Diff 399796

mlir/test/Integration/Dialect/SparseTensor/taco/MTTKRP_test.py

This file was added.

				# RUN: SUPPORTLIB=%mlir_runner_utils_dir/libmlir_c_runner_utils%shlibext %PYTHON %s \| FileCheck %s

				import numpy as np
				import os
				import sys
				import tempfile
				aartbikUnsubmitted Done Reply Inline Actions There are quite a few modifications around the core. Can you move this comment to the exact place where we use the original TACO part, so <code> This PyTACO part is taken from the TACO open-source project. PyTaco <code> aartbik: There are quite a few modifications around the core. Can you move this comment to the exact…

				_SCRIPT_PATH = os.path.dirname(os.path.abspath(__file__))
				sys.path.append(_SCRIPT_PATH)
				from tools import mlir_pytaco_api as pt


				# This PyTACO part is taken from the TACO open-source project.
				# See http://tensor-compiler.org/docs/data_analytics/index.html.
				compressed = pt.compressed
				dense = pt.dense

				# Define fmts for storing the sparse tensor and dense matrices.
				csf = pt.format([compressed, compressed, compressed])
				rm = pt.format([dense, dense])

				# Load a sparse three-dimensional tensor from file (stored in the FROSTT
				# format) and store it as a compressed sparse fiber tensor. We use a small
				# tensor for the purpose of testing. To run the program using the data from
				# the real application, please download the data from:
				# http://frostt.io/tensors/nell-2/
				B = pt.read(os.path.join(_SCRIPT_PATH, "data/nell-2.tns"), csf)

				# These two lines have been modified from the original program to use static
				# data to support result comparison.
				aartbikUnsubmitted Done Reply Inline Actions Modify - >This line has been modified from the original program to .... ? aartbik: Modify - >This line has been modified from the original program to .... ?
				C = pt.from_array(np.full((B.shape[1], 25), 1, dtype=np.float64))
				D = pt.from_array(np.full((B.shape[2], 25), 2, dtype=np.float64))

				# Declare the result to be a dense matrix.
				A = pt.tensor([B.shape[0], 25], rm)
				aartbikUnsubmitted Not Done Reply Inline Actions please do not use commented out code; the test should run as is, and the comment should reflect what is done; if we want to test the other cases too, we should add more tests aartbik: please do not use commented out code; the test should run as is, and the comment should reflect…
				bixiaAuthorUnsubmitted Done Reply Inline Actions Remove this comment. bixia: Remove this comment.

				# Declare index vars.
				i, j, k, l = pt.get_index_vars(4)

				# Define the MTTKRP computation.
				A[i, j] = B[i, k, l] * D[l, j] * C[k, j]


				# CHECK: Compare result True
				# Perform the MTTKRP computation and write the result to file.
				with tempfile.TemporaryDirectory() as test_dir:
				actual_file = os.path.join(test_dir, "A.tns")
				pt.write(actual_file, A)
				actual = np.loadtxt(actual_file, np.float64)
				expected = np.loadtxt(os.path.join(_SCRIPT_PATH, "data/gold_A.tns"),
				np.float64)
				print(f"Compare result {np.allclose(actual, expected, rtol=0.01)}")

mlir/test/Integration/Dialect/SparseTensor/taco/README.md

This file was added.

# MLIR-PyTACO: Implementing PyTACO with MLIR

TACO (http://tensor-compiler.org/) is a tensor algebra compiler. TACO defines

PyTACO, a domain specific language in Python, for writing tensor algebra

applications.

This directory contains the implementation of PyTACO using MLIR. In particular,

we implement a Python layer that accepts the PyTACO language, generates MLIR

linalg.generic OPs with sparse tensor annotation to represent the tensor

zero9178Unsubmitted

Done

This directory contains the implementation of PyTACO using MLIR. In particular,

- we implememt a Python layer that accepts the PyTACO lauguage, generates MLIR

+ we implement a Python layer that accepts the PyTACO language, generates MLIR

linalg.generic OPs with sparse tensor annotation to represent the tensor

zero9178:

computation, and invokes the MLIR sparse tensor code generator

(https://mlir.llvm.org/docs/Dialects/SparseTensorOps/) as well as other MLIR

compilation passes to generate an executable. Then, we invoke the MLIR execution

engine to execute the program and pass the result back to the Python layer.

aartbikUnsubmitted

Not Done

machine code -> an executable, or runnable code or something like that?

aartbik: machine code -> an executable, or runnable code or something like that?

bixiaAuthorUnsubmitted

Done

machine code -> an executable

bixia: machine code -> an executable

As can be seen from the tests in this directory, in order to port a PyTACO

program to MLIR-PyTACO, we basically only need to replace this line that

imports PyTACO:

```python

import pytaco as pt

```

with this line to import MLIR-PyTACO:

```python

from tools import mlir_pytaco_api as pt

```

mlir/test/Integration/Dialect/SparseTensor/taco/SpMV_test.py

This file was added.

				# RUN: SUPPORTLIB=%mlir_runner_utils_dir/libmlir_c_runner_utils%shlibext %PYTHON %s \| FileCheck %s

				import numpy as np
				import os
				aartbikUnsubmitted Done Reply Inline Actions same, make it very specific what kernel part is from PyTACO example aartbik: same, make it very specific what kernel part is from PyTACO example
				import sys
				import tempfile

				_SCRIPT_PATH = os.path.dirname(os.path.abspath(__file__))
				sys.path.append(_SCRIPT_PATH)
				from tools import mlir_pytaco_api as pt


				# This PyTACO part is taken from the TACO open-source project.
				# See http://tensor-compiler.org/docs/scientific_computing/index.html.
				compressed = pt.compressed
				dense = pt.dense

				# Define formats for storing the sparse matrix and dense vectors.
				csr = pt.format([dense, compressed])
				dv = pt.format([dense])

				# Load a sparse matrix stored in the matrix market format) and store it
				# as a CSR matrix. The matrix in this test is a reduced version of the data
				# downloaded from here:
				# https://www.cise.ufl.edu/research/sparse/MM/Boeing/pwtk.tar.gz
				# In order to run the program using the matrix above, you can download the
				# matrix and replace this path to the actual path to the file.
				A = pt.read(os.path.join(_SCRIPT_PATH, "data/pwtk.mtx"), csr)

				# These two lines have been modified from the original program to use static
				# data to support result comparison.
				aartbikUnsubmitted Done Reply Inline Actions Modify - >This line has been modified from the original program to .... ? aartbik: Modify - >This line has been modified from the original program to .... ?
				x = pt.from_array(np.full((A.shape[1],), 1, dtype=np.float64))
				z = pt.from_array(np.full((A.shape[0],), 2, dtype=np.float64))

				# Declare the result to be a dense vector
				y = pt.tensor([A.shape[0]], dv)
				aartbikUnsubmitted Done Reply Inline Actions remove commented out code aartbik: remove commented out code

				# Declare index vars
				i, j = pt.get_index_vars(2)

				# Define the SpMV computation
				y[i] = A[i, j] * x[j] + z[i]


				# CHECK: Compare result True
				# Perform the SpMV computation and write the result to file
				with tempfile.TemporaryDirectory() as test_dir:
				actual_file = os.path.join(test_dir, "y.tns")
				pt.write(actual_file, y)
				actual = np.loadtxt(actual_file, np.float64)
				expected = np.loadtxt(os.path.join(_SCRIPT_PATH, "data/gold_y.tns"),
				np.float64)
				print(f"Compare result {np.allclose(actual, expected, rtol=0.01)}")

mlir/test/Integration/Dialect/SparseTensor/taco/data/gold_A.tns

This file was added.

				1 1 12
				1 2 12
				1 3 12
				1 4 12
				1 5 12
				1 6 12
				1 7 12
				1 8 12
				1 9 12
				1 10 12
				1 11 12
				1 12 12
				1 13 12
				1 14 12
				1 15 12
				1 16 12
				1 17 12
				1 18 12
				1 19 12
				1 20 12
				1 21 12
				1 22 12
				1 23 12
				1 24 12
				1 25 12
				2 1 6
				2 2 6
				2 3 6
				2 4 6
				2 5 6
				2 6 6
				2 7 6
				2 8 6
				2 9 6
				2 10 6
				2 11 6
				2 12 6
				2 13 6
				2 14 6
				2 15 6
				2 16 6
				2 17 6
				2 18 6
				2 19 6
				2 20 6
				2 21 6
				2 22 6
				2 23 6
				2 24 6
				2 25 6

mlir/test/Integration/Dialect/SparseTensor/taco/data/gold_y.tns

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				# See http://frostt.io/tensors/file-formats.html for FROSTT (.tns) format
				1 37102
				2 -20.4138
				3 804927

mlir/test/Integration/Dialect/SparseTensor/taco/data/nell-2.tns

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				1 1 1 1.0
				1 2 2 2.0
				1 3 4 3.0
				2 1 1 1.0
				2 4 3 2.0

mlir/test/Integration/Dialect/SparseTensor/taco/data/pwtk.mtx

This file was added.

				%%MatrixMarket matrix coordinate real symmetric
				%-------------------------------------------------------------------------------
				% To download a matrix for a real world application
				% https://math.nist.gov/MatrixMarket/
				%-------------------------------------------------------------------------------
				3 3 5
				1 1 37423.0879671
				2 1 -22.4050781162
				3 1 -300.654980157
				3 2 -.00869762944058
				3 3 805225.750212

mlir/test/Integration/Dialect/SparseTensor/taco/simple_tensor_algebra_test.py

This file was added.

				# RUN: SUPPORTLIB=%mlir_runner_utils_dir/libmlir_c_runner_utils%shlibext %PYTHON %s \| FileCheck %s

				import os
				import sys

				_SCRIPT_PATH = os.path.dirname(os.path.abspath(__file__))
				sys.path.append(_SCRIPT_PATH)
				from tools import mlir_pytaco_api as pt

				compressed = pt.compressed
				dense = pt.dense

				# Ensure that we can run an unmodified PyTACO program with a simple tensor
				# algebra expression using tensor index notation, and produce the expected
				# result.
				i, j = pt.get_index_vars(2)
				A = pt.tensor([2, 3])
				B = pt.tensor([2, 3])
				C = pt.tensor([2, 3])
				D = pt.tensor([2, 3], dense)
				A.insert([0, 1], 10)
				A.insert([1, 2], 40)
				B.insert([0, 0], 20)
				B.insert([1, 2], 30)
				C.insert([0, 1], 5)
				C.insert([1, 2], 7)
				D[i, j] = A[i, j] + B[i, j] - C[i, j]

				# CHECK: [20. 5. 0. 0. 0. 63.]
				aartbikUnsubmitted Done Reply Inline Actions maybe empty line before this CHECK aartbik: maybe empty line before this CHECK
				print(D.to_array().reshape(6))

mlir/test/Integration/Dialect/SparseTensor/taco/tools/lit.local.cfg

This file was added.

				# Files in this directory are tools, not tests.
				config.unsupported = True

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco.py

This file was added.

				# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
				# See https://llvm.org/LICENSE.txt for license information.
				# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception

				"""Experimental MLIR-PyTACO with sparse tensor support.

				See http://tensor-compiler.org/ for TACO tensor compiler.

