTER,
 	*sim_grid.BL_REGISTER,
 	*sim_grid_axis.BL_REGISTER,
-	*sim_domain.BL_REGISTER,
+	*source.BL_REGISTER,
+	*structure.BL_REGISTER,
+	*temporal_shape.BL_REGISTER,
 ]

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/maxwell/monitor_data.py

@@ -0,0 +1,25 @@
+from ... import contracts as ct
+from .. import base
+
+
+class MaxwellMonitorDataBLSocket(base.MaxwellSimSocket):
+	socket_type = ct.SocketType.MaxwellMonitorData
+	bl_label = 'Maxwell Monitor Data'
+
+
+####################
+# - Socket Configuration
+####################
+class MaxwellMonitorDataSocketDef(base.SocketDef):
+	socket_type: ct.SocketType = ct.SocketType.MaxwellMonitorData
+
+	def init(self, bl_socket: MaxwellMonitorDataBLSocket) -> None:
+		pass
+
+
+####################
+# - Blender Registration
+####################
+BL_REGISTER = [
+	MaxwellMonitorDataBLSocket,
+]

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/physical/__init__.py

@@ -1,9 +1,9 @@
-from . import pol, unit_system
+from . import pol  # , unit_system
 
 PhysicalPolSocketDef = pol.PhysicalPolSocketDef
 
 
 BL_REGISTER = [
-	*unit_system.BL_REGISTER,
+	# *unit_system.BL_REGISTER,
 	*pol.BL_REGISTER,
 ]

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/physical/pol.py

@@ -3,12 +3,12 @@ import sympy as sp
 import sympy.physics.optics.polarization as spo_pol
 import sympy.physics.units as spu
 
-from blender_maxwell.utils.pydantic_sympy import SympyExpr
+from blender_maxwell.utils import extra_sympy_units as spux
 
 from ... import contracts as ct
 from .. import base
 
-StokesVector = SympyExpr
+StokesVector = spux.SympyExpr
 
 
 class PhysicalPolBLSocket(base.MaxwellSimSocket):

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/physical/unit_system.py

@@ -1,6 +1,6 @@
 import bpy
 
-from blender_maxwell.utils.pydantic_sympy import SympyExpr
+#from blender_maxwell.utils.pydantic_sympy import SympyExpr
 
 from ... import contracts as ct
 from .. import base

src/blender_maxwell/utils/__init__.py

@@ -1,16 +1,22 @@
 from ..nodeps.utils import blender_type_enum, pydeps
 from . import (
-	analyze_geonodes,
+	bl_cache,
 	extra_sympy_units,
+	image_ops,
 	logger,
-	pydantic_sympy,
+	sci_constants,
+	serialize,
+	staticproperty,
 )
 
 __all__ = [
-	'pydeps',
-	'analyze_geonodes',
 	'blender_type_enum',
+	'pydeps',
+	'bl_cache',
 	'extra_sympy_units',
+	'image_ops',
 	'logger',
-	'pydantic_sympy',
+	'sci_constants',
+	'serialize',
+	'staticproperty',
 ]

src/blender_maxwell/utils/analyze_geonodes.py

@@ -1,30 +0,0 @@
-import typing as typ
-
-import bpy
-
-INVALID_BL_SOCKET_TYPES = {
-	'NodeSocketGeometry',
-}
-
-
-def interface(
-	geonodes: bpy.types.GeometryNodeTree,  ## TODO: bpy type
-	direc: typ.Literal['INPUT', 'OUTPUT'],
-):
-	"""Returns 'valid' GeoNodes interface sockets.
-
-	- The Blender socket type is not something invalid (ex. "Geometry").
-	- The socket has a default value.
-	- The socket's direction (input/output) matches the requested direction.
-	"""
-	return {
-		interface_item_name: bl_interface_socket
-		for interface_item_name, bl_interface_socket in (
-			geonodes.interface.items_tree.items()
-		)
-		if (
-			bl_interface_socket.socket_type not in INVALID_BL_SOCKET_TYPES
-			and hasattr(bl_interface_socket, 'default_value')
-			and bl_interface_socket.in_out == direc
-		)
-	}

src/blender_maxwell/utils/bl_cache.py

@@ -10,6 +10,7 @@ import uuid
 from pathlib import Path
 
 import bpy
+import numpy as np
 
 from blender_maxwell import contracts as ct
 from blender_maxwell.utils import logger, serialize
@@ -515,6 +516,7 @@ class BLField:
 			use_prop_update: Configures the BLField to run `bl_instance.on_prop_changed(attr_name)` whenever value is set.
 				This is done by setting the `update` method.
 			enum_cb: Method used to generate new enum elements whenever `Signal.ResetEnum` is presented.
+			matrix_rowmajor: Blender's UI stores matrices flattened,
 
