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ckpts/universal/global_step120/zero/16.mlp.dense_h_to_4h.weight/fp32.pt

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ckpts/universal/global_step120/zero/16.mlp.dense_h_to_4h_swiglu.weight/fp32.pt

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ckpts/universal/global_step120/zero/4.attention.dense.weight/fp32.pt

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+size 16778317

venv/lib/python3.10/site-packages/torch/_logging/__init__.py

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+# Top level logging module for torch logging
+# Design doc: https://docs.google.com/document/d/1ZRfTWKa8eaPq1AxaiHrq4ASTPouzzlPiuquSBEJYwS8/edit#
+# Simple setup for onboarding (see above doc for more detail):
+# 1. register any top-level log qualified name for your module in torch._logging._registrations (see there for examples)
+# 2. register any artifacts (<artifact_name> below) in torch._logging._registrations
+#   a. call getArtifactLogger(__name__, <artifact_name>) at your logging site instead of the standard logger to log your artifact
+import torch._logging._registrations
+from ._internal import (
+    _init_logs,
+    DEFAULT_LOGGING,
+    getArtifactLogger,
+    LazyString,
+    set_logs,
+    trace_structured,
+    warning_once,
+)

venv/lib/python3.10/site-packages/torch/_logging/_internal.py

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+import functools
+import hashlib
+import itertools
+import json
+import logging
+import os
+import os.path
+import re
+import tempfile
+from dataclasses import dataclass, field
+from importlib import __import__
+from typing import Any, Callable, Dict, List, Optional, Set, Tuple, Union
+from weakref import WeakSet
+
+log = logging.getLogger(__name__)
+
+# This is a synthetic logger which doesn't correspond to an actual logger,
+# but handles all of our "tracing" logging, which is structured and doesn't go
+# to stderr but always goes to a dedicated log file.  We don't put these
+# loggers in the classic module hierarchy, because we don't want a suppression
+# of logs to also cause a trace to get suppressed (traces typically are not
+# collected, unless we are in prod, in which case they always are collected.)
+#
+# TODO: Maybe we should allow for some sub-hierarchy so you can control which
+# traces you want to collect, for performance reasons.
+#
+# See https://docs.google.com/document/d/1CX_hJ0PNy9f3R1y8TJrfkSeLkvGjjjLU84BSXgS2AZ8/edit
+trace_log = logging.getLogger("torch.__trace")
+
+DEFAULT_LOG_LEVEL = logging.WARNING
+LOG_ENV_VAR = "TORCH_LOGS"
+LOG_OUT_ENV_VAR = "TORCH_LOGS_OUT"
+LOG_FORMAT_ENV_VAR = "TORCH_LOGS_FORMAT"
+TRACE_ENV_VAR = "TORCH_TRACE"
+
+
+@dataclass
+class LogRegistry:
+    # shorthand name to log qualified name
+    # Note: this only contains loggers registered
+    # from register_log
+    # e.g. "dynamo" -> "torch._dynamo"
+    log_alias_to_log_qnames: Dict[str, List[str]] = field(default_factory=dict)
+
+    # artifact logger qualified names,
+    # this is populated lazily, as calls to getArtifactLogger
+    # currently formatted as <module>.__<artifact_name>
+    # e.g. "torch._dynamo.convert_frame.__guards"
+    artifact_log_qnames: Set[str] = field(default_factory=set)
+
+    # child logs of registered logs if specified via open
+    # registration by the user (ie placing "torch._dynamo.output_graph" in the env var)
+    # these need to be tracked so their levels can be reset properly
+    # e.g. "torch._dynamo.output_graph"
+    child_log_qnames: Set[str] = field(default_factory=set)
+
+    # artifact names, populated by register_artifact
+    # e.g. "guards"
+    artifact_names: Set[str] = field(default_factory=set)
+
+    # Artifacts that should be visible by default in the error message
+    visible_artifacts: Set[str] = field(default_factory=set)
+
+    # A short description of each artifact
+    artifact_descriptions: Dict[str, str] = field(default_factory=dict)
+
+    # artifacts which are not displayed unless explicitly named in the
+    # settings. Ex. output_code is NOT displayed even if the inductor
+    # log level is set to DEBUG. It must be explicitly named in the settings
+    off_by_default_artifact_names: Set[str] = field(default_factory=set)
+
+    # logging format string for artifacts
+    artifact_log_formatters: Dict[str, logging.Formatter] = field(default_factory=dict)
+
+    def is_artifact(self, name):
+        return name in self.artifact_names
+
+    def is_log(self, alias):
+        return alias in self.log_alias_to_log_qnames
+
+    # register a log with an alias
+    def register_log(self, alias, log_qnames: Union[str, List[str]]):
+        if isinstance(log_qnames, str):
+            log_qnames = [log_qnames]
+        self.log_alias_to_log_qnames[alias] = log_qnames
+
+    # register an artifact name
+    def register_artifact_name(
+        self, name, description, visible, off_by_default, log_format
+    ):
+        self.artifact_names.add(name)
+        if visible:
+            self.visible_artifacts.add(name)
+        self.artifact_descriptions[name] = description
+
+        # if off by default, don't enable it
+        # when log_name's log_level is set to DEBUG
+        if off_by_default:
+            self.off_by_default_artifact_names.add(name)
+
+        if log_format is not None:
+            self.artifact_log_formatters[name] = logging.Formatter(log_format)
+
+    # register the qualified name of an artifact log
+    # this is needed to know which logs need to be reset
+    # whenever the log_state is changed
+    def register_artifact_log(self, artifact_log_qname):
+        self.artifact_log_qnames.add(artifact_log_qname)
+
+    def register_child_log(self, log_qname):
+        self.child_log_qnames.add(log_qname)
+
+    # flattens all the qnames together (TODO: consider memoizing?)
+    def get_log_qnames(self) -> Set[str]:
+        return {
+            qname
+            for qnames in self.log_alias_to_log_qnames.values()
+            for qname in qnames
+        }
+
+    def get_artifact_log_qnames(self):
+        return set(self.artifact_log_qnames)
+
+    def get_child_log_qnames(self):
+        return set(self.child_log_qnames)
+
+    def is_off_by_default(self, artifact_qname):
+        return artifact_qname in self.off_by_default_artifact_names
+
+
+@dataclass
+class LogState:
+    # qualified log names -> currently set log level
+    log_qname_to_level: Dict[str, str] = field(default_factory=dict)
+
+    # the set of currently enabled artifacts
+    artifact_names: Set[str] = field(default_factory=set)
+
+    def enable_artifact(self, artifact_name):
+        self.artifact_names.add(artifact_name)
+
+    def is_artifact_enabled(self, name):
+        return name in self.artifact_names
+
+    def enable_log(self, log_qnames, log_level):
+        if isinstance(log_qnames, str):
+            log_qnames = [log_qnames]
+        for log_qname in log_qnames:
+            self.log_qname_to_level[log_qname] = log_level
+
+    def get_log_level_pairs(self):
+        """Returns all qualified module names for which the user requested
+        explicit logging settings.
+
+        .. warning:
+
+            This function used to return all loggers, regardless of whether
+            or not the user specified them or not; it now only returns logs
+            which were explicitly mentioned by the user (and torch, which
+            always is implicitly requested when we initialize our logging
+            subsystem.)
+        """
+        return self.log_qname_to_level.items()
+
+    def clear(self):
+        self.log_qname_to_level.clear()
+        self.artifact_names.clear()
+
+
+log_registry = LogRegistry()
+log_state = LogState()
+
+# sample usage: torch._logging.set_logs(**torch._logging.DEFAULT_LOGGING)
+DEFAULT_LOGGING = {
+    "dynamo": logging.DEBUG,
+    "aot": logging.DEBUG,
+    "inductor": logging.DEBUG,
+    "ddp_graphs": True,
+    "graph_breaks": True,
+    "guards": True,
+    "recompiles": True,
+    "dynamic": logging.INFO,
+}
+
+
+def set_logs(
+    *,
+    all: Optional[int] = None,
+    dynamo: Optional[int] = None,
+    aot: Optional[int] = None,
+    autograd: Optional[int] = None,
+    dynamic: Optional[int] = None,
+    inductor: Optional[int] = None,
+    distributed: Optional[int] = None,
+    dist_c10d: Optional[int] = None,
+    dist_ddp: Optional[int] = None,
+    dist_fsdp: Optional[int] = None,
+    onnx: Optional[int] = None,
+    bytecode: bool = False,
+    aot_graphs: bool = False,
+    aot_joint_graph: bool = False,
+    ddp_graphs: bool = False,
+    graph: bool = False,
+    graph_code: bool = False,
+    graph_breaks: bool = False,
+    graph_sizes: bool = False,
+    guards: bool = False,
+    recompiles: bool = False,
+    recompiles_verbose: bool = False,
+    trace_source: bool = False,
+    trace_call: bool = False,
+    output_code: bool = False,
+    schedule: bool = False,
+    perf_hints: bool = False,
+    post_grad_graphs: bool = False,
+    onnx_diagnostics: bool = False,
+    fusion: bool = False,
+    overlap: bool = False,
+    export: Optional[int] = None,
+    modules: Optional[Dict[str, Union[int, bool]]] = None,
+    cudagraphs: bool = False,
+    sym_node: bool = False,
+):
+    """
+    Sets the log level for individual components and toggles individual log
+    artifact types.
+
+    .. warning:: This feature is a prototype and may have compatibility
+        breaking changes in the future.
+
+    .. note:: The ``TORCH_LOGS`` environment variable has complete precedence
+        over this function, so if it was set, this function does nothing.
+
+    A component is a set of related features in PyTorch. All of the log
+    messages emitted from a given component have their own log levels. If the
+    log level of a particular message has priority greater than or equal to its
+    component's log level setting, it is emitted. Otherwise, it is suppressed.
+    This allows you to, for instance, silence large groups of log messages that
+    are not relevant to you and increase verbosity of logs for components that
+    are relevant. The expected log level values, ordered from highest to lowest
+    priority, are:
+
+        * ``logging.CRITICAL``
+        * ``logging.ERROR``
+        * ``logging.WARNING``
+        * ``logging.INFO``
+        * ``logging.DEBUG``
+        * ``logging.NOTSET``
+
+    See documentation for the Python ``logging`` module for more information on
+    log levels: `<https://docs.python.org/3/library/logging.html#logging-levels>`_
+
+    An artifact is a particular type of log message. Each artifact is assigned
+    to a parent component. A component can emit many different kinds of
+    artifacts. In general, an artifact is emitted if either its corresponding
+    setting in the argument list below is turned on or if its parent component
+    is set to a log level less than or equal to the log level of the artifact.
+
+    Keyword args:
+        all (:class:`Optional[int]`):
+            The default log level for all components. Default: ``logging.WARN``
+
+        dynamo (:class:`Optional[int]`):
+            The log level for the TorchDynamo component. Default: ``logging.WARN``
+
+        aot (:class:`Optional[int]`):
+            The log level for the AOTAutograd component. Default: ``logging.WARN``
+
+        autograd (:class:`Optional[int]`):
+            The log level for autograd. Default: ``logging.WARN``
+
+        inductor (:class:`Optional[int]`):
+            The log level for the TorchInductor component. Default: ``logging.WARN``
+
+        dynamic (:class:`Optional[int]`):
+            The log level for dynamic shapes. Default: ``logging.WARN``
+
+        distributed (:class:`Optional[int]`):
+            Whether to log c10d communication operations and other debug info from PyTorch Distributed components.
+            Default: ``logging.WARN``
+
+        dist_c10d (:class:`Optional[int]`):
+            Whether to log c10d communication operations related debug info in PyTorch Distributed components.
+            Default: ``logging.WARN``
+
+        dist_ddp (:class:`Optional[int]`):
+            Whether to log debug info related to ``DistributedDataParallel``(DDP) from PyTorch Distributed components.
+            Default: ``logging.WARN``
+
+        dist_fsdp (:class:`Optional[int]`):
+            Whether to log debug info related to ``FullyShardedDataParallel``(FSDP) in PyTorch Distributed components.
+            Default: ``logging.WARN``
+
+        onnx (:class:`Optional[int]`):
+            The log level for the ONNX exporter component. Default: ``logging.WARN``
+
+        bytecode (:class:`bool`):
+            Whether to emit the original and generated bytecode from TorchDynamo.
+            Default: ``False``
+
+        aot_graphs (:class:`bool`):
+            Whether to emit the graphs generated by AOTAutograd. Default: ``False``
+
+        aot_joint_graph (:class:`bool`):
+            Whether to emit the joint forward-backward graph generated by AOTAutograd. Default: ``False``
+
+        inductor (:class:`Optional[int]`):
+            Whether to log information from inductor cudagraphs. Default: ``logging.WARN``
+
+        ddp_graphs (:class:`bool`):
+            Whether to emit graphs generated by DDPOptimizer. Default: ``False``
+
+        graph (:class:`bool`):
+            Whether to emit the graph captured by TorchDynamo in tabular format.
+            Default: ``False``
+
+        graph_code (:class:`bool`):
+            Whether to emit the python source of the graph captured by TorchDynamo.
+            Default: ``False``
+
+        graph_breaks (:class:`bool`):