				This module implements the Python classes for PyTACO index notation. These
				include classes for data types, tensor dimension formats (aka mode formats),
				tensor dimension orderings (aka mode ordering), tensor storage formats, and
				tensors.

				The PyTACO API doesn't follow the naming conversion required by the style guide
				for this module. As such, we first implement the supporting classes and routines
				following the style guide, and then define the type aliases and constants to
				support the PyTACO API in the pytaco_api module.
				"""


				from typing import Any, Callable, Dict, Iterable, List, Optional, Set, Tuple, Union

				import abc
				aartbikUnsubmitted Done Reply Inline Actions empty line after from aartbik: empty line after from
				import ctypes
				import dataclasses
				import enum
				import numpy as np
				import functools
				import operator
				import os
				import threading

				# Import MLIR related modules.
				from mlir import all_passes_registration # Register MLIR compiler passes.
				from mlir import execution_engine
				from mlir import ir
				from mlir import runtime
				from mlir.dialects import arith
				from mlir.dialects import builtin
				from mlir.dialects import linalg
				from mlir.dialects import std
				from mlir.dialects import sparse_tensor
				from mlir.dialects.linalg.opdsl import lang
				from mlir.passmanager import PassManager

				from . import mlir_pytaco_utils as utils


				# TACO naming prefixes.
				_TACO_INDEX_PREFIX = "i"
				_TACO_TENSOR_PREFIX = "A"

				# Bitwidths for pointers and indices.
				_POINTER_BIT_WIDTH = 0
				_INDEX_BIT_WIDTH = 0
				# The name for the environment variable that provides the full path for the
				# supporting library.
				_SUPPORTLIB_ENV_VAR = "SUPPORTLIB"
				# The default supporting library if the environment variable is not provided.
				_DEFAULT_SUPPORTLIB = "libmlir_c_runner_utils.so"
				# The JIT compiler optimization level.
				_OPT_LEVEL = 2
				# The entry point to the JIT compiled program.
				_ENTRY_NAME = "main"

				# Type aliases for type annotation.
				_BinaryOp = Callable[[Any, Any], Any]
				_ExprVisitor = Callable[..., None]
				_ExprInfoDict = Dict["IndexExpr", "_ExprInfo"]
				_LogicalOp = Callable[[bool, bool], bool]
				_ModeFormatOp = Callable[["ModeFormat", "ModeFormat"], "ModeFormat"]
				_SubtreeLeafChecker = Optional[Callable[..., bool]]


				class Type(enum.Enum):
				"""The data types supported by TACO.

				We use numpy data types to implement the enum data types.
				"""
				INT16 = np.int16
				INT32 = np.int32
				INT64 = np.int64
				# numpy _ctype_from_dtype_scalar can't handle float16 yet.
				FLOAT32 = np.float32
				FLOAT64 = np.float64


				# All floating point type enums.
				_FLOAT_TYPES = (Type.FLOAT32, Type.FLOAT64)
				# All integral type enums.
				_INT_TYPES = (Type.INT16, Type.INT32, Type.INT64)
				# Type alias for any numpy type used to implement the runtime support for the
				# enum data types.
				_AnyRuntimeType = Union[np.int16, np.int32, np.int64, np.float32, np.float64]


				@dataclasses.dataclass(frozen=True)
				class DType:
				"""The data type class.

				We support the TACO API dtype class with an alias of this class.

				The following methods are defined by the TACO API:
				is_float: Returns whether the data type represents a floating point value.
				is_int: Returns whether the data type represents an integral value.

				Attributes:
				kind: A Type enum representing the data type.
				value: The numpy data type for the TACO data type.
				"""
				kind: Type = Type.FLOAT64

				def is_float(self) -> bool:
				"""Returns whether the data type represents a floating point value."""
				return self.kind in _FLOAT_TYPES

				def is_int(self) -> bool:
				"""Returns whether the data type represents an integral value."""
				return self.kind in _INT_TYPES

				@property
				def value(self) -> _AnyRuntimeType:
				"""Returns the numpy dtype for the data type."""
				return self.kind.value


				def _mlir_type_from_taco_type(dtype: DType) -> ir.Type:
				"""Returns the MLIR type corresponding to the given TACO type."""
				dtype_to_irtype = {
				Type.INT16: ir.IntegerType.get_signless(16),
				Type.INT32: ir.IntegerType.get_signless(32),
				Type.INT64: ir.IntegerType.get_signless(64),
				Type.FLOAT32: ir.F32Type.get(),
				Type.FLOAT64: ir.F64Type.get()
				}
				return dtype_to_irtype[dtype.kind]


				def _compile_mlir(module: ir.Module) -> ir.Module:
				"""Compiles an MLIR module and returns the compiled module."""
				pipeline = (
				f"sparsification,"
				f"sparse-tensor-conversion,"
				f"builtin.func(linalg-bufferize,convert-linalg-to-loops,convert-vector-to-scf),"
				f"convert-scf-to-std,"
				f"func-bufferize,"
				f"tensor-constant-bufferize,"
				f"builtin.func(tensor-bufferize,std-bufferize,finalizing-bufferize),"
				f"convert-vector-to-llvm{{reassociate-fp-reductions=1 enable-index-optimizations=1}},"
				f"lower-affine,"
				f"convert-memref-to-llvm,"
				f"convert-std-to-llvm,"
				f"reconcile-unrealized-casts")
				PassManager.parse(pipeline).run(module)
				return module


				@functools.lru_cache()
				def _get_support_lib_name() -> str:
				"""Returns the string for the supporting C shared library."""
				return os.getenv(_SUPPORTLIB_ENV_VAR, _DEFAULT_SUPPORTLIB)


				def _ctype_pointer_from_array(array: np.ndarray) -> ctypes.pointer:
				"""Returns the ctype pointer for the given numpy array."""
				return ctypes.pointer(
				ctypes.pointer(runtime.get_ranked_memref_descriptor(array)))


				class ModeFormat(enum.Enum):
				"""The tensor dimension storage format class.

				We support the TACO API mode_format class with an alias of this class.

				In TACO, a tensor dimension is called a mode and the storage format for a
				tensor dimension is called a mode format.
				"""
				DENSE = sparse_tensor.DimLevelType.dense
				COMPRESSED = sparse_tensor.DimLevelType.compressed


				def _mode_format_operation(a: ModeFormat, b: ModeFormat,
				op: _LogicalOp) -> ModeFormat:
				"""Implements the given operator on ModeFormat."""
				return (ModeFormat.COMPRESSED
				if op(a == ModeFormat.COMPRESSED, b == ModeFormat.COMPRESSED) else
				ModeFormat.DENSE)


				def _mode_format_estimator(op: _BinaryOp) -> _ModeFormatOp:
				"""Produces a ModeFormat operator for the given binary operator.

				The ModeFormat operator is used as a heuristic to derive the destination
				dimension sparsity from the source dimension sparsity. In particular, if the
				binary operator produces a disjunction of the zero values from its source
				operands, such as the MUL operator, we return a ModeFormat operator that
				uses operator.or_. That is, we estimate that a dimension for the MUL
				operation result to be sparse if either of its source operands is sparse.

				On the other hand, if the binary operator produces a conjunction of the
				zero values from its source operands, such as the ADD operator, we return
				a ModeFormat operator that uses operator.and_. In this case, we estimate
				that a dimension for the ADD operation result to be sparse if both of its
				source operands are sparse.

				Args:
				op: A _BinaryOp object representing a supporting operator on tensors.

				Returns:
				A ModeFormatOp for estimating the destination dimension sparsity from
				the source dimension sparsity.
				"""
				conjunction = functools.partial(_mode_format_operation, op=operator.and_)
				disjunction = functools.partial(_mode_format_operation, op=operator.or_)
				return conjunction if op(0, 1) != 0 else disjunction


				def _all_instance_of(collection: Iterable, cls: Any) -> bool:
				"""Returns true if all elements of the iterable is an instance of cls."""
				return all(isinstance(e, cls) for e in collection)


				def _identity_ordering(rank: int) -> List[int]:
				"""Returns the identity ordering for tensor of given rank."""
				return list(range(rank))


				@dataclasses.dataclass(frozen=True)
				class ModeOrdering:
				"""The tensor dimension ordering class.

				We support the the TACO API mode_ordering class with an alias of this class.

				Attributes:
				ordering: A list of integers representing the ordering of the tensor
				dimensions.
				"""
				ordering: List[int]

				def __post_init__(self) -> None:
				"""Verifies the value in ordering.

				Raises:
				ValueError: If ordering is not a list of integers.
				"""
				if (not isinstance(self.ordering, list) or
				not _all_instance_of(self.ordering, int)):
				raise ValueError("Ordering must be a list of integers: "
				f"{self.ordering}")
				# Check that ordering is a permutation of the dimension numbers.
				if sorted(self.ordering) != _identity_ordering(self.rank()):
				raise ValueError(f"Invalid ordering: {self.ordering} != "
				f"permutation{_identity_ordering(self.rank())}.")

				def rank(self) -> int:
				"""Returns the number of dimensions represented by the ordering."""
				return len(self.ordering)

				@dataclasses.dataclass(frozen=True)
				class ModeFormatPack:
				"""The tensor dimension format class.

				We support the TACO API mode_format_pack class with an alias of this class.

				The storage format of a tensor contains one mode_format for each tensor
				dimension.

				Attributes:
				formats: A list of ModeFormat representing the storage format for each of
				the tensor dimension.
				"""
				formats: List[ModeFormat]

				def __post_init__(self) -> None:
				"""Verifies the value in formats.

				Raises:
				ValueError: If formats is not a list of ModeFormats.
				"""
				if (not isinstance(self.formats, list) or
				not _all_instance_of(self.formats, ModeFormat)):
				raise ValueError("Formats must be a list of ModeFormat: "
				f"{self.formats}")

				def rank(self) -> int:
				"""Returns the number of dimensions represented by the format pack."""
				return len(self.formats)


				@dataclasses.dataclass
				class Format:
				"""The tensor format class defined by the TACO API.

				Attributes:
				format_pack: A ModeFormatPack representing the storage format for the tensor
				dimensions.
				ordering: A ModeOrdering representing the tensor dimension ordering in the
				storage.
				"""
				format_pack: ModeFormatPack
				ordering: Optional[ModeOrdering] = None

				def __post_init__(self) -> None:
				"""Verifies and fixes up the values in format_pack and ordering.

				Verifies and fixes up the values in format_pack and ordering to supports the
				initializer syntax defined by the TACO API. If format_pack is a list of
				ModeFormat, replaces it with ModeFormatPack constructed from the list. If
				ordering is not provided, set ordering to the natural ordering for the rank
				corresponding to format_pack.