 		"""
 		log.debug(
@@ -528,8 +530,8 @@ class BLField:
 		## Static
 		self._prop_ui = prop_ui
 		self._prop_flags = prop_flags
-		self._min = abs_min
+		self._abs_min = abs_min
-		self._max = abs_max
+		self._abs_max = abs_max
 		self._soft_min = soft_min
 		self._soft_max = soft_max
 		self._float_step = float_step
@@ -545,6 +547,12 @@ class BLField:
 		self._str_cb = str_cb
 		self._enum_cb = enum_cb
 
+		## Vector/Matrix Identity
+		## -> Matrix Shape assists in the workaround for Matrix Display Bug
+		self._is_vector = False
+		self._is_matrix = False
+		self._matrix_shape = None
+
 		## HUGE TODO: Persist these
 		self._str_cb_cache = {}
 		self._enum_cb_cache = {}
@@ -637,6 +645,7 @@ class BLField:
 
 		## Reusable Snippets
 		def _add_min_max_kwargs():
+			nonlocal kwargs_prop  ## I've heard legends of needing this!
 			kwargs_prop |= {'min': self._abs_min} if self._abs_min is not None else {}
 			kwargs_prop |= {'max': self._abs_max} if self._abs_max is not None else {}
 			kwargs_prop |= (
@@ -647,6 +656,7 @@ class BLField:
 			)
 
 		def _add_float_kwargs():
+			nonlocal kwargs_prop
 			kwargs_prop |= (
 				{'step': self._float_step} if self._float_step is not None else {}
 			)
@@ -684,6 +694,7 @@ class BLField:
 			default_value = self._default_value
 			BLProp = bpy.props.BoolVectorProperty
 			kwargs_prop |= {'size': len(typ.get_args(AttrType))}
+			self._is_vector = True
 
 		## Vector Int
 		elif typ.get_origin(AttrType) is tuple and all(
@@ -693,6 +704,7 @@ class BLField:
 			BLProp = bpy.props.IntVectorProperty
 			_add_min_max_kwargs()
 			kwargs_prop |= {'size': len(typ.get_args(AttrType))}
+			self._is_vector = True
 
 		## Vector Float
 		elif typ.get_origin(AttrType) is tuple and all(
@@ -703,6 +715,59 @@ class BLField:
 			_add_min_max_kwargs()
 			_add_float_kwargs()
 			kwargs_prop |= {'size': len(typ.get_args(AttrType))}
+			self._is_vector = True
+
+		## Matrix Bool
+		elif typ.get_origin(AttrType) is tuple and all(
+			all(V is bool for V in typ.get_args(T)) for T in typ.get_args(AttrType)
+		):
+			# Workaround for Matrix Display Bug
+			## - Also requires __get__ support to read consistently.
+			rows = len(typ.get_args(AttrType))
+			cols = len(typ.get_args(typ.get_args(AttrType)[0]))
+			default_value = (
+				np.array(self._default_value, dtype=bool)
+				.flatten()
+				.reshape([cols, rows])
+			).tolist()
+			BLProp = bpy.props.BoolVectorProperty
+			kwargs_prop |= {'size': (cols, rows), 'subtype': 'MATRIX'}
+			## 'size' has column-major ordering (Matrix Display Bug).
+			self._is_matrix = True
+			self._matrix_shape = (rows, cols)
+
+		## Matrix Int
+		elif typ.get_origin(AttrType) is tuple and all(
+			all(V is int for V in typ.get_args(T)) for T in typ.get_args(AttrType)
+		):
+			_add_min_max_kwargs()
+			rows = len(typ.get_args(AttrType))
+			cols = len(typ.get_args(typ.get_args(AttrType)[0]))
+			default_value = (
+				np.array(self._default_value, dtype=int).flatten().reshape([cols, rows])
+			).tolist()
+			BLProp = bpy.props.IntVectorProperty
+			kwargs_prop |= {'size': (cols, rows), 'subtype': 'MATRIX'}
+			self._is_matrix = True
+			self._matrix_shape = (rows, cols)
+
+		## Matrix Float
+		elif typ.get_origin(AttrType) is tuple and all(
+			all(V is float for V in typ.get_args(T)) for T in typ.get_args(AttrType)
+		):
+			_add_min_max_kwargs()
+			_add_float_kwargs()
+			rows = len(typ.get_args(AttrType))
+			cols = len(typ.get_args(typ.get_args(AttrType)[0]))
+			default_value = (
+				np.array(self._default_value, dtype=float)
+				.flatten()
+				.reshape([cols, rows])
+			).tolist()
+			BLProp = bpy.props.FloatVectorProperty
+			kwargs_prop |= {'size': (cols, rows), 'subtype': 'MATRIX'}
+			self._is_matrix = True
+			self._matrix_shape = (rows, cols)
 