+            Whether to emit the graph breaks encountered by TorchDynamo.
+            Default: ``False``
+
+        graph_sizes (:class:`bool`):
+            Whether to emit tensor sizes of the graph captured by TorchDynamo.
+            Default: ``False``
+
+        guards (:class:`bool`):
+            Whether to emit the guards generated by TorchDynamo for each compiled
+            function. Default: ``False``
+
+        recompiles (:class:`bool`):
+            Whether to emit a guard failure reason and message every time
+            TorchDynamo recompiles a function. Default: ``False``
+
+        recompiles_verbose (:class:`bool`):
+            Whether to emit all guard failure reasons when TorchDynamo recompiles
+            a function, even those that are not actually run. Default: ``False``
+
+        trace_source (:class:`bool`):
+            Whether to emit when TorchDynamo begins tracing a new line. Default: ``False``
+
+        trace_call (:class:`bool`):
+            Whether to emit detailed line location when TorchDynamo creates an FX node
+            corresponding to function call. Python 3.11+ only. Default: ``False``
+
+        output_code (:class:`bool`):
+            Whether to emit the TorchInductor output code. Default: ``False``
+
+        schedule (:class:`bool`):
+            Whether to emit the TorchInductor schedule. Default: ``False``
+
+        perf_hints (:class:`bool`):
+            Whether to emit the TorchInductor perf hints. Default: ``False``
+
+        post_grad_graphs (:class:`bool`):
+            Whether to emit the graphs generated by after post grad passes. Default: ``False``
+
+        onnx_diagnostics (:class:`bool`):
+            Whether to emit the ONNX exporter diagnostics in logging. Default: ``False``
+
+        fusion (:class:`bool`):
+            Whether to emit detailed Inductor fusion decisions. Default: ``False``
+
+        overlap (:class:`bool`):
+            Whether to emit detailed Inductor compute/comm overlap decisions. Default: ``False``
+
+        sym_node (:class:`bool`):
+            Whether to emit debug info for various SymNode opterations. Default: ``False``
+
+        export (:class:`Optional[int]`):
+            The log level for export. Default: ``logging.WARN``
+
+        modules (dict):
+            This argument provides an alternate way to specify the above log
+            component and artifact settings, in the format of a keyword args
+            dictionary given as a single argument. There are two cases
+            where this is useful (1) if a new log component or artifact has
+            been registered but a keyword argument for it has not been added
+            to this function and (2) if the log level for an unregistered module
+            needs to be set. This can be done by providing the fully-qualified module
+            name as the key, with the log level as the value. Default: ``None``
+
+
+    Example::
+
+        >>> # xdoctest: +SKIP
+        >>> import logging
+
+        # The following changes the "dynamo" component to emit DEBUG-level
+        # logs, and to emit "graph_code" artifacts.
+
+        >>> torch._logging.set_logs(dynamo=logging.DEBUG, graph_code=True)
+
+        # The following enables the logs for a different module
+
+        >>> torch._logging.set_logs(modules={"unregistered.module.name": logging.DEBUG})
+    """
+    # ignore if env var is set
+    if LOG_ENV_VAR in os.environ:
+        log.warning(
+            "Using TORCH_LOGS environment variable for log settings, ignoring call to set_logs"
+        )
+        return
+
+    log_state.clear()
+
+    modules = modules or {}
+
+    def _set_logs(**kwargs):
+        for alias, val in itertools.chain(kwargs.items(), modules.items()):  # type: ignore[union-attr]
+            if val is None:
+                continue
+
+            if log_registry.is_artifact(alias):
+                if not isinstance(val, bool):
+                    raise ValueError(
+                        f"Expected bool to enable artifact {alias}, received {val}"
+                    )
+
+                if val:
+                    log_state.enable_artifact(alias)
+            elif log_registry.is_log(alias) or alias in log_registry.child_log_qnames:
+                if val not in logging._levelToName:
+                    raise ValueError(
+                        f"Unrecognized log level for log {alias}: {val}, valid level values "
+                        f"are: {','.join([str(k) for k in logging._levelToName.keys()])}"
+                    )
+
+                log_state.enable_log(
+                    log_registry.log_alias_to_log_qnames.get(alias, alias), val
+                )
+            else:
+                raise ValueError(
+                    f"Unrecognized log or artifact name passed to set_logs: {alias}"
+                )
+
+        _init_logs()
+
+    _set_logs(
+        torch=all,
+        dynamo=dynamo,
+        aot=aot,
+        autograd=autograd,
+        inductor=inductor,
+        dynamic=dynamic,
+        bytecode=bytecode,
+        aot_graphs=aot_graphs,
+        aot_joint_graph=aot_joint_graph,
+        ddp_graphs=ddp_graphs,
+        distributed=distributed,
+        dist_c10d=dist_c10d,
+        dist_ddp=dist_ddp,
+        dist_fsdp=dist_fsdp,
+        graph=graph,
+        graph_code=graph_code,
+        graph_breaks=graph_breaks,
+        graph_sizes=graph_sizes,
+        guards=guards,
+        recompiles=recompiles,
+        recompiles_verbose=recompiles_verbose,
+        trace_source=trace_source,
+        trace_call=trace_call,
+        output_code=output_code,
+        schedule=schedule,
+        perf_hints=perf_hints,
+        post_grad_graphs=post_grad_graphs,
+        onnx=onnx,
+        onnx_diagnostics=onnx_diagnostics,
+        fusion=fusion,
+        overlap=overlap,
+        sym_node=sym_node,
+        export=export,
+        cudagraphs=cudagraphs,
+    )
+
+
+def get_loggers():
+    """
+    Returns: a list of all registered loggers
+    """
+    return [logging.getLogger(qname) for qname in log_registry.get_log_qnames()]
+
+
+def register_log(setting_name, log_name):
+    """
+    Enables a log to be controlled by the env var and user API with the setting_name
+    Args:
+        setting_name:  the shorthand name used in the env var and user API
+        log_name:  the log name that the setting_name is associated with
+    """
+    log_registry.register_log(setting_name, log_name)
+
+
+def register_artifact(
+    setting_name, description, visible=False, off_by_default=False, log_format=None
+):
+    """
+    Enables an artifact to be controlled by the env var and user API with name
+    Args:
+        setting_name: the shorthand name used in the env var and user API
+        description: A description of what this outputs
+        visible: Whether it gets suggested to users by default
+        off_by_default: whether this artifact should be logged when the ancestor loggers
+            are enabled at level DEBUG
+    """
+    log_registry.register_artifact_name(
+        setting_name, description, visible, off_by_default, log_format
+    )
+
+
+def getArtifactLogger(module_qname, artifact_name):
+    if artifact_name not in log_registry.artifact_names:
+        raise ValueError(
+            f"Artifact name: {repr(artifact_name)} not registered,"
+            f"please call register_artifact({repr(artifact_name)}) in torch._logging.registrations."
+        )
+    qname = module_qname + f".__{artifact_name}"
+    log = logging.getLogger(qname)
+    log.artifact_name = artifact_name  # type: ignore[attr-defined]
+    log_registry.register_artifact_log(qname)
+    configure_artifact_log(log)
+    return log
+
+
+INCR_VERBOSITY_CHAR = "+"
+DECR_VERBOSITY_CHAR = "-"
+VERBOSITY_REGEX = (
+    "("
+    + "|".join([re.escape(INCR_VERBOSITY_CHAR), re.escape(DECR_VERBOSITY_CHAR)])
+    + "?)"
+)
+
+
+def configure_artifact_log(log):
+    # If the artifact is off by default, then it should only be logged when explicitly
+    # enabled; set propagate to False so that this artifact is not propagated
+    # to its ancestor logger
+    if log_registry.is_off_by_default(log.artifact_name):
+        log.propagate = False
+
+    # enable artifact logging when explicitly enabled
+    if log_state.is_artifact_enabled(log.artifact_name):
+        log.setLevel(logging.DEBUG)
+        log.propagate = True
+
+
+# match a comma separated list of loggable names (whitespace allowed after commas)
+def _gen_settings_regex():
+    return re.compile(r"((\+|-)?[\w\.]+,\s*)*(\+|-)?[\w\.]+?")
+
+
+def _validate_settings(settings):
+    return re.fullmatch(_gen_settings_regex(), settings) is not None
+
+
+def help_message(verbose=False):
+    def pad_to(s, length=30):
+        assert len(s) <= length
+        return s + " " * (length - len(s))
+
+    if verbose:
+        printed_artifacts = log_registry.artifact_names
+    else:
+        printed_artifacts = log_registry.visible_artifacts
+
+    if verbose:
+        heading = "All registered names"
+    else:
+        heading = "Visible registered names (use TORCH_LOGS='+help' for full list)"
+    lines = (
+        ["all"]
+        + sorted(log_registry.log_alias_to_log_qnames.keys())
+        + sorted(
+            [
+                f"{pad_to(name)}\t{log_registry.artifact_descriptions[name]}"
+                for name in printed_artifacts
+            ]
+        )
+    )
+    setting_info = "  " + "\n  ".join(lines)
+    examples = """
+Examples:
+  TORCH_LOGS="+dynamo,aot" will set the log level of TorchDynamo to
+  logging.DEBUG and AOT to logging.INFO
+
+  TORCH_LOGS="-dynamo,+inductor" will set the log level of TorchDynamo to
+  logging.ERROR and TorchInductor to logging.DEBUG
+
+  TORCH_LOGS="aot_graphs" will enable the aot_graphs artifact
+
+  TORCH_LOGS="+dynamo,schedule" will enable set the log level of TorchDynamo
+  to logging.DEBUG and enable the schedule artifact
+
+  TORCH_LOGS="+some.random.module,schedule" will set the log level of
+  some.random.module to logging.DEBUG and enable the schedule artifact
+
+  TORCH_LOGS_FORMAT="%(levelname)s: %(message)s" or any provided format
+  string will set the output format
+  Valid keys are "levelname", "message", "pathname", "levelno", "lineno",
+  "filename" and "name".
+
+  TORCH_LOGS_OUT=/tmp/output.txt will output the logs to /tmp/output.txt as
+  well. This is useful when the output is long.
+"""  # flake8: noqa: B950
+    msg = f"""
+TORCH_LOGS Info
+{examples}
+
+{heading}
+{setting_info}
+"""
+    return msg
+
+
+def _invalid_settings_err_msg(settings, verbose=False):
+    valid_settings = ", ".join(
+        ["all"]
+        + list(log_registry.log_alias_to_log_qnames.keys())
+        + list(log_registry.artifact_names)
+    )
+    msg = f"""
+Invalid log settings: {settings}, must be a comma separated list of fully
+qualified module names, registered log names or registered artifact names.
+For more info on various settings, try TORCH_LOGS="help"
+Valid settings:
+{valid_settings}
+"""
+    return msg
+
+
+@functools.lru_cache
+def _parse_log_settings(settings):
+    if settings == "":
+        return dict()
+
+    if settings == "help":
+        raise ValueError(help_message(verbose=False))
+    elif settings == "+help":
+        raise ValueError(help_message(verbose=True))
+    if not _validate_settings(settings):
+        raise ValueError(_invalid_settings_err_msg(settings))
+
+    settings = re.sub(r"\s+", "", settings)
+    log_names = settings.split(",")
+
+    def get_name_level_pair(name):
+        clean_name = name.replace(INCR_VERBOSITY_CHAR, "")
+        clean_name = clean_name.replace(DECR_VERBOSITY_CHAR, "")
+
+        if name[0] == INCR_VERBOSITY_CHAR:
+            level = logging.DEBUG
+        elif name[0] == DECR_VERBOSITY_CHAR:
+            level = logging.ERROR
+        else:
+            level = logging.INFO
+
+        return clean_name, level
+
+    log_state = LogState()
+
+    for name in log_names:
+        name, level = get_name_level_pair(name)
+
+        if name == "all":
+            name = "torch"
+
+        if log_registry.is_log(name):
+            assert level is not None
+            log_qnames = log_registry.log_alias_to_log_qnames[name]
+            log_state.enable_log(log_qnames, level)
+        elif log_registry.is_artifact(name):
+            log_state.enable_artifact(name)
+        elif _is_valid_module(name):
+            if not _has_registered_parent(name):
+                log_registry.register_log(name, name)
+            else:
+                log_registry.register_child_log(name)
+            log_state.enable_log(name, level)
+        else:
+            raise ValueError(_invalid_settings_err_msg(settings))
+
+    return log_state
+
+
+def _is_valid_module(qname):
+    try:
+        __import__(qname)
+        return True
+    except ImportError:
+        return False
+
+
+def _update_log_state_from_env():
+    global log_state
+    log_setting = os.environ.get(LOG_ENV_VAR, None)
+    if log_setting is not None:
+        log_state = _parse_log_settings(log_setting)
+
+
+def _has_registered_parent(log_qname):
+    cur_log = logging.getLogger(log_qname)
+
+    registered_log_qnames = log_registry.get_log_qnames()
+
+    while cur_log.parent:
+        if cur_log.name in registered_log_qnames:
+            return True
+        cur_log = cur_log.parent
+
+    return False
+
+
+# apply custom formats to artifacts when necessary
+class TorchLogsFormatter(logging.Formatter):
+    def __init__(self, *, trace: bool = False):
+        super().__init__()
+        self._is_trace = trace
+
+    def format(self, record):
+        artifact_name = getattr(logging.getLogger(record.name), "artifact_name", None)
