feat: transform node w/sane `DataChanged`-chaining

We also implemented a JIT-based `rescale` for `ArrayFlow`, where the
same function as for `LazyArrayRangeFlow` passes through and can do an
arbitrary symbolic shift/rescale/order-preserving whatever.
To make this fast for `ArrayFlow`, we utilize a "test" variable `a`,
put it through the function and rescale/strip its units, then `lambdify`
it and broadcast the function onto `ArrayFlow.values`.

It's an immensely clean way of working.
The `lambdify` seems fast, interestingly, but ideally we would of course
also cache that somehow.

Some details remain:

- Fourier Transform index bounds / length are currently not presumed
  known before actually computing them; it's unclear what's best here,
  as the design cross-section of physical expectation, mathematical
  correctness, and ease of implementation (especially trying to keep
  actual data out of the `InfoFlow` hot-path). For now, the `0..\infty`
  bounds **will probably break** the `Viz` node.
- We've reverted the notion that particular `sim_symbol`s must have a
  unit pre-defined, which causes a little more complexity for nodes like
  `TemporalShape`. This question is going to need resolving
- The whole `InfoFlow` object really seems to be at the heart of certain
  lagginess when it comes to the math system. It, together with the
  index representations, would benefit greatly from a principled
  refactor.
- The `Viewer` node is broken for 3D preview; see #70.

Closes #59. Progress on #54.

TODO.md

@@ -2,15 +2,15 @@
 - [x] Wave Constant
 - Sources
 	- [x] Temporal Shapes / Continuous Wave Temporal Shape
-	- [ ] Temporal Shapes / Symbolic Temporal Shape
-	- [ ] Plane Wave Source
+	- [x] Temporal Shapes / Symbolic Temporal Shape
+	- [x] Plane Wave Source
 	- [ ] TFSF Source
-	- [ ] Gaussian Beam Source
+	- [x] Gaussian Beam Source
 	- [ ] Astig. Gauss Beam
 - Monitors
 	- [x] EH Field
 	- [x] Power Flux
-	- [ ] Permittivity
+	- [x] Permittivity
 	- [ ] Diffraction
 - Tidy3D / Integration
 	- [ ] Exporter
@@ -23,7 +23,7 @@
 	- [ ] Uniform
 	- [ ] Data
 - Structures
-	- [ ] Cylinder
+	- [x] Cylinder
 	- [ ] Cylinder Array
 	- [ ] L-Cavity Cylinder
 	- [ ] H-Cavity Cylinder
@@ -31,10 +31,10 @@
 	- [ ] BCC Lattice
 	- [ ] Monkey
 - Expr Socket
-	- [ ] Array Mode
+	- [x] LVF Mode
 - Math Nodes
 	- [ ] Reduce Math
-	- [ ] Transform Math - reindex freq->wl
+	- [x] Transform Math - reindex freq->wl
 - Material Data Fitting
 	- [ ] Data File Import
 	- [ ] DataFit Medium
@@ -47,10 +47,10 @@
 	- [ ] Debye Medium
 	- [ ] Anisotropic Medium
 - Integration
-	- [ ] Simulation and Analysis of Maxim's Cavity
+	- [x] Simulation and Analysis of Maxim's Cavity
 - Constants
 	- [x] Number Constant
 	- [x] Vector Constant
 	- [x] Physical Constant
 
-- [ ] Fix many problems by persisting `_enum_cb_cache` and `_str_cb_cache`.
+- [x] Fix many problems by persisting `_enum_cb_cache` and `_str_cb_cache`.

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

@@ -20,6 +20,7 @@ import typing as typ
 
 import jaxtyping as jtyp
 import numpy as np
+import sympy as sp
 import sympy.physics.units as spu
 
 from blender_maxwell.utils import extra_sympy_units as spux
@@ -110,3 +111,24 @@ class ArrayFlow:
 
 		msg = f'Tried to rescale unitless LazyDataValueRange to unit {unit}'
 		raise ValueError(msg)
+
+	def rescale(
+		self, rescale_func, reverse: bool = False, new_unit: spux.Unit | None = None
+	) -> typ.Self:
+		# Compile JAX-Compatible Rescale Function
+		a = sp.Symbol('a')
+		rescale_expr = (
+			spux.scale_to_unit(rescale_func(a * self.unit), new_unit)
+			if self.unit is not None
+			else rescale_func(a * self.unit)
+		)
+		log.critical([self.unit, new_unit, rescale_expr])
+		_rescale_func = sp.lambdify(a, rescale_expr, 'jax')
+		values = _rescale_func(self.values)
+
+		# Return ArrayFlow
+		return ArrayFlow(
+			values=values[::-1] if reverse else values,
+			unit=new_unit,
+			is_sorted=self.is_sorted,
+		)

