Updates:
- some unsupported modes are now going to report a match failure for
unsupported coordinate transformation modes.
- fixes a bug that was introduced in the last patch for resize (my
bad...)
- uses actual x and y coordinates for computing weights in bilinear
interpolation (rather than eps modified values)
- slightly simplifies the bilinear interpolation payload for readability
and performance
- passes coordinate transformation mode information from an onnx.Resize
op to the mode string for the aten._interpolate op. This allows us to
perform custom logic in the torch->linalg lowering to support
onnx.Resize options without losing the default behaviors of the
interpolate op.
This PR fixes the bugs for `Torch::AtenOneHotOp` by:
1) Using `Torch::kUnknownSize` as the default value for `numClasses` in
the pattern matching stage in `DecomposeAtenOneHotOp`
2) Adding `AtenIntScalarOp` to the patterns in `TorchToArith`
3) Handling both `int` and `float` types for `off` and `on` values in
`TorchOnnxToTorch` conversion
It also includes:
1) A new test in `TorchToArith/basic.mlir`, for `torch.aten.Int.Scalar`,
and
2) A new test in `decompose-complex-ops.mlir`, for `torch.aten.one_hot`
**Dependencies**
This PR is dependent on #3334.
I am trying to eliminate 'getWithLeastStaticInformation' in
DecomposeAtenTriuOp. Could you provide me with some suggestions?
@qingyunqu @zjgarvey
See issue https://github.com/llvm/torch-mlir/issues/3312
Discord Thread:
https://discord.com/channels/636084430946959380/1238330633328005243
## Context:
[This](https://github.com/llvm/torch-mlir/blob/main/python/torch_mlir/fx.py#L61)
was updated to support e2e tests for the TorchDynamo frontend in
Torch-MLIR, where we run FX decompositions and import the FX IR to
generate Torch dialect, followed by
`torch-function-to-torch-backend-pipeline`, skipping only the shape/type
refinement for now. However, we should be able to skip many of the torch
simplification passes, as depicted in the [frontend
roadmap](https://github.com/llvm/torch-mlir/blob/main/docs/images/roadmap_frontend.png).
Based on IREE's TorchDynamo
[pipeline](https://github.com/iree-org/iree/blob/main/compiler/plugins/input/Torch/InputConversion/Passes.cpp#L29),
the only two passes we seem to require are: `ReduceOpVariantsPass` and
`DecomposeComplexOpsPass`. This is inline with our findings as well
based on initial exploration.
This PR creates a dedicated frontend simplification pipeline for
TorchDynamo / FX Importer which calls only `ReduceOpVariantsPass` and
`DecomposeComplexOpsPass`. We rely on the e2e fx_importer tests to
ensure we're not regressing by removing many of the passes that were
historically needed for TorchScript.
One notable change here is that we do not call the
`LowerToBackendContractPass` anymore, which used to call
`TorchSimplificationPipeline` iteratively until VerifyBackendContract
was clean. Some of this was required for the shape/type refinement to
converge, which seems a non-issue for Dynamo frontend. Do we anticipate
this (the iterative invocation of TorchSimplificationPipeline followed
by VerifyBackendContract) to be worth retaining in the Dynamo frontend
pipeline? If so, I can make those changes, PLMK.
In constant folding progress, a new constant op will be created
according to the origin op's result type.
See the code in TorchDialect.cpp.
```cpp
Operation *TorchDialect::materializeConstant(OpBuilder &builder,
Attribute value, Type type,
Location loc) {
if (auto integerType = dyn_cast<Torch::IntType>(type))
return builder.create<Torch::ConstantIntOp>(loc, cast<IntegerAttr>(value));
if (auto floatType = dyn_cast<Torch::FloatType>(type))
return builder.create<Torch::ConstantFloatOp>(loc, cast<FloatAttr>(value));
if (auto numberType = dyn_cast<Torch::NumberType>(type)) {
if (auto floatValue = dyn_cast<mlir::FloatAttr>(value)) {
return builder.create<Torch::ConstantNumberOp>(loc, floatValue);
} else if (auto intValue = dyn_cast<mlir::IntegerAttr>(value)) {
return builder.create<Torch::ConstantNumberOp>(loc, intValue);
}
}
if (isa<Torch::BoolType>(type)) {
return builder.create<Torch::ConstantBoolOp>(loc, cast<IntegerAttr>(value));
}
if (isa<Torch::NoneType>(type))
return builder.create<ConstantNoneOp>(loc);
if (auto stringAttr = dyn_cast<StringAttr>(value))
return builder.create<ConstantStrOp>(loc, stringAttr);
if (auto elementsAttr = dyn_cast<ElementsAttr>(value)) {
// Only !torch.vtensor can be constant folded. !torch.tensor has
// non-trivial aliasing semantics which prevent deduplicating it.
