feat: implemented data loading w/new math ops

We implemented a node to load various kinds of data, notably `.npy`,
`.txt`, `.txt.gz`, and `.csv`. The `DataFileImporterNode` really should
expose some settings for setting name/mathtype/physical type/unit of
each unit, and/or treating a column from 2D data as index coordinates.
But the nuances of doing this in a manner general enough to deal with
!=2D data was a lot, and we needed similar abilities in the general math
system anyway.

So, we delved back into the `FilterMathNode` and a little into the
`TransformMathNode`. Fundamentally, a few difficult operations came out
of this:

- Filter:SliceIdx: Slice an array using the usual syntax, as baked into the
  function.
- Filter:PinIdx: Pin an axis by its actual index.
- Filter:SetDim: Set the `InfoFlow` index coordinates of an axis to a specific,
  loose-socket provided 1D array, and use a common symbol to set the
  name+physical type (and allow specifying an appropriate unit).
- Transform:IntDimToComplex: Fold a last length-2 integer-indexed axis
  into a real output type, which removes the dimension and produces a
  complex output type. Essentially, this is equivalent to folding it as
  a vector and treating the `R^2` numbers as real/imaginary, except this
  is more explicit.

By combining all of these, we managed to process and constrain the medium data to
be a well-suited, unit-aware (**though not on the output (yet)**) `wl->C` tensor.
In particular, the slicing is nice for avoiding discontinuities.

Workflow-wise, we'll see how important these are / what else we might
want. Also, it turns out Blender's text editor is really quite nice for
light data-text viewing.

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

@@ -122,7 +122,6 @@ class ArrayFlow:
 			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)
 
@@ -132,3 +131,13 @@ class ArrayFlow:
 			unit=new_unit,
 			is_sorted=self.is_sorted,
 		)
+
+	def __getitem__(self, subscript: slice):
+		if isinstance(subscript, slice):
+			return ArrayFlow(
+				values=self.values[subscript],
+				unit=self.unit,
+				is_sorted=self.is_sorted,
+			)
+
+		raise NotImplementedError

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

@@ -39,6 +39,16 @@ class InfoFlow:
 		default_factory=dict
 	)  ## TODO: Rename to dim_idxs
 
+	@functools.cached_property
+	def dim_has_coords(self) -> dict[str, int]:
+		return {
+			dim_name: not (
+				isinstance(dim_idx, LazyArrayRangeFlow)
+				and (dim_idx.start.is_infinite or dim_idx.stop.is_infinite)
+			)
+			for dim_name, dim_idx in self.dim_idx.items()
+		}
+
 	@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()}
@@ -99,9 +109,29 @@ class InfoFlow:
 	####################
 	# - Methods
 	####################
+	def slice_dim(self, dim_name: str, slice_tuple: tuple[int, int, int]) -> typ.Self:
+		return InfoFlow(
+			# Dimensions
+			dim_names=self.dim_names,
+			dim_idx={
+				_dim_name: (
+					dim_idx
+					if _dim_name != dim_name
+					else dim_idx[slice_tuple[0] : slice_tuple[1] : slice_tuple[2]]
+				)
+				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 replace_dim(
 		self, old_dim_name: str, new_dim_idx: tuple[str, ArrayFlow | LazyArrayRangeFlow]
 	) -> typ.Self:
+		"""Replace a dimension (and its indexing) with a new name and index array/range."""
 		return InfoFlow(
 			# Dimensions
 			dim_names=[
@@ -122,6 +152,7 @@ class InfoFlow:
 		)
 
 	def rescale_dim_idxs(self, new_dim_idxs: dict[str, LazyArrayRangeFlow]) -> typ.Self:
+		"""Replace several dimensional indices with new index arrays/ranges."""
 		return InfoFlow(
 			# Dimensions
 			dim_names=self.dim_names,
@@ -156,7 +187,7 @@ class InfoFlow:
 		)
 
 	def swap_dimensions(self, dim_0_name: str, dim_1_name: str) -> typ.Self:
-		"""Delete a dimension."""
+		"""Swap the position of two dimensions."""
 
 		# Compute Swapped Dimension Name List
 		def name_swapper(dim_name):
@@ -181,7 +212,7 @@ class InfoFlow:
 		)
 
 	def set_output_mathtype(self, output_mathtype: spux.MathType) -> typ.Self:
-		"""Set the MathType of a particular output name."""
+		"""Set the MathType of the output."""
 		return InfoFlow(
 			dim_names=self.dim_names,
 			dim_idx=self.dim_idx,
@@ -198,6 +229,7 @@ class InfoFlow:
 		collapsed_mathtype: spux.MathType,
 		collapsed_unit: spux.Unit,
 	) -> typ.Self:
+		"""Replace the (scalar) output with the given corrected values."""
 		return InfoFlow(
 			# Dimensions
 			dim_names=self.dim_names,

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

@@ -418,7 +418,11 @@ class LazyArrayRangeFlow:
 		self,
 		symbol_values: dict[spux.Symbol, typ.Any] = MappingProxyType({}),
 	) -> ArrayFlow | LazyValueFuncFlow:
-		return (self.realize_stop() - self.realize_start()) / self.steps
+		raw_step_size = (self.realize_stop() - self.realize_start() + 1) / self.steps
+
+		if self.mathtype is spux.MathType.Integer and raw_step_size.is_integer():
+			return int(raw_step_size)
+		return raw_step_size
 
 	def realize(
 		self,
@@ -463,3 +467,28 @@ class LazyArrayRangeFlow:
 	@functools.cached_property
 	def realize_array(self) -> ArrayFlow:
 		return self.realize()
+
+	def __getitem__(self, subscript: slice):
+		if isinstance(subscript, slice) and self.scaling == ScalingMode.Lin:
+			# Parse Slice
+			start = subscript.start if subscript.start is not None else 0
+			stop = subscript.stop if subscript.stop is not None else self.steps
+			step = subscript.step if subscript.step is not None else 1
+
+			slice_steps = (stop - start + step - 1) // step
+
+			# Compute New Start/Stop
+			step_size = self.realize_step_size()
+			new_start = step_size * start
+			new_stop = new_start + step_size * slice_steps
+
+			return LazyArrayRangeFlow(
+				start=sp.S(new_start),
+				stop=sp.S(new_stop),
+				steps=slice_steps,
+				scaling=self.scaling,
+				unit=self.unit,
+				symbols=self.symbols,
+			)
+
+		raise NotImplementedError