				Raises:
				ValueError: If format_pack is not an instance of ModeFormatPack or if
				ordering is not an instance of ModeOrdering.
				"""
				if isinstance(self.format_pack, list):
				if not _all_instance_of(self.format_pack, ModeFormat):
				raise ValueError(f"Expected a list of ModeFormat: {self.format_pack}")
				self.format_pack = ModeFormatPack(self.format_pack)
				if not isinstance(self.format_pack, ModeFormatPack):
				raise ValueError(f"Expected ModeFormatpack: {self.format_pack}")

				if self.ordering is None:
				self.ordering = ModeOrdering(list(range(self.rank())))
				if not isinstance(self.ordering, ModeOrdering):
				raise ValueError(f"Expected ModeOrdering: {self.ordering}")

				if self.format_pack.rank() != self.ordering.rank():
				raise ValueError("Inconsistent ModeFormatPack and ModeOrdering: "
				f"len({self.format_pack}) != "
				f"len({self.ordering})")

				def is_dense(self) -> bool:
				"""Returns true if all the Tensor dimensions have a dense format."""
				return all([f == ModeFormat.DENSE for f in self.format_pack.formats])

				def rank(self) -> int:
				"""Returns the number of dimensions represented by the format."""
				return self.format_pack.rank()

				def mlir_tensor_attr(self) -> Optional[sparse_tensor.EncodingAttr]:
				"""Constructs the MLIR attributes for the tensor format."""
				if self.is_dense():
				return None

				order = (
				range(self.rank()) if
				(self.ordering is None) else self.ordering.ordering)
				mlir_storage_format = [f.value for f in self.format_pack.formats]
				return sparse_tensor.EncodingAttr.get(mlir_storage_format,
				ir.AffineMap.get_permutation(order),
				_POINTER_BIT_WIDTH, _INDEX_BIT_WIDTH)


				def _make_format(formats: List[ModeFormat],
				ordering: Optional[List[int]] = None) -> Format:
				"""Constructs a format from a list of ModeFormat and an optional ordering.

				Args:
				formats: A list of ModeFormat, one for each dimension of a tensor.
				ordering: An optional list of integer, for the ordering of the tensor
				dimensions. When an ordering is not given, the identity ordering is used.

				Returns:
				A tensor format object.

				Raises:
				ValueError: If formats is not a list of ModeFormat or the length of formats
				is not consistent with the len of ordering.
				"""
				ordering = ordering or _identity_ordering(len(formats))
				return Format(ModeFormatPack(formats), ModeOrdering(ordering))


				class _AtomicCounter:
				"""An atomic counter."""

				def __init__(self):
				self._counter = 0
				self._counter_lock = threading.Lock()

				def increment(self) -> int:
				"""Increments the counter by one and returns the old value."""
				old_value = self._counter
				with self._counter_lock:
				self._counter = self._counter + 1
				return old_value


				class IndexVar:
				"""The tensor index class.

				We support the TACO API index_var class with an alias of this class.

				An IndexVar object represents an index variable in tensor index notation.

				Attributes:
				name: A unique string name of the IndexVar.
				"""
				_counter = _AtomicCounter()

				def __init__(self):
				id = self._counter.increment()
				self._name = f"{_TACO_INDEX_PREFIX}{id}"

				def __repr__(self) -> str:
				return f"IndexVar(name={repr(self._name)})"

				@property
				def name(self) -> str:
				"""Returns the name of the IndexVar."""
				return self._name


				def get_index_vars(n: int) -> List[IndexVar]:
				"""Returns a list of n IndexVar.

				This routine is defined by the TACO API.

				Args:
				n: An interger representing the number of IndexVar to get.

				Returns:
				A list of IndexVar.

				Raises:
				ValueError: if n is not a positive integer.
				"""
				if not isinstance(n, int) or n <= 0:
				raise ValueError(f"Expected an integer: {n}.")
				# If lock contention ever becomes an issue, we could implement a bulk getter
				# that returns a range by only claiming the lock once.
				return [IndexVar() for i in range(n)]


				def _mlir_symbols_from_index_vars(
				index_vars: Tuple[IndexVar, ...]) -> Tuple[lang.SymbolDef, ...]:
				"""Returns a tuple of MLIR symbols for the given tuple of index_var."""
				return tuple(getattr(lang.S, i.name) for i in index_vars)


				def _mlir_dimensions_from_index_vars(
				index_vars: Tuple[IndexVar, ...]) -> Tuple[lang.DimDef, ...]:
				"""Returns a tuple of MLIR dimensions for the given tuple of index_var."""
				return tuple(getattr(lang.D, i.name) for i in index_vars)


				def _mlir_tensor_type(
				dtype: DType, shape: Tuple[int, ...],
				attr: Optional[sparse_tensor.EncodingAttr]) -> ir.RankedTensorType:
				"""Returns an MLIR tensor type.

				Args:
				dtype: An DType object for the element data type of the tensor.
				shape: A tuple of integer for the shape of the tensor.
				attr: An optional MLIR sparse tensor attribute, only provided if the tensor
				is a sparse tensor.

				Returns:
				An MLIR ranked tensor type.
				"""
				ir_type = _mlir_type_from_taco_type(dtype)
				return ir.RankedTensorType.get(shape, ir_type, attr)


				def _verify_and_normalize_indices(indices) -> Tuple[IndexVar, ...]:
				"""Verifies and normalizes the indices for a tensor access.

				Args:
				indices: The index expression used to access a tensor, which could be any
				Python object from user inputs.

				Returns:
				A tuple of IndexVar.

				Raises:
				ValueError: If indices is not an IndexVar or a tuple of IndexVar.
				"""
				if isinstance(indices, IndexVar):
				return (indices,)
				elif isinstance(indices, tuple) and _all_instance_of(indices, IndexVar):
				return indices

				raise ValueError(f"Expected IndexVars: {indices}")


				@dataclasses.dataclass(frozen=True)
				class _StructOpInfo:
				"""Information for generating a structured op in the linalg dialect.

				This information is associated with an expression node that serves as the
				root for an expression subtree implemented with a structured op.

				Attributes:
				dst_indices: A tuple of IndexVar, representing the result dimensions of the
				structured op. This is used to construct the temporary variable for the
				tensor to hold the structured op result.
				dst_dims: A tuple of int, representing the result shape of the structured
				op.
				dst_dtype: A DType representing the data type of the structured op result.
				dst_name: A string representing the name of the structured op result.
				dst_format: A Format object representing the destination tensor format.
				"""
				dst_indices: Tuple[IndexVar, ...]
				dst_dims: Tuple[int, ...]
				dst_dtype: DType
				dst_name: str
				dst_format: Format

				def __post_init__(self) -> None:
				"""Verifies the integrity of the attribute values."""
				assert len(self.dst_indices) == len(self.dst_dims)
				assert self.dst_format is not None

				def emit_tensor_init(self) -> ir.RankedTensorType:
				"""Returns an initialization for the destination tensor."""
				if self.dst_format.is_dense():
				# Initialize the dense tensor.
				ir_type = _mlir_type_from_taco_type(self.dst_dtype)
				tensor = linalg.InitTensorOp(self.dst_dims, ir_type).result
				zero = arith.ConstantOp(ir_type, 0.0)
				return linalg.FillOp(output=tensor, value=zero).results[0]

				# Initialize the sparse tensor.
				mlir_type = _mlir_tensor_type(self.dst_dtype, self.dst_dims,
				self.dst_format.mlir_tensor_attr())
				index_type = ir.IndexType.get()
				dims = [arith.ConstantOp(index_type, d).result for d in mlir_type.shape]
				return sparse_tensor.InitOp(mlir_type, dims)


				class _Stats:
				"""Information to describe how a tensor expression is implemented.

				Currently, we only record the temporary tensors introduced for splitting the
				original expression.
				"""

				def __init__(self):
				self._temps = []

				def __repr__(self) -> str:
				return f"_Stats({repr(self._temps)})"

				def add_element(self, structop: _StructOpInfo):
				"""Adds a temporary tensor."""
				self._temps.append(structop)

				def get_total(self) -> int:
				"""Gets the total number of temporary tensors."""
				return len(self._temps)

				def _get_element(self, idx: int) -> _StructOpInfo:
				"""Gets the ith temporary tensor."""
				assert idx < self.get_total()
				return self._temps[idx]

				def get_dimensions(self, idx: int) -> Tuple[int]:
				"""Gets the dimensions for the ith temporary tensor."""
				return self._get_element(idx).dst_dims

				def get_formats(self, idx: int) -> Tuple[ModeFormat]:
				"""Gets the ModeFormats for the ith temporary tensor."""
				return tuple(self._get_element(idx).dst_format.format_pack.formats)


				class Tensor:
				"""The tensor class.

				We support the TACO API tensor class with an alias of this class.

				This class is part of the TACO API with the following methods:
				insert: Inserts a value to the given coordinate in the tensor.
				to_array: Returns a numpy ndarray for the tensor.

				TACO API also defines the following arrtibutes for the class:
				dtype: A dtype object representing the data type of the tensor.
				format: A format object representing the storage format of the tensor.
				name: A string object representing the name of the tensor.
				order: An integral rank of the tensor.
				shape: A list of integers representing the shape of the tensor.

				We currently ignore the tensor dimension ordering for dense tensor.
				"""
				_counter = _AtomicCounter()

				def _get_unique_name(self) -> str:
				"""Returns a unique name for creating a new Tensor."""
				return f"{_TACO_TENSOR_PREFIX}{self._counter.increment()}"

				def _init_format(self, fmt: Union[ModeFormat, List[ModeFormat],
				Format]) -> None:
				"""Process the fmt argument for the Tensor constructor.

				Args:
				fmt: This argument can be a ModeFormat, List[ModeFormat], or format. If
				this argument is a ModeFormat, uses this ModeFormat for all the tensor
				dimensions. If this argument is a list of ModeFormat, the len of the
				list should equal to the rank of the tensor. If this argument is a
				format, uses it for the format of the tensor.

				Raises:
				ValueError: If fmt is not one of the expected type or is inconsistent
				with the rank of the tensor. This is because fmt could be an users
				input.
				"""
				if isinstance(fmt, ModeFormat):
				self._format = _make_format([fmt] * self.order)
				elif isinstance(fmt, list):
				if len(fmt) == self.order and isinstance(fmt[0], ModeFormat):
				self._format = _make_format(fmt)
				else:
				raise ValueError("Inconsistent shape and format: "
				f"{self._shape}, {fmt}.")
				elif isinstance(fmt, Format):
				if fmt.rank() != self.order:
				raise ValueError("Inconsistent shape and format: "
				f"{self._shape}, {fmt}.")
				else:
				self._format = fmt
				else:
				raise ValueError(f"Invalid format argument: {fmt}.")

				def __init__(self,
				value_or_shape: Optional[Union[List[int], Tuple[int, ...], float,
				int]] = None,
				fmt: Optional[Union[ModeFormat, List[ModeFormat],
				Format]] = None,
				dtype: Optional[DType] = None,
				name: Optional[str] = None):
				"""The tensor constructor interface defined by TACO API.

				Args:
				value_or_shape: This argument is optional and can be int, float,
				List[int], or Tuple[int, ...]. If this argument is an int or float,
				creates a scalar tensor and initializes it with the value. If this
				argument is a list or tuple of int, uses it as the shape to create a
				tensor.
				fmt: This argument can be a ModeFormat, List[ModeFormat], or format. If
				this argument is a ModeFormat, uses this ModeFormat for all the tensor
				dimensions. If this argument is a list of ModeFormat, the len of the
				list should equal to the rank of the tensor. If this argument is a
				format, uses it for the format of the tensor.
				dtype: An object of dtype, representing the data type of the tensor.
				name: A string name of the tensor. If a name is not given, creates a
				unique name for the tensor.