+        if artifact_name is not None:
+            artifact_formatter = log_registry.artifact_log_formatters.get(
+                artifact_name, None
+            )
+            if artifact_formatter is not None:
+                return artifact_formatter.format(record)
+
+        record.message = record.getMessage()
+        record.asctime = self.formatTime(record, "%m%d %H:%M:%S")
+
+        # exception handling - copied from logging.Formatter.format
+        s = record.message
+        if record.exc_info:
+            # Cache the traceback text to avoid converting it multiple times
+            # (it's constant anyway)
+            if not record.exc_text:
+                record.exc_text = self.formatException(record.exc_info)
+        if record.exc_text:
+            if s[-1:] != "\n":
+                s = s + "\n"
+            s = s + record.exc_text
+        if record.stack_info:
+            if s[-1:] != "\n":
+                s = s + "\n"
+            s = s + self.formatStack(record.stack_info)
+
+        record.rankprefix = ""
+        if not self._is_trace and dist.is_available() and dist.is_initialized():
+            record.rankprefix = f"[rank{dist.get_rank()}]:"
+
+        record.traceid = ""
+        if (
+            not self._is_trace
+            and (trace_id := torch._guards.CompileContext.current_trace_id())
+            is not None
+        ):
+            record.traceid = f" [{trace_id}]"
+
+        glog_level_to_abbr = {
+            "DEBUG": "V",  # V is for VERBOSE in glog
+            "INFO": "I",
+            "WARNING": "W",
+            "ERROR": "E",
+            "CRITICAL": "C",
+        }
+
+        shortlevel = glog_level_to_abbr.get(record.levelname, record.levelname)
+
+        record.artifactprefix = ""
+        if artifact_name is not None:
+            record.artifactprefix = f" [__{artifact_name}]"
+
+        prefix = (
+            f"{record.rankprefix}{shortlevel}{record.asctime}.{int(record.msecs*1000):06d} {record.thread} "
+            f"{os.path.relpath(record.pathname, os.path.dirname(os.path.dirname(torch.__file__)))}:"
+            f"{record.lineno}]{record.traceid}{record.artifactprefix}"
+        )
+        if self._is_trace:
+            assert s == ""
+            r = f"{prefix} {json.dumps(record.metadata)}"
+            if record.payload is not None:
+                r += "".join(f"\n\t{l}" for l in record.payload.split("\n"))
+            return r
+        else:
+            lines = s.split("\n")
+            return "\n".join(f"{prefix} {l}" for l in lines)
+
+
+def _default_formatter():
+    fmt = os.environ.get(LOG_FORMAT_ENV_VAR, None)
+    if fmt is None:
+        return TorchLogsFormatter()
+    else:
+        if fmt in ("short", "basic"):
+            fmt = logging.BASIC_FORMAT
+        return logging.Formatter(fmt)
+
+
+DEFAULT_FORMATTER = _default_formatter()
+
+
+def _setup_handlers(create_handler_fn, log):
+    debug_handler = _track_handler(create_handler_fn())
+    debug_handler.setFormatter(DEFAULT_FORMATTER)
+    debug_handler.setLevel(logging.DEBUG)
+    log.addHandler(debug_handler)
+
+
+handlers = WeakSet()  # type: ignore[var-annotated]
+
+
+# mark handlers that we've created
+# so we don't modify user handlers
+def _track_handler(handler):
+    handlers.add(handler)
+    return handler
+
+
+def _is_torch_handler(handler):
+    return handler in handlers
+
+
+# clears all torch handlers on specified loggers
+def _clear_handlers(log):
+    to_remove = [handler for handler in log.handlers if _is_torch_handler(handler)]
+    for handler in to_remove:
+        log.removeHandler(handler)
+
+
+def _reset_logs():
+    # reset all registered logs
+    for log_qname in log_registry.get_log_qnames():
+        log = logging.getLogger(log_qname)
+        log.setLevel(logging.WARNING)
+        log.propagate = False
+        _clear_handlers(log)
+
+    # reset all artifact and child logs
+    for artifact_log_qname in itertools.chain(
+        log_registry.get_artifact_log_qnames(), log_registry.get_child_log_qnames()
+    ):
+        log = logging.getLogger(artifact_log_qname)
+        log.setLevel(logging.NOTSET)
+        log.propagate = True
+
+    trace_log.propagate = False
+    _clear_handlers(trace_log)
+
+
+def _get_log_state():
+    return log_state
+
+
+def _set_log_state(state):
+    global log_state
+    log_state = state
+
+
+def _init_logs(log_file_name=None):
+    _reset_logs()
+    _update_log_state_from_env()
+
+    out = os.environ.get(LOG_OUT_ENV_VAR, None)
+    if out is not None:
+        log_file_name = out
+
+    # First, reset all known (registered) loggers to NOTSET, so that they
+    # respect their parent log level
+    for log_qname in log_registry.get_log_qnames():
+        # But not the top level torch level: this defaults to WARNING so
+        # that our log messages don't leak to the lower levels
+        if log_qname == "torch":
+            continue
+        log = logging.getLogger(log_qname)
+        log.setLevel(logging.NOTSET)
+
+    # Now, for all loggers which the user requested to have non-standard
+    # logging behavior, modify their log levels
+    for log_qname, level in log_state.get_log_level_pairs():
+        log = logging.getLogger(log_qname)
+        log.setLevel(level)
+
+    # Finally, setup handlers for all registered loggers
+    for log_qname in log_registry.get_log_qnames():
+        log = logging.getLogger(log_qname)
+        _setup_handlers(
+            logging.StreamHandler,
+            log,
+        )
+
+        if log_file_name is not None:
+            _setup_handlers(
+                lambda: logging.FileHandler(log_file_name),
+                log,
+            )
+
+    # configure artifact loggers, note: this must happen last
+    # since the levels of ancestor loggers are taken into account
+    for artifact_log_qname in log_registry.get_artifact_log_qnames():
+        log = logging.getLogger(artifact_log_qname)
+        configure_artifact_log(log)
+
+    # Setup handler for the special trace_log, with different default
+    # configuration
+    trace_dir_name = os.environ.get(TRACE_ENV_VAR, None)
+    # This handler may remove itself if trace_dir_name is None and we are not
+    # actually in an FB environment.  This allows us to defer actually
+    # initializing it until we actually need to log anything.  This is
+    # important because JK initializes a C++ singleton, which will pork our
+    # process if we subsequently fork.
+    handler = LazyTraceHandler(trace_dir_name)
+    # This log is ALWAYS at debug level.  We will additionally test if there
+    # are any handlers before deciding to actually call logging on this.  Do
+    # not manually call
+    trace_log.setLevel(logging.DEBUG)
+    trace_log_handler = _track_handler(handler)
+    trace_log_handler.setFormatter(TorchLogsFormatter(trace=True))
+    trace_log.addHandler(trace_log_handler)
+
+
+class LazyTraceHandler(logging.StreamHandler):
+    """Like FileHandler, but the file is allocated lazily only upon the first log message"""
+
+    def __init__(self, root_dir: Optional[str]):
+        # This is implemented in the same way that delay is implemented on
+        # FileHandler
+        self.root_dir = root_dir
+        logging.Handler.__init__(self)
+        self.stream = None
+        self._builtin_open = open
+
+    # cloned from FileHandler in cpython
+    def close(self):
+        self.acquire()
+        try:
+            try:
+                if self.stream:
+                    try:
+                        self.flush()
+                    finally:
+                        stream = self.stream
+                        self.stream = None
+                        if hasattr(stream, "close"):
+                            stream.close()
+            finally:
+                # Issue #19523: call unconditionally to
+                # prevent a handler leak when delay is set
+                # Also see Issue #42378: we also rely on
+                # self._closed being set to True there
+                logging.StreamHandler.close(self)
+        finally:
+            self.release()
+
+    def emit(self, record):
+        if self.stream is None:
+            ok = False
+            if self.root_dir is None:
+                TRACE_LOG_DIR = "/logs"
+                open_func = self._builtin_open
+
+                import torch.version as torch_version
+
+                if hasattr(torch_version, "git_version"):
+                    log.info("LazyTraceHandler: disabled because not fbcode")
+                elif not torch._utils_internal.justknobs_check("pytorch/trace:enable"):
+                    log.info(
+                        "LazyTraceHandler: disabled because justknobs_check('pytorch/trace:enable') returned False"
+                    )
+                elif not os.path.exists(TRACE_LOG_DIR):
+                    log.info(
+                        "LazyTraceHandler: disabled because %s does not exist",
+                        TRACE_LOG_DIR,
+                    )
+                elif not os.access(TRACE_LOG_DIR, os.W_OK):
+                    log.info(
+                        "LazyTraceHandler: disabled because %s is not writeable",
+                        TRACE_LOG_DIR,
+                    )
+                else:
+                    self.root_dir = TRACE_LOG_DIR
+
+            if self.root_dir is not None:
+                os.makedirs(self.root_dir, exist_ok=True)
+                ranksuffix = ""
+                if dist.is_available() and dist.is_initialized():
+                    ranksuffix = f"rank_{dist.get_rank()}_"
+                self.stream = tempfile.NamedTemporaryFile(
+                    mode="w+",
+                    suffix=".log",
+                    prefix=f"dedicated_log_torch_trace_{ranksuffix}",
+                    dir=self.root_dir,
+                    delete=False,
+                )
+                log.info("LazyTraceHandler: logging to %s", self.stream.name)
+            else:
+                # We go poof, remove and no-op
+                trace_log.removeHandler(self)
+                return
+        if self.stream:
+            super().emit(record)
+
+
+@functools.lru_cache(None)
+def warning_once(logger_obj, *args, **kwargs):
+    """
+    This function is similar to `logger.warning()`, but will emit the warning with the same message only once
+    Note: The cache is for the function arguments, so 2 different callers using the same arguments will hit the cache.
+    The assumption here is that all warning messages are unique across the code. If they aren't then need to switch to
+    another type of cache that includes the caller frame information in the hashing function.
+    """
+    logger_obj.warning(*args, **kwargs)
+
+
+class LazyString:
+    def __init__(self, func, *args, **kwargs):
+        self.func = func
+        self.args = args
+        self.kwargs = kwargs
+
+    def __str__(self):
+        return self.func(*self.args, **self.kwargs)
+
+
+def trace_structured(
+    name: str,
+    # NB: metadata expected to be dict so adding more info is forward compatible
+    # Tuple[str, int] is a special case for string interning
+    metadata_fn: Callable[[], Union[Dict[str, Any], Tuple[str, int]]] = dict,
+    *,
+    payload_fn: Callable[[], Optional[Union[str, object]]] = lambda: None,
+    suppress_context: bool = False,
+):
+    """
+    metadata is an arbitrary JSON compatible struct, but it's expected to not be
+    too long (e.g., less than 1MB)
+
+    payload is an arbitrary string, which can be arbitrarily long (but expected to have
+    newlines so no lines are too long)
+    """
+    assert "name" not in ["rank", "frame_id", "frame_compile_id", "attempt"]
+    assert callable(
+        metadata_fn
+    ), f"metadata_fn should be callable, but got {type(metadata_fn)}"
+    assert callable(
+        payload_fn
+    ), f"payload_fn should be callable, but got {type(payload_fn)}"
+    # trace_log never propagates and is ALWAYS DEBUG, so also check that there
+    # are handlers instead of checking the log level
+    if trace_log.handlers:
+        record: Dict[str, object] = {}
+        record[name] = metadata_fn()
+        if not suppress_context:
+            # TODO: Actually, the rank probably should just be emitted once at
+            # the top, and not repeatedly spammed in all the logs, since it
+            # never changes and we assume no interleaving
+            if dist.is_available() and dist.is_initialized():
+                record["rank"] = dist.get_rank()
+            if (
+                trace_id := torch._guards.CompileContext.current_trace_id()
+            ) is not None:
+                record["frame_id"] = trace_id.compile_id.frame_id
+                record["frame_compile_id"] = trace_id.compile_id.frame_compile_id
+                record["attempt"] = trace_id.attempt
+        payload = payload_fn()
+        if payload is not None:
+            if not isinstance(payload, str):
+                if isinstance(payload, list):
+                    # special case to look better
+                    payload = "[\n" + ",\n".join(json.dumps(i) for i in payload) + "\n]"
+                else:
+                    # force newlines so we are unlikely to overflow line limit
+                    payload = json.dumps(payload, indent=0)
+            h = hashlib.md5()
+            h.update(payload.encode("utf-8"))
+            record["has_payload"] = h.hexdigest()
+        trace_log.debug(
+            "", extra={"metadata": record, "payload": payload}, stacklevel=2
+        )
+
+
+import torch._guards
+import torch._utils_internal
+import torch.distributed as dist