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

@@ -58,9 +58,11 @@ class ParamsFlow:
 
 		## TODO: MutableDenseMatrix causes error with 'in' check bc it isn't hashable.
 		return [
+			(
 				spux.scale_to_unit_system(arg, unit_system, use_jax_array=True)
 				if arg not in symbol_values
 				else symbol_values[arg]
+			)
 			for arg in self.func_args
 		]
 

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

@@ -20,9 +20,11 @@ import enum
 import typing as typ
 
 import bpy
+import jax.lax as jlax
 import jax.numpy as jnp
+import sympy as sp
 
-from blender_maxwell.utils import bl_cache, logger
+from blender_maxwell.utils import bl_cache, logger, sim_symbols
 from blender_maxwell.utils import extra_sympy_units as spux
 
 from .... import contracts as ct
@@ -43,64 +45,201 @@ class FilterOperation(enum.StrEnum):
 		Swap: Swap the positions of two dimensions.
 	"""
 
-	# Dimensions
+	# Slice
+	SliceIdx = enum.auto()
+
+	# Pin
 	PinLen1 = enum.auto()
 	Pin = enum.auto()
+	PinIdx = enum.auto()
+
+	# Reinterpret
 	Swap = enum.auto()
+	SetDim = enum.auto()
 
-	# Fold
-	DimToVec = enum.auto()
-	DimsToMat = enum.auto()
-
+	####################
+	# - UI
+	####################
 	@staticmethod
 	def to_name(value: typ.Self) -> str:
 		FO = FilterOperation
 		return {
-			# Dimensions
+			# Slice
+			FO.SliceIdx: 'a[...]',
+			# Pin
 			FO.PinLen1: 'pinₐ =1',
 			FO.Pin: 'pinₐ ≈v',
+			FO.PinIdx: 'pinₐ =a[v]',
+			# Reinterpret
 			FO.Swap: 'a₁ ↔ a₂',
-			# Interpret
-			FO.DimToVec: '→ Vector',
-			FO.DimsToMat: '→ Matrix',
+			FO.SetDim: 'setₐ =v',
 		}[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 bl_enum_element(self, i: int) -> ct.BLEnumElement:
+		FO = FilterOperation
+		return (
+			str(self),
+			FO.to_name(self),
+			FO.to_name(self),
+			FO.to_icon(self),
+			i,
 		)
 
-	def jax_func(self, axis_0: int | None, axis_1: int | None):
+	####################
+	# - Ops from Info
+	####################
+	@staticmethod
+	def by_info(info: ct.InfoFlow) -> list[typ.Self]:
+		FO = FilterOperation
+		operations = []
+
+		# Slice
+		if info.dim_names:
+			operations.append(FO.SliceIdx)
+
+		# Pin
+		## PinLen1
+		## -> There must be a dimension with length 1.
+		if 1 in list(info.dim_lens.values()):
+			operations.append(FO.PinLen1)
+
+		## Pin | PinIdx
+		## -> There must be a dimension, full stop.
+		if info.dim_names:
+			operations += [FO.Pin, FO.PinIdx]
+
+		# Reinterpret
+		## Swap
+		## -> There must be at least two dimensions.
+		if len(info.dim_names) >= 2:  # noqa: PLR2004
+			operations.append(FO.Swap)
+
+		## SetDim
+		## -> There must be a dimension to correct.
+		if info.dim_names:
+			operations.append(FO.SetDim)
+
+		return operations
+
+	####################
+	# - Computed Properties
+	####################
+	@property
+	def func_args(self) -> list[spux.MathType]:
+		FO = FilterOperation
 		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),
+			# Pin
+			FO.Pin: [spux.MathType.Integer],
+			FO.PinIdx: [spux.MathType.Integer],
+		}.get(self, [])
+
+	####################
+	# - Methods
+	####################
+	@property
+	def num_dim_inputs(self) -> None:
+		FO = FilterOperation
+		return {
+			# Slice
+			FO.SliceIdx: 1,
+			# Pin
+			FO.PinLen1: 1,
+			FO.Pin: 1,
+			FO.PinIdx: 1,
+			# Reinterpret
+			FO.Swap: 2,
+			FO.SetDim: 1,
 		}[self]
 
-	def transform_info(self, info: ct.InfoFlow, dim_0: str, dim_1: str):
+	def valid_dims(self, info: ct.InfoFlow) -> list[typ.Self]:
+		FO = FilterOperation
+		match self:
+			case FO.SliceIdx:
+				return info.dim_names
+
+			# PinLen1: Only allow dimensions with length=1.
+			case FO.PinLen1:
+				return [
+					dim_name
+					for dim_name in info.dim_names
+					if info.dim_lens[dim_name] == 1
+				]
+
+			# Pin: Only allow dimensions with known indexing.
+			case FO.Pin:
+				return [
+					dim_name
+					for dim_name in info.dim_names
+					if info.dim_has_coords[dim_name] != 0
+				]
+
+			case FO.PinIdx | FO.Swap:
+				return info.dim_names
+
+			case FO.SetDim:
+				return [
+					dim_name
+					for dim_name in info.dim_names
+					if info.dim_mathtypes[dim_name] == spux.MathType.Integer
+				]
+
+		return []
+
+	def are_dims_valid(
+		self, info: ct.InfoFlow, dim_0: str | None, dim_1: str | None
+	) -> bool:
+		"""Check whether the given dimension inputs are valid in the context of this operation, and of the information."""
+		return (self.num_dim_inputs in [1, 2] and dim_0 in self.valid_dims(info)) or (
+			self.num_dim_inputs == 2 and dim_1 in self.valid_dims(info)
+		)
+
+	####################
+	# - UI
+	####################
+	def jax_func(
+		self,
+		axis_0: int | None,
+		axis_1: int | None,
+		slice_tuple: tuple[int, int, int] | None = None,
+	):
+		FO = FilterOperation
 		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),
+			# Pin
+			FO.SliceIdx: lambda expr: jlax.slice_in_dim(
+				expr, slice_tuple[0], slice_tuple[1], slice_tuple[2], axis=axis_0
+			),
+			# Pin
+			FO.PinLen1: lambda expr: jnp.squeeze(expr, axis_0),
+			FO.Pin: lambda expr, idx: jnp.take(expr, idx, axis=axis_0),
+			FO.PinIdx: lambda expr, idx: jnp.take(expr, idx, axis=axis_0),
+			# Reinterpret
+			FO.Swap: lambda expr: jnp.swapaxes(expr, axis_0, axis_1),
+			FO.SetDim: lambda expr: expr,
+		}[self]
+
+	def transform_info(
+		self,
+		info: ct.InfoFlow,
+		dim_0: str,
+		dim_1: str,
+		slice_tuple: tuple[int, int, int] | None = None,
+		corrected_dim: tuple[str, tuple[str, ct.ArrayFlow | ct.LazyArrayRangeFlow]]
+		| None = None,
+	):
+		FO = FilterOperation
+		return {
+			FO.SliceIdx: lambda: info.slice_dim(dim_0, slice_tuple),
+			# Pin
+			FO.PinLen1: lambda: info.delete_dimension(dim_0),
+			FO.Pin: lambda: info.delete_dimension(dim_0),
+			FO.PinIdx: lambda: info.delete_dimension(dim_0),
+			# Reinterpret
+			FO.Swap: lambda: info.swap_dimensions(dim_0, dim_1),
+			FO.SetDim: lambda: info.replace_dim(*corrected_dim),
 		}[self]()
 