				Raises:
				ValueError: If there is any inconsistency among the input arguments.
				"""
				# Take care of the argument default values.
				fmt = fmt or ModeFormat.COMPRESSED
				dtype = dtype or DType(Type.FLOAT64)
				self._name = name or self._get_unique_name()

				self._dtype = dtype
				# We currently use _coords and _values to host the sparse tensor value with
				# COO format, and _dense_storage to host the dense tensor value. We haven't
				# implement the conversion between the two storages yet. This will be
				# improved in a follow up CL.
				self._coords = []
				self._values = []
				self._dense_storage = None
				self._stats = _Stats()
				if value_or_shape is None or isinstance(value_or_shape, int) or isinstance(
				value_or_shape, float):
				# Create a scalar tensor and ignore the fmt parameter.
				self._shape = []
				self._format = _make_format([], [])
				if value_or_shape is not None:
				self._dense_storage = np.array(value_or_shape, dtype=self._dtype.value)
				elif (isinstance(value_or_shape, tuple) or isinstance(
				value_or_shape, list)) and _all_instance_of(value_or_shape, int):
				# Create a tensor with the specified shape and format.
				self._shape = list(value_or_shape)
				self._init_format(fmt)
				else:
				raise ValueError("Invalid first argument. "
				"Must be a tuple or list for a shape or a single value"
				f"if initializing a scalar tensor: {value_or_shape}.")

				def __repr__(self) -> str:
				value_str = (f"{repr(self._dense_storage)})" if self.is_dense() else
				f"{repr(self._coords)} {repr(self._values)})")
				return (f"Tensor(_name={repr(self._name)} "
				f"_dtype={repr(self._dtype)} : ") + value_str

				def insert(self, coords: List[int], val: Union[float, int]) -> None:
				"""Inserts a value to the given coordinate.

				Args:
				coords: A list of integer coordinates. The length of the list must be the
				same as the rank of the tensor.
				val: A value being inserted. It is either an integral or a floating point
				value. This value will be converted to the data type of the tensor.

				Raises:
				ValueError: When there is any problem in the parameters.
				"""
				if not isinstance(coords, list):
				raise ValueError(f"Non list coordinate detected: {coords}.")
				if not _all_instance_of(coords, int):
				raise ValueError(f"Non integer coordinate detected: {coords}.")
				if (len(coords) != self.order or
				any([c < 0 or c >= self._shape[i] for i, c in enumerate(coords)])):
				raise ValueError("Invalid coordinate for rank: "
				f"{self.order}, {coords}.")

				if not isinstance(val, int) and not isinstance(val, float):
				raise ValueError(f"Value is neither int nor float: {val}.")

				self._coords.append(tuple(coords))
				self._values.append(self._dtype.value(val))

				def is_dense(self) -> bool:
				"""Returns true if all the Tensor dimensions have a dense format."""
				return self._format.is_dense()

				def to_array(self) -> np.ndarray:
				"""Returns the numpy array for the Tensor.

				This is currenly only implemented for dense Tensor.
				"""
				if not self.is_dense():
				raise ValueError("Conversion from non-dense Tensor "
				"to numpy array not supported yet.")
				return self._dense_storage

				@staticmethod
				def from_array(array: np.ndarray) -> "Tensor":
				"""Returns a dense tensor with the value copied from the input array.

				We currently only support the conversion of float64 numpy arrays to Tensor.

				Args:
				array: The numpy array that provides the data type, shape and value for
				the tensor.

				Returns:
				A Tensor object.

				Raises:
				ValueError if the data type of the numpy array is not float64.
				"""
				if array.dtype != np.float64:
				raise ValueError(f"Expected float64 value type: {array.dtype}.")
				tensor = Tensor(array.shape, ModeFormat.DENSE)
				tensor._dense_storage = np.copy(array)
				return tensor

				@staticmethod
				def from_coo(
				coordinates: List[Tuple[int, ...]],
				values: List[_AnyRuntimeType],
				fmt: Format,
				dtype: DType,
				) -> "Tensor":
				"""Converts coordinates and values to a sparse tensor representation.

				Args:
				coordinates: A list of coordinates with non-zero values.
				values: The non-zero values.
				fmt: The tensor storage format.
				dtype: The tensor element data type.

				Returns:
				A tensor with the given non-zero values and storage format. The shape of
				the tensor has the minimum size for each dimension to make the given
				coordinates valid.
				"""
				assert (isinstance(coordinates, List) and
				_all_instance_of(coordinates, Tuple))
				assert (isinstance(values, List) and _all_instance_of(values, dtype.value))
				assert isinstance(fmt, Format)

				rank = fmt.rank()
				assert all(len(c) == rank and _all_instance_of(c, int) for c in coordinates)

				# Find the maximum coordinate value for each dimension.
				max_coordinate = list(map(max, zip(*coordinates)))
				# The size of each dimension is one more that such a maximum coordinate
				# value.
				shape = [c + 1 for c in max_coordinate]
				tensor = Tensor(shape, fmt)
				tensor._coords = coordinates
				tensor._values = values

				return tensor


				@property
				def dtype(self) -> DType:
				"""Returns the data type for the Tensor."""
				return self._dtype

				@property
				def format(self) -> Format:
				"""Returns the storage format for the Tensor."""
				return self._format

				@property
				def name(self) -> str:
				"""Returns the name for the Tensor."""
				return self._name

				@property
				def order(self) -> int:
				"""Returns the rank of the Tensor."""
				return len(self._shape)

				@property
				def shape(self) -> List[int]:
				"""Returns the shape of the Tensor."""
				return self._shape

				def __getitem__(self, key) -> "Access":
				"""Verifies and processes a tensor access.

				In the tensor index notation, a tensor access T[i, j] is represented as
				retrieving a value with key (i, j) from the tensor object T in Python. This
				routine verifies the key for the tensor access and returns a tensor access
				object.

				Args:
				key: The key used to access the tensor, which could be any Python object
				from user inputs.

				Returns:
				The corresponding tensor access object.

				Raises:
				ValueError: If key is not an IndexVar or a tuple of IndexVar.
				"""
				indices = _verify_and_normalize_indices(key)
				return Access(self, indices)

				def __setitem__(self, key, value) -> None:
				"""Verifies and processes a tensor assignment.

				In the tensor index notation, a tensor assignment "T[i, j] = ..." is
				represented as setting a value for a tensor object T via key (i, j) in
				Python. This routine verifies the key, evaluates the value, and assigns the
				value to the tensor.

				We only support assignment of dense tensor currently.

				Args:
				key: The key used to access the tensor, which could be any Python object
				from user inputs.
				value: The value assigned to the tensor, which could be any Python object
				from user inputs.

				Raises:
				ValueError: If tensor is not a dense tensor, or the key is not an IndexVar
				or a tuple of IndexVar, or the length of the indices is not the same as
				the rank of the tensor.
				"""
				indices = _verify_and_normalize_indices(key)
				if len(indices) != self.order:
				raise ValueError("Mismatch between indices and tensor rank: "
				f"len({indices}) != {self.order}.")

				result = value.evaluate(self, indices)
				if self.is_dense():
				assert isinstance(result, np.ndarray)
				self._dense_storage = result
				else:
				assert _all_instance_of(result, np.ndarray) and len(result) == 2
				assert (result[0].ndim, result[1].ndim) == (1, 2)
				(self._values, self._coords) = result

				def mlir_tensor_type(self) -> ir.RankedTensorType:
				"""Returns the MLIR type for the tensor."""
				return _mlir_tensor_type(self._dtype, tuple(self._shape),
				self._format.mlir_tensor_attr())

				def dense_dst_ctype_pointer(self) -> ctypes.pointer:
				"""Returns the ctypes pointer for the pointer to an MemRefDescriptor.

				For a dense tensor output, the MLIR compiler allocates the storage for
				the tensor. This routine returns the pointer to an MLIR MemRefDescriptor for
				receiving the tensor.
				"""
				assert self.is_dense()
				mem_ref_desc = runtime.make_nd_memref_descriptor(
				self.order, np.ctypeslib.as_ctypes_type(self.dtype.value))()
				return ctypes.pointer(ctypes.pointer(mem_ref_desc))

				def ctype_pointer(self) -> ctypes.pointer:
				"""Returns the ctypes pointer for the pointer to the input tensor."""
				if self.is_dense():
				if self._dense_storage is None:
				self._dense_storage = np.zeros(self._shape, self._dtype.value)
				return _ctype_pointer_from_array(self._dense_storage)

				shape = np.array(self._shape, np.int64)
				indices = np.array(self._coords, np.int64)
				values = np.array(self._values, self._dtype.value)
				ptr = utils.coo_tensor_to_sparse_tensor(_get_support_lib_name(), shape,
				values, indices)
				return ctypes.pointer(ctypes.cast(ptr, ctypes.c_void_p))

				def get_coordinates_and_values(
				self) -> Tuple[List[Tuple[int, ...]], List[_AnyRuntimeType]]:
				"""Returns the coordinates and values for the non-zero elements."""
				if not self.is_dense():
				return (self._coords, self._values)

				# Coordinates for non-zero elements, grouped by dimensions.
				coords_by_dims = self._dense_storage.nonzero()
				# Coordinates for non-zero elements, grouped by elements.
				coords = np.transpose(coords_by_dims)
				values = self._dense_storage[coords_by_dims]
				return (coords, values)

				def _record_stats(self, structop: "_StructOpInfo"):
				"""Collects information for temporary tensors."""
				# Exclude user specified destination tensors.
				if structop.dst_name == self.name:
				return

				self._stats.add_element(structop)


				def _emit_operand(op_def: lang.LinalgOpDef, indices: Tuple[IndexVar, ...],
				name: str, kind: lang.OperandKind) -> lang.OperandDef:
				"""Emits an operand for a tensor access in the current linalg operation.

				Args:
				op_def: A LinalgOpDef representing the current linalg dialect operation.
				indices: A tuple of IndexVar used to access the tensor.
				name: A unique string name of the tensor.
				kind: An OperandKind for the operand.

				Returns:
				An OperandDef representing the operand.
				"""
				dim_sym = _mlir_symbols_from_index_vars(indices)
				opnd = lang.OperandDef(kind, lang.T, dim_sym)
				op_def.add_operand(name, opnd)
				return opnd


				@dataclasses.dataclass(frozen=True)
				class _DimInfo:
				"""Information for an operand dimension.

				Attributes:
				dim: An integer for the size of the dimension.
				mode_format: A ModeFormat for the dimension sparsity.
				"""
				dim: int
				mode_format: ModeFormat


				@dataclasses.dataclass()
				class _ExprInfo:
				"""Expression information for validation and code generation.

				Attributes:
				src_indices: A tuple of IndexVar for the indices used by the tensors in the
				expression tree.
				dim_infos: A tuple of _DimInfo, representing the dimension information
				corresponding to the src_indices.
				reduce_indices: A set of IndexVar for the indices reduced by the expression.
				acc_reduce_indices: An accumulated set of IndexVar for the indices reduced
				by the expression and its children.
				structop_info: Information to support the code generation for a structured
				op in the linalg dialect, if the corresponding expression node is the root
				of a subtree for a structured op.
				mlir_value: The MLIR value generated for the structured op.
				"""
				src_indices: Tuple[IndexVar, ...]
				dim_infos: Tuple[_DimInfo, ...]
				reduce_indices: Optional[Set[IndexVar]] = None
				acc_reduce_indices: Optional[Set[IndexVar]] = None
				structop_info: Optional[_StructOpInfo] = None
				mlir_value: Optional[ir.Value] = None

				def __post_init__(self) -> None:
				"""Verifies and fix up attribute values.