venv/lib/python3.10/site-packages/torch/_logging/_registrations.py

@@ -0,0 +1,134 @@
+# flake8: noqa: B950
+from ._internal import register_artifact, register_log
+
+DYNAMIC = ["torch.fx.experimental.symbolic_shapes", "torch.fx.experimental.sym_node"]
+DISTRIBUTED = [
+    "torch.distributed",
+    "torch._dynamo.backends.distributed",
+    "torch.nn.parallel.distributed",
+]
+
+register_log("dynamo", ["torch._dynamo", *DYNAMIC])
+register_log("aot", ["torch._functorch.aot_autograd", "torch._functorch._aot_autograd"])
+register_log("autograd", "torch.autograd")
+register_log("inductor", ["torch._inductor", "torch._inductor.cudagraph_trees"])
+
+register_artifact(
+    "cudagraphs",
+    "Logs information from wrapping inductor generated code with cudagraphs.",
+)
+
+register_log("dynamic", DYNAMIC)
+register_log("torch", "torch")
+register_log("distributed", DISTRIBUTED)
+register_log(
+    "dist_c10d", ["torch.distributed.distributed_c10d", "torch.distributed.rendezvous"]
+)
+register_log(
+    "dist_ddp", ["torch.nn.parallel.distributed", "torch._dynamo.backends.distributed"]
+)
+register_log("dist_fsdp", ["torch.distributed.fsdp"])
+register_log("onnx", "torch.onnx")
+register_log("export", ["torch._dynamo", "torch.export", *DYNAMIC])
+
+register_artifact(
+    "guards",
+    "This prints the guards for every compiled Dynamo frame. It does not tell you where the guards come from.",
+    visible=True,
+)
+register_artifact("verbose_guards", "", off_by_default=True)
+register_artifact(
+    "bytecode",
+    "Prints the original and modified bytecode from Dynamo. Mostly useful if you're debugging our bytecode generation in Dynamo.",
+    off_by_default=True,
+)
+register_artifact(
+    "graph",
+    "Prints the dynamo traced graph (prior to AOTDispatch) in a table. If you prefer python code use `graph_code` instead. ",
+)
+register_artifact("graph_code", "Like `graph`, but gives you the Python code instead.")
+register_artifact(
+    "graph_sizes", "Prints the sizes of all FX nodes in the dynamo graph."
+)
+register_artifact(
+    "trace_source",
+    "As we execute bytecode, prints the file name / line number we are processing and the actual source code. Useful with `bytecode`",
+)
+register_artifact(
+    "trace_call",
+    "Like trace_source, but it will give you the per-expression blow-by-blow if your Python is recent enough.",
+)
+register_artifact(
+    "aot_graphs",
+    "Prints the FX forward and backward graph generated by AOTDispatch, after partitioning. Useful to understand what's being given to Inductor",
+    visible=True,
+)
+register_artifact(
+    "aot_joint_graph",
+    "Print FX joint graph from AOTAutograd, prior to partitioning. Useful for debugging partitioning",
+)
+register_artifact(
+    "post_grad_graphs",
+    "Prints the FX graph generated by post grad passes. Useful to understand what's being given to Inductor after post grad passes",
+)
+register_artifact(
+    "compiled_autograd",
+    "Prints various logs in compiled_autograd, including but not limited to the graphs. Useful for debugging compiled_autograd.",
+    visible=True,
+)
+register_artifact(
+    "ddp_graphs",
+    "Only relevant for compiling DDP. DDP splits into multiple graphs to trigger comms early. This will print each individual graph here.",
+)
+register_artifact(
+    "recompiles",
+    "Prints the reason why we recompiled a graph. Very, very useful.",
+    visible=True,
+)
+register_artifact(
+    "recompiles_verbose",
+    "Prints all guard checks that fail during a recompilation. "
+    "At runtime, Dynamo will stop at the first failed check for each failing guard. "
+    "So not all logged failing checks are actually ran by Dynamo.",
+    visible=True,
+    off_by_default=True,
+)
+register_artifact(
+    "graph_breaks",
+    "Prints whenever Dynamo decides that it needs to graph break (i.e. create a new graph). Useful for debugging why torch.compile has poor performance",
+    visible=True,
+)
+register_artifact(
+    "not_implemented",
+    "Prints log messages whenever we return NotImplemented in a multi-dispatch, letting you trace through each object we attempted to dispatch to",
+)
+register_artifact(
+    "output_code",
+    "Prints the code that Inductor generates (either Triton or C++)",
+    off_by_default=True,
+    visible=True,
+)
+register_artifact(
+    "schedule",
+    "Inductor scheduler information. Useful if working on Inductor fusion algo",
+    off_by_default=True,
+)
+register_artifact("perf_hints", "", off_by_default=True)
+register_artifact("onnx_diagnostics", "", off_by_default=True)
+register_artifact(
+    "fusion",
+    "Detailed Inductor fusion decisions. More detailed than 'schedule'",
+    off_by_default=True,
+)
+register_artifact(
+    "overlap",
+    "Detailed Inductor compute/comm overlap decisions",
+    off_by_default=True,
+)
+register_artifact(
+    "sym_node",
+    "Logs extra info for various SymNode operations",
+    off_by_default=True,
+)
+
+register_artifact("custom_format_test_artifact", "Testing only", log_format="")

venv/lib/python3.10/site-packages/torch/_logging/structured.py

@@ -0,0 +1,37 @@
+"""
+Utilities for converting data types into structured JSON for dumping.
+"""
+
+import traceback
+from typing import Dict, Sequence
+
+import torch._logging._internal
+
+
+INTERN_TABLE: Dict[str, int] = {}
+
+
+def intern_string(s: str) -> int:
+    r = INTERN_TABLE.get(s, None)
+    if r is None:
+        r = len(INTERN_TABLE)
+        INTERN_TABLE[s] = r
+        torch._logging._internal.trace_structured(
+            "str", lambda: (s, r), suppress_context=True
+        )
+    return r
+
+
+def from_traceback(tb: Sequence[traceback.FrameSummary]) -> object:
+    r = []
+    for frame in tb:
+        # dict naming convention here coincides with
+        # python/combined_traceback.cpp
+        r.append(
+            {
+                "line": frame.lineno,
+                "name": frame.name,
+                "filename": intern_string(frame.filename),
+            }
+        )
+    return r

venv/lib/python3.10/site-packages/torch/_numpy/__init__.py

@@ -0,0 +1,30 @@
+# mypy: ignore-errors
+
+from . import fft, linalg, random
+from ._dtypes import *  # noqa: F403
+from ._funcs import *  # noqa: F403
+from ._getlimits import finfo, iinfo
+from ._ndarray import (
+    array,
+    asarray,
+    ascontiguousarray,
+    can_cast,
+    from_dlpack,
+    ndarray,
+    newaxis,
+    result_type,
+)
+from ._ufuncs import *  # noqa: F403
+from ._util import AxisError, UFuncTypeError
+
+# from . import testing
+
+alltrue = all
+sometrue = any
+
+inf = float("inf")
+nan = float("nan")
+from math import pi, e  # isort: skip
+
+False_ = False
+True_ = True

venv/lib/python3.10/site-packages/torch/_numpy/_binary_ufuncs_impl.py

@@ -0,0 +1,86 @@
+# mypy: ignore-errors
+
+"""Export torch work functions for binary ufuncs, rename/tweak to match numpy.
+This listing is further exported to public symbols in the `torch._numpy/_ufuncs.py` module.
+"""
+
+import torch
+
+from torch import (  # noqa: F401
+    add,  # noqa: F401
+    arctan2,  # noqa: F401
+    bitwise_and,  # noqa: F401
+    bitwise_left_shift as left_shift,  # noqa: F401
+    bitwise_or,  # noqa: F401
+    bitwise_right_shift as right_shift,  # noqa: F401
+    bitwise_xor,  # noqa: F401
+    copysign,  # noqa: F401
+    divide,  # noqa: F401
+    eq as equal,  # noqa: F401
+    float_power,  # noqa: F401
+    floor_divide,  # noqa: F401
+    fmax,  # noqa: F401
+    fmin,  # noqa: F401
+    fmod,  # noqa: F401
+    gcd,  # noqa: F401
+    greater,  # noqa: F401
+    greater_equal,  # noqa: F401
+    heaviside,  # noqa: F401
+    hypot,  # noqa: F401
+    lcm,  # noqa: F401
+    ldexp,  # noqa: F401
+    less,  # noqa: F401
+    less_equal,  # noqa: F401
+    logaddexp,  # noqa: F401
+    logaddexp2,  # noqa: F401
+    logical_and,  # noqa: F401
+    logical_or,  # noqa: F401
+    logical_xor,  # noqa: F401
+    maximum,  # noqa: F401
+    minimum,  # noqa: F401
+    multiply,  # noqa: F401
+    nextafter,  # noqa: F401
+    not_equal,  # noqa: F401
+    pow as power,  # noqa: F401
+    remainder,  # noqa: F401
+    remainder as mod,  # noqa: F401
+    subtract,  # noqa: F401
+    true_divide,  # noqa: F401
+)
+
+from . import _dtypes_impl, _util
+
+
+# work around torch limitations w.r.t. numpy
+def matmul(x, y):
+    # work around:
+    #  - RuntimeError: expected scalar type Int but found Double
+    #  - RuntimeError: "addmm_impl_cpu_" not implemented for 'Bool'
+    #  - RuntimeError: "addmm_impl_cpu_" not implemented for 'Half'
+    dtype = _dtypes_impl.result_type_impl(x, y)
+    is_bool = dtype == torch.bool
+    is_half = (x.dtype == torch.float16 or y.dtype == torch.float16) and (
+        x.is_cpu or y.is_cpu
+    )
+
+    work_dtype = dtype
+    if is_bool:
+        work_dtype = torch.uint8
+    if is_half:
+        work_dtype = torch.float32
+
+    x = _util.cast_if_needed(x, work_dtype)
+    y = _util.cast_if_needed(y, work_dtype)
+
+    result = torch.matmul(x, y)
+
+    if work_dtype != dtype:
+        result = result.to(dtype)
+
+    return result
+
+
+# a stub implementation of divmod, should be improved after
+# https://github.com/pytorch/pytorch/issues/90820 is fixed in pytorch
+def divmod(x, y):
+    return x // y, x % y