 
@@ -133,115 +272,192 @@ class FilterMathNode(base.MaxwellSimNode):
 	}
 
 	####################
-	# - Properties
+	# - Properties: Expr InfoFlow
 	####################
-	operation: FilterOperation = bl_cache.BLField(
-		FilterOperation.PinLen1,
-		prop_ui=True,
+	@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
 		)
 
-	# Dimension Selection
-	dim_0: enum.StrEnum = bl_cache.BLField(enum_cb=lambda self, _: self.search_dims())
-	dim_1: enum.StrEnum = bl_cache.BLField(enum_cb=lambda self, _: self.search_dims())
+		if has_info and not info_pending:
+			self.expr_info = bl_cache.Signal.InvalidateCache
 
-	####################
-	# - Computed
-	####################
-	@property
-	def data_info(self) -> ct.InfoFlow | None:
-		info = self._compute_input('Expr', kind=ct.FlowKind.Info)
-		if not ct.FlowSignal.check(info):
+	@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
 
 	####################
-	# - Search Dimensions
+	# - Properties: Operation
 	####################
+	operation: FilterOperation = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_operations(),
+		cb_depends_on={'expr_info'},
+	)
+
+	def search_operations(self) -> list[ct.BLEnumElement]:
+		if self.expr_info is not None:
+			return [
+				operation.bl_enum_element(i)
+				for i, operation in enumerate(FilterOperation.by_info(self.expr_info))
+			]
+		return []
+
+	####################
+	# - Properties: Dimension Selection
+	####################
+	dim_0: enum.StrEnum = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_dims(),
+		cb_depends_on={'operation', 'expr_info'},
+	)
+	dim_1: enum.StrEnum = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_dims(),
+		cb_depends_on={'operation', 'expr_info'},
+	)
+
 	def search_dims(self) -> list[ct.BLEnumElement]:
-		if self.data_info is None:
+		if self.expr_info is not None and self.operation is not None:
+			return [
+				(dim_name, dim_name, dim_name, '', i)
+				for i, dim_name in enumerate(self.operation.valid_dims(self.expr_info))
+			]
 		return []
 
-		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
+	####################
+	# - Properties: Slice
+	####################
+	slice_tuple: tuple[int, int, int] = bl_cache.BLField([0, 1, 1])
+
+	####################
+	# - Properties: Unit
+	####################
+	set_dim_symbol: sim_symbols.CommonSimSymbol = bl_cache.BLField(
+		sim_symbols.CommonSimSymbol.X
+	)
+
+	set_dim_active_unit: enum.StrEnum = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_valid_units(),
+		cb_depends_on={'set_dim_symbol'},
+	)
+
+	def search_valid_units(self) -> list[ct.BLEnumElement]:
+		"""Compute Blender enum elements of valid units for the current `physical_type`."""
+		physical_type = self.set_dim_symbol.sim_symbol.physical_type
+		if physical_type is not spux.PhysicalType.NonPhysical:
+			return [
+				(sp.sstr(unit), spux.sp_to_str(unit), sp.sstr(unit), '', i)
+				for i, unit in enumerate(physical_type.valid_units)
 			]
-		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
-			]
-		else:
 		return []
 
-		return [(*dim, '', i) for i, dim in enumerate(dims)]
+	@bl_cache.cached_bl_property(depends_on={'set_dim_active_unit'})
+	def set_dim_unit(self) -> spux.Unit | None:
+		if self.set_dim_active_unit is not None:
+			return spux.unit_str_to_unit(self.set_dim_active_unit)
+
+		return None
 
 	####################
 	# - UI
 	####################
 	def draw_label(self):
 		FO = FilterOperation
-		labels = {
-			FO.PinLen1: lambda: f'Filter: Pin {self.dim_0} (len=1)',
-			FO.Pin: lambda: f'Filter: Pin {self.dim_0}',
-			FO.Swap: lambda: f'Filter: Swap {self.dim_0}|{self.dim_1}',
-			FO.DimToVec: lambda: 'Filter: -> Vector',
-			FO.DimsToMat: lambda: 'Filter: -> Matrix',
-		}
+		match self.operation:
+			# Slice
+			case FO.SliceIdx:
+				slice_str = ':'.join([str(v) for v in self.slice_tuple])
+				return f'Filter: {self.dim_0}[{slice_str}]'
 
-		if (label := labels.get(self.operation)) is not None:
-			return label()
+			# Pin
+			case FO.PinLen1:
+				return f'Filter: Pin {self.dim_0}[0]'
+			case FO.Pin:
+				return f'Filter: Pin {self.dim_0}[...]'
+			case FO.PinIdx:
+				pin_idx_axis = self._compute_input(
+					'Axis', kind=ct.FlowKind.Value, optional=True
+				)
+				has_pin_idx_axis = not ct.FlowSignal.check(pin_idx_axis)
+				if has_pin_idx_axis:
+					return f'Filter: Pin {self.dim_0}[{pin_idx_axis}]'
+				return self.bl_label
 
+			# Reinterpret
+			case FO.Swap:
+				return f'Filter: Swap [{self.dim_0}]|[{self.dim_1}]'
+			case FO.SetDim:
+				return f'Filter: Set [{self.dim_0}]'
+
+			case _:
 				return self.bl_label
 
 	def draw_props(self, _: bpy.types.Context, layout: bpy.types.UILayout) -> None:
 		layout.prop(self, self.blfields['operation'], text='')
 