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

@@ -31,7 +31,9 @@ log = logger.get(__name__)
 
 @dataclasses.dataclass(frozen=True, kw_only=True)
 class InfoFlow:
-	# Dimension Information
+	####################
+	# - Covariant Input
+	####################
 	dim_names: list[str] = dataclasses.field(default_factory=list)
 	dim_idx: dict[str, ArrayFlow | LazyArrayRangeFlow] = dataclasses.field(
 		default_factory=dict
@@ -67,6 +69,9 @@ class InfoFlow:
 			for dim_idx in self.dim_idx.values()
 		]
 
+	####################
+	# - Contravariant Output
+	####################
 	# Output Information
 	## TODO: Add PhysicalType
 	output_name: str = dataclasses.field(default_factory=list)
@@ -94,6 +99,28 @@ class InfoFlow:
 	####################
 	# - Methods
 	####################
+	def replace_dim(
+		self, old_dim_name: str, new_dim_idx: tuple[str, ArrayFlow | LazyArrayRangeFlow]
+	) -> typ.Self:
+		return InfoFlow(
+			# Dimensions
+			dim_names=[
+				dim_name if dim_name != old_dim_name else new_dim_idx[0]
+				for dim_name in self.dim_names
+			],
+			dim_idx={
+				(dim_name if dim_name != old_dim_name else new_dim_idx[0]): (
+					dim_idx if dim_name != old_dim_name else new_dim_idx[1]
+				)
+				for dim_name, dim_idx in self.dim_idx.items()
+			},
+			# Outputs
+			output_name=self.output_name,
+			output_shape=self.output_shape,
+			output_mathtype=self.output_mathtype,
+			output_unit=self.output_unit,
+		)
+
 	def rescale_dim_idxs(self, new_dim_idxs: dict[str, LazyArrayRangeFlow]) -> typ.Self:
 		return InfoFlow(
 			# Dimensions

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

@@ -268,6 +268,32 @@ class LazyArrayRangeFlow:
 	####################
 	# - Bound Operations
 	####################
+	def rescale(
+		self, rescale_func, reverse: bool = False, new_unit: spux.Unit | None = None
+	) -> typ.Self:
+		new_pre_start = self.start if not reverse else self.stop
+		new_pre_stop = self.stop if not reverse else self.start
+
+		new_start = rescale_func(new_pre_start * self.unit)
+		new_stop = rescale_func(new_pre_stop * self.unit)
+
+		return LazyArrayRangeFlow(
+			start=(
+				spux.scale_to_unit(new_start, new_unit)
+				if new_unit is not None
+				else new_start
+			),
+			stop=(
+				spux.scale_to_unit(new_stop, new_unit)
+				if new_unit is not None
+				else new_stop
+			),
+			steps=self.steps,
+			scaling=self.scaling,
+			unit=new_unit,
+			symbols=self.symbols,
+		)
+
 	def rescale_bounds(
 		self,
 		rescale_func: typ.Callable[

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

@@ -566,7 +566,9 @@ class ExtractDataNode(base.MaxwellSimNode):
 				}
 				| {
 					c: ct.ArrayFlow(
-						values=xarr.get_index(c).values, unit=spu.radian, is_sorted=True
+						values=xarr.get_index(c).values,
+						unit=spu.radian,
+						is_sorted=True,
 					)
 					for c in ['r', 'theta', 'phi']
 				}

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

@@ -14,19 +14,19 @@
 # You should have received a copy of the GNU Affero General Public License
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
-from . import filter_math, map_math, operate_math  # , #reduce_math, transform_math
+from . import filter_math, map_math, operate_math, transform_math
 
 BL_REGISTER = [
 	*operate_math.BL_REGISTER,
 	*map_math.BL_REGISTER,
 	*filter_math.BL_REGISTER,
 	# *reduce_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,
-	# **transform_math.BL_NODES,
+	**transform_math.BL_NODES,
 }