assert(isa<ValueTensorType>(type) && "should be a vtensor type!");
return builder.create<ValueTensorLiteralOp>(loc, elementsAttr);
}
return nullptr;
}
```
So when the op has a tensor result type, it must be "ValueTensorType"
due to the **assert** statement. However, many fold methods in
TorchOps.cpp only have a judgment of "BaseTensorType".
After running the model tests in SHARK-TestSuite, I noticed a few model
failures due to half-fusion.
Notably, RDN_pytorch_vaiq_int8 had a depth=5 convolution chain with
multiple AtenViewOp's.
This change enables more customization with operand quantization, and
generalizes the patterns QuantizeOperands and QuantizeTransposeOperands
to QuantizeOperandsPastCommutingOps.
This allows for passing quantization through operations which are
functionally unaffected by quantization, such as view-like ops. The
purpose of this change is to address a myriad of quantization issues
seen in quantized onnx models that have some reshape-like operations
sandwiched in between a dequant and something like a matmul (whose other
operand is immediately quantizable).
While playing with TorchDynamo on ResNet18. I notice following issues:
- `prims.convert_element_type` can’t be canonicalized even if the input
and the output share the same type
- `aten.max_pool2d_with_indices` is always used instead of
`aten.max_pool2d`, even if the second returned output (indices) has no
user
This PR fixes above issues by adding a folder to the
PrimsConvertElementTypeOp and a canonicalizer to the
AtenMaxPool2dWithIndicesOp
Lit test:
`cmake --build build --target check-torch-mlir-all`
---------
Co-authored-by: Ze Zhang <ze.zhang@getcruise.com>
This is part 1 of ~3, formatting all miscellaneous text files and CPP files matched by a first run of pre-commit. These tend to be low change-traffic and are likely not disruptive.
Subsequent patches will format Python files and remaining CPP files.
A choice was made to quantize the return type of Relu with a scale and
zero point copied from the input's quantization scheme. With this
choice, the torch-to-linalg conversion of quantized Relu essentially
computes max(input, zeroPoint) in the elementwise payload.
Decomposition RepeatInterleaveSelfInt with following ops:
```python
def my_repeat_interleave(input, repeats, dim=None):
if dim is None:
# Flatten the input and then repeat
return input.flatten().unsqueeze(-1).tile((1, repeats)).flatten()
else:
# Calculate the shape after repeat
expanded_shape = list(input.shape)
expanded_shape[dim] *= repeats
# Repeat the tensor along the specified dimension
repeat_shape = [1] * (input.dim() + 1)
repeat_shape[dim + 1] = repeats
input = input.unsqueeze(-1)
# Tile and then reshape
tiled = torch.tile(input, repeat_shape)
# Rearrange and reshape
repeated = tiled.reshape(*expanded_shape)
return repeated
```
I passed the tests of stablehlo and linalg. When testing onnx, strange
things happened.
In torch-mlir's CI **torch_nightly** and my own
environment(torch==2.4.0.dev20240318+cpu), it can **pass the pass**.
In torch-mlir's CI **torch_stable**, it **failed**.
The test case is `RepeatInterleaveSelfIntNoDimModule_basic`, the result
shape should be [120].
```python
class RepeatInterleaveSelfIntNoDimModule(torch.nn.Module):
def __init__(self):
super().__init__()
@export
@annotate_args([
None,
([3, 4, 5], torch.float32, True),
])
def forward(self, x):
return x.repeat_interleave(2)
@register_test_case(module_factory=lambda: RepeatInterleaveSelfIntNoDimModule())
def RepeatInterleaveSelfIntNoDimModule_basic(module, tu: TestUtils):
module.forward(tu.rand(3, 4, 5))
```
The error log is as follows:
```
Unexpected outcome summary: (onnx)
****** Failed tests - 1 tests
FAIL - "RepeatInterleaveSelfIntNoDimModule_basic"
@ trace item #0 - call to "forward"
@ output of call to "forward"
ERROR: shape (torch.Size([6, 4, 5])) is not equal to golden shape (torch.Size([120]))
```
@rsuderman
Would you please help me check what's wrong with my PR? Thanks a lot.