-		if self.operation in [FilterOperation.PinLen1, FilterOperation.Pin]:
+		if self.operation is not None:
+			match self.operation.num_dim_inputs:
+				case 1:
 					layout.prop(self, self.blfields['dim_0'], text='')
-
-		if self.operation == FilterOperation.Swap:
+				case 2:
 					row = layout.row(align=True)
 					row.prop(self, self.blfields['dim_0'], text='')
 					row.prop(self, self.blfields['dim_1'], text='')
 
+			if self.operation is FilterOperation.SliceIdx:
+				layout.prop(self, self.blfields['slice_tuple'], text='')
+
+			if self.operation is FilterOperation.SetDim:
+				row = layout.row(align=True)
+				row.prop(self, self.blfields['set_dim_symbol'], text='')
+				row.prop(self, self.blfields['set_dim_active_unit'], text='')
+
 	####################
 	# - Events
 	####################
 	@events.on_value_changed(
 		# Trigger
 		socket_name='Expr',
-		prop_name={'operation'},
-		run_on_init=True,
-	)
-	def on_input_changed(self) -> None:
-		self.dim_0 = bl_cache.Signal.ResetEnumItems
-		self.dim_1 = bl_cache.Signal.ResetEnumItems
-
-	@events.on_value_changed(
-		# Trigger
-		socket_name='Expr',
-		prop_name={'dim_0', 'dim_1', 'operation'},
-		run_on_init=True,
+		prop_name={'operation', 'dim_0', 'dim_1'},
 		# Loaded
 		props={'operation', 'dim_0', 'dim_1'},
 		input_sockets={'Expr'},
 		input_socket_kinds={'Expr': ct.FlowKind.Info},
 	)
-	def on_pin_changed(self, props: dict, input_sockets: dict):
+	def on_pin_factors_changed(self, props: dict, input_sockets: dict):
+		"""Synchronize loose input sockets to match the dimension-pinning method declared in `self.operation`.
+
+		To "pin" an axis, a particular index must be chosen to "extract".
+		One might choose axes of length 1 ("squeeze"), choose a particular index, or choose a coordinate that maps to a particular index.
+
+		Those last two options requires more information from the user: Which index?
+		Which coordinate?
+		To answer these questions, we create an appropriate loose input socket containing this data, so the user can make their decision.
+		"""
 		info = input_sockets['Expr']
 		has_info = not ct.FlowSignal.check(info)
 		if not has_info:
 			return
 
-		# "Dimensions"|"PIN": Add/Remove Input Socket
-		if props['operation'] == FilterOperation.Pin and props['dim_0'] is not None:
+		# Pin Dim by-Value: Synchronize Input Socket
+		## -> The user will be given a socket w/correct mathtype, unit, etc. .
+		## -> Internally, this value will map to a particular index.
+		if props['operation'] is FilterOperation.Pin and props['dim_0'] is not None:
+			# Deduce Pinned Information
 			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
@@ -250,9 +466,11 @@ class FilterMathNode(base.MaxwellSimNode):
 			)
 
 			# Get Current and Wanted Socket Defs
+			## -> 'Value' may already exist. If not, all is well.
 			current_bl_socket = self.loose_input_sockets.get('Value')
 
-			# Determine Whether to Declare New Loose Input SOcket
+			# Determine Whether to Construct
+			## -> If nothing needs to change, then nothing changes.
 			if (
 				current_bl_socket is None
 				or current_bl_socket.size is not spux.NumberSize1D.Scalar
@@ -262,22 +480,68 @@ class FilterMathNode(base.MaxwellSimNode):
 				self.loose_input_sockets = {
 					'Value': sockets.ExprSocketDef(
 						active_kind=ct.FlowKind.Value,
-						size=spux.NumberSize1D.Scalar,
 						physical_type=pinned_physical_type,
 						mathtype=wanted_mathtype,
 						default_unit=pinned_unit,
 					),
 				}
+
+		# Pin Dim by-Index: Synchronize Input Socket
+		## -> The user will be given a simple integer socket.
+		elif (
+			props['operation'] is FilterOperation.PinIdx and props['dim_0'] is not None
+		):
+			current_bl_socket = self.loose_input_sockets.get('Axis')
+			if (
+				current_bl_socket is None
+				or current_bl_socket.size is not spux.NumberSize1D.Scalar
+				or current_bl_socket.physical_type != spux.PhysicalType.NonPhysical
+				or current_bl_socket.mathtype != spux.MathType.Integer
+			):
+				self.loose_input_sockets = {
+					'Axis': sockets.ExprSocketDef(
+						active_kind=ct.FlowKind.Value,
+						mathtype=spux.MathType.Integer,
+					)
+				}
+
+		# Set Dim: Synchronize Input Socket
+		## -> The user must provide a (ℤ) -> ℝ array.
+		## -> It must be of identical length to the replaced axis.
+		elif (
+			props['operation'] is FilterOperation.SetDim
+			and props['dim_0'] is not None
+			and info.dim_mathtypes[props['dim_0']] is spux.MathType.Integer
+			and info.dim_physical_types[props['dim_0']] is spux.PhysicalType.NonPhysical
+		):
+			# Deduce Axis Information
+			current_bl_socket = self.loose_input_sockets.get('Dim')
+			if (
+				current_bl_socket is None
+				or current_bl_socket.active_kind != ct.FlowKind.LazyValueFunc
+				or current_bl_socket.mathtype != spux.MathType.Real
+				or current_bl_socket.physical_type != spux.PhysicalType.NonPhysical
+			):
+				self.loose_input_sockets = {
+					'Dim': sockets.ExprSocketDef(
+						active_kind=ct.FlowKind.LazyValueFunc,
+						mathtype=spux.MathType.Real,
+						physical_type=spux.PhysicalType.NonPhysical,
+						show_info_columns=True,
+					)
+				}
+
+		# No Loose Value: Remove Input Sockets
 		elif self.loose_input_sockets:
 			self.loose_input_sockets = {}
 