				Verifies the consistency of the attributes and modifies the default values
				to support convenient initializer syntax.
				"""
				assert len(self.src_indices) == len(self.dim_infos)
				self.reduce_indices = self.reduce_indices or set()
				self.acc_reduce_indices = self.acc_reduce_indices or set()

				class IndexExpr(abc.ABC):
				"""The index notation base class.

				We support the TACO API index_expression class with an alias of this class.
				"""

				def _verify_operand_and_build_expr(self, rhs, op: _BinaryOp) -> "_BinaryExpr":
				"""Verifies the RHS operand and returns a binary expression.

				Args:
				rhs: The RHS of the binary operation, which could be any Python object
				from user inputs.
				op: A _BinaryOp object representing the binary operator.

				Raises:
				ValueError: If rhs is not an IndexExpr.
				"""
				if not isinstance(rhs, IndexExpr):
				raise ValueError(f"Expected IndexExpr: {rhs}")
				return _BinaryExpr(op, self, rhs)

				def __add__(self, rhs) -> "_BinaryExpr":
				"""Defines the operator +.

				Args:
				rhs: The value being added, which could be any Python object from user
				inputs.

				Returns:
				A _BinaryExpr object representing the operation.

				Raises:
				ValueError: If rhs is not an IndexExpr.
				"""
				return self._verify_operand_and_build_expr(rhs, operator.add)

				def __mul__(self, rhs) -> "_BinaryExpr":
				"""Defines the operator *.

				Args:
				rhs: The value being multiplied, which could be any Python object from
				user inputs.

				Returns:
				A _BinaryExpr object representing the operation.

				Raises:
				ValueError: If rhs is not an IndexExpr.
				"""
				return self._verify_operand_and_build_expr(rhs, operator.mul)

				def __sub__(self, rhs) -> "_BinaryExpr":
				"""Defines the operator -.

				Args:
				rhs: The value being subtracted, which could be any Python object from
				user inputs.

				Returns:
				A _BinaryExpr object representing the operation.

				Raises:
				ValueError: If rhs is not an IndexExpr.
				"""
				return self._verify_operand_and_build_expr(rhs, operator.sub)

				@abc.abstractmethod
				def _visit(self,
				func: _ExprVisitor,
				args,
				*,
				leaf_checker: _SubtreeLeafChecker = None) -> None:
				"""A post-order visitor.

				Args:
				func: A callable applied to each node in the expression tree.
				args: The variable-length arguments passed to the callable. These
				arguments are grouped as an iterable and will be unpacked before passing
				to the callable. This is to enable the keyword argument only syntax
				after this argument.
				leaf_checker: A callable object to identify nodes that should be treated
				as leaf nodes to support partial tree visiting.
				"""
				pass

				@abc.abstractmethod
				def _emit_expression(
				self,
				expr_to_opnd: Dict["IndexExpr", lang.OperandDef],
				expr_to_info: _ExprInfoDict,
				) -> lang.ScalarExpression:
				"""Emits MLIR for the expression tree.

				Args:
				expr_to_opnd: A dictionary for looking up structured op input operands for
				the input nodes of the structured op.
				expr_to_info: A dictionary for looking up code generation information for
				expressions.

				Returns:
				A linalg dialect ScalarExpression for the expression.
				"""
				pass

				@abc.abstractmethod
				def dtype(self) -> DType:
				"""Returns the data type for the result of the expression."""
				pass

				def _emit_structured_op(self, expr_to_info: _ExprInfoDict) -> None:
				"""Emits a structured op in the linalg dialect for the expression tree.

				We define a DefineOpcallable in the domain specific language for the linalg
				dialect and execute the callable to generate the structured op. Self is the
				root of the expression tree for the structured op.

				Args:
				expr_to_info: A dictionary for looking up code generation information for
				expressions.
				"""
				op_info = expr_to_info[self].structop_info
				op_name = op_info.dst_name
				op_def = lang.LinalgOpDef(name=op_name)
				op_callable = lang.DefinedOpCallable(op_name, op_def)

				# Collect the input expression nodes for the structured op.
				expr_inputs = []
				self._visit(
				_gather_structured_op_input,
				(self, expr_to_info, expr_inputs),
				leaf_checker=_is_structured_op_leaf,
				)

				# Create a linalg structured op operand for each input expression node and
				# build a dictionary for looking up the information.
				expr_to_input_opnd = {
				e: _emit_structured_op_input(e, expr_to_info, op_def)
				for e in expr_inputs
				}

				# Emit the expression tree, which produces the value assigned to the
				# destination tensor.
				value = self._emit_expression(expr_to_input_opnd, expr_to_info)
				# Emit the structured op representation for the destination tensor.
				dst_opnd = _emit_operand(op_def, op_info.dst_indices, op_info.dst_name,
				lang.OperandKind.OutputTensor)
				dst_dim_syms = _mlir_dimensions_from_index_vars(op_info.dst_indices)
				dst_use = lang.TensorUse(dst_opnd, dst_dim_syms)

				expr_info = expr_to_info[self]
				# If the structured op reduces some indices, explicitly represent the
				# reduction. This is done by generating a ReduceFn for the dimensions being
				# reduced in the linalg dialect and calling the function with the value
				# being reduced. We only support add reduction currently.
				if expr_info.reduce_indices:
				reduce_dims = _mlir_dimensions_from_index_vars(expr_info.reduce_indices)
				value = lang.ReduceFn.add[reduce_dims](value)

				# Emit the assignment as a comprehension in the linalg dialect.
				comp = lang.Comprehension((dst_use, value))
				op_def.comprehensions.append(comp)

				# The structured op in the linalg dialect requires an explicit
				# initialization for the destination tensor. Emit MLIR to initialize the
				# destination tensor.
				init = op_info.emit_tensor_init()

				# Collect MLIR values for the linalg input operands, with the assumption
				# that dictionary preserves the insertion order.
				args = [
				expr_to_info[expr].mlir_value
				for expr, opnd in expr_to_input_opnd.items()
				]
				# Execute the DefineOpcallable object for the linalg dialect operation to
				# emit MLIR for the linalg structured op.
				expr_info.mlir_value = op_callable(*args, outs=[init])

				def _identify_structured_ops(
				self,
				expr_to_info: _ExprInfoDict,
				dst: Tensor,
				dst_indices: Tuple[IndexVar, ...],
				) -> List["IndexExpr"]:
				"""Returns expression nodes for the roots of the identified structured ops.

				A structured op in the linalg dialect only supports reduction performed on
				the whole expression. If the expression tree contains reduction that are
				performed on part of the expression tree, the expression tree needs to be
				implemented with multiple structured ops. This routine identifies all the
				expression nodes that contain reduction as the root of structured ops in the
				linalg dialect.

				Args:
				expr_to_info: A dictionary for looking up code generation information for
				expressions.
				dst: A destination Tensor that accepts the value of the expression tree.
				dst_indices: The indices used by the destination index expression.

				Returns:
				An ordered list of IndexExpr for the root expressions of the structured
				ops, where child expressions go before parent expressions that use their
				results.
				"""
				reduce_indices = tuple(
				set(expr_to_info[self].src_indices) - set(dst_indices))
				for reduce_index in reduce_indices:
				_mark_structured_op_root(self, reduce_index, expr_to_info)

				self._visit(_accumulate_reduce_indices, (expr_to_info,))
				structop_roots = []
				self._visit(_gather_structured_op, (expr_to_info, structop_roots))

				# Handle the root of the top level expression.
				if not structop_roots or structop_roots[-1] != self:
				# The top level expression is not a reduction. Add the top level
				# expression as a structured op root.
				structop_roots.append(self)

				# Use user specified information for the destination tensor to build an
				# _StructOpInfo for the top level expression.
				expr_to_info[self].structop_info = _StructOpInfo(dst_indices,
				tuple(dst.shape),
				self.dtype(), dst.name,
				dst.format)

				return structop_roots

				def _validate_and_collect_expr_info(
				self,
				dst: Tensor,
				dst_indices: Tuple[IndexVar, ...],
				) -> _ExprInfoDict:
				"""Propagates expression information for validation.

				Propagates the indices used by child expression nodes to parent expression
				nodes. Also collects and validates the sizes for the dimensions
				corresponding to the indices.

				Args:
				dst: A destination Tensor that accepts the value of the expression tree.
				dst_indices: The indices used by the destination index expression.

				Raises:
				ValueError if there is any inconsistency in indices or dimensional
				values.

				Returns:
				A dictionary of (IndexExpr, _ExprInfo).
				"""
				expr_to_info = {}
				# Validate the expression tree and construct expression information.
				self._visit(_validate_and_collect_expr_info, (expr_to_info,))

				# Validate the destination dimension information.
				info = expr_to_info[self]
				index_to_dim_info = {i: d for i, d in zip(info.src_indices, info.dim_infos)}
				for i, d, in zip(dst_indices, dst.shape):
				if i not in index_to_dim_info:
				raise ValueError("Destination IndexVar not used in the "
				f"source expression: {i}")
				else:
				if d != index_to_dim_info[i].dim:
				raise ValueError(f"Inconsistent destination dimension for {i}: "
				f"{d} vs {index_to_dim_info[i].dim}")

				return expr_to_info

				def _emit_assignment(
				self,
				module: ir.Module,
				dst: Tensor,
				dst_indices: Tuple[IndexVar, ...],
				expr_to_info: _ExprInfoDict,
				input_accesses: List["Access"],
				) -> None:
				"""Emits an MLIR function for assigning the expression to a tensor."""
				input_types = [a.tensor.mlir_tensor_type() for a in input_accesses]

				# Build the kernel for the operations.
				with ir.InsertionPoint(module.body):

				@builtin.FuncOp.from_py_func(*input_types, name=_ENTRY_NAME)
				def linalg_funcop(*args):
				# Set up the mapping from the Access nodes to their MLIR values.
				for e, mlir in zip(input_accesses, args):
				expr_to_info[e].mlir_value = mlir

				# Emit structured ops in the linalg dialect to implement the assignment.
				for structop_root in self._identify_structured_ops(
				expr_to_info, dst, dst_indices):
				structop_root._emit_structured_op(expr_to_info)
				dst._record_stats(expr_to_info[structop_root].structop_info)

				# The function returns the MLIR value of the root expression.
				return expr_to_info[self].mlir_value

				linalg_funcop.func_op.attributes[
				"llvm.emit_c_interface"] = ir.UnitAttr.get()

				def evaluate(
				self,
				dst: Tensor,
				dst_indices: Tuple[IndexVar, ...],
				) -> Union[np.ndarray, Tuple[np.ndarray, np.ndarray]]:
				"""Evaluates tensor assignment dst[dst_indices] = expression.

				Args:
				dst: The destination tensor.
				dst_indices: The tuple of IndexVar used to access the destination tensor.

				Returns:
				The result of the dense tensor represented in numpy ndarray or the sparse
				tensor represented by two numpy ndarray for its non-zero values and
				indices.