1. onnx.MatMulInteger now converts to aten.matmul instead of aten.mm
2. aten.matmul, for ranks >=2, now allows quantized inputs and will
lower to linalg::quantized_matmul or linalg::quantized_batch_matmul.
3. added AtenMatmulOp to the FuseQuantizeOps rewrite patters
QuantizeOperands, QuantizeTransposedOperands, and QuantizeAccumulator
4. added several tests, including some to test AtenMmOp with varying
quantization signed-ness.
5. a quantized matmul mat-vec test is added to verify the failure to
lower to linalg; cleaned of out-of-date code related to common
torch-mlir lowering xfails.
6. in debugging a real model with quantized matmuls, I found a bug on
the scalarize-shapes pass which resulted from the aten.full op folder
returning an incompatible result type. This is fixed by the small change
here to
[lib/Dialect/Torch/IR/TorchOps.cpp](https://github.com/llvm/torch-mlir/compare/main...zjgarvey:torch-mlir:MatMulIntegerFix?expand=1#diff-dc8ed165c207918e606490eee3984b1ad51d7034e6aac36fc046bf47f6f03f4f).
- Added linalg lowering for `AtenFloorDivideScalarOp`
- Needed `AtenDivScalarModeOp` for the decomp.
- Added linalg lowering for `AtenDivScalarModeOp`
- Moved linalg payload logic to `createDivModePayload()` since the logic
was nearly identical for both `AtenDivScalarModeOp` and
`AtenDivTensorModeOp`. Just a template function
- Added `AtenDivScalarModeOp` lowering for stablehlo
Pytorch's
[`torch.floor_divide()`](https://pytorch.org/docs/stable/generated/torch.floor_divide.html)
in a previous version (for a reason unknown to me) preformed a
truncation instead of "floor". The already implemented op
`AtenFloorDivideTensorOp` was done before this change. However, this
wasn't caught because our testcases only tested positive floor division.
I changed this to floor as well as adding a few test cases.
Fix the case PrimListUnpackOp's result num is not equal to PrimList
length.
See the following example:
```python
def forward(self, x):
if len(x.shape) == 5:
b0, t, c0, h0, w0 = x.shape
b, c, h, w = torch.mul(b0, t), c0, h0, w0
else:
b1, c1, h1, w1 = x.shape
b, c, h, w = b1, c1, h1, w1
res = torch.reshape(x, [b, c, h, w])
return res
```
Without this fix, the following error message will occur:
```
/root/torch-mlir/externals/llvm-project/mlir/lib/IR/PatternMatch.cpp:118: virtual void mlir::RewriterBase::replaceOp(mlir::Operation *, mlir::ValueRange): Assertion `op->getNumResults() == newValues.size() && "incorrect # of replacement values"' failed.
```
Previously, it could only handle the situations where outputsize == (1,
1) or outputsize == (input_H, input_W). Now it supports all situations
where input_H % output_H== 0 && input_W % output_W == 0
Shapes can be processed as tensors to represent the set of dimensions.
As reshapes take a list of scalars this can result in a single dynamic
dimension blocking the adjacent static dimensions.
This pass attempts to de-couple tensor computations related to shapes
and propagate values to better support lowering scalar tensor
computations.
See the related issues here:
[SHARK-Turbine#556](https://github.com/nod-ai/SHARK-Turbine/issues/556)
1. Adds uint8 casting to onnx.Cast op
2. Fixes an issue with onnx.DequantizeLinear when the scale comes with
shape [1].
3. Adds support for unsigned types in an AtenItemOp folder
4. Adds a simpler quantized model for easier debugging
5. Adds a fusion pass to convert [quant -> dequant -> transpose -> mm]
patterns to [transpose -> quant -> mm].
6. Moved some xfails that are still not passing, but for different
reasons than onnx.cast failures.
Fix bug of DecomposeAtenSelectIntOp. Because it may use resultTy when
resultTy has not been inferred.