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

@@ -48,7 +48,7 @@ class FilterOperation(enum.StrEnum):
 	Pin = enum.auto()
 	Swap = enum.auto()
 
-	# Interpret
+	# Fold
 	DimToVec = enum.auto()
 	DimsToMat = enum.auto()
 

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

@@ -439,7 +439,7 @@ class MapMathNode(base.MaxwellSimNode):
 
 	@bl_cache.cached_bl_property()
 	def expr_output_shape(self) -> ct.InfoFlow | None:
-		info = self._compute_input('Expr', kind=ct.FlowKind.Info)
+		info = self._compute_input('Expr', kind=ct.FlowKind.Info, optional=True)
 		has_info = not ct.FlowSignal.check(info)
 		if has_info:
 			return info.output_shape
@@ -491,9 +491,9 @@ class MapMathNode(base.MaxwellSimNode):
 		# Compute Sympy Function
 		## -> The operation enum directly provides the appropriate function.
 		if has_expr_value and operation is not None:
-			operation.sp_func(expr)
+			return operation.sp_func(expr)
 
-		return ct.Flowsignal.FlowPending
+		return ct.FlowSignal.FlowPending
 
 	@events.computes_output_socket(
 		'Expr',
@@ -529,7 +529,7 @@ class MapMathNode(base.MaxwellSimNode):
 		input_sockets={'Expr'},
 		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:
 		operation = props['operation']
 		info = input_sockets['Expr']
 
@@ -546,8 +546,11 @@ class MapMathNode(base.MaxwellSimNode):
 		input_sockets={'Expr'},
 		input_socket_kinds={'Expr': ct.FlowKind.Params},
 	)
-	def compute_data_params(self, input_sockets: dict) -> ct.ParamsFlow | ct.FlowSignal:
-		return input_sockets['Expr']
+	def compute_params(self, input_sockets: dict) -> ct.ParamsFlow | ct.FlowSignal:
+		has_params = not ct.FlowSignal.check(input_sockets['Expr'])
+		if has_params:
+			return input_sockets['Expr']
+		return ct.FlowSignal.FlowPending
 
 
 ####################

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

@@ -20,9 +20,12 @@ import enum
 import typing as typ
 
 import bpy
-import jax
+import jax.numpy as jnp
+import sympy as sp
+import sympy.physics.units as spu
 
-from blender_maxwell.utils import bl_cache, logger
+from blender_maxwell.utils import bl_cache, logger, sci_constants, sim_symbols
+from blender_maxwell.utils import extra_sympy_units as spux
 
 from .... import contracts as ct
 from .... import sockets
@@ -31,6 +34,164 @@ from ... import base, events
 log = logger.get(__name__)
 