				Raises:
				ValueError: If the expression is not proper or not supported.
				"""
				expr_to_info = self._validate_and_collect_expr_info(dst, dst_indices)

				# Compute a list of input accesses.
				input_accesses = []
				self._visit(_gather_input_accesses_index_vars, (input_accesses,))

				support_lib = _get_support_lib_name()
				# Build and compile the module to produce the execution engine.
				with ir.Context(), ir.Location.unknown():
				module = ir.Module.create()
				self._emit_assignment(module, dst, dst_indices, expr_to_info,
				input_accesses)
				compiled_module = _compile_mlir(module)

				# We currently rely on an environment to pass in the full path of a
				# supporting library for the execution engine.
				engine = execution_engine.ExecutionEngine(
				compiled_module, opt_level=_OPT_LEVEL, shared_libs=[support_lib])

				# Gather the pointers for the input buffers.
				input_pointers = [a.tensor.ctype_pointer() for a in input_accesses]
				if dst.is_dense():
				# The pointer to receive dense output is the first argument to the
				# execution engine.
				arg_pointers = [dst.dense_dst_ctype_pointer()] + input_pointers
				else:
				# The pointer to receive sparse output is the last argument to the
				# execution engine. The pointer to receive a sparse tensor output is a
				# pointer to pointer of char.
				arg_pointers = input_pointers + [
				ctypes.pointer(ctypes.pointer(ctypes.c_char(0)))
				]

				# Invoke the execution engine to run the module and return the result.
				engine.invoke(_ENTRY_NAME, *arg_pointers)

				if dst.is_dense():
				return runtime.ranked_memref_to_numpy(arg_pointers[0][0])

				# Check and return the sparse tensor output.
				rank, nse, shape, values, indices = utils.sparse_tensor_to_coo_tensor(
				support_lib,
				ctypes.cast(arg_pointers[-1][0], ctypes.c_void_p),
				np.float64,
				)
				assert (np.equal(rank, dst.order) and np.equal(shape, dst.shape) and
				np.equal(values.ndim, 1) and np.equal(values.shape[0], nse) and
				np.equal(indices.ndim, 2) and np.equal(indices.shape[0], nse) and
				np.equal(indices.shape[1], rank))
				return (values, indices)

				@dataclasses.dataclass(frozen=True)
				class Access(IndexExpr):
				"""The tensor access class.

				We support the TACO API access class with an alias of this class.

				Attributes:
				tensor: A Tensor being accessed.
				indices: A tuple of IndexVar, representing the indices used to access the
				Tensor.
				"""
				tensor: Tensor
				indices: Tuple[IndexVar, ...]

				def __post_init__(self) -> None:
				"""Verifies the tensor and indices for a tensor access.

				Raises:
				ValueError: If indices is not a list of IndexVar or the len of indices
				doesn't equal to the rank of the tensor.
				"""
				if (not isinstance(self.indices, tuple) or
				not _all_instance_of(self.indices, IndexVar)):
				raise ValueError(f"Indices contain non IndexVar: {str(self.indices)}.")
				if self.tensor.order != len(self.indices):
				raise ValueError("Invalid indices for rank: "
				f"str{self.tensor.order} != len({str(self.indices)}).")

				def _emit_expression(
				self,
				expr_to_opnd: Dict[IndexExpr, lang.OperandDef],
				expr_to_info: _ExprInfoDict,
				) -> lang.ScalarExpression:
				"""Emits a linalg dialect TensorUse expression for the tensor access."""
				assert self in expr_to_opnd
				dims = _mlir_dimensions_from_index_vars(self.indices)
				return lang.TensorUse(expr_to_opnd[self], dims)

				def _visit(self,
				func: _ExprVisitor,
				args,
				*,
				leaf_checker: _SubtreeLeafChecker = None) -> None:
				if leaf_checker:
				assert leaf_checker(self, *args)
				func(self, *args)

				def dtype(self) -> DType:
				return self.tensor.dtype


				def _gather_input_accesses_index_vars(
				expr: IndexExpr,
				input_accesses: List[Access],
				) -> None:
				"""Collects Access nodes."""
				if isinstance(expr, Access) and expr not in input_accesses:
				input_accesses.append(expr)


				def _op_to_callable(op: _BinaryOp) -> lang.ArithFnType:
				"""Returns the linalg dialect function object for the given operation."""
				op_to_callable = {
				operator.add: lang.ArithFn.add,
				operator.sub: lang.ArithFn.sub,
				operator.mul: lang.ArithFn.mul,
				}
				return op_to_callable[op]


				@dataclasses.dataclass(frozen=True)
				class _BinaryExpr(IndexExpr):
				"""The representation for a binary operation.

				Attributes:
				op: A _BinaryOp representing the binary operation.
				a: An IndexExpr representing the first operand of the operation.
				b: An IndexExpr representing the second operand of the operation.
				"""
				op: _BinaryOp
				a: IndexExpr
				b: IndexExpr

				def __post_init__(self) -> None:
				"""Verifies that the operands being added are IndexExpr."""
				assert isinstance(self.a, IndexExpr) and isinstance(self.b, IndexExpr)

				def _emit_expression(
				self,
				expr_to_opnd: Dict[IndexExpr, lang.OperandDef],
				expr_to_info: _ExprInfoDict,
				) -> lang.ScalarExpression:
				"""Emits the expression tree and returns the expression."""
				# The current expression node is an internal node of the structured op.
				if self not in expr_to_opnd:
				a = self.a._emit_expression(expr_to_opnd, expr_to_info)
				b = self.b._emit_expression(expr_to_opnd, expr_to_info)
				return _op_to_callable(self.op)(a, b)

				# The current expression is a leaf node of the structured op. That is, it is
				# a temporary tensor generated by its child structured op.
				op_info = expr_to_info[self].structop_info
				assert op_info is not None
				dims = _mlir_dimensions_from_index_vars(op_info.dst_indices)
				return lang.TensorUse(expr_to_opnd[self], dims)

				def _visit(self,
				func: _ExprVisitor,
				args,
				*,
				leaf_checker: _SubtreeLeafChecker = None) -> None:
				"""A post-order visitor."""
				if leaf_checker is None or not leaf_checker(self, *args):
				self.a._visit(func, args, leaf_checker=leaf_checker)
				self.b._visit(func, args, leaf_checker=leaf_checker)
				func(self, *args)

				def dtype(self) -> DType:
				"""Returns the data type of the binary operation."""
				return self.a.dtype()


				def _validate_and_collect_dim_info(
				index_to_dim_info: Dict[IndexVar, _DimInfo],
				indices: Tuple[IndexVar, ...],
				dim_infos: Tuple[_DimInfo, ...],
				expr: _BinaryExpr,
				) -> None:
				"""Validates and collects the dimension information for an index notation.

				Validates (indices, dim_infos) against the information collected from other
				source operands and is represented by index_to_dim_info. In particular, we
				ensure that each IndexVar corresponds to only one dimension size. We also
				aggregate the new information represented in (indices, dim_infos) to
				index_to_dim_info.

				Args:
				index_to_dim: A dictionary of (IndexVar, _DimInfo) collected from the
				previous operands.
				indices: The IndexVars to be validated.
				dim_infos: The dimension information for the IndexVars to be validated.
				expr: The binary expression where (indices, dim_infos) is used.

				Raises:
				ValueError if there is any problem in the IndexVars or dimensional values.
				"""
				assert len(indices) == len(dim_infos)
				for i, d in zip(indices, dim_infos):
				if i not in index_to_dim_info:
				index_to_dim_info[i] = d
				else:
				if d.dim != index_to_dim_info[i].dim:
				raise ValueError(f"Inconsistent source dimension for {i}: "
				f"{d.dim} vs {index_to_dim_info[i].dim}")
				mode_format = _mode_format_estimator(expr.op)(
				index_to_dim_info[i].mode_format, d.mode_format)
				index_to_dim_info[i] = _DimInfo(d.dim, mode_format)


				def _validate_and_collect_expr_info(
				expr: IndexExpr,
				expr_to_info: _ExprInfoDict,
				) -> None:
				"""Validates dimension information and constructs _ExprInfo.

				Validates that dimensional values for the same IndexVar are the same. Collects
				a list of IndexVar used by the expression and their corresponding dimensional
				values. Constructs an _ExprInfo object to record the information for the
				IndexExpr.

				This routine is passed to the post-order visitor as an _ExprVisitor object.

				Args:
				expr: The IndexExpr being validated.
				expr_to_info: The dictionary of (IndexExpr, _ExprInfo) for recording the
				expression information.

				Raises:
				ValueError if there is any problem in the IndexVars or dimensional values.
				"""
				# Objects of class Access can be shared by different expressions. Avoid
				# processing Access objects multiple times by skipping the processing if expr
				# is already in the dictionary.
				if expr in expr_to_info:
				return

				if isinstance(expr, Access):
				src_indices = expr.indices
				src_dims = tuple(expr.tensor.shape)
				mode_formats = tuple(expr.tensor.format.format_pack.formats)
				assert len(src_dims) == len(mode_formats)
				dim_infos = tuple([_DimInfo(d, m) for d, m in zip(src_dims, mode_formats)])
				else:
				assert isinstance(expr, _BinaryExpr)
				a_info = expr_to_info[expr.a]
				index_to_dim_info = {
				i: d for i, d in zip(a_info.src_indices, a_info.dim_infos)
				}
				b_info = expr_to_info[expr.b]
				_validate_and_collect_dim_info(index_to_dim_info, b_info.src_indices,
				b_info.dim_infos, expr)
				# Here we rely on the fact that dictionaries keep the insertion order for
				# keys and values.
				src_indices = tuple(index_to_dim_info.keys())
				dim_infos = tuple(index_to_dim_info.values())

				expr_to_info[expr] = _ExprInfo(src_indices, dim_infos)


				def _mark_structured_op_root(
				expr: IndexExpr,
				reduce_index: IndexVar,
				expr_to_info: _ExprInfoDict,
				) -> None:
				"""Identifies the root expression for a structured op in the linalg dialect.

				An linalg structured op can only perform reduction on the whole expression.
				For a TACO tensor algebra expression, the reduction on an IndexVar is done at
				the smallest expression that contains all the uses of the IndexVar. If such an
				expression is only part of the whole expression, we need to split this
				sub-expression tree out from its parent and implement the sub-expression as a
				structured op.

				This routine identifies the root expression node for performing a reduction on
				the given IndexVar. If the reduction of the given IndexVar should be performed
				on expression X, then the IndexVar is added to expr_to_info[X].reduce_indices

				Args:
				expr: The root IndexExpr for the tensor algebra expression.
				reduce_index: The IndexVar which we want to find out the proper expression
				to perform a reduction.
				expr_to_info: The dictionary to look up _ExprInfo for IndexExpr.
				"""
				assert (isinstance(expr, _BinaryExpr))
				a_info = expr_to_info[expr.a]
				b_info = expr_to_info[expr.b]
				expr_info = expr_to_info[expr]

				if reduce_index in a_info.src_indices and reduce_index in b_info.src_indices:
				expr_info.reduce_indices.add(reduce_index)
				return

				if reduce_index in a_info.src_indices:
				_mark_structured_op_root(expr.a, reduce_index, expr_to_info)
				elif reduce_index in b_info.src_indices:
				_mark_structured_op_root(expr.b, reduce_index, expr_to_info)
				else:
				assert False, "Unreachable path"


				def _accumulate_reduce_indices(
				expr: IndexExpr,
				expr_to_info: _ExprInfoDict,
				) -> None:
				"""Propagates reduction indices from child expressions to parent expressions.