 		## Generic String
 		elif AttrType is str:
@@ -732,7 +797,7 @@ class BLField:
 			}
 
 		## StrEnum
-		elif issubclass(AttrType, enum.StrEnum):
+		elif inspect.isclass(AttrType) and issubclass(AttrType, enum.StrEnum):
 			default_value = self._default_value
 			BLProp = bpy.props.EnumProperty
 			kwargs_prop |= {
@@ -792,6 +857,7 @@ class BLField:
 		)  ## TODO: Mine description from owner class __doc__
 
 		# Define Property Getter
+		## Serialized properties need to deserialize in the getter.
 		if prop_is_serialized:
 
 			def getter(_self: BLInstance) -> AttrType:
@@ -802,6 +868,7 @@ class BLField:
 				return getattr(_self, bl_attr_name)
 
 		# Define Property Setter
+		## Serialized properties need to serialize in the setter.
 		if prop_is_serialized:
 
 			def setter(_self: BLInstance, value: AttrType) -> None:
@@ -821,7 +888,40 @@ class BLField:
 	def __get__(
 		self, bl_instance: BLInstance | None, owner: type[BLInstance]
 	) -> typ.Any:
-		return self._cached_bl_property.__get__(bl_instance, owner)
+		value = self._cached_bl_property.__get__(bl_instance, owner)
+
+		# enum.Enum: Cast Auto-Injected Dynamic Enum 'NONE' -> None
+		## As far a Blender is concerned, dynamic enum props can't be empty.
+		## -> Well, they can... But bad things happen. So they can't.
+		## So in the interest of the user's sanity, we always ensure one entry.
+		## -> This one entry always has the one, same, id: 'NONE'.
+		## Of course, we often want to check for this "there was nothing" case.
+		## -> Aka, we want to do a `None` check, semantically speaking.
+		## -> ...But because it's a special thingy, we must check 'NONE'?
+		## Nonsense. Let the user just check `None`, as Guido intended.
+		if self._enum_cb is not None and value == 'NONE':
+			## TODO: Perhaps check if the unsafe callback was actually [].
+			## -> In case the user themselves want to return 'NONE'.
+			## -> Why would they do this? Because they are users!
+			return None
+
+		# Sized Vectors/Matrices
+		## Why not just yeet back a np.array?
+		## -> Type-annotating a shaped numpy array is... "rough".
+		## -> Type-annotation tuple[] of known shape is super easy.
+		## -> Even list[] won't do; its size varies, after all!
+		## -> Reject modernity. Return to tuple[].
+		if self._is_vector:
+			## -> tuple()ify the np.array to respect tuple[] type annotation.
+			return tuple(np.array(value))
+
+		if self._is_matrix:
+			# Matrix Display Bug: Correctly Read Row-Major Values w/Reshape
+			return tuple(
+				map(tuple, np.array(value).flatten().reshape(self._matrix_shape))
+			)
+
+		return value
 
 	def __set__(self, bl_instance: BLInstance | None, value: typ.Any) -> None:
 		if value == Signal.ResetEnumItems:

src/blender_maxwell/utils/jarray.py

@@ -1,61 +0,0 @@
-import dataclasses
-import typing as typ
-from types import MappingProxyType
-
-import jax
-import jax.numpy as jnp
-
-# import jaxtyping as jtyp
-import sympy.physics.units as spu
-import xarray
-
-from . import logger
-
-log = logger.get(__name__)
-
-DimName: typ.TypeAlias = str
-Number: typ.TypeAlias = int | float | complex
-NumberRange: typ.TypeAlias = jax.Array
-
-
-@dataclasses.dataclass(kw_only=True)
-class JArray:
-	"""Very simple wrapper for JAX arrays, which includes information about the dimension names and bounds."""
-
-	array: jax.Array
-	dims: dict[DimName, NumberRange]
-	dim_units: dict[DimName, spu.Quantity]
-
-	####################
-	# - Constructor
-	####################
-	@classmethod
-	def from_xarray(
-		cls,
-		xarr: xarray.DataArray,
-		dim_units: dict[DimName, spu.Quantity] = MappingProxyType({}),
-		sort_axis: int = -1,
-	) -> typ.Self:
-		return cls(
-			array=jnp.sort(jnp.array(xarr.data), axis=sort_axis),
-			dims={
-				dim_name: jnp.array(xarr.get_index(dim_name).values)
-				for dim_name in xarr.dims
-			},
-			dim_units={dim_name: dim_units.get(dim_name) for dim_name in xarr.dims},
-		)
-
-	def idx(self, dim_name: DimName, dim_value: Number) -> int:
-		found_idx = jnp.searchsorted(self.dims[dim_name], dim_value)
-		if found_idx == 0:
-			return found_idx
-		if found_idx == len(self.dims[dim_name]):
-			return found_idx - 1
-
-		left = self.dims[dim_name][found_idx - 1]
-		right = self.dims[dim_name][found_idx - 1]
-		return found_idx - 1 if (dim_value - left) <= (right - dim_value) else found_idx
-
-	@property
-	def dtype(self) -> jnp.dtype:
-		return self.array.dtype