```
auto resultTy = op.getType().cast<BaseTensorType>();
if (sliceTy.getSizes().size() == resultTy.getSizes().size()) {
rewriter.replaceOp(op, slice);
return success();
}
```
So I add restriction.
Reshaping tensors depend on directly matching individual dimensions to
their corresponding dim in the `torch.view` reshape dimensions. This
involves decoupling dynamic dimensions from their static counterparts
and support cleanup / canonicalization.
The previous conversions for AtenAdaptiveAvgPool1dOp and
AtenAdaptiveMaxPool2dOp are refactored into a general templated
conversion that works for all of the AtenAdaptive...PoolNdOp's.
New support is added for the following ops:
1. AtenAdaptiveMaxPool1d
2. AtenAdaptiveMaxPool3d
3. AtenAdaptiveAvgPool3d
Support is also provided for passing inputs without batch dimensions.
For example, applying adaptive_avg_pool2d to an input tensor of rank 3.
After [pytorch #118162](https://github.com/pytorch/pytorch/pull/118162)
gets down to torch-mlir, I'll add a test for AdaptiveMaxPool1d with
return_indices (which will pass with that upstream fix).
---------
Co-authored-by: James Newling <james.newling@gmail.com>
This folds small version of the tensor-scalar comparison operators as
they are commonly used for shape computations. This includes le, lt, ge,
gt, eq, and ne.
This mostly copy-pastes the reduce minimum implementation to reduce max
to improve test coverage. We also improve the aten lowering for min/max
dim for unsigned types.
Current implementation depends on using `aten.view` which has issues
inferring tensor collapse/expand operations during the lowering to
`linalg`. Using flatten and unsqueeze better infers what the later
reshape behavior.
Add e2d support for `aten.linalg_norm` by decompose it to
`aten.linalg_vector_norm`.
Lowering to `aten.linalg_matrix_norm` is still unsupported.
To Test:
`python -m e2e_testing.main -v`
---------
Co-authored-by: Ze Zhang <ze.zhang@getcruise.com>
A handful of operations are commonly used in shape calculations (slice,
concat, broadcast). Added these additional folders to better propagate
simple shape computations.
Existing lowering via aten.view does not work as well for dynamic shapes
as the lowering to tensor.expand must re-infer dynamic shape matching.
Better to directly lower.
Finish supporting importing the vast majority of `onnx` operations. This
includes:
- region support
- region value inherentance
- `torch.string` support
- `torch.list` support
- `torch.optional` support
A bunch of small fixes are interlinked and trigger crashes if not
addressed as a group. This includes:
- aten view when expand from a rank-0 tensor
- slice folder with negative indices
- `aten._shape_as_tensor` folder on a rank-0 tensor
- `aten.cat` of a tensor with a length-0 tensor
The decomposition only suports a NCHW lowering however the operation can
support arbitrary spatial dimensions. Updated the lowering to better
support spatial dimensions.
Torch lowering only supported the most recent version. Refactored the
lowering so more easily handle default values and optional operands /
attributes.
Strided slicing can occur with a negative stride. In these cases we need
to bound end differently. This included removing a function that was
generating bad limits.
Simple folder for limited size aten tensor operations. This is primarily
useful for shape computation folding as they unfortunately can use
`aten` operators. Add, sub, mul are common examples of these folders.
This commit adds the OnnxToTorch lowering for cosh, acosh, asin, asinh,
and atanh op.
This commit also adds the TorchToLinalg lowering for acosh, asin, asinh,
and atanh op.
Signed-Off By: Vivek Khandelwal <vivekkhandelwal1424@gmail.com>
Some operations include a backend matcher for specialized operations. We
map these back to generics so they appropriately match to the high
performance versions. This is done for the attention operation.
The lowering decomposes AtenTraceOp into an AtenDiagonalOp followed by
AtenSumOp.
The progress is tracked in
https://github.com/nod-ai/SHARK-Turbine/issues/333.
---------
Co-authored-by: Franz Haniel <franz.haniel@amd.com>
Folds aten::index_select ops under the following conditions:
1. If the input and output are the same shape, the indexing operation is
a NOP, so just return the input.
2. If the input has shape <1x1x...xNx...x1> (all 1's except for one
dim), and the output shape is <1x1x...x1> (all 1's), then there is a
single index, so extract the single element value and return a tensor
with that value.