				This routine is passed to the post-order visitor as an _ExprVisitor object.

				Args:
				expr: The IndexExpr being visited.
				expr_to_info: The dictionary of (IndexExpr, _ExprInfo) for recording the
				expression information.
				"""
				assert expr in expr_to_info
				expr_info = expr_to_info[expr]

				if isinstance(expr, _BinaryExpr):
				a_info = expr_to_info[expr.a]
				b_info = expr_to_info[expr.b]
				expr_info.acc_reduce_indices = (
				a_info.acc_reduce_indices \| b_info.acc_reduce_indices
				\| expr_info.reduce_indices)
				else:
				assert isinstance(expr, Access)


				def _gather_structured_op(
				expr: IndexExpr,
				expr_to_info: _ExprInfoDict,
				structop_roots: List[IndexExpr],
				) -> None:
				"""Adds structured op root expression information to structop_roots.

				This routine is passed to the post-order visitor as an _ExprVisitor object.

				Args:
				expr: The IndexExpr being visited.
				expr_to_info: The dictionary to look up _ExprInfo for IndexExpr.
				structop_roots: The resulting list of IndexExpr that are the roots for
				linalg structured ops.
				"""
				if not expr_to_info[expr].reduce_indices:
				return

				# If the expression is the root for reducing some indices, collect the indices
				# and dimensions for the reduction result.
				dst_indices = []
				dst_dims = []
				mode_fmts = []
				for i, d in zip(expr_to_info[expr].src_indices, expr_to_info[expr].dim_infos):
				if i not in expr_to_info[expr].acc_reduce_indices:
				dst_indices.append(i)
				dst_dims.append(d.dim)
				mode_fmts.append(d.mode_format)

				# Add the information to the dictionary.
				op_info = _StructOpInfo(
				tuple(dst_indices),
				tuple(dst_dims),
				expr.dtype(),
				f"temp{len(structop_roots)}",
				_make_format(mode_fmts),
				)
				expr_to_info[expr].structop_info = op_info

				# Add the expression to the list of structured op roots.
				structop_roots.append(expr)


				def _is_structured_op_leaf(
				expr: IndexExpr,
				root: IndexExpr,
				expr_to_info: _ExprInfoDict,
				*unused_args,
				) -> bool:
				"""Returns true iff the expression is a leaf node for a structured op.

				The root of a structured op is a leaf of its parent structured op that uses
				its result. An expression node is a leaf node for the current structured op if
				it is an Access node or the root for a structured op that is not the current
				structured op.

				This routine is passed to the post-order visitor as a _SubtreeLeafChecker
				object. Because the post-order visitor pass the same parameters to both
				_SubtreeLeafChecker and _ExprVisitor, this routine may received unused
				parameters.

				Args:
				expr: The IndexExpr being visited.
				root: The root of the current structured op.
				expr_to_info: The dictionary to look up _ExprInfo for IndexExpr.

				Returns:
				True if the current IndexExpr is a leaf for the current structured op.
				"""
				return (expr != root and
				expr_to_info[expr].structop_info is not None) or isinstance(
				expr, Access)


				def _gather_structured_op_input(
				expr: IndexExpr,
				root: IndexExpr,
				expr_to_info: _ExprInfoDict,
				structop_inputs: List[IndexExpr],
				) -> None:
				"""Adds the IndexExpr to structop_inputs if it is an input.

				If the current IndexExpr is an input for the current structured op, adds it to
				structop_inputs. The current IndexExpr is an input if it is an Access node or
				if it is the root for a structured op that is not the current structured op.

				This routine is passed to the post-order visitor as an _ExprVisitor object.

				Args:
				expr: The IndexExpr being visited.
				root: The root of the current structured op.
				expr_to_info: The dictionary to look up _ExprInfo for IndexExpr.
				structop_inputs: The resulting list of IndexExpr that provide input to the
				current structured op.
				"""
				if (expr != root and expr not in structop_inputs) and (
				isinstance(expr, Access) or
				(expr in expr_to_info and expr_to_info[expr].structop_info)):
				structop_inputs.append(expr)


				def _emit_structured_op_input(
				expr: IndexExpr,
				expr_to_info: _ExprInfoDict,
				op_def: lang.LinalgOpDef,
				) -> lang.OperandDef:
				"""Emits OperandDef in the linalg dialect for the input IndexExpr.

				Args:
				expr: The input IndexExpr for the current structured op.
				expr_to_info: The dictionary to look up _ExprInfo for IndexExpr.
				op_def: The linalg operation for the current structured op.

				Returns:
				An OperandDef in the linalg dialect for the input IndexExpr.
				"""
				op_info = expr_to_info[expr].structop_info
				if op_info:
				# The input is a temporary tensor produced by another structured op.
				indices = op_info.dst_indices
				name = op_info.dst_name
				else:
				# The input is a user provided tensor.
				assert isinstance(expr, Access)
				indices = expr.indices
				name = expr.tensor.name

				dim_sym = _mlir_symbols_from_index_vars(indices)
				opnd = lang.OperandDef(lang.OperandKind.InputTensor, lang.T, dim_sym)
				op_def.add_operand(name, opnd)
				return opnd

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco_api.py

This file was added.

				# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
				# See https://llvm.org/LICENSE.txt for license information.
				# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception

				"""Supports the PyTACO API with the MLIR-PyTACO implementation.

				See http://tensor-compiler.org/ for TACO tensor compiler.

				This module exports the MLIR-PyTACO implementation through the language defined
				by PyTACO. In particular, it defines the function and type aliases and constants
				needed for the PyTACO API to support the execution of PyTACO programs using the
				MLIR-PyTACO implementation.
				"""

				from . import mlir_pytaco
				from . import mlir_pytaco_io

				# Functions defined by PyTACO API.
				get_index_vars = mlir_pytaco.get_index_vars
				from_array = mlir_pytaco.Tensor.from_array
				read = mlir_pytaco_io.read
				write = mlir_pytaco_io.write

				# Classes defined by PyTACO API.
				dtype = mlir_pytaco.DType
				mode_format = mlir_pytaco.ModeFormat
				mode_ordering = mlir_pytaco.ModeOrdering
				mode_format_pack = mlir_pytaco.ModeFormatPack
				format = mlir_pytaco.Format
				index_var = mlir_pytaco.IndexVar
				tensor = mlir_pytaco.Tensor
				index_expression = mlir_pytaco.IndexExpr
				access = mlir_pytaco.Access

				# Data type constants defined by PyTACO API.
				int16 = mlir_pytaco.DType(mlir_pytaco.Type.INT16)
				int32 = mlir_pytaco.DType(mlir_pytaco.Type.INT32)
				int64 = mlir_pytaco.DType(mlir_pytaco.Type.INT64)
				float32 = mlir_pytaco.DType(mlir_pytaco.Type.FLOAT32)
				float64 = mlir_pytaco.DType(mlir_pytaco.Type.FLOAT64)

				# Storage format constants defined by the PyTACO API. In PyTACO, each storage
				# format constant has two aliasing names.
				compressed = mlir_pytaco.ModeFormat.COMPRESSED
				Compressed = mlir_pytaco.ModeFormat.COMPRESSED
				dense = mlir_pytaco.ModeFormat.DENSE
				Dense = mlir_pytaco.ModeFormat.DENSE

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco_io.py

This file was added.

				# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
				# See https://llvm.org/LICENSE.txt for license information.
				# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception

				"""Experimental MLIR-PyTACO with sparse tensor support.

				See http://tensor-compiler.org/ for TACO tensor compiler.

				This module implements the PyTACO API for writing a tensor to a file or reading
				a tensor from a file.

				See the following links for Matrix Market Exchange (.mtx) format and FROSTT
				(.tns) format:
				https://math.nist.gov/MatrixMarket/formats.html
				http://frostt.io/tensors/file-formats.html
				"""

				from typing import List, TextIO

				from . import mlir_pytaco

				# Define the type aliases so that we can write the implementation here as if
				# it were part of mlir_pytaco.py.
				Tensor = mlir_pytaco.Tensor
				Format = mlir_pytaco.Format
				DType = mlir_pytaco.DType
				Type = mlir_pytaco.Type

				# Constants used in the implementation.
				_MTX_FILENAME_SUFFIX = ".mtx"
				_TNS_FILENAME_SUFFIX = ".tns"

				_MTX_HEAD = "%%MatrixMarket"
				_MTX_MATRIX = "matrix"
				_MTX_COORDINATE = "coordinate"
				_MTX_REAL = "real"
				_MTX_SYMMETRY = "symmetric"
				_MTX_GENERAL = "general"
				_SYMMETRY_FIELD_ID = 4

				# The TACO supported header for .mtx has the following five fields:
				# . %%MatrixMarket
				# . matrix \| tensor
				# . coordinate \| array
				# . real
				# . symmetric \| general
				#
				# This is what we support currently.
				_SUPPORTED_HEADER_FIELDS = ((_MTX_HEAD,), (_MTX_MATRIX,), (_MTX_COORDINATE,),
				(_MTX_REAL,), (_MTX_GENERAL, _MTX_SYMMETRY))

				_A_SPACE = " "
				_MTX_COMMENT = "%"
				_TNS_COMMENT = "#"


				def _coordinate_from_strings(strings: List[str]) -> List[int]:
				""""Return the coordinate represented by the input strings."""
				# Coordinates are 1-based in the text file and 0-based in memory.
				return [int(s) - 1 for s in strings]


				def _read_coordinate_format(file: TextIO, tensor: Tensor,
				is_symmetric: bool) -> None:
				"""Reads tensor values in coordinate format."""
				rank = tensor.order
				# Process the data for the tensor.
				for line in file:
				if not line:
				continue

				fields = line.split(_A_SPACE)
				if rank != len(fields) - 1:
				raise ValueError("The format and data have mismatched ranks: "
				f"{rank} vs {len(fields)-1}.")
				coordinate = _coordinate_from_strings(fields[:-1])
				value = float(fields[-1])
				tensor.insert(coordinate, value)
				if is_symmetric and coordinate[0] != coordinate[-1]:
				coordinate.reverse()
				tensor.insert(coordinate, value)


				def _read_mtx(file: TextIO, fmt: Format) -> Tensor:
				"""Inputs tensor from a text file with .mtx format."""
				# The first line should have this five fields:
				# head tensor-kind format data-type symmetry
				fields = file.readline().rstrip("\n").split(_A_SPACE)
				tuple_to_str = lambda x: "\|".join(x)
				if len(fields) != len(_SUPPORTED_HEADER_FIELDS):
				raise ValueError(
				"Expected first line with theses fields "
				f"{' '.join(map(tuple_to_str, _SUPPORTED_HEADER_FIELDS))}: "
				f"{' '.join(fields)}")

				for i, values in enumerate(_SUPPORTED_HEADER_FIELDS):
				if fields[i] not in values:
				raise ValueError(f"The {i}th field can only be one of these values "
				f"{tuple_to_str(values)}: {fields[i]}")

				is_symmetric = (fields[_SYMMETRY_FIELD_ID] == _MTX_SYMMETRY)
				# Skip leading empty lines or comment lines.
				line = file.readline()
				while not line or line[0] == _MTX_COMMENT:
				line = file.readline()