 	####################
-	# - Output
+	# - FlowKind.Value|LazyValueFunc
 	####################
 	@events.computes_output_socket(
 		'Expr',
 		kind=ct.FlowKind.LazyValueFunc,
-		props={'operation', 'dim_0', 'dim_1'},
+		props={'operation', 'dim_0', 'dim_1', 'slice_tuple'},
 		input_sockets={'Expr'},
 		input_socket_kinds={'Expr': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Info}},
 	)
@@ -296,82 +560,120 @@ class FilterMathNode(base.MaxwellSimNode):
 			has_lazy_value_func
 			and has_info
 			and operation is not None
-			and operation.are_dims_valid(dim_0, dim_1)
+			and operation.are_dims_valid(info, dim_0, dim_1)
 		):
 			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 is not None else None
+			slice_tuple = (
+				props['slice_tuple']
+				if self.operation is FilterOperation.SliceIdx
+				else None
+			)
 
 			return lazy_value_func.compose_within(
-				operation.jax_func(axis_0, axis_1),
-				enclosing_func_args=[int] if operation == FilterOperation.Pin else [],
+				operation.jax_func(axis_0, axis_1, slice_tuple),
+				enclosing_func_args=operation.func_args,
 				supports_jax=True,
 			)
 		return ct.FlowSignal.FlowPending
 
-	@events.computes_output_socket(
-		'Expr',
-		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
-
 	####################
-	# - Auxiliary: Info
+	# - FlowKind.Info
 	####################
 	@events.computes_output_socket(
 		'Expr',
 		kind=ct.FlowKind.Info,
-		props={'dim_0', 'dim_1', 'operation'},
-		input_sockets={'Expr'},
-		input_socket_kinds={'Expr': ct.FlowKind.Info},
+		props={
+			'dim_0',
+			'dim_1',
+			'operation',
+			'slice_tuple',
+			'set_dim_symbol',
+			'set_dim_active_unit',
+		},
+		input_sockets={'Expr', 'Dim'},
+		input_socket_kinds={
+			'Expr': ct.FlowKind.Info,
+			'Dim': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Params, ct.FlowKind.Info},
+		},
+		input_sockets_optional={'Dim': True},
 	)
-	def compute_info(self, props: dict, input_sockets: dict) -> ct.InfoFlow:
+	def compute_info(self, props, input_sockets) -> ct.InfoFlow:
 		operation = props['operation']
 		info = input_sockets['Expr']
+		dim_coords = input_sockets['Dim'][ct.FlowKind.LazyValueFunc]
+		dim_params = input_sockets['Dim'][ct.FlowKind.Params]
+		dim_info = input_sockets['Dim'][ct.FlowKind.Info]
+		dim_symbol = props['set_dim_symbol']
+		dim_active_unit = props['set_dim_active_unit']
 
 		has_info = not ct.FlowSignal.check(info)
+		has_dim_coords = not ct.FlowSignal.check(dim_coords)
+		has_dim_params = not ct.FlowSignal.check(dim_params)
+		has_dim_info = not ct.FlowSignal.check(dim_info)
 
 		# Dimension(s)
 		dim_0 = props['dim_0']
 		dim_1 = props['dim_1']
+		slice_tuple = props['slice_tuple']
+		if has_info and operation is not None:
+			# Set Dimension: Retrieve Array
+			if props['operation'] is FilterOperation.SetDim:
 				if (
-			has_info
-			and operation is not None
-			and operation.are_dims_valid(dim_0, dim_1)
+					dim_0 is not None
+					# Check Replaced Dimension
+					and has_dim_coords
+					and len(dim_coords.func_args) == 1
+					and dim_coords.func_args[0] is spux.MathType.Integer
+					and not dim_coords.func_kwargs
+					and dim_coords.supports_jax
+					# Check Params
+					and has_dim_params
+					and len(dim_params.func_args) == 1
+					and not dim_params.func_kwargs
+					# Check Info
+					and has_dim_info
 				):
-			return operation.transform_info(info, dim_0, dim_1)
+					# Retrieve Dimension Coordinate Array
+					## -> It must be strictly compatible.
+					values = dim_coords.func_jax(int(dim_params.func_args[0]))
+					if (
+						len(values.shape) != 1
+						or values.shape[0] != info.dim_lens[dim_0]
+					):
+						return ct.FlowSignal.FlowPending
 
+					# Transform Info w/Corrected Dimension
+					## -> The existing dimension will be replaced.
+					if dim_active_unit is not None:
+						dim_unit = spux.unit_str_to_unit(dim_active_unit)
+					else:
+						dim_unit = None
+
+					new_dim_idx = ct.ArrayFlow(
+						values=values,
+						unit=dim_unit,
+					)
+					corrected_dim = [dim_0, (dim_symbol.name, new_dim_idx)]
+					return operation.transform_info(
+						info, dim_0, dim_1, corrected_dim=corrected_dim
+					)
+				return ct.FlowSignal.FlowPending
+			return operation.transform_info(info, dim_0, dim_1, slice_tuple=slice_tuple)
 		return ct.FlowSignal.FlowPending
 
 	####################
-	# - Auxiliary: Params
+	# - FlowKind.Params
 	####################
 	@events.computes_output_socket(
 		'Expr',
 		kind=ct.FlowKind.Params,
 		props={'dim_0', 'dim_1', 'operation'},
-		input_sockets={'Expr', 'Value'},
-		input_socket_kinds={'Expr': {ct.FlowKind.Info, ct.FlowKind.Params}},
-		input_sockets_optional={'Value': True},
+		input_sockets={'Expr', 'Value', 'Axis'},
+		input_socket_kinds={
+			'Expr': {ct.FlowKind.Info, ct.FlowKind.Params},
+		},
+		input_sockets_optional={'Value': True, 'Axis': True},
 	)
 	def compute_params(self, props: dict, input_sockets: dict) -> ct.ParamsFlow:
 		operation = props['operation']
@@ -388,20 +690,30 @@ class FilterMathNode(base.MaxwellSimNode):
 			has_info
 			and has_params
 			and operation is not None
-			and operation.are_dims_valid(dim_0, dim_1)
+			and operation.are_dims_valid(info, dim_0, dim_1)
 		):
-			## Pinned Value
+			# Retrieve Pinned Value
 			pinned_value = input_sockets['Value']
 			has_pinned_value = not ct.FlowSignal.check(pinned_value)
 
-			if props['operation'] == FilterOperation.Pin and has_pinned_value:
+			pinned_axis = input_sockets['Axis']
+			has_pinned_axis = not ct.FlowSignal.check(pinned_axis)
+
+			# Pin by-Value: Compute Nearest IDX
+			## -> Presume a sorted index array to be able to use binary search.
+			if props['operation'] is FilterOperation.Pin and has_pinned_value:
 				nearest_idx_to_value = info.dim_idx[dim_0].nearest_idx_of(
 					pinned_value, require_sorted=True
 				)
 
 				return params.compose_within(enclosing_func_args=[nearest_idx_to_value])
 