 
+####################
+# - Operation Enum
+####################
+class TransformOperation(enum.StrEnum):
+	"""Valid operations for the `MapMathNode`.
+
+	Attributes:
+		FreqToVacWL: Transform frequency axes to be indexed by vacuum wavelength.
+		VacWLToFreq: Transform vacuum wavelength axes to be indexed by frequency.
+		FFT: Compute the fourier transform of the input expression.
+		InvFFT: Compute the inverse fourier transform of the input expression.
+	"""
+
+	# Index
+	FreqToVacWL = enum.auto()
+	VacWLToFreq = enum.auto()
+	# Fourier
+	FFT1D = enum.auto()
+	InvFFT1D = enum.auto()
+	# Affine
+	## TODO
+
+	####################
+	# - UI
+	####################
+	@staticmethod
+	def to_name(value: typ.Self) -> str:
+		TO = TransformOperation
+		return {
+			# By Number
+			TO.FreqToVacWL: '𝑓 → λᵥ',
+			TO.VacWLToFreq: 'λᵥ → 𝑓',
+			TO.FFT1D: 't → 𝑓',
+			TO.InvFFT1D: '𝑓 → t',
+		}[value]
+
+	@staticmethod
+	def to_icon(value: typ.Self) -> str:
+		return ''
+
+	def bl_enum_element(self, i: int) -> ct.BLEnumElement:
+		TO = TransformOperation
+		return (
+			str(self),
+			TO.to_name(self),
+			TO.to_name(self),
+			TO.to_icon(self),
+			i,
+		)
+
+	####################
+	# - Ops from Shape
+	####################
+	@staticmethod
+	def by_element_shape(info: ct.InfoFlow) -> list[typ.Self]:
+		TO = TransformOperation
+		operations = []
+
+		# Freq <-> VacWL
+		for dim_name in info.dim_names:
+			if info.dim_physical_types[dim_name] == spux.PhysicalType.Freq:
+				operations.append(TO.FreqToVacWL)
+
+			if info.dim_physical_types[dim_name] == spux.PhysicalType.Freq:
+				operations.append(TO.VacWLToFreq)
+
+		# 1D Fourier
+		if info.dim_names:
+			last_physical_type = info.dim_physical_types[info.dim_names[-1]]
+			if last_physical_type == spux.PhysicalType.Time:
+				operations.append(TO.FFT1D)
+			if last_physical_type == spux.PhysicalType.Freq:
+				operations.append(TO.InvFFT1D)
+
+		return operations
+
+	####################
+	# - Function Properties
+	####################
+	@property
+	def sp_func(self):
+		TO = TransformOperation
+		return {
+			# Index
+			TO.FreqToVacWL: lambda expr: expr,
+			TO.VacWLToFreq: lambda expr: expr,
+			# Fourier
+			TO.FFT1D: lambda expr: sp.fourier_transform(
+				expr, sim_symbols.t, sim_symbols.freq
+			),
+			TO.InvFFT1D: lambda expr: sp.fourier_transform(
+				expr, sim_symbols.freq, sim_symbols.t
+			),
+		}[self]
+
+	@property
+	def jax_func(self):
+		TO = TransformOperation
+		return {
+			# Index
+			TO.FreqToVacWL: lambda expr: expr,
+			TO.VacWLToFreq: lambda expr: expr,
+			# Fourier
+			TO.FFT1D: lambda expr: jnp.fft(expr),
+			TO.InvFFT1D: lambda expr: jnp.ifft(expr),
+		}[self]
+
+	def transform_info(self, info: ct.InfoFlow | None) -> ct.InfoFlow | None:
+		TO = TransformOperation
+		if not info.dim_names:
+			return None
+		return {
+			# Index
+			TO.FreqToVacWL: lambda: info.replace_dim(
+				(f_dim := info.dim_names[-1]),
+				[
+					'wl',
+					info.dim_idx[f_dim].rescale(
+						lambda el: sci_constants.vac_speed_of_light / el,
+						reverse=True,
+						new_unit=spu.nanometer,
+					),
+				],
+			),
+			TO.VacWLToFreq: lambda: info.replace_dim(
+				(wl_dim := info.dim_names[-1]),
+				[
+					'f',
+					info.dim_idx[wl_dim].rescale(
+						lambda el: sci_constants.vac_speed_of_light / el,
+						reverse=True,
+						new_unit=spux.THz,
+					),
+				],
+			),
+			# Fourier
+			TO.FFT1D: lambda: info.replace_dim(
+				info.dim_names[-1],
+				[
+					'f',
+					ct.LazyArrayRangeFlow(start=0, stop=sp.oo, steps=0, unit=spu.hertz),
+				],
+			),
+			TO.InvFFT1D: info.replace_dim(
+				info.dim_names[-1],
+				[
+					't',
+					ct.LazyArrayRangeFlow(
+						start=0, stop=sp.oo, steps=0, unit=spu.second
+					),
+				],
+			),
+		}.get(self, lambda: info)()
+
+
+####################
+# - Node
+####################
 class TransformMathNode(base.MaxwellSimNode):
 	r"""Applies a function to the array as a whole, with arbitrary results.
 