venv/lib/python3.10/site-packages/torch/_numpy/_casting_dicts.py

@@ -0,0 +1,881 @@
+# mypy: ignore-errors
+
+import torch
+
+# These two dicts are autogenerated with autogen/gen_dtypes.py,
+# using numpy version 1.23.5.
+
+_can_cast_dict = {
+    "no": {
+        torch.float16: {
+            torch.float16: True,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.float32: {
+            torch.float16: False,
+            torch.float32: True,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.float64: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: True,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.complex64: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: True,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.complex128: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.uint8: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: True,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.int8: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: True,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.int16: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: True,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.int32: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: True,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.int64: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.bool: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: True,
+        },
+    },
+    "equiv": {
+        torch.float16: {
+            torch.float16: True,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.float32: {
+            torch.float16: False,
+            torch.float32: True,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.float64: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: True,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.complex64: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: True,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.complex128: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.uint8: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: True,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.int8: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: True,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.int16: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: True,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.int32: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: True,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.int64: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.bool: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: False,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: True,
+        },
+    },
+    "safe": {
+        torch.float16: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.float32: {
+            torch.float16: False,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.float64: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: True,
+            torch.complex64: False,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.complex64: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.complex128: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: False,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.uint8: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: False,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.int8: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.int16: {
+            torch.float16: False,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.int32: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: True,
+            torch.complex64: False,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.int64: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: True,
+            torch.complex64: False,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.bool: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+    },
+    "same_kind": {
+        torch.float16: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.float32: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.float64: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.complex64: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.complex128: {
+            torch.float16: False,
+            torch.float32: False,
+            torch.float64: False,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: False,
+            torch.int16: False,
+            torch.int32: False,
+            torch.int64: False,
+            torch.bool: False,
+        },
+        torch.uint8: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.int8: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.int16: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.int32: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.int64: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: False,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: False,
+        },
+        torch.bool: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+    },
+    "unsafe": {
+        torch.float16: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+        torch.float32: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+        torch.float64: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+        torch.complex64: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+        torch.complex128: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+        torch.uint8: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+        torch.int8: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+        torch.int16: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+        torch.int32: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+        torch.int64: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+        torch.bool: {
+            torch.float16: True,
+            torch.float32: True,
+            torch.float64: True,
+            torch.complex64: True,
+            torch.complex128: True,
+            torch.uint8: True,
+            torch.int8: True,
+            torch.int16: True,
+            torch.int32: True,
+            torch.int64: True,
+            torch.bool: True,
+        },
+    },
+}
+
+
+_result_type_dict = {
+    torch.float16: {
+        torch.float16: torch.float16,
+        torch.float32: torch.float32,
+        torch.float64: torch.float64,
+        torch.complex64: torch.complex64,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.float16,
+        torch.int8: torch.float16,
+        torch.int16: torch.float32,
+        torch.int32: torch.float64,
+        torch.int64: torch.float64,
+        torch.bool: torch.float16,
+    },
+    torch.float32: {
+        torch.float16: torch.float32,
+        torch.float32: torch.float32,
+        torch.float64: torch.float64,
+        torch.complex64: torch.complex64,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.float32,
+        torch.int8: torch.float32,
+        torch.int16: torch.float32,
+        torch.int32: torch.float64,
+        torch.int64: torch.float64,
+        torch.bool: torch.float32,
+    },
+    torch.float64: {
+        torch.float16: torch.float64,
+        torch.float32: torch.float64,
+        torch.float64: torch.float64,
+        torch.complex64: torch.complex128,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.float64,
+        torch.int8: torch.float64,
+        torch.int16: torch.float64,
+        torch.int32: torch.float64,
+        torch.int64: torch.float64,
+        torch.bool: torch.float64,
+    },
+    torch.complex64: {
+        torch.float16: torch.complex64,
+        torch.float32: torch.complex64,
+        torch.float64: torch.complex128,
+        torch.complex64: torch.complex64,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.complex64,
+        torch.int8: torch.complex64,
+        torch.int16: torch.complex64,
+        torch.int32: torch.complex128,
+        torch.int64: torch.complex128,
+        torch.bool: torch.complex64,
+    },
+    torch.complex128: {
+        torch.float16: torch.complex128,
+        torch.float32: torch.complex128,
+        torch.float64: torch.complex128,
+        torch.complex64: torch.complex128,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.complex128,
+        torch.int8: torch.complex128,
+        torch.int16: torch.complex128,
+        torch.int32: torch.complex128,
+        torch.int64: torch.complex128,
+        torch.bool: torch.complex128,
+    },
+    torch.uint8: {
+        torch.float16: torch.float16,
+        torch.float32: torch.float32,
+        torch.float64: torch.float64,
+        torch.complex64: torch.complex64,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.uint8,
+        torch.int8: torch.int16,
+        torch.int16: torch.int16,
+        torch.int32: torch.int32,
+        torch.int64: torch.int64,
+        torch.bool: torch.uint8,
+    },
+    torch.int8: {
+        torch.float16: torch.float16,
+        torch.float32: torch.float32,
+        torch.float64: torch.float64,
+        torch.complex64: torch.complex64,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.int16,
+        torch.int8: torch.int8,
+        torch.int16: torch.int16,
+        torch.int32: torch.int32,
+        torch.int64: torch.int64,
+        torch.bool: torch.int8,
+    },
+    torch.int16: {
+        torch.float16: torch.float32,
+        torch.float32: torch.float32,
+        torch.float64: torch.float64,
+        torch.complex64: torch.complex64,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.int16,
+        torch.int8: torch.int16,
+        torch.int16: torch.int16,
+        torch.int32: torch.int32,
+        torch.int64: torch.int64,
+        torch.bool: torch.int16,
+    },
+    torch.int32: {
+        torch.float16: torch.float64,
+        torch.float32: torch.float64,
+        torch.float64: torch.float64,
+        torch.complex64: torch.complex128,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.int32,
+        torch.int8: torch.int32,
+        torch.int16: torch.int32,
+        torch.int32: torch.int32,
+        torch.int64: torch.int64,
+        torch.bool: torch.int32,
+    },
+    torch.int64: {
+        torch.float16: torch.float64,
+        torch.float32: torch.float64,
+        torch.float64: torch.float64,
+        torch.complex64: torch.complex128,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.int64,
+        torch.int8: torch.int64,
+        torch.int16: torch.int64,
+        torch.int32: torch.int64,
+        torch.int64: torch.int64,
+        torch.bool: torch.int64,
+    },
+    torch.bool: {
+        torch.float16: torch.float16,
+        torch.float32: torch.float32,
+        torch.float64: torch.float64,
+        torch.complex64: torch.complex64,
+        torch.complex128: torch.complex128,
+        torch.uint8: torch.uint8,
+        torch.int8: torch.int8,
+        torch.int16: torch.int16,
+        torch.int32: torch.int32,
+        torch.int64: torch.int64,
+        torch.bool: torch.bool,
+    },
+}

venv/lib/python3.10/site-packages/torch/_numpy/_dtypes.py

@@ -0,0 +1,434 @@
+# mypy: ignore-errors
+
+""" Define analogs of numpy dtypes supported by pytorch.
+Define the scalar types and supported dtypes and numpy <--> torch dtype mappings.
+"""
+import builtins
+
+import torch
+
+from . import _dtypes_impl
+
+
+# ### Scalar types ###
+
+
+class generic:
+    name = "generic"
+
+    def __new__(cls, value):
+        # NumPy scalars are modelled as 0-D arrays
+        # so a call to np.float32(4) produces a 0-D array.
+
+        from ._ndarray import asarray, ndarray
+
+        if isinstance(value, str) and value in ["inf", "nan"]:
+            value = {"inf": torch.inf, "nan": torch.nan}[value]
+
+        if isinstance(value, ndarray):
+            return value.astype(cls)
+        else:
+            return asarray(value, dtype=cls)
+
+
+##################
+# abstract types #
+##################
+
+
+class number(generic):
+    name = "number"
+
+
+class integer(number):
+    name = "integer"
+
+
+class inexact(number):
+    name = "inexact"
+
+
+class signedinteger(integer):
+    name = "signedinteger"
+
+
+class unsignedinteger(integer):
+    name = "unsignedinteger"
+
+
+class floating(inexact):
+    name = "floating"
+
+
+class complexfloating(inexact):
+    name = "complexfloating"
+
+
+_abstract_dtypes = [
+    "generic",
+    "number",
+    "integer",
+    "signedinteger",
+    "unsignedinteger",
+    "inexact",
+    "floating",
+    "complexfloating",
+]
+
+# ##### concrete types
+
+# signed integers
+
+
+class int8(signedinteger):
+    name = "int8"
+    typecode = "b"
+    torch_dtype = torch.int8
+
+
+class int16(signedinteger):
+    name = "int16"
+    typecode = "h"
+    torch_dtype = torch.int16
+
+
+class int32(signedinteger):
+    name = "int32"
+    typecode = "i"
+    torch_dtype = torch.int32
+
+
+class int64(signedinteger):
+    name = "int64"
+    typecode = "l"
+    torch_dtype = torch.int64
+
+
+# unsigned integers
+
+
+class uint8(unsignedinteger):
+    name = "uint8"
+    typecode = "B"
+    torch_dtype = torch.uint8
+
+
+# floating point
+
+
+class float16(floating):
+    name = "float16"
+    typecode = "e"
+    torch_dtype = torch.float16
+
+
+class float32(floating):
+    name = "float32"
+    typecode = "f"
+    torch_dtype = torch.float32
+
+
+class float64(floating):
+    name = "float64"
+    typecode = "d"
+    torch_dtype = torch.float64
+
+
+class complex64(complexfloating):
+    name = "complex64"
+    typecode = "F"
+    torch_dtype = torch.complex64
+
+
+class complex128(complexfloating):
+    name = "complex128"
+    typecode = "D"
+    torch_dtype = torch.complex128
+
+
+class bool_(generic):
+    name = "bool_"
+    typecode = "?"
+    torch_dtype = torch.bool
+
+
+# name aliases
+_name_aliases = {
+    "intp": int64,
+    "int_": int64,
+    "intc": int32,
+    "byte": int8,
+    "short": int16,
+    "longlong": int64,  # XXX: is this correct?
+    "ubyte": uint8,
+    "half": float16,
+    "single": float32,
+    "double": float64,
+    "float_": float64,
+    "csingle": complex64,
+    "singlecomplex": complex64,
+    "cdouble": complex128,
+    "cfloat": complex128,
+    "complex_": complex128,
+}
+# We register float_ = float32 and so on
+for name, obj in _name_aliases.items():
+    vars()[name] = obj
+
+
+# Replicate this NumPy-defined way of grouping scalar types,
+# cf tests/core/test_scalar_methods.py
+sctypes = {
+    "int": [int8, int16, int32, int64],
+    "uint": [uint8],
+    "float": [float16, float32, float64],
+    "complex": [complex64, complex128],
+    "others": [bool_],
+}
+
+
+# Support mappings/functions
+
+_names = {st.name: st for cat in sctypes for st in sctypes[cat]}
+_typecodes = {st.typecode: st for cat in sctypes for st in sctypes[cat]}
+_torch_dtypes = {st.torch_dtype: st for cat in sctypes for st in sctypes[cat]}
+
+
+_aliases = {
+    "u1": uint8,
+    "i1": int8,
+    "i2": int16,
+    "i4": int32,
+    "i8": int64,
+    "b": int8,  # XXX: srsly?
+    "f2": float16,
+    "f4": float32,
+    "f8": float64,
+    "c8": complex64,
+    "c16": complex128,
+    # numpy-specific trailing underscore
+    "bool_": bool_,
+}
+
+
+_python_types = {
+    int: int64,
+    float: float64,
+    complex: complex128,
+    builtins.bool: bool_,
+    # also allow stringified names of python types
+    int.__name__: int64,
+    float.__name__: float64,
+    complex.__name__: complex128,
+    builtins.bool.__name__: bool_,
+}
+
+
+def sctype_from_string(s):
+    """Normalize a string value: a type 'name' or a typecode or a width alias."""
+    if s in _names:
+        return _names[s]
+    if s in _name_aliases.keys():
+        return _name_aliases[s]
+    if s in _typecodes:
+        return _typecodes[s]
+    if s in _aliases:
+        return _aliases[s]
+    if s in _python_types:
+        return _python_types[s]
+    raise TypeError(f"data type {s!r} not understood")
+
+
+def sctype_from_torch_dtype(torch_dtype):
+    return _torch_dtypes[torch_dtype]
+
+
+# ### DTypes. ###
+
+
+def dtype(arg):
+    if arg is None:
+        arg = _dtypes_impl.default_dtypes().float_dtype
+    return DType(arg)
+
+
+class DType:
+    def __init__(self, arg):
+        # a pytorch object?
+        if isinstance(arg, torch.dtype):
+            sctype = _torch_dtypes[arg]
+        elif isinstance(arg, torch.Tensor):
+            sctype = _torch_dtypes[arg.dtype]
+        # a scalar type?
+        elif issubclass_(arg, generic):
+            sctype = arg
+        # a dtype already?
+        elif isinstance(arg, DType):
+            sctype = arg._scalar_type
+        # a has a right attribute?
+        elif hasattr(arg, "dtype"):
+            sctype = arg.dtype._scalar_type
+        else:
+            sctype = sctype_from_string(arg)
+        self._scalar_type = sctype
+
+    @property
+    def name(self):
+        return self._scalar_type.name
+
+    @property
+    def type(self):
+        return self._scalar_type
+
+    @property
+    def kind(self):
+        # https://numpy.org/doc/stable/reference/generated/numpy.dtype.kind.html
+        return _torch_dtypes[self.torch_dtype].name[0]
+
+    @property
+    def typecode(self):
+        return self._scalar_type.typecode
+
+    def __eq__(self, other):
+        if isinstance(other, DType):
+            return self._scalar_type == other._scalar_type
+        try:
+            other_instance = DType(other)
+        except TypeError:
+            return False
+        return self._scalar_type == other_instance._scalar_type
+
+    @property
+    def torch_dtype(self):
+        return self._scalar_type.torch_dtype
+
+    def __hash__(self):
+        return hash(self._scalar_type.name)
+
+    def __repr__(self):
+        return f'dtype("{self.name}")'
+
+    __str__ = __repr__
+
+    @property
+    def itemsize(self):
+        elem = self.type(1)
+        return elem.tensor.element_size()
+
+    def __getstate__(self):
+        return self._scalar_type
+
+    def __setstate__(self, value):
+        self._scalar_type = value
+
+
+typecodes = {
+    "All": "efdFDBbhil?",
+    "AllFloat": "efdFD",
+    "AllInteger": "Bbhil",
+    "Integer": "bhil",
+    "UnsignedInteger": "B",
+    "Float": "efd",
+    "Complex": "FD",
+}
+
+
+# ### Defaults and dtype discovery
+
+
+def set_default_dtype(fp_dtype="numpy", int_dtype="numpy"):
+    """Set the (global) defaults for fp, complex, and int dtypes.
+
+    The complex dtype is inferred from the float (fp) dtype. It has
+    a width at least twice the width of the float dtype,
+    i.e., it's complex128 for float64 and complex64 for float32.
+
+    Parameters
+    ----------
+    fp_dtype
+        Allowed values are "numpy", "pytorch" or dtype_like things which
+        can be converted into a DType instance.
+        Default is "numpy" (i.e. float64).
+    int_dtype
+        Allowed values are "numpy", "pytorch" or dtype_like things which
+        can be converted into a DType instance.
+        Default is "numpy" (i.e. int64).
+
+    Returns
+    -------
+    The old default dtype state: a namedtuple with attributes ``float_dtype``,
+    ``complex_dtypes`` and ``int_dtype``. These attributes store *pytorch*
+    dtypes.
+
+    Notes
+    ------------
+    This functions has a side effect: it sets the global state with the provided dtypes.
+
+    The complex dtype has bit width of at least twice the width of the float
+    dtype, i.e. it's complex128 for float64 and complex64 for float32.
+
+    """
+    if fp_dtype not in ["numpy", "pytorch"]:
+        fp_dtype = dtype(fp_dtype).torch_dtype
+    if int_dtype not in ["numpy", "pytorch"]:
+        int_dtype = dtype(int_dtype).torch_dtype
+
+    if fp_dtype == "numpy":
+        float_dtype = torch.float64
+    elif fp_dtype == "pytorch":
+        float_dtype = torch.float32
+    else:
+        float_dtype = fp_dtype
+
+    complex_dtype = {
+        torch.float64: torch.complex128,
+        torch.float32: torch.complex64,
+        torch.float16: torch.complex64,
+    }[float_dtype]
+
+    if int_dtype in ["numpy", "pytorch"]:
+        int_dtype = torch.int64
+    else:
+        int_dtype = int_dtype
+
+    new_defaults = _dtypes_impl.DefaultDTypes(
+        float_dtype=float_dtype, complex_dtype=complex_dtype, int_dtype=int_dtype
+    )
+
+    # set the new global state and return the old state
+    old_defaults = _dtypes_impl.default_dtypes
+    _dtypes_impl._default_dtypes = new_defaults
+    return old_defaults
+
+
+def issubclass_(arg, klass):
+    try:
+        return issubclass(arg, klass)
+    except TypeError:
+        return False
+
+
+def issubdtype(arg1, arg2):
+    # cf https://github.com/numpy/numpy/blob/v1.24.0/numpy/core/numerictypes.py#L356-L420
+
+    # We also accept strings even if NumPy doesn't as dtypes are serialized as their
+    # string representation in dynamo's graph
+    def str_to_abstract(t):
+        if isinstance(t, str) and t in _abstract_dtypes:
+            return globals()[t]
+        return t
+
+    arg1 = str_to_abstract(arg1)
+    arg2 = str_to_abstract(arg2)
+
+    if not issubclass_(arg1, generic):
+        arg1 = dtype(arg1).type
+    if not issubclass_(arg2, generic):
+        arg2 = dtype(arg2).type
+    return issubclass(arg1, arg2)
+
+
+__all__ = ["dtype", "DType", "typecodes", "issubdtype", "set_default_dtype", "sctypes"]
+__all__ += list(_names.keys())  # noqa: PLE0605
+__all__ += list(_name_aliases.keys())  # noqa: PLE0605
+__all__ += _abstract_dtypes  # noqa: PLE0605