+			# Pin by-Index
+			if props['operation'] is FilterOperation.PinIdx and has_pinned_axis:
+				return params.compose_within(enclosing_func_args=[pinned_axis])
+
 			return params
+
 		return ct.FlowSignal.FlowPending
 
 

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

@@ -21,6 +21,7 @@ import typing as typ
 
 import bpy
 import jax.numpy as jnp
+import jaxtyping as jtyp
 import sympy as sp
 import sympy.physics.units as spu
 
@@ -47,13 +48,20 @@ class TransformOperation(enum.StrEnum):
 		InvFFT: Compute the inverse fourier transform of the input expression.
 	"""
 
-	# Index
+	# Covariant Transform
 	FreqToVacWL = enum.auto()
 	VacWLToFreq = enum.auto()
+
+	# Fold
+	IntDimToComplex = enum.auto()
+	DimToVec = enum.auto()
+	DimsToMat = enum.auto()
+
 	# Fourier
 	FFT1D = enum.auto()
 	InvFFT1D = enum.auto()
-	# Affine
+
+	# TODO: Affine
 	## TODO
 
 	####################
@@ -63,9 +71,14 @@ class TransformOperation(enum.StrEnum):
 	def to_name(value: typ.Self) -> str:
 		TO = TransformOperation
 		return {
-			# By Number
+			# Covariant Transform
 			TO.FreqToVacWL: '𝑓 → λᵥ',
 			TO.VacWLToFreq: 'λᵥ → 𝑓',
+			# Fold
+			TO.IntDimToComplex: '→ ℂ',
+			TO.DimToVec: '→ Vector',
+			TO.DimsToMat: '→ Matrix',
+			# Fourier
 			TO.FFT1D: 't → 𝑓',
 			TO.InvFFT1D: '𝑓 → t',
 		}[value]
@@ -92,7 +105,8 @@ class TransformOperation(enum.StrEnum):
 		TO = TransformOperation
 		operations = []
 
-		# Freq <-> VacWL
+		# Covariant Transform
+		## Freq <-> VacWL
 		for dim_name in info.dim_names:
 			if info.dim_physical_types[dim_name] == spux.PhysicalType.Freq:
 				operations.append(TO.FreqToVacWL)
@@ -100,7 +114,23 @@ class TransformOperation(enum.StrEnum):
 			if info.dim_physical_types[dim_name] == spux.PhysicalType.Freq:
 				operations.append(TO.VacWLToFreq)
 
-		# 1D Fourier
+		# Fold
+		## (Last) Int Dim (=2) to Complex
+		if len(info.dim_names) >= 1:
+			last_dim_name = info.dim_names[-1]
+			if info.dim_lens[last_dim_name] == 2:  # noqa: PLR2004
+				operations.append(TO.IntDimToComplex)
+
+		## To Vector
+		if len(info.dim_names) >= 1:
+			operations.append(TO.DimToVec)
+
+		## To Matrix
+		if len(info.dim_names) >= 2:  # noqa: PLR2004
+			operations.append(TO.DimsToMat)
+
+		# Fourier
+		## 1D Fourier
 		if info.dim_names:
 			last_physical_type = info.dim_physical_types[info.dim_names[-1]]
 			if last_physical_type == spux.PhysicalType.Time:
@@ -117,9 +147,13 @@ class TransformOperation(enum.StrEnum):
 	def sp_func(self):
 		TO = TransformOperation
 		return {
-			# Index
+			# Covariant Transform
 			TO.FreqToVacWL: lambda expr: expr,
 			TO.VacWLToFreq: lambda expr: expr,
+			# Fold
+			# TO.IntDimToComplex: lambda expr: expr,  ## TODO: Won't work?
+			TO.DimToVec: lambda expr: expr,
+			TO.DimsToMat: lambda expr: expr,
 			# Fourier
 			TO.FFT1D: lambda expr: sp.fourier_transform(
 				expr, sim_symbols.t, sim_symbols.freq
@@ -133,15 +167,26 @@ class TransformOperation(enum.StrEnum):
 	def jax_func(self):
 		TO = TransformOperation
 		return {
-			# Index
+			# Covariant Transform
 			TO.FreqToVacWL: lambda expr: expr,
 			TO.VacWLToFreq: lambda expr: expr,
+			# Fold
+			## -> To Complex: With a little imagination, this is a noop :)
+			## -> **Requires** dims[-1] to be integer-indexed w/length of 2.
+			TO.IntDimToComplex: lambda expr: expr.view(dtype=jnp.complex64).squeeze(),
+			TO.DimToVec: lambda expr: expr,
+			TO.DimsToMat: 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:
+	def transform_info(
+		self,
+		info: ct.InfoFlow | None,
+		data: jtyp.Shaped[jtyp.Array, '...'] | None = None,
+		unit: spux.Unit | None = None,
+	) -> ct.InfoFlow | None:
 		TO = TransformOperation
 		if not info.dim_names:
 			return None
@@ -169,6 +214,12 @@ class TransformOperation(enum.StrEnum):
 					),
 				],
 			),
+			# Fold
+			TO.IntDimToComplex: lambda: info.delete_dimension(
+				info.dim_names[-1]
+			).set_output_mathtype(spux.MathType.Complex),
+			TO.DimToVec: lambda: info.shift_last_input,
+			TO.DimsToMat: lambda: info.shift_last_input.shift_last_input,
 			# Fourier
 			TO.FFT1D: lambda: info.replace_dim(
 				info.dim_names[-1],
@@ -216,7 +267,7 @@ class TransformMathNode(base.MaxwellSimNode):
 	}
 
 	####################
-	# - Properties
+	# - Properties: Expr InfoFlow
 	####################
 	@events.on_value_changed(
 		socket_name={'Expr'},
@@ -243,6 +294,9 @@ class TransformMathNode(base.MaxwellSimNode):
 
 		return None
 
+	####################
+	# - Properties: Operation
+	####################
 	operation: TransformOperation = bl_cache.BLField(
 		enum_cb=lambda self, _: self.search_operations(),
 		cb_depends_on={'expr_info'},
@@ -258,9 +312,6 @@ class TransformMathNode(base.MaxwellSimNode):
 			]
 		return []
 
-	def draw_props(self, _: bpy.types.Context, layout: bpy.types.UILayout) -> None:
-		layout.prop(self, self.blfields['operation'], text='')
-
 	####################
 	# - UI
 	####################
@@ -339,6 +390,7 @@ class TransformMathNode(base.MaxwellSimNode):
 