src/blender_maxwell/utils/pydantic_sympy.py

@@ -1,164 +0,0 @@
-import typing as typ
-
-import pydantic as pyd
-import sympy as sp
-import sympy.physics.units as spu
-import typing_extensions as typx
-from pydantic_core import core_schema as pyd_core_schema
-
-from . import extra_sympy_units as spux
-
-####################
-# - Missing Basics
-####################
-AllowedSympyExprs = sp.Expr | sp.MatrixBase | sp.MutableDenseMatrix
-Complex = typx.Annotated[
-	complex,
-	pyd.GetPydanticSchema(
-		lambda tp, handler: pyd_core_schema.no_info_after_validator_function(
-			lambda x: x, handler(tp)
-		)
-	),
-]
-
-
-####################
-# - Custom Pydantic Type for sp.Expr
-####################
-class _SympyExpr:
-	@classmethod
-	def __get_pydantic_core_schema__(
-		cls,
-		_source_type: AllowedSympyExprs,
-		_handler: pyd.GetCoreSchemaHandler,
-	) -> pyd_core_schema.CoreSchema:
-		def validate_from_str(value: str) -> AllowedSympyExprs:
-			if not isinstance(value, str):
-				return value
-
-			try:
-				expr = sp.sympify(value)
-			except ValueError as ex:
-				msg = f'Value {value} is not a `sympify`able string'
-				raise ValueError(msg) from ex
-
-			return expr.subs(spux.ALL_UNIT_SYMBOLS)
-
-		def validate_from_expr(value: AllowedSympyExprs) -> AllowedSympyExprs:
-			if not (isinstance(value, sp.Expr | sp.MatrixBase)):
-				msg = f'Value {value} is not a `sympy` expression'
-				raise ValueError(msg)
-
-			return value
-
-		sympy_expr_schema = pyd_core_schema.chain_schema(
-			[
-				pyd_core_schema.no_info_plain_validator_function(validate_from_str),
-				pyd_core_schema.no_info_plain_validator_function(validate_from_expr),
-				pyd_core_schema.is_instance_schema(AllowedSympyExprs),
-			]
-		)
-		return pyd_core_schema.json_or_python_schema(
-			json_schema=sympy_expr_schema,
-			python_schema=sympy_expr_schema,
-			serialization=pyd_core_schema.plain_serializer_function_ser_schema(
-				lambda instance: sp.srepr(instance)
-			),
-		)
-
-
-####################
-# - Configurable Expression Validation
-####################
-SympyExpr = typx.Annotated[
-	AllowedSympyExprs,
-	_SympyExpr,
-]
-
-
-def ConstrSympyExpr(
-	# Feature Class
-	allow_variables: bool = True,
-	allow_units: bool = True,
-	# Structure Class
-	allowed_sets: set[typ.Literal['integer', 'rational', 'real', 'complex']]
-	| None = None,
-	allowed_structures: set[typ.Literal['scalar', 'matrix']] | None = None,
-	# Element Class
-	allowed_symbols: set[sp.Symbol] | None = None,
-	allowed_units: set[spu.Quantity] | None = None,
-	# Shape Class
-	allowed_matrix_shapes: set[tuple[int, int]] | None = None,
-):
-	## See `sympy` predicates:
-	## - <https://docs.sympy.org/latest/guides/assumptions.html#predicates>
-	def validate_expr(expr: AllowedSympyExprs):
-		if not (isinstance(expr, sp.Expr | sp.MatrixBase),):
-			## NOTE: Must match AllowedSympyExprs union elements.
-			msg = f"expr '{expr}' is not an allowed Sympy expression ({AllowedSympyExprs})"
-			raise ValueError(msg)
-
-		msgs = set()
-
-		# Validate Feature Class
-		if (not allow_variables) and (len(expr.free_symbols) > 0):
-			msgs.add(
-				f'allow_variables={allow_variables} does not match expression {expr}.'
-			)
-		if (not allow_units) and spux.uses_units(expr):
-			msgs.add(f'allow_units={allow_units} does not match expression {expr}.')
-
-		# Validate Structure Class
-		if (
-			allowed_sets
-			and isinstance(expr, sp.Expr)
-			and not any(
-				{
-					'integer': expr.is_integer,
-					'rational': expr.is_rational,
-					'real': expr.is_real,
-					'complex': expr.is_complex,
-				}[allowed_set]
-				for allowed_set in allowed_sets
-			)
-		):
-			msgs.add(
-				f"allowed_sets={allowed_sets} does not match expression {expr} (remember to add assumptions to symbols, ex. `x = sp.Symbol('x', real=True))"
-			)
-		if allowed_structures and not any(
-			{
-				'matrix': isinstance(expr, sp.MatrixBase),
-			}[allowed_set]
-			for allowed_set in allowed_structures
-			if allowed_structures != 'scalar'
-		):
-			msgs.add(
-				f"allowed_structures={allowed_structures} does not match expression {expr} (remember to add assumptions to symbols, ex. `x = sp.Symbol('x', real=True))"
-			)
-
-		# Validate Element Class
-		if allowed_symbols and expr.free_symbols.issubset(allowed_symbols):
-			msgs.add(
-				f'allowed_symbols={allowed_symbols} does not match expression {expr}'
-			)
-		if allowed_units and spux.get_units(expr).issubset(allowed_units):
-			msgs.add(f'allowed_units={allowed_units} does not match expression {expr}')
-
-		# Validate Shape Class
-		if (
-			allowed_matrix_shapes and isinstance(expr, sp.MatrixBase)
-		) and expr.shape not in allowed_matrix_shapes:
-			msgs.add(
-				f'allowed_matrix_shapes={allowed_matrix_shapes} does not match expression {expr} with shape {expr.shape}'
-			)
-
-		# Error or Return
-		if msgs:
-			raise ValueError(str(msgs))
-		return expr
-
-	return typx.Annotated[
-		AllowedSympyExprs,
-		_SympyExpr,
-		pyd.AfterValidator(validate_expr),
-	]

src/blender_maxwell/utils/serialize.py

@@ -141,7 +141,7 @@ def _dec_hook(_type: type, obj: NaivelyEncodableType) -> typ.Any:
 		is_representation(obj) and obj[0] == TypeID.SympyType
 	):
 		obj_value = obj[2]
-		return sp.sympify(obj_value).subs(spux.ALL_UNIT_SYMBOLS)
+		return sp.sympify(obj_value).subs(spux.UNIT_BY_SYMBOL)
 
 	if hasattr(_type, 'parse_as_msgspec') and (
 		is_representation(obj) and obj[0] in [TypeID.SocketDef, TypeID.ManagedObj]