@@ -48,125 +209,153 @@ class TransformMathNode(base.MaxwellSimNode):
 	bl_label = 'Transform Math'
 
 	input_sockets: typ.ClassVar = {
-		'Data': sockets.DataSocketDef(format='jax'),
-	}
-	input_socket_sets: typ.ClassVar = {
-		'Fourier': {},
-		'Affine': {},
-		'Convolve': {},
+		'Expr': sockets.ExprSocketDef(active_kind=ct.FlowKind.LazyValueFunc),
 	}
 	output_sockets: typ.ClassVar = {
-		'Data': sockets.DataSocketDef(format='jax'),
+		'Expr': sockets.ExprSocketDef(active_kind=ct.FlowKind.LazyValueFunc),
 	}
 
 	####################
 	# - Properties
 	####################
-	operation: enum.StrEnum = bl_cache.BLField(
-		enum_cb=lambda self, _: self.search_operations()
+	@events.on_value_changed(
+		socket_name={'Expr'},
+		input_sockets={'Expr'},
+		input_socket_kinds={'Expr': ct.FlowKind.Info},
+		input_sockets_optional={'Expr': True},
+	)
+	def on_input_exprs_changed(self, input_sockets) -> None:  # noqa: D102
+		has_info = not ct.FlowSignal.check(input_sockets['Expr'])
+
+		info_pending = ct.FlowSignal.check_single(
+			input_sockets['Expr'], ct.FlowSignal.FlowPending
+		)
+
+		if has_info and not info_pending:
+			self.expr_info = bl_cache.Signal.InvalidateCache
+
+	@bl_cache.cached_bl_property()
+	def expr_info(self) -> ct.InfoFlow | None:
+		info = self._compute_input('Expr', kind=ct.FlowKind.Info, optional=True)
+		has_info = not ct.FlowSignal.check(info)
+		if has_info:
+			return info
+
+		return None
+
+	operation: TransformOperation = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_operations(),
+		cb_depends_on={'expr_info'},
 	)
 
 	def search_operations(self) -> list[ct.BLEnumElement]:
-		if self.active_socket_set == 'Fourier':  # noqa: SIM114
-			items = []
-		elif self.active_socket_set == 'Affine':  # noqa: SIM114
-			items = []
-		elif self.active_socket_set == 'Convolve':
-			items = []
-		else:
-			msg = f'Active socket set {self.active_socket_set} is unknown'
-			raise RuntimeError(msg)
-
-		return [(*item, '', i) for i, item in enumerate(items)]
+		if self.expr_info is not None:
+			return [
+				operation.bl_enum_element(i)
+				for i, operation in enumerate(
+					TransformOperation.by_element_shape(self.expr_info)
+				)
+			]
+		return []
 
 	def draw_props(self, _: bpy.types.Context, layout: bpy.types.UILayout) -> None:
 		layout.prop(self, self.blfields['operation'], text='')
 
 	####################
-	# - Events
+	# - UI
 	####################
-	@events.on_value_changed(
-		prop_name='active_socket_set',
-	)
-	def on_socket_set_changed(self):
-		self.operation = bl_cache.Signal.ResetEnumItems
+	def draw_label(self):
+		if self.operation is not None:
+			return 'Transform: ' + TransformOperation.to_name(self.operation)
+
+		return self.bl_label
+
+	def draw_props(self, _: bpy.types.Context, layout: bpy.types.UILayout) -> None:
+		layout.prop(self, self.blfields['operation'], text='')
 
 	####################
 	# - Compute: LazyValueFunc / Array
 	####################
 	@events.computes_output_socket(
-		'Data',
-		kind=ct.FlowKind.LazyValueFunc,
-		props={'active_socket_set', 'operation'},
-		input_sockets={'Data'},
-		input_socket_kinds={
-			'Data': ct.FlowKind.LazyValueFunc,
-		},
+		'Expr',
+		kind=ct.FlowKind.Value,
+		props={'operation'},
+		input_sockets={'Expr'},
 	)
-	def compute_data(self, props: dict, input_sockets: dict):
-		has_data = not ct.FlowSignal.check(input_sockets['Data'])
-		if not has_data or props['operation'] == 'NONE':
-			return ct.FlowSignal.FlowPending
+	def compute_value(self, props, input_sockets) -> ct.ValueFlow | ct.FlowSignal:
+		operation = props['operation']
+		expr = input_sockets['Expr']
 
-		mapping_func: typ.Callable[[jax.Array], jax.Array] = {
-			'Fourier': {},
-			'Affine': {},
-			'Convolve': {},
-		}[props['active_socket_set']][props['operation']]
+		has_expr_value = not ct.FlowSignal.check(expr)
 
-		# Compose w/Lazy Root Function Data
-		return input_sockets['Data'].compose_within(
-			mapping_func,
-			supports_jax=True,
-		)
+		# Compute Sympy Function
+		## -> The operation enum directly provides the appropriate function.
+		if has_expr_value and operation is not None:
+			return operation.sp_func(expr)
+
+		return ct.Flowsignal.FlowPending
 