 		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

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

@@ -14,11 +14,13 @@
 # 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 tidy_3d_file_importer
+from . import data_file_importer, tidy_3d_file_importer
 
 BL_REGISTER = [
+	*data_file_importer.BL_REGISTER,
 	*tidy_3d_file_importer.BL_REGISTER,
 ]
 BL_NODES = {
+	**data_file_importer.BL_NODES,
 	**tidy_3d_file_importer.BL_NODES,
 }

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/file_importers/data_file_importer.py

@@ -0,0 +1,356 @@
+# blender_maxwell
+# Copyright (C) 2024 blender_maxwell Project Contributors
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Affero General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Affero General Public License for more details.
+#
+# 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/>.
+
+import enum
+import typing as typ
+from pathlib import Path
+
+import bpy
+import jax.numpy as jnp
+import jaxtyping as jtyp
+import numpy as np
+import pandas as pd
+import sympy as sp
+import tidy3d as td
+
+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
+from ... import base, events
+
+log = logger.get(__name__)
+
+####################
+# - Data File Extensions
+####################
+_DATA_FILE_EXTS = {
+	'.txt',
+	'.txt.gz',
+	'.csv',
+	'.npy',
+}
+
+
+class DataFileExt(enum.StrEnum):
+	Txt = enum.auto()
+	TxtGz = enum.auto()
+	Csv = enum.auto()
+	Npy = enum.auto()
+
+	####################
+	# - Enum Elements
+	####################
+	@staticmethod
+	def to_name(v: typ.Self) -> str:
+		return DataFileExt(v).extension
+
+	@staticmethod
+	def to_icon(v: typ.Self) -> str:
+		return ''
+
+	####################
+	# - Computed Properties
+	####################
+	@property
+	def extension(self) -> str:
+		"""Map to the actual string extension."""
+		E = DataFileExt
+		return {
+			E.Txt: '.txt',
+			E.TxtGz: '.txt.gz',
+			E.Csv: '.csv',
+			E.Npy: '.npy',
+		}[self]
+
+	@property
+	def loader(self) -> typ.Callable[[Path], jtyp.Shaped[jtyp.Array, '...']]:
+		def load_txt(path: Path):
+			return jnp.asarray(np.loadtxt(path))
+
+		def load_csv(path: Path):
+			return jnp.asarray(pd.read_csv(path).values)
+
+		def load_npy(path: Path):
+			return jnp.load(path)
+
+		E = DataFileExt
+		return {
+			E.Txt: load_txt,
+			E.TxtGz: load_txt,
+			E.Csv: load_csv,
+			E.Npy: load_npy,
+		}[self]
+
+	@property
+	def loader_is_jax_compatible(self) -> bool:
+		E = DataFileExt
+		return {
+			E.Txt: True,
+			E.TxtGz: True,
+			E.Csv: False,
+			E.Npy: True,
+		}[self]
+
+	####################
+	# - Creation
+	####################
+	@staticmethod
+	def from_ext(ext: str) -> typ.Self | None:
+		return {
+			_ext: _data_file_ext
+			for _data_file_ext, _ext in {
+				k: k.extension for k in list(DataFileExt)
+			}.items()
+		}.get(ext)
+
+	@staticmethod
+	def from_path(path: Path) -> typ.Self | None:
+		if DataFileExt.is_path_compatible(path):
+			data_file_ext = DataFileExt.from_ext(''.join(path.suffixes))
+			if data_file_ext is not None:
+				return data_file_ext
+
+			msg = f'DataFileExt: Path "{path}" is compatible, but could not find valid extension'
+			raise RuntimeError(msg)
+
+		return None
+
+	####################
+	# - Compatibility
+	####################
+	@staticmethod
+	def is_ext_compatible(ext: str):
+		return ext in _DATA_FILE_EXTS
+
+	@staticmethod
+	def is_path_compatible(path: Path):
+		return path.is_file() and DataFileExt.is_ext_compatible(''.join(path.suffixes))
+
+
+####################
+# - Node
+####################
+class DataFileImporterNode(base.MaxwellSimNode):
+	node_type = ct.NodeType.DataFileImporter
+	bl_label = 'Data File Importer'
+
+	input_sockets: typ.ClassVar = {
+		'File Path': sockets.FilePathSocketDef(),
+	}
+	output_sockets: typ.ClassVar = {
+		'Expr': sockets.ExprSocketDef(active_kind=ct.FlowKind.LazyValueFunc),
+	}
+
+	####################
+	# - Properties
+	####################
+	@events.on_value_changed(
+		socket_name={'File Path'},
+		input_sockets={'File Path'},
+		input_socket_kinds={'File Path': ct.FlowKind.Value},
+		input_sockets_optional={'File Path': True},
+	)
+	def on_input_exprs_changed(self, input_sockets) -> None:  # noqa: D102
+		has_file_path = not ct.FlowSignal.check(input_sockets['File Path'])
+
+		has_file_path = ct.FlowSignal.check_single(
+			input_sockets['File Path'], ct.FlowSignal.FlowPending
+		)
+
+		if has_file_path:
+			self.file_path = bl_cache.Signal.InvalidateCache
+
+	@bl_cache.cached_bl_property()
+	def file_path(self) -> Path:
+		"""Retrieve the input file path."""
+		file_path = self._compute_input(
+			'File Path', kind=ct.FlowKind.Value, optional=True
+		)
+		has_file_path = not ct.FlowSignal.check(file_path)
+		if has_file_path:
+			return file_path
+
+		return None
+
+	@bl_cache.cached_bl_property(depends_on={'file_path'})
+	def data_file_ext(self) -> DataFileExt | None:
+		"""Retrieve the file extension by concatenating all suffixes."""
+		if self.file_path is not None:
+			return DataFileExt.from_path(self.file_path)
+		return None
+
+	####################
+	# - Output Info
+	####################
+	@bl_cache.cached_bl_property(depends_on={'file_path'})
+	def expr_info(self) -> ct.InfoFlow | None:
+		"""Retrieve the output expression's `InfoFlow`."""
+		info = self.compute_output('Expr', kind=ct.FlowKind.Info)
+		has_info = not ct.FlowKind.check(info)
+		if has_info:
+			return info
+		return None
+
+	####################
+	# - UI
+	####################
+	def draw_label(self):
+		"""Show the extracted file name (w/extension) in the node's header label.
+
+		Notes:
+			Called by Blender to determine the text to place in the node's header.
+		"""
+		if self.file_path is not None:
+			return 'Load File: ' + self.file_path.name
+
+		return self.bl_label
+
+	def draw_info(self, _: bpy.types.Context, layout: bpy.types.UILayout) -> None:
+		"""Show information about the loaded file."""
+		if self.data_file_ext is not None:
+			box = layout.box()
+			row = box.row()
+			row.alignment = 'CENTER'
+			row.label(text='Data File')
+
+			row = box.row()
+			row.alignment = 'CENTER'
+			row.label(text=self.file_path.name)
+
+	def draw_props(self, _: bpy.types.Context, layout: bpy.types.UILayout) -> None:
+		pass
+
+	####################
+	# - Events
+	####################
+	@events.on_value_changed(
+		socket_name='File Path',
+		input_sockets={'File Path'},
+	)
+	def on_file_changed(self, input_sockets) -> None:
+		pass
+
+	####################
+	# - FlowKind.Array|LazyValueFunc
+	####################
+	@events.computes_output_socket(
+		'Expr',
+		kind=ct.FlowKind.LazyValueFunc,
+		input_sockets={'File Path'},
+	)
+	def compute_func(self, input_sockets: dict) -> td.Simulation:
+		"""Declare a lazy, composable function that returns the loaded data.
+
+		Returns:
+			A completely empty `ParamsFlow`, ready to be composed.
+		"""
+		file_path = input_sockets['File Path']
+
+		has_file_path = not ct.FlowSignal.check(input_sockets['File Path'])
+
+		if has_file_path:
+			data_file_ext = DataFileExt.from_path(file_path)
+			if data_file_ext is not None:
+				# Jax Compatibility: Lazy Data Loading
+				## -> Delay loading of data from file as long as we can.
+				if data_file_ext.loader_is_jax_compatible:
+					return ct.LazyValueFuncFlow(
+						func=lambda: data_file_ext.loader(file_path),
+						supports_jax=True,
+					)
+
+				# No Jax Compatibility: Eager Data Loading
+				## -> Load the data now and bind it.
+				data = data_file_ext.loader(file_path)
+				return ct.LazyValueFuncFlow(func=lambda: data, supports_jax=True)
+			return ct.FlowSignal.FlowPending
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind.Params|Info
+	####################
+	@events.computes_output_socket(
+		'Expr',
+		kind=ct.FlowKind.Params,
+	)
+	def compute_params(self) -> ct.ParamsFlow:
+		"""Declare an empty `Data:Params`, to indicate the start of a function-composition pipeline.
+
+		Returns:
+			A completely empty `ParamsFlow`, ready to be composed.
+		"""
+		return ct.ParamsFlow()
+
+	@events.computes_output_socket(
+		'Expr',
+		kind=ct.FlowKind.Info,
+		output_sockets={'Expr'},
+		output_socket_kinds={'Expr': ct.FlowKind.LazyValueFunc},
+	)
+	def compute_info(self, output_sockets) -> ct.InfoFlow:
+		"""Declare an `InfoFlow` based on the data shape.
+
+		This currently requires computing the data.
+		Note, however, that the incremental cache causes this computation only to happen once when a file is selected.
+
+		Returns:
+			A completely empty `ParamsFlow`, ready to be composed.
+		"""
+		expr = output_sockets['Expr']
+
+		has_expr_func = not ct.FlowSignal.check(expr)
+
+		if has_expr_func:
+			data = expr.func_jax()
+
+			# Deduce Dimensionality
+			_shape = data.shape
+			shape = _shape if _shape is not None else ()
+			dim_names = [f'a{i}' for i in range(len(shape))]
+
+			# Return InfoFlow
+			## -> TODO: How to interpret the data should be user-defined.
+			## -> -- This may require those nice dynamic symbols.
+			return ct.InfoFlow(
+				dim_names=dim_names,  ## TODO: User
+				dim_idx={
+					dim_name: ct.LazyArrayRangeFlow(
+						start=sp.S(0),  ## TODO: User
+						stop=sp.S(shape[i] - 1),  ## TODO: User
+						steps=shape[dim_names.index(dim_name)],
+						unit=None,  ## TODO: User
+					)
+					for i, dim_name in enumerate(dim_names)
+				},
+				output_name='_',
+				output_shape=None,
+				output_mathtype=spux.MathType.Real,  ## TODO: User
+				output_unit=None,  ## TODO: User
+			)
+		return ct.FlowSignal.FlowPending
+
+
+####################
+# - Blender Registration
+####################
+BL_REGISTER = [
+	DataFileImporterNode,
+]
+BL_NODES = {
+	ct.NodeType.DataFileImporter: (ct.NodeCategory.MAXWELLSIM_INPUTS_FILEIMPORTERS)
+}