				# Process the first data line with dimensions and number of non-zero values.
				fields = line.split(_A_SPACE)
				rank = fmt.rank()
				if rank != len(fields) - 1:
				raise ValueError("The format and data have mismatched ranks: "
				f"{rank} vs {len(fields)-1}.")
				shape = fields[:-1]
				shape = [int(s) for s in shape]
				num_non_zero = float(fields[-1])

				# Read the tensor values in coordinate format.
				tensor = Tensor(shape, fmt)
				_read_coordinate_format(file, tensor, is_symmetric)
				return tensor


				def _read_tns(file: TextIO, fmt: Format) -> Tensor:
				"""Inputs tensor from a text file with .tns format."""
				rank = fmt.rank()
				coordinates = []
				values = []
				dtype = DType(Type.FLOAT64)

				for line in file:
				# Skip empty lines and comment lines.
				if not line or line[0] == _TNS_COMMENT:
				continue

				# Process each line with a coordinate and the value at the coordinate.
				fields = line.split(_A_SPACE)
				if rank != len(fields) - 1:
				raise ValueError("The format and data have mismatched ranks: "
				f"{rank} vs {len(fields)-1}.")
				coordinates.append(tuple(_coordinate_from_strings(fields[:-1])))
				values.append(dtype.value(fields[-1]))

				return Tensor.from_coo(coordinates, values, fmt, dtype)


				def _write_tns(file: TextIO, tensor: Tensor) -> None:
				"""Outputs a tensor to a file using .tns format."""
				coords, non_zeros = tensor.get_coordinates_and_values()
				assert len(coords) == len(non_zeros)
				# Output a coordinate and the corresponding value in a line.
				for c, v in zip(coords, non_zeros):
				# The coordinates are 1-based in the text file and 0-based in memory.
				plus_one_to_str = lambda x: str(x + 1)
				file.write(f"{' '.join(map(plus_one_to_str,c))} {v}\n")


				def read(filename: str, fmt: Format) -> Tensor:
				"""Inputs a tensor from a given file.

				The name suffix of the file specifies the format of the input tensor. We
				currently only support .mtx format for support sparse tensors.

				Args:
				filename: A string input filename.
				fmt: The storage format of the tensor.

				Raises:
				ValueError: If filename doesn't end with .mtx or .tns, or fmt is not an
				instance of Format or fmt is not a sparse tensor.
				"""
				if (not isinstance(filename, str) or
				(not filename.endswith(_MTX_FILENAME_SUFFIX) and
				not filename.endswith(_TNS_FILENAME_SUFFIX))):
				raise ValueError("Expected string filename ends with "
				f"{_MTX_FILENAME_SUFFIX} or {_TNS_FILENAME_SUFFIX}: "
				f"{filename}.")
				if not isinstance(fmt, Format) or fmt.is_dense():
				raise ValueError(f"Expected a sparse Format object: {fmt}.")

				with open(filename, "r") as file:
				return (_read_mtx(file, fmt) if filename.endswith(_MTX_FILENAME_SUFFIX) else
				_read_tns(file, fmt))


				def write(filename: str, tensor: Tensor) -> None:
				"""Outputs a tensor to a given file.

				The name suffix of the file specifies the format of the output. We currently
				only support .tns format.

				Args:
				filename: A string output filename.
				tensor: The tensor to output.

				Raises:
				ValueError: If filename doesn't end with .tns or tensor is not a Tensor.
				"""
				if (not isinstance(filename, str) or
				not filename.endswith(_TNS_FILENAME_SUFFIX)):
				raise ValueError("Expected string filename ends with"
				f" {_TNS_FILENAME_SUFFIX}: {filename}.")
				if not isinstance(tensor, Tensor):
				raise ValueError(f"Expected a Tensor object: {tensor}.")

				with open(filename, "w") as file:
				return _write_tns(file, tensor)

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco_utils.py

This file was added.

				# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
				# See https://llvm.org/LICENSE.txt for license information.
				# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception

				# This file contains the utilities to process sparse tensor outputs.

				from typing import Tuple
				import ctypes
				import functools
				import numpy as np


				@functools.lru_cache()
				def _get_c_shared_lib(lib_name: str) -> ctypes.CDLL:
				"""Loads and returns the requested C shared library.

				Args:
				lib_name: A string representing the C shared library.

				Returns:
				The C shared library.

				Raises:
				OSError: If there is any problem in loading the shared library.
				ValueError: If the shared library doesn't contain the needed routines.
				"""
				# This raises OSError exception if there is any problem in loading the shared
				# library.
				c_lib = ctypes.CDLL(lib_name)

				try:
				c_lib.convertToMLIRSparseTensor.restype = ctypes.c_void_p
				except Exception as e:
				raise ValueError("Missing function convertToMLIRSparseTensor from "
				f"the supporting C shared library: {e} ") from e

				try:
				c_lib.convertFromMLIRSparseTensor.restype = ctypes.c_void_p
				except Exception as e:
				raise ValueError("Missing function convertFromMLIRSparseTensor from "
				f"the C shared library: {e} ") from e

				return c_lib


				def sparse_tensor_to_coo_tensor(
				lib_name: str,
				sparse_tensor: ctypes.c_void_p,
				dtype: np.dtype,
				) -> Tuple[int, int, np.ndarray, np.ndarray, np.ndarray]:
				"""Converts an MLIR sparse tensor to a COO-flavored format tensor.

				Args:
				lib_name: A string for the supporting C shared library.
				sparse_tensor: A ctypes.c_void_p to the MLIR sparse tensor descriptor.
				dtype: The numpy data type for the tensor elements.

				Returns:
				A tuple that contains the following values for the COO-flavored format
				tensor:
				rank: An integer for the rank of the tensor.
				nse: An interger for the number of non-zero values in the tensor.
				shape: A 1D numpy array of integers, for the shape of the tensor.
				values: A 1D numpy array, for the non-zero values in the tensor.
				indices: A 2D numpy array of integers, representing the indices for the
				non-zero values in the tensor.

				Raises:
				OSError: If there is any problem in loading the shared library.
				ValueError: If the shared library doesn't contain the needed routines.
				"""
				c_lib = _get_c_shared_lib(lib_name)

				rank = ctypes.c_ulonglong(0)
				nse = ctypes.c_ulonglong(0)
				shape = ctypes.POINTER(ctypes.c_ulonglong)()
				values = ctypes.POINTER(np.ctypeslib.as_ctypes_type(dtype))()
				indices = ctypes.POINTER(ctypes.c_ulonglong)()
				c_lib.convertFromMLIRSparseTensor(sparse_tensor, ctypes.byref(rank),
				ctypes.byref(nse), ctypes.byref(shape),
				ctypes.byref(values), ctypes.byref(indices))

				# Convert the returned values to the corresponding numpy types.
				shape = np.ctypeslib.as_array(shape, shape=[rank.value])
				values = np.ctypeslib.as_array(values, shape=[nse.value])
				indices = np.ctypeslib.as_array(indices, shape=[nse.value, rank.value])
				return rank, nse, shape, values, indices


				def coo_tensor_to_sparse_tensor(lib_name: str, np_shape: np.ndarray,
				np_values: np.ndarray,
				np_indices: np.ndarray) -> int:
				"""Converts a COO-flavored format sparse tensor to an MLIR sparse tensor.

				Args:
				lib_name: A string for the supporting C shared library.
				np_shape: A 1D numpy array of integers, for the shape of the tensor.
				np_values: A 1D numpy array, for the non-zero values in the tensor.
				np_indices: A 2D numpy array of integers, representing the indices for the
				non-zero values in the tensor.

				Returns:
				An integer for the non-null ctypes.c_void_p to the MLIR sparse tensor
				descriptor.

				Raises:
				OSError: If there is any problem in loading the shared library.
				ValueError: If the shared library doesn't contain the needed routines.
				"""

				rank = ctypes.c_ulonglong(len(np_shape))
				nse = ctypes.c_ulonglong(len(np_values))
				shape = np_shape.ctypes.data_as(ctypes.POINTER(ctypes.c_ulonglong))
				values = np_values.ctypes.data_as(
				ctypes.POINTER(np.ctypeslib.as_ctypes_type(np_values.dtype)))
				indices = np_indices.ctypes.data_as(ctypes.POINTER(ctypes.c_ulonglong))

				c_lib = _get_c_shared_lib(lib_name)
				ptr = c_lib.convertToMLIRSparseTensor(rank, nse, shape, values, indices)
				assert ptr is not None, "Problem with calling convertToMLIRSparseTensor"
				return ptr

This is an archive of the discontinued LLVM Phabricator instance.

Upstream MLIR PyTACO implementation.
ClosedPublic

Details

Diff Detail

Event Timeline

This PyTACO part is taken from the TACO open-source project.

Revision Contents

Diff 399796

mlir/test/Integration/Dialect/SparseTensor/taco/MTTKRP_test.py

This PyTACO part is taken from the TACO open-source project.

mlir/test/Integration/Dialect/SparseTensor/taco/README.md

mlir/test/Integration/Dialect/SparseTensor/taco/SpMV_test.py

mlir/test/Integration/Dialect/SparseTensor/taco/data/gold_A.tns

mlir/test/Integration/Dialect/SparseTensor/taco/data/gold_y.tns

mlir/test/Integration/Dialect/SparseTensor/taco/data/nell-2.tns

mlir/test/Integration/Dialect/SparseTensor/taco/data/pwtk.mtx

mlir/test/Integration/Dialect/SparseTensor/taco/simple_tensor_algebra_test.py

mlir/test/Integration/Dialect/SparseTensor/taco/tools/lit.local.cfg

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco.py

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco_api.py

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco_io.py

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco_utils.py

This is an archive of the discontinued LLVM Phabricator instance.

Upstream MLIR PyTACO implementation.ClosedPublic

Details

Diff Detail

Event Timeline

This PyTACO part is taken from the TACO open-source project.

Revision Contents

Diff 399796

mlir/test/Integration/Dialect/SparseTensor/taco/MTTKRP_test.py

This PyTACO part is taken from the TACO open-source project.

mlir/test/Integration/Dialect/SparseTensor/taco/README.md

mlir/test/Integration/Dialect/SparseTensor/taco/SpMV_test.py

mlir/test/Integration/Dialect/SparseTensor/taco/data/gold_A.tns

mlir/test/Integration/Dialect/SparseTensor/taco/data/gold_y.tns

mlir/test/Integration/Dialect/SparseTensor/taco/data/nell-2.tns

mlir/test/Integration/Dialect/SparseTensor/taco/data/pwtk.mtx

mlir/test/Integration/Dialect/SparseTensor/taco/simple_tensor_algebra_test.py

mlir/test/Integration/Dialect/SparseTensor/taco/tools/lit.local.cfg

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco.py

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco_api.py

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco_io.py

mlir/test/Integration/Dialect/SparseTensor/taco/tools/mlir_pytaco_utils.py

Upstream MLIR PyTACO implementation.
ClosedPublic