 	@events.computes_output_socket(
-		'Data',
-		kind=ct.FlowKind.Array,
-		output_sockets={'Data'},
-		output_socket_kinds={
-			'Data': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Params},
+		'Expr',
+		kind=ct.FlowKind.LazyValueFunc,
+		props={'operation'},
+		input_sockets={'Expr'},
+		input_socket_kinds={
+			'Expr': ct.FlowKind.LazyValueFunc,
 		},
 	)
-	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]
+	def compute_func(
+		self, props, input_sockets
+	) -> ct.LazyValueFuncFlow | ct.FlowSignal:
+		operation = props['operation']
+		expr = input_sockets['Expr']
 
-		if all(not ct.FlowSignal.check(inp) for inp in [lazy_value_func, params]):
-			return ct.ArrayFlow(
-				values=lazy_value_func.func_jax(
-					*params.func_args, **params.func_kwargs
-				),
-				unit=None,
+		has_expr = not ct.FlowSignal.check(expr)
+
+		if has_expr and operation is not None:
+			return expr.compose_within(
+				operation.jax_func,
+				supports_jax=True,
 			)
-
 		return ct.FlowSignal.FlowPending
 
 	####################
-	# - Compute Auxiliary: Info / Params
+	# - FlowKind.Info|Params
 	####################
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.Info,
-		props={'active_socket_set', 'operation'},
-		input_sockets={'Data'},
-		input_socket_kinds={'Data': ct.FlowKind.Info},
+		props={'operation'},
+		input_sockets={'Expr'},
+		input_socket_kinds={'Expr': ct.FlowKind.Info},
 	)
-	def compute_data_info(self, props: dict, input_sockets: dict) -> ct.InfoFlow:
-		info = input_sockets['Data']
-		if ct.FlowSignal.check(info):
-			return ct.FlowSignal.FlowPending
+	def compute_info(
+		self, props: dict, input_sockets: dict
+	) -> ct.InfoFlow | typ.Literal[ct.FlowSignal.FlowPending]:
+		operation = props['operation']
+		info = input_sockets['Expr']
 
-		return info
+		has_info = not ct.FlowSignal.check(info)
+
+		if has_info and operation is not None:
+			transformed_info = operation.transform_info(info)
+			if transformed_info is None:
+				return ct.FlowSignal.FlowPending
+			return transformed_info
+
+		return ct.FlowSignal.FlowPending
 
 	@events.computes_output_socket(
-		'Data',
+		'Expr',
 		kind=ct.FlowKind.Params,
-		input_sockets={'Data'},
-		input_socket_kinds={'Data': ct.FlowKind.Params},
+		input_sockets={'Expr'},
+		input_socket_kinds={'Expr': ct.FlowKind.Params},
 	)
-	def compute_data_params(self, input_sockets: dict) -> ct.ParamsFlow | ct.FlowSignal:
-		return input_sockets['Data']
+	def compute_params(self, input_sockets: dict) -> ct.ParamsFlow | ct.FlowSignal:
+		has_params = not ct.FlowSignal.check(input_sockets['Expr'])
+		if has_params:
+			return input_sockets['Expr']
+		return ct.FlowSignal.FlowPending
 
 
 ####################

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

@@ -225,8 +225,24 @@ class VizNode(base.MaxwellSimNode):
 	#####################
 	## - Properties
 	#####################
+	@events.on_value_changed(
+		socket_name={'Expr'},
+		input_sockets={'Expr'},
+		input_socket_kinds={'Expr': ct.FlowKind.Info},
+		input_sockets_optional={'Expr': True},
+	)
+	def on_input_exprs_changed(self, input_sockets) -> None:  # noqa: D102
+		has_info = not ct.FlowSignal.check(input_sockets['Expr'])
+
+		info_pending = ct.FlowSignal.check_single(
+			input_sockets['Expr'], ct.FlowSignal.FlowPending
+		)
+
+		if has_info and not info_pending:
+			self.expr_info = bl_cache.Signal.InvalidateCache
+
 	@bl_cache.cached_bl_property()
-	def input_info(self) -> ct.InfoFlow | None:
+	def expr_info(self) -> ct.InfoFlow | None:
 		info = self._compute_input('Expr', kind=ct.FlowKind.Info)
 		if not ct.FlowSignal.check(info):
 			return info
@@ -235,7 +251,7 @@ class VizNode(base.MaxwellSimNode):
 