src/blender_maxwell/utils/image_ops.py

@@ -234,7 +234,7 @@ def plot_curves_2d(
 	y_unit = info.output_unit
 
 	for category in range(data.shape[1]):
-		ax.plot(data[:, 0], data[:, 1])
+		ax.plot(info.dim_idx_arrays[0], data[:, category])
 
 	ax.set_title('2D Curves')
 	ax.set_xlabel(f'{x_name}' + (f'({x_unit})' if x_unit is not None else ''))
@@ -250,8 +250,9 @@ def plot_filled_curves_2d(
 	y_name = info.output_name
 	y_unit = info.output_unit
 
-	ax.fill_between(info.dim_arrays[0], data[:, 0], info.dim_arrays[0], data[:, 1])
-	ax.set_title('2D Curves')
+	shared_x_idx = info.dim_idx_arrays[0]
+	ax.fill_between(shared_x_idx, data[:, 0], shared_x_idx, data[:, 1])
+	ax.set_title('2D Filled Curves')
 	ax.set_xlabel(f'{x_name}' + (f'({x_unit})' if x_unit is not None else ''))
 	ax.set_ylabel(f'{y_name}' + (f'({y_unit})' if y_unit is not None else ''))
 

src/blender_maxwell/utils/sim_symbols.py

@@ -109,6 +109,10 @@ class SimSymbol:
 	####################
 	# - Properties
 	####################
+	@property
+	def name(self) -> str:
+		return self.sim_node_name.name
+
 	@property
 	def domain(self) -> sp.Interval | sp.Set:
 		"""Return the domain of valid values for the symbol.
@@ -235,6 +239,10 @@ class CommonSimSymbol(enum.StrEnum):
 	####################
 	# - Properties
 	####################
+	@property
+	def name(self) -> str:
+		return self.sim_symbol.name
+
 	@property
 	def sim_symbol_name(self) -> str:
 		SSN = SimSymbolName