---------
Co-authored-by: Dave Liddell <dliddell@xilinx.com>
Lowering of torch.aten.all.dim to linalg.
Per PyTorch documentation:
> This function matches the behaviour of NumPy in returning output of
dtype bool for all supported dtypes except uint8. For uint8 the dtype of
output is uint8 itself.
Since there is no support for ui8 in torch-mlir currently
(https://github.com/llvm/torch-mlir/pull/1384#issuecomment-1260011334)
implementation returns failure for that case.
If a tensor is initialized by a list with a single constant integer,
this folder turns it into a torch.vtensor.literal
---------
Co-authored-by: Dave Liddell <dliddell@xilinx.com>
Leaning on the QDQ functionality in torch we can support the QLinearConv
operation by piggybacking through `torch.Convolution`. This includes
some changes such as allowing the `onnx` rewriter to run recursively.
Doing so allows `QLinearConv` to decopmose to `onnx.Convolution` which
is then lowered to `torch`.
So that the CumSum Op in OPT can get the constant that it requires to be lowered to TMTensor
---------
Co-authored-by: Rob Suderman <rob.suderman@gmail.com>
Co-authored-by: Xida Ren <xida.ren.dev@gmail.com>
Linalg has quantized specific operations. We can lower to these
operations when there is a known zeropoint and scale operations. This
allows the `convolution` to occur with lower bitwidth's, improving the
overall performance.
We were seeing some assertion failures after some checks around folders
were tightened up in LLVM:
https://github.com/llvm/llvm-project/pull/75887 . This PR essentially
moves the logic that used to be applied at the LLVM level into the
folder, which seems to be the suggested fix.
I'm not sure if the IR that caused issues for us _should_ be valid?
```
%1 = torch.aten.detach %arg0 : !torch.tensor<[1],f32> -> !torch.tensor
```
A better fix might be to create a verifier ensuring the result of
`aten.detach` has the same type as its operand.
---------
Co-authored-by: aaron-stgeorge <aaron.stgeorge@getcruise.com>
After noticing a number of commits with unrelated formatting changes,
I think something was changed with clang-format at one point and we're
seeing a number of unrelated changes. Doing a refresh can help avoid
this.
The changes made here came from
```
find lib -iname *.h -o -iname *.cpp | xargs clang-format -i --style=llvm
find include -iname *.h -o -iname *.cpp | xargs clang-format -i --style=llvm
find projects -iname *.h -o -iname *.cpp | xargs clang-format -i --style=llvm
```
This preserves sparsity at the most obvious places of lowering TORCH
tensors to MLIR RankedTensorType tensors. Other places are marked for
audit. With some initial lowering tests.
This adds an encoding field to the torch type, using the interfaces for
printing, parsing, and verification. Note that although this change
prepares adding sparsity to the torch type (as illustrated by the round
trip and invalid tests), nothing in this change depends on the actual
contents of the encoding field!
This includes custom op matching for decomposed operations and fusing
dequantization into dense operations. As a validation we compare
to the dequant+mm torch implementation.
The logic here is very similar to the conversion for AdaptiveAvgPool1d
#2661 with a few modifications:
1. buffVal = -inf instead of 0
2. the main linalg generic op accumulates a max, instead of a sum, to
the first output tensor
3. avg pooling requires dividing the sum pool by the kernel width, which
we stored as an auxilliary tensor (kSizeTensor). Here, the auxiliary
tensor will be recording the indices. Strangely enough, the only
signature available for this function is to return indices, and it
appears that they must be computed whether the user desires them or not.
See
[pytorch/torch/nn/functional.py](https://github.com/pytorch/pytorch/blob/main/torch/nn/functional.py#L1174).
Before writing other adaptive pooling conversions, the logic of this
decomposition should be rolled into a helper function that will work for
both max and avg pooling ops. Even the auxiliary tensor should likely be
automated. This code was written in a slightly more tedious way than
strictly necessary (often using loops to fill SmallVectors up to rank-2,
which is only two in this case), in order to more easily facilitate the
transition to a helper function.
convolution with [time,batch,channel] ordering, as opposed to the
default [batch, channel, time]. Currently implementing by transposing
the input and output, but may need to get its own implementation in the
future because this is supposed to be an op that gives a speedup. This
is used by fairseq
(https://github.com/facebookresearch/fairseq/issues/172).