 	viz_mode: enum.StrEnum = bl_cache.BLField(
 		enum_cb=lambda self, _: self.search_viz_modes(),
-		cb_depends_on={'input_info'},
+		cb_depends_on={'expr_info'},
 	)
 	viz_target: enum.StrEnum = bl_cache.BLField(
 		enum_cb=lambda self, _: self.search_targets(),
@@ -251,7 +267,7 @@ class VizNode(base.MaxwellSimNode):
 	## - Searchers
 	#####################
 	def search_viz_modes(self) -> list[ct.BLEnumElement]:
-		if self.input_info is not None:
+		if self.expr_info is not None:
 			return [
 				(
 					viz_mode,
@@ -260,7 +276,7 @@ class VizNode(base.MaxwellSimNode):
 					VizMode.to_icon(viz_mode),
 					i,
 				)
-				for i, viz_mode in enumerate(VizMode.valid_modes_for(self.input_info))
+				for i, viz_mode in enumerate(VizMode.valid_modes_for(self.expr_info))
 			]
 
 		return []
@@ -284,6 +300,12 @@ class VizNode(base.MaxwellSimNode):
 	#####################
 	## - UI
 	#####################
+	def draw_label(self):
+		if self.viz_mode is not None:
+			return 'Viz: ' + self.sim_node_name
+
+		return self.bl_label
+
 	def draw_props(self, _: bpy.types.Context, col: bpy.types.UILayout):
 		col.prop(self, self.blfields['viz_mode'], text='')
 		col.prop(self, self.blfields['viz_target'], text='')
@@ -338,11 +360,23 @@ class VizNode(base.MaxwellSimNode):
 		elif self.loose_input_sockets:
 			self.loose_input_sockets = {}
 
-		self.input_info = bl_cache.Signal.InvalidateCache
-
 	#####################
 	## - Plotting
 	#####################
+	@events.computes_output_socket(
+		'Preview',
+		kind=ct.FlowKind.Value,
+		# Loaded
+		props={'viz_mode', 'viz_target', 'colormap'},
+		input_sockets={'Expr'},
+		input_socket_kinds={
+			'Expr': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Info, ct.FlowKind.Params}
+		},
+		all_loose_input_sockets=True,
+	)
+	def compute_dummy_value(self, props, input_sockets, loose_input_sockets):
+		return ct.FlowSignal.NoFlow
+
 	@events.on_show_plot(
 		managed_objs={'plot'},
 		props={'viz_mode', 'viz_target', 'colormap'},

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

@@ -787,7 +787,7 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 		altered_socket_kinds = set()
 
 		# Invalidate Caches on DataChanged
-		if event == ct.FlowEvent.DataChanged:
+		if event is ct.FlowEvent.DataChanged:
 			input_socket_name = socket_name  ## Trigger direction is forwards
 
 			# Invalidate Input Socket Cache
@@ -861,8 +861,18 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 			# )
 			event_method(self)
 
+		# DataChanged Propagation Stop: No Altered Socket Kinds
+		## -> If no FlowKinds were altered, then propagation makes no sense.
+		## -> Semantically, **nothing has changed** == no DataChanged!
+		if event is ct.FlowEvent.DataChanged and not altered_socket_kinds:
+			return
+
+		# Constrain ShowPlot to First Node: Workaround
+		if event is ct.FlowEvent.ShowPlot:
+			return
+
 		# Propagate Event to All Sockets in "Trigger Direction"
-		## The trigger chain goes node/socket/node/socket/...
+		## -> The trigger chain goes node/socket/socket/node/socket/...
 		if not stop_propagation:
 			direc = ct.FlowEvent.flow_direction[event]
 			triggered_sockets = self._bl_sockets(direc=direc)

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/outputs/viewer.py

@@ -139,8 +139,10 @@ class ViewerNode(base.MaxwellSimNode):
 