venv/lib/python3.10/site-packages/torch/_numpy/_dtypes_impl.py

@@ -0,0 +1,216 @@
+# mypy: ignore-errors
+
+"""Dtypes/scalar type implementaions with torch dtypes.
+
+Here `dtype` is always a torch.dtype, this module knows nothing about
+scalar types, wrapper dtypes or anything like that. PyTorch only.
+"""
+from collections import namedtuple
+
+import torch
+
+# defaults : mimic NumPy, allow user control
+DefaultDTypes = namedtuple(
+    "DefaultDTypes", ["float_dtype", "complex_dtype", "int_dtype"]
+)
+
+# a global state
+# We set it the first time we call default_dtypes() to avoid importing
+# torch._dynamo.config and create a circular reference
+_default_dtypes = None
+
+
+def default_dtypes():
+    global _default_dtypes
+    if _default_dtypes is None:
+        import torch._dynamo.config as config
+
+        _default_dtypes = DefaultDTypes(
+            float_dtype=getattr(torch, config.numpy_default_float),
+            complex_dtype=getattr(torch, config.numpy_default_complex),
+            int_dtype=getattr(torch, config.numpy_default_int),
+        )
+        assert isinstance(_default_dtypes.float_dtype, torch.dtype)
+        assert isinstance(_default_dtypes.complex_dtype, torch.dtype)
+        assert isinstance(_default_dtypes.int_dtype, torch.dtype)
+    return _default_dtypes
+
+
+def get_default_dtype_for(dtype):
+    """Default scalar type given sctype category."""
+    if dtype == torch.bool:
+        return dtype
+    if dtype.is_complex:
+        return default_dtypes().complex_dtype
+    if dtype.is_floating_point:
+        return default_dtypes().float_dtype
+    # else, it must be (some) integer
+    return default_dtypes().int_dtype
+
+
+from . import _casting_dicts as _cd
+
+
+def can_cast_impl(from_torch_dtype, to_torch_dtype, casting):
+    return _cd._can_cast_dict[casting][from_torch_dtype][to_torch_dtype]
+
+
+def result_type_impl(*tensors):
+    # NB: torch dtypes here
+    dtyp = tensors[0].dtype
+    if len(tensors) == 1:
+        return dtyp
+
+    for curr in tensors[1:]:
+        dtyp = _cd._result_type_dict[dtyp][curr.dtype]
+
+    return dtyp
+
+
+def python_type_for_torch(dtyp):
+    """Get a python scalar type a torch dtype"""
+    if dtyp.is_floating_point:
+        typ = float
+    elif dtyp.is_complex:
+        typ = complex
+    elif dtyp == torch.bool:
+        typ = bool
+    else:
+        typ = int
+    return typ
+
+
+# ### NEP 50 helpers ###
+
+_SCALAR_TYPES = (int, bool, float, complex)
+
+_SCALAR_AND_SYMBOLIC_TYPES = (
+    *_SCALAR_TYPES,
+    torch.SymInt,
+    torch.SymFloat,
+    torch.SymBool,
+)
+
+_NEP50_FUNCS_TENSOR_ONLY = (
+    "minimum",
+    "maximum",
+    "logaddexp",
+    "logaddexp2",
+    "lcm",
+    "gcd",
+    "hypot",
+    "heaviside",
+    "fmod",
+    "fmin",
+    "fmax",
+    "copysign",
+    "arctan2",
+)
+
+
+def is_scalar(x):
+    return isinstance(x, _SCALAR_TYPES)
+
+
+def is_scalar_or_symbolic(x):
+    return isinstance(x, _SCALAR_AND_SYMBOLIC_TYPES)
+
+
+def _dtype_for_scalar(py_type):
+    return {
+        bool: torch.bool,
+        torch.SymBool: torch.bool,
+        int: torch.int64,
+        torch.SymInt: torch.int64,
+        float: torch.float64,
+        torch.SymFloat: torch.float64,
+        complex: torch.complex128,
+    }[py_type]
+
+
+def _dtype_for_scalar_or_tensor(x):
+    return x.dtype if isinstance(x, torch.Tensor) else _dtype_for_scalar(type(x))
+
+
+def is_float_or_fp_tensor(x):
+    return _dtype_for_scalar_or_tensor(x).is_floating_point
+
+
+def is_complex_or_complex_tensor(x):
+    return _dtype_for_scalar_or_tensor(x).is_complex
+
+
+def _category(dtype):
+    return {
+        torch.bool: 0,
+        torch.SymBool: 0,
+        # int
+        torch.uint8: 1,
+        torch.int8: 1,
+        torch.int16: 1,
+        torch.int32: 1,
+        torch.int64: 1,
+        torch.SymInt: 1,
+        # float
+        torch.float16: 2,
+        torch.float32: 2,
+        torch.float64: 2,
+        torch.SymFloat: 2,
+        # complex
+        torch.complex64: 3,
+        torch.complex128: 3,
+    }[dtype]
+
+
+def nep50_to_tensors(x1, x2, handle_weaks, function_name):
+    """If either of inputs is a python scalar, type-promote with NEP 50."""
+
+    def to_tensor(scalar, dtype=None):
+        if dtype is None:
+            dtype = _dtype_for_scalar(type(scalar))
+            dtype = get_default_dtype_for(dtype)
+        return torch.as_tensor(scalar, dtype=dtype)
+
+    x1_is_weak = not isinstance(x1, torch.Tensor)
+    x2_is_weak = not isinstance(x2, torch.Tensor)
+    if not handle_weaks or (x1_is_weak and x2_is_weak):
+        x1 = to_tensor(x1) if x1_is_weak else x1
+        x2 = to_tensor(x2) if x2_is_weak else x2
+        return x1, x2
+
+    # scalar <op> tensor: NEP 50
+    assert x1_is_weak != x2_is_weak
+
+    weak, not_weak = (x1, x2) if x1_is_weak else (x2, x1)
+
+    # find the dtype for the weak's type
+    weak_dtype = _dtype_for_scalar(type(weak))
+
+    cat_weak = _category(weak_dtype)
+    cat_not_weak = _category(not_weak.dtype)
+
+    dt = not_weak.dtype if cat_weak <= cat_not_weak else None
+
+    # special-case complex + float32
+    if weak_dtype.is_complex and not_weak.dtype == torch.float32:
+        dt = torch.complex64
+
+    # detect overflows: in PyTorch, uint8(-1) wraps around to 255,
+    # while NEP50 mandates an exception.
+    #
+    # Note that we only check if each element of the binop overflows,
+    # not the result. Consider, e.g. `uint8(100) + 200`. Operands are OK
+    # in uint8, but the result overflows and wrap around 255.
+    # Numpy emits a RuntimeWarning, PyTorch does not, and we do not either.
+    if cat_weak == 1 and cat_not_weak == 1:
+        # integers
+        iinfo = torch.iinfo(not_weak.dtype)
+        if not (iinfo.min <= weak <= iinfo.max):
+            raise OverflowError(
+                f"Python integer {weak} out of bounds for {not_weak.dtype}"
+            )
+    if weak_dtype != dt or function_name in _NEP50_FUNCS_TENSOR_ONLY:
+        # finally, can make `weak` into a 0D tensor, if both parameters are required to be tensor.
+        weak = to_tensor(weak, dt)
+
+    return (weak, not_weak) if x1_is_weak else (not_weak, weak)