(in case you were wondering like me, this is different from transposed
convolution. Transposed convolution has fractional strides).
---------
Co-authored-by: Xida Ren <xida.ren.dev@gmail.com>
Co-authored-by: Frederik Harwath <frederik.harwath@amd.com>
Handle both `torch.dequantize` and `torch.quantize_per_tensor` including
the op based quantization parameter tracking. This includes adding
`qint32` to torch types as it was missing during the initial type
inclusion.
For testing we only have `torch.int8` and `torch.float` types on
function boundaries as the `qint8` types require passing the scale
and zero point quantization information which is not supported yet.
Adds a lowering to Linalg for reflection_pad1d. Based on ideas/code from draft PR
https://github.com/llvm/torch-mlir/pull/2693.
---------
Co-authored-by: Kumar Deepak <kumar@xilinx.com>
The expression for HardSigmoid in Onnx
(https://onnx.ai/onnx/operators/onnx__HardSigmoid.html): max(0, min(1,
alpha * x + beta))
is inherently different from HardSigmoid in Torch
(https://pytorch.org/docs/stable/generated/torch.nn.Hardsigmoid.html)
which is: if x < -3 -> 0
elif x > 3 -> 1
else x/6 + 1/2
That being said, it was just better to compute out the entire expression
when translating the Onnx expression to Torch mlir, which is done in
this PR. Some of the logic is shared from the files in
`DecomposeComplexOps`. Therefore, refactored some shared logic between
`DecomposeComplexOps` and `DefaultDomainGToP` and put it in a `Utils`
file.
`AtenStackOp` defines this folder for list operand containing single
element:
```
OpFoldResult AtenStackOp::fold(FoldAdaptor adaptor) {
auto list = getOperand(0).getDefiningOp<PrimListConstructOp>();
if (!list || !list->hasOneUse() || list.getElements().size() != 1)
return nullptr;
return list.getElements()[0];
}
```
However, unlike `AtenCatOp`, `AtenStackOp` cannot be folded away for
single element list operand because the result from a stack operation
contains an additional dimension (of size 1, like expand_shape).
This PR removes the `AtenStackOp::fold` method, and adds an e2e test for
single element list input case, which fails on current `main` as
follows:
```
Unexpected outcome summary: (linalg)
****** Failed tests - 1 tests
FAIL - "TensorsStackSingleElementListModule_basic"
@ trace item #0 - call to "forward"
@ output of call to "forward"
ERROR: shape (torch.Size([10, 32])) is not equal to golden shape (torch.Size([10, 1, 32]))
```
Thanks Chris Lalau Keraly for the bug report.
This commit adds the OnnxToTorch support for BitwiseXor, BitwiseOr, Div, Equal, Cast,
Ceil, Floor, Cos, and Clip op.
This commit also adds the TorchToLinalg support for aten.clamp.Tensor and aten.clamp_min.Tensor op.
Signed-Off By: vivekkhandelwal1424@gmail.com
Adds a lowering for the torch.aten.argmin operator to linalg via decomposition into torch.aten.min.dim.
---------
Co-authored-by: Franz Haniel <franz.haniel@amd.com>
The function `getTypeForScalarType` currently takes an argument to
specify the signedness of integer types. This is leakage of backend
specific requirements into the torch dialect world. Because
`getTypeForScalarType` is a utility function for the torch dialect, it
should only produce types that match the sign conventions used by
PyTorch (regular integers are signed and unsigned integers are
unsigned).
This commit removes the signedness argument from
`getTypeForScalarType`, and moves the backend specific handling of
integer types to the backend code.
This commit adds the OnnxToTorch support for Atan, Bitshift, BitwiseAnd,
and BitwiseNot op.
This commit also adds the TorchToLinalg support for AtenBitwiseLeftShiftTensorOp.
Signed-Off By: vivekkhandelwal@nod-labs.com
The aten.reshape ops in the decomposition are replaced with prims.collapse
and prims.split_dim ops, which means that the cases where the lowering of
reshape from torch to linalg which are not supported, are avoided.
Essentially, by using the collapse and split_dim ops instead of the
reshape ops, we are not "losing" the information that the reshapes do not
arbitrarily mix dimensions. Which makes lowering easy.
3 additional tests added:
- fully dynamic,
- dynamic only the spatial dimensions,
- dynamic only in the non-spatial dimensions.