 		# Unset Plot if Nothing Plotted
 		with node_tree.replot():
-			if props['auto_plot']:
-				self.trigger_event(ct.FlowEvent.ShowPlot)
+			if props['auto_plot'] and self.inputs['Any'].is_linked:
+				self.inputs['Any'].links[0].from_socket.node.trigger_event(
+					ct.FlowEvent.ShowPlot
+				)
 
 	@events.on_value_changed(
 		socket_name='Any',

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/sources/temporal_shape.py

@@ -82,8 +82,8 @@ class TemporalShapeNode(base.MaxwellSimNode):
 				default_steps=100,
 			),
 			'Envelope': sockets.ExprSocketDef(
-				default_symbols=[sim_symbols.t_ps],
-				default_value=10 * sim_symbols.t_ps.sp_symbol,
+				default_symbols=[sim_symbols.t],
+				default_value=10 * sim_symbols.t.sp_symbol,
 			),
 		},
 	}

src/blender_maxwell/utils/bl_instance.py

@@ -251,7 +251,8 @@ class BLInstance:
 			if prop_name in deps:
 				for dst_prop_name in deps[prop_name]:
 					log.debug(
-						'Property %s is invalidating %s',
+						'%s: "%s" is invalidating "%s"',
+						self.bl_label,
 						prop_name,
 						dst_prop_name,
 					)

src/blender_maxwell/utils/sim_symbols.py

@@ -204,9 +204,9 @@ class CommonSimSymbol(enum.StrEnum):
 	"""
 
 	X = enum.auto()
-	TimePS = enum.auto()
-	WavelengthNM = enum.auto()
-	FrequencyTHZ = enum.auto()
+	Time = enum.auto()
+	Wavelength = enum.auto()
+	Frequency = enum.auto()
 
 	@staticmethod
 	def to_name(v: typ.Self) -> str:
@@ -241,9 +241,9 @@ class CommonSimSymbol(enum.StrEnum):
 		CSS = CommonSimSymbol
 		return {
 			CSS.X: SSN.LowerX,
-			CSS.TimePS: SSN.LowerT,
-			CSS.WavelengthNM: SSN.Wavelength,
-			CSS.FrequencyTHZ: SSN.Frequency,
+			CSS.Time: SSN.LowerT,
+			CSS.Wavelength: SSN.Wavelength,
+			CSS.Frequency: SSN.Frequency,
 		}[self]
 
 	@property
@@ -260,7 +260,7 @@ class CommonSimSymbol(enum.StrEnum):
 				interval_inf=(True, True),
 				interval_closed=(False, False),
 			),
-			CSS.TimePS: SimSymbol(
+			CSS.Time: SimSymbol(
 				sim_node_name=self.sim_symbol_name,
 				mathtype=spux.MathType.Real,
 				physical_type=spux.PhysicalType.Time,
@@ -269,7 +269,7 @@ class CommonSimSymbol(enum.StrEnum):
 				interval_inf=(False, True),
 				interval_closed=(True, False),
 			),
-			CSS.WavelengthNM: SimSymbol(
+			CSS.Wavelength: SimSymbol(
 				sim_node_name=self.sim_symbol_name,
 				mathtype=spux.MathType.Real,
 				physical_type=spux.PhysicalType.Length,
@@ -278,11 +278,10 @@ class CommonSimSymbol(enum.StrEnum):
 				interval_inf=(False, True),
 				interval_closed=(False, False),
 			),
-			CSS.FrequencyTHZ: SimSymbol(
+			CSS.Frequency: SimSymbol(
 				sim_node_name=self.sim_symbol_name,
 				mathtype=spux.MathType.Real,
 				physical_type=spux.PhysicalType.Freq,
-				## TODO: Unit of THz
 				interval_finite=(0, sys.float_info.max),
 				interval_inf=(False, True),
 				interval_closed=(False, False),
@@ -294,6 +293,6 @@ class CommonSimSymbol(enum.StrEnum):
 # - Selected Direct Access
 ####################
 x = CommonSimSymbol.X.sim_symbol
-t_ps = CommonSimSymbol.TimePS.sim_symbol
-wl_nm = CommonSimSymbol.WavelengthNM.sim_symbol
-freq_thz = CommonSimSymbol.FrequencyTHZ.sim_symbol
+t = CommonSimSymbol.Time.sim_symbol
+wl = CommonSimSymbol.Wavelength.sim_symbol
+freq = CommonSimSymbol.Frequency.sim_symbol