venv/lib/python3.10/site-packages/torch/_numpy/_funcs.py

@@ -0,0 +1,75 @@
+# mypy: ignore-errors
+
+import inspect
+import itertools
+
+from . import _funcs_impl, _reductions_impl
+from ._normalizations import normalizer
+
+# _funcs_impl.py contains functions which mimic NumPy's eponymous equivalents,
+# and consume/return PyTorch tensors/dtypes.
+# They are also type annotated.
+# Pull these functions from _funcs_impl and decorate them with @normalizer, which
+# - Converts any input `np.ndarray`, `torch._numpy.ndarray`, list of lists, Python scalars, etc into a `torch.Tensor`.
+# - Maps NumPy dtypes to PyTorch dtypes
+# - If the input to the `axis` kwarg is an ndarray, it maps it into a tuple
+# - Implements the semantics for the `out=` arg
+# - Wraps back the outputs into `torch._numpy.ndarrays`
+
+
+def _public_functions(mod):
+    def is_public_function(f):
+        return inspect.isfunction(f) and not f.__name__.startswith("_")
+
+    return inspect.getmembers(mod, is_public_function)
+
+
+# We fill in __all__ in the loop below
+__all__ = []
+
+# decorate implementer functions with argument normalizers and export to the top namespace
+for name, func in itertools.chain(
+    _public_functions(_funcs_impl), _public_functions(_reductions_impl)
+):
+    if name in ["percentile", "quantile", "median"]:
+        decorated = normalizer(func, promote_scalar_result=True)
+    elif name == "einsum":
+        # normalized manually
+        decorated = func
+    else:
+        decorated = normalizer(func)
+
+    decorated.__qualname__ = name
+    decorated.__name__ = name
+    vars()[name] = decorated
+    __all__.append(name)
+
+
+"""
+Vendored objects from numpy.lib.index_tricks
+"""
+
+
+class IndexExpression:
+    """
+    Written by Konrad Hinsen <[email protected]>
+    last revision: 1999-7-23
+
+    Cosmetic changes by T. Oliphant 2001
+    """
+
+    def __init__(self, maketuple):
+        self.maketuple = maketuple
+
+    def __getitem__(self, item):
+        if self.maketuple and not isinstance(item, tuple):
+            return (item,)
+        else:
+            return item
+
+
+index_exp = IndexExpression(maketuple=True)
+s_ = IndexExpression(maketuple=False)
+
+
+__all__ += ["index_exp", "s_"]

venv/lib/python3.10/site-packages/torch/_numpy/_funcs_impl.py

@@ -0,0 +1,2053 @@
+# mypy: ignore-errors
+
+"""A thin pytorch / numpy compat layer.
+
+Things imported from here have numpy-compatible signatures but operate on
+pytorch tensors.
+"""
+# Contents of this module ends up in the main namespace via _funcs.py
+# where type annotations are used in conjunction with the @normalizer decorator.
+from __future__ import annotations
+
+import builtins
+import itertools
+import operator
+from typing import Optional, Sequence
+
+import torch
+
+from . import _dtypes_impl, _util
+from ._normalizations import (
+    ArrayLike,
+    ArrayLikeOrScalar,
+    CastingModes,
+    DTypeLike,
+    NDArray,
+    NotImplementedType,
+    OutArray,
+)
+
+
+def copy(
+    a: ArrayLike, order: NotImplementedType = "K", subok: NotImplementedType = False
+):
+    return a.clone()
+
+
+def copyto(
+    dst: NDArray,
+    src: ArrayLike,
+    casting: Optional[CastingModes] = "same_kind",
+    where: NotImplementedType = None,
+):
+    (src,) = _util.typecast_tensors((src,), dst.dtype, casting=casting)
+    dst.copy_(src)
+
+
+def atleast_1d(*arys: ArrayLike):
+    res = torch.atleast_1d(*arys)
+    if isinstance(res, tuple):
+        return list(res)
+    else:
+        return res
+
+
+def atleast_2d(*arys: ArrayLike):
+    res = torch.atleast_2d(*arys)
+    if isinstance(res, tuple):
+        return list(res)
+    else:
+        return res
+
+
+def atleast_3d(*arys: ArrayLike):
+    res = torch.atleast_3d(*arys)
+    if isinstance(res, tuple):
+        return list(res)
+    else:
+        return res
+
+
+def _concat_check(tup, dtype, out):
+    if tup == ():
+        raise ValueError("need at least one array to concatenate")
+
+    """Check inputs in concatenate et al."""
+    if out is not None and dtype is not None:
+        # mimic numpy
+        raise TypeError(
+            "concatenate() only takes `out` or `dtype` as an "
+            "argument, but both were provided."
+        )
+
+
+def _concat_cast_helper(tensors, out=None, dtype=None, casting="same_kind"):
+    """Figure out dtypes, cast if necessary."""
+
+    if out is not None or dtype is not None:
+        # figure out the type of the inputs and outputs
+        out_dtype = out.dtype.torch_dtype if dtype is None else dtype
+    else:
+        out_dtype = _dtypes_impl.result_type_impl(*tensors)
+
+    # cast input arrays if necessary; do not broadcast them agains `out`
+    tensors = _util.typecast_tensors(tensors, out_dtype, casting)
+
+    return tensors
+
+
+def _concatenate(
+    tensors, axis=0, out=None, dtype=None, casting: Optional[CastingModes] = "same_kind"
+):
+    # pure torch implementation, used below and in cov/corrcoef below
+    tensors, axis = _util.axis_none_flatten(*tensors, axis=axis)
+    tensors = _concat_cast_helper(tensors, out, dtype, casting)
+    return torch.cat(tensors, axis)
+
+
+def concatenate(
+    ar_tuple: Sequence[ArrayLike],
+    axis=0,
+    out: Optional[OutArray] = None,
+    dtype: Optional[DTypeLike] = None,
+    casting: Optional[CastingModes] = "same_kind",
+):
+    _concat_check(ar_tuple, dtype, out=out)
+    result = _concatenate(ar_tuple, axis=axis, out=out, dtype=dtype, casting=casting)
+    return result
+
+
+def vstack(
+    tup: Sequence[ArrayLike],
+    *,
+    dtype: Optional[DTypeLike] = None,
+    casting: Optional[CastingModes] = "same_kind",
+):
+    _concat_check(tup, dtype, out=None)
+    tensors = _concat_cast_helper(tup, dtype=dtype, casting=casting)
+    return torch.vstack(tensors)
+
+
+row_stack = vstack
+
+
+def hstack(
+    tup: Sequence[ArrayLike],
+    *,
+    dtype: Optional[DTypeLike] = None,
+    casting: Optional[CastingModes] = "same_kind",
+):
+    _concat_check(tup, dtype, out=None)
+    tensors = _concat_cast_helper(tup, dtype=dtype, casting=casting)
+    return torch.hstack(tensors)
+
+
+def dstack(
+    tup: Sequence[ArrayLike],
+    *,
+    dtype: Optional[DTypeLike] = None,
+    casting: Optional[CastingModes] = "same_kind",
+):
+    # XXX: in numpy 1.24 dstack does not have dtype and casting keywords
+    # but {h,v}stack do.  Hence add them here for consistency.
+    _concat_check(tup, dtype, out=None)
+    tensors = _concat_cast_helper(tup, dtype=dtype, casting=casting)
+    return torch.dstack(tensors)
+
+
+def column_stack(
+    tup: Sequence[ArrayLike],
+    *,
+    dtype: Optional[DTypeLike] = None,
+    casting: Optional[CastingModes] = "same_kind",
+):
+    # XXX: in numpy 1.24 column_stack does not have dtype and casting keywords
+    # but row_stack does. (because row_stack is an alias for vstack, really).
+    # Hence add these keywords here for consistency.
+    _concat_check(tup, dtype, out=None)
+    tensors = _concat_cast_helper(tup, dtype=dtype, casting=casting)
+    return torch.column_stack(tensors)
+
+
+def stack(
+    arrays: Sequence[ArrayLike],
+    axis=0,
+    out: Optional[OutArray] = None,
+    *,
+    dtype: Optional[DTypeLike] = None,
+    casting: Optional[CastingModes] = "same_kind",
+):
+    _concat_check(arrays, dtype, out=out)
+
+    tensors = _concat_cast_helper(arrays, dtype=dtype, casting=casting)
+    result_ndim = tensors[0].ndim + 1
+    axis = _util.normalize_axis_index(axis, result_ndim)
+    return torch.stack(tensors, axis=axis)
+
+
+def append(arr: ArrayLike, values: ArrayLike, axis=None):
+    if axis is None:
+        if arr.ndim != 1:
+            arr = arr.flatten()
+        values = values.flatten()
+        axis = arr.ndim - 1
+    return _concatenate((arr, values), axis=axis)
+
+
+# ### split ###
+
+
+def _split_helper(tensor, indices_or_sections, axis, strict=False):
+    if isinstance(indices_or_sections, int):
+        return _split_helper_int(tensor, indices_or_sections, axis, strict)
+    elif isinstance(indices_or_sections, (list, tuple)):
+        # NB: drop split=..., it only applies to split_helper_int
+        return _split_helper_list(tensor, list(indices_or_sections), axis)
+    else:
+        raise TypeError("split_helper: ", type(indices_or_sections))
+
+
+def _split_helper_int(tensor, indices_or_sections, axis, strict=False):
+    if not isinstance(indices_or_sections, int):
+        raise NotImplementedError("split: indices_or_sections")
+
+    axis = _util.normalize_axis_index(axis, tensor.ndim)
+
+    # numpy: l%n chunks of size (l//n + 1), the rest are sized l//n
+    l, n = tensor.shape[axis], indices_or_sections
+
+    if n <= 0:
+        raise ValueError()
+
+    if l % n == 0:
+        num, sz = n, l // n
+        lst = [sz] * num
+    else:
+        if strict:
+            raise ValueError("array split does not result in an equal division")
+
+        num, sz = l % n, l // n + 1
+        lst = [sz] * num
+
+    lst += [sz - 1] * (n - num)
+
+    return torch.split(tensor, lst, axis)
+
+
+def _split_helper_list(tensor, indices_or_sections, axis):
+    if not isinstance(indices_or_sections, list):
+        raise NotImplementedError("split: indices_or_sections: list")
+    # numpy expects indices, while torch expects lengths of sections
+    # also, numpy appends zero-size arrays for indices above the shape[axis]
+    lst = [x for x in indices_or_sections if x <= tensor.shape[axis]]
+    num_extra = len(indices_or_sections) - len(lst)
+
+    lst.append(tensor.shape[axis])
+    lst = [
+        lst[0],
+    ] + [a - b for a, b in zip(lst[1:], lst[:-1])]
+    lst += [0] * num_extra
+
+    return torch.split(tensor, lst, axis)
+
+
+def array_split(ary: ArrayLike, indices_or_sections, axis=0):
+    return _split_helper(ary, indices_or_sections, axis)
+
+
+def split(ary: ArrayLike, indices_or_sections, axis=0):
+    return _split_helper(ary, indices_or_sections, axis, strict=True)
+
+
+def hsplit(ary: ArrayLike, indices_or_sections):
+    if ary.ndim == 0:
+        raise ValueError("hsplit only works on arrays of 1 or more dimensions")
+    axis = 1 if ary.ndim > 1 else 0
+    return _split_helper(ary, indices_or_sections, axis, strict=True)
+
+
+def vsplit(ary: ArrayLike, indices_or_sections):
+    if ary.ndim < 2:
+        raise ValueError("vsplit only works on arrays of 2 or more dimensions")
+    return _split_helper(ary, indices_or_sections, 0, strict=True)
+
+
+def dsplit(ary: ArrayLike, indices_or_sections):
+    if ary.ndim < 3:
+        raise ValueError("dsplit only works on arrays of 3 or more dimensions")
+    return _split_helper(ary, indices_or_sections, 2, strict=True)
+
+
+def kron(a: ArrayLike, b: ArrayLike):
+    return torch.kron(a, b)
+
+
+def vander(x: ArrayLike, N=None, increasing=False):
+    return torch.vander(x, N, increasing)
+
+
+# ### linspace, geomspace, logspace and arange ###
+
+
+def linspace(
+    start: ArrayLike,
+    stop: ArrayLike,
+    num=50,
+    endpoint=True,
+    retstep=False,
+    dtype: Optional[DTypeLike] = None,
+    axis=0,
+):
+    if axis != 0 or retstep or not endpoint:
+        raise NotImplementedError
+    if dtype is None:
+        dtype = _dtypes_impl.default_dtypes().float_dtype
+    # XXX: raises TypeError if start or stop are not scalars
+    return torch.linspace(start, stop, num, dtype=dtype)
+
+
+def geomspace(
+    start: ArrayLike,
+    stop: ArrayLike,
+    num=50,
+    endpoint=True,
+    dtype: Optional[DTypeLike] = None,
+    axis=0,
+):
+    if axis != 0 or not endpoint:
+        raise NotImplementedError
+    base = torch.pow(stop / start, 1.0 / (num - 1))
+    logbase = torch.log(base)
+    return torch.logspace(
+        torch.log(start) / logbase,
+        torch.log(stop) / logbase,
+        num,
+        base=base,
+    )
+
+
+def logspace(
+    start,
+    stop,
+    num=50,
+    endpoint=True,
+    base=10.0,
+    dtype: Optional[DTypeLike] = None,
+    axis=0,
+):
+    if axis != 0 or not endpoint:
+        raise NotImplementedError
+    return torch.logspace(start, stop, num, base=base, dtype=dtype)
+
+
+def arange(
+    start: Optional[ArrayLikeOrScalar] = None,
+    stop: Optional[ArrayLikeOrScalar] = None,
+    step: Optional[ArrayLikeOrScalar] = 1,
+    dtype: Optional[DTypeLike] = None,
+    *,
+    like: NotImplementedType = None,
+):
+    if step == 0:
+        raise ZeroDivisionError
+    if stop is None and start is None:
+        raise TypeError
+    if stop is None:
+        # XXX: this breaks if start is passed as a kwarg:
+        # arange(start=4) should raise (no stop) but doesn't
+        start, stop = 0, start
+    if start is None:
+        start = 0
+
+    # the dtype of the result
+    if dtype is None:
+        dtype = (
+            _dtypes_impl.default_dtypes().float_dtype
+            if any(_dtypes_impl.is_float_or_fp_tensor(x) for x in (start, stop, step))
+            else _dtypes_impl.default_dtypes().int_dtype
+        )
+    work_dtype = torch.float64 if dtype.is_complex else dtype
+
+    # RuntimeError: "lt_cpu" not implemented for 'ComplexFloat'. Fall back to eager.
+    if any(_dtypes_impl.is_complex_or_complex_tensor(x) for x in (start, stop, step)):
+        raise NotImplementedError
+
+    if (step > 0 and start > stop) or (step < 0 and start < stop):
+        # empty range
+        return torch.empty(0, dtype=dtype)
+
+    result = torch.arange(start, stop, step, dtype=work_dtype)
+    result = _util.cast_if_needed(result, dtype)
+    return result
+
+
+# ### zeros/ones/empty/full ###
+
+
+def empty(
+    shape,
+    dtype: Optional[DTypeLike] = None,
+    order: NotImplementedType = "C",
+    *,
+    like: NotImplementedType = None,
+):
+    if dtype is None:
+        dtype = _dtypes_impl.default_dtypes().float_dtype
+    return torch.empty(shape, dtype=dtype)
+
+
+# NB: *_like functions deliberately deviate from numpy: it has subok=True
+# as the default; we set subok=False and raise on anything else.
+
+
+def empty_like(
+    prototype: ArrayLike,
+    dtype: Optional[DTypeLike] = None,
+    order: NotImplementedType = "K",
+    subok: NotImplementedType = False,
+    shape=None,
+):
+    result = torch.empty_like(prototype, dtype=dtype)
+    if shape is not None:
+        result = result.reshape(shape)
+    return result
+
+
+def full(
+    shape,
+    fill_value: ArrayLike,
+    dtype: Optional[DTypeLike] = None,
+    order: NotImplementedType = "C",
+    *,
+    like: NotImplementedType = None,
+):
+    if isinstance(shape, int):
+        shape = (shape,)
+    if dtype is None:
+        dtype = fill_value.dtype
+    if not isinstance(shape, (tuple, list)):
+        shape = (shape,)
+    return torch.full(shape, fill_value, dtype=dtype)
+
+
+def full_like(
+    a: ArrayLike,
+    fill_value,
+    dtype: Optional[DTypeLike] = None,
+    order: NotImplementedType = "K",
+    subok: NotImplementedType = False,
+    shape=None,
+):
+    # XXX: fill_value broadcasts
+    result = torch.full_like(a, fill_value, dtype=dtype)
+    if shape is not None:
+        result = result.reshape(shape)
+    return result
+
+
+def ones(
+    shape,
+    dtype: Optional[DTypeLike] = None,
+    order: NotImplementedType = "C",
+    *,
+    like: NotImplementedType = None,
+):
+    if dtype is None:
+        dtype = _dtypes_impl.default_dtypes().float_dtype
+    return torch.ones(shape, dtype=dtype)
+
+
+def ones_like(
+    a: ArrayLike,
+    dtype: Optional[DTypeLike] = None,
+    order: NotImplementedType = "K",
+    subok: NotImplementedType = False,
+    shape=None,
+):
+    result = torch.ones_like(a, dtype=dtype)
+    if shape is not None:
+        result = result.reshape(shape)
+    return result
+
+
+def zeros(
+    shape,
+    dtype: Optional[DTypeLike] = None,
+    order: NotImplementedType = "C",
+    *,
+    like: NotImplementedType = None,
+):
+    if dtype is None:
+        dtype = _dtypes_impl.default_dtypes().float_dtype
+    return torch.zeros(shape, dtype=dtype)
+
+
+def zeros_like(
+    a: ArrayLike,
+    dtype: Optional[DTypeLike] = None,
+    order: NotImplementedType = "K",
+    subok: NotImplementedType = False,
+    shape=None,
+):
+    result = torch.zeros_like(a, dtype=dtype)
+    if shape is not None:
+        result = result.reshape(shape)
+    return result
+
+
+# ### cov & corrcoef ###
+
+
+def _xy_helper_corrcoef(x_tensor, y_tensor=None, rowvar=True):
+    """Prepare inputs for cov and corrcoef."""
+
+    # https://github.com/numpy/numpy/blob/v1.24.0/numpy/lib/function_base.py#L2636
+    if y_tensor is not None:
+        # make sure x and y are at least 2D
+        ndim_extra = 2 - x_tensor.ndim
+        if ndim_extra > 0:
+            x_tensor = x_tensor.view((1,) * ndim_extra + x_tensor.shape)
+        if not rowvar and x_tensor.shape[0] != 1:
+            x_tensor = x_tensor.mT
+        x_tensor = x_tensor.clone()
+
+        ndim_extra = 2 - y_tensor.ndim
+        if ndim_extra > 0:
+            y_tensor = y_tensor.view((1,) * ndim_extra + y_tensor.shape)
+        if not rowvar and y_tensor.shape[0] != 1:
+            y_tensor = y_tensor.mT
+        y_tensor = y_tensor.clone()
+
+        x_tensor = _concatenate((x_tensor, y_tensor), axis=0)
+
+    return x_tensor
+
+
+def corrcoef(
+    x: ArrayLike,
+    y: Optional[ArrayLike] = None,
+    rowvar=True,
+    bias=None,
+    ddof=None,
+    *,
+    dtype: Optional[DTypeLike] = None,
+):
+    if bias is not None or ddof is not None:
+        # deprecated in NumPy
+        raise NotImplementedError
+    xy_tensor = _xy_helper_corrcoef(x, y, rowvar)
+
+    is_half = (xy_tensor.dtype == torch.float16) and xy_tensor.is_cpu
+    if is_half:
+        # work around torch's "addmm_impl_cpu_" not implemented for 'Half'"
+        dtype = torch.float32
+
+    xy_tensor = _util.cast_if_needed(xy_tensor, dtype)
+    result = torch.corrcoef(xy_tensor)
+
+    if is_half:
+        result = result.to(torch.float16)
+
+    return result
+
+
+def cov(
+    m: ArrayLike,
+    y: Optional[ArrayLike] = None,
+    rowvar=True,
+    bias=False,
+    ddof=None,
+    fweights: Optional[ArrayLike] = None,
+    aweights: Optional[ArrayLike] = None,
+    *,
+    dtype: Optional[DTypeLike] = None,
+):
+    m = _xy_helper_corrcoef(m, y, rowvar)
+
+    if ddof is None:
+        ddof = 1 if bias == 0 else 0
+
+    is_half = (m.dtype == torch.float16) and m.is_cpu
+    if is_half:
+        # work around torch's "addmm_impl_cpu_" not implemented for 'Half'"
+        dtype = torch.float32
+
+    m = _util.cast_if_needed(m, dtype)
+    result = torch.cov(m, correction=ddof, aweights=aweights, fweights=fweights)
+
+    if is_half:
+        result = result.to(torch.float16)
+
+    return result
+
+
+def _conv_corr_impl(a, v, mode):
+    dt = _dtypes_impl.result_type_impl(a, v)
+    a = _util.cast_if_needed(a, dt)
+    v = _util.cast_if_needed(v, dt)
+
+    padding = v.shape[0] - 1 if mode == "full" else mode
+
+    if padding == "same" and v.shape[0] % 2 == 0:
+        # UserWarning: Using padding='same' with even kernel lengths and odd
+        # dilation may require a zero-padded copy of the input be created
+        # (Triggered internally at pytorch/aten/src/ATen/native/Convolution.cpp:1010.)
+        raise NotImplementedError("mode='same' and even-length weights")
+
+    # NumPy only accepts 1D arrays; PyTorch requires 2D inputs and 3D weights
+    aa = a[None, :]
+    vv = v[None, None, :]
+
+    result = torch.nn.functional.conv1d(aa, vv, padding=padding)
+
+    # torch returns a 2D result, numpy returns a 1D array
+    return result[0, :]
+
+
+def convolve(a: ArrayLike, v: ArrayLike, mode="full"):
+    # NumPy: if v is longer than a, the arrays are swapped before computation
+    if a.shape[0] < v.shape[0]:
+        a, v = v, a
+
+    # flip the weights since numpy does and torch does not
+    v = torch.flip(v, (0,))
+
+    return _conv_corr_impl(a, v, mode)
+
+
+def correlate(a: ArrayLike, v: ArrayLike, mode="valid"):
+    v = torch.conj_physical(v)
+    return _conv_corr_impl(a, v, mode)
+
+
+# ### logic & element selection ###
+
+
+def bincount(x: ArrayLike, /, weights: Optional[ArrayLike] = None, minlength=0):
+    if x.numel() == 0:
+        # edge case allowed by numpy
+        x = x.new_empty(0, dtype=int)
+
+    int_dtype = _dtypes_impl.default_dtypes().int_dtype
+    (x,) = _util.typecast_tensors((x,), int_dtype, casting="safe")
+
+    return torch.bincount(x, weights, minlength)
+
+
+def where(
+    condition: ArrayLike,
+    x: Optional[ArrayLikeOrScalar] = None,
+    y: Optional[ArrayLikeOrScalar] = None,
+    /,
+):
+    if (x is None) != (y is None):
+        raise ValueError("either both or neither of x and y should be given")
+
+    if condition.dtype != torch.bool:
+        condition = condition.to(torch.bool)
+
+    if x is None and y is None:
+        result = torch.where(condition)
+    else:
+        result = torch.where(condition, x, y)
+    return result
+
+
+# ###### module-level queries of object properties
+
+
+def ndim(a: ArrayLike):
+    return a.ndim
+
+
+def shape(a: ArrayLike):
+    return tuple(a.shape)
+
+
+def size(a: ArrayLike, axis=None):
+    if axis is None:
+        return a.numel()
+    else:
+        return a.shape[axis]
+
+
+# ###### shape manipulations and indexing
+
+
+def expand_dims(a: ArrayLike, axis):
+    shape = _util.expand_shape(a.shape, axis)
+    return a.view(shape)  # never copies
+
+
+def flip(m: ArrayLike, axis=None):
+    # XXX: semantic difference: np.flip returns a view, torch.flip copies
+    if axis is None:
+        axis = tuple(range(m.ndim))
+    else:
+        axis = _util.normalize_axis_tuple(axis, m.ndim)
+    return torch.flip(m, axis)
+
+
+def flipud(m: ArrayLike):
+    return torch.flipud(m)
+
+
+def fliplr(m: ArrayLike):
+    return torch.fliplr(m)
+
+
+def rot90(m: ArrayLike, k=1, axes=(0, 1)):
+    axes = _util.normalize_axis_tuple(axes, m.ndim)
+    return torch.rot90(m, k, axes)
+
+
+# ### broadcasting and indices ###
+
+
+def broadcast_to(array: ArrayLike, shape, subok: NotImplementedType = False):
+    return torch.broadcast_to(array, size=shape)
+
+
+# This is a function from tuples to tuples, so we just reuse it
+from torch import broadcast_shapes
+
+
+def broadcast_arrays(*args: ArrayLike, subok: NotImplementedType = False):
+    return torch.broadcast_tensors(*args)
+
+
+def meshgrid(*xi: ArrayLike, copy=True, sparse=False, indexing="xy"):
+    ndim = len(xi)
+
+    if indexing not in ["xy", "ij"]:
+        raise ValueError("Valid values for `indexing` are 'xy' and 'ij'.")
+
+    s0 = (1,) * ndim
+    output = [x.reshape(s0[:i] + (-1,) + s0[i + 1 :]) for i, x in enumerate(xi)]
+
+    if indexing == "xy" and ndim > 1:
+        # switch first and second axis
+        output[0] = output[0].reshape((1, -1) + s0[2:])
+        output[1] = output[1].reshape((-1, 1) + s0[2:])
+
+    if not sparse:
+        # Return the full N-D matrix (not only the 1-D vector)
+        output = torch.broadcast_tensors(*output)
+
+    if copy:
+        output = [x.clone() for x in output]
+
+    return list(output)  # match numpy, return a list
+
+
+def indices(dimensions, dtype: Optional[DTypeLike] = int, sparse=False):
+    # https://github.com/numpy/numpy/blob/v1.24.0/numpy/core/numeric.py#L1691-L1791
+    dimensions = tuple(dimensions)
+    N = len(dimensions)
+    shape = (1,) * N
+    if sparse:
+        res = tuple()
+    else:
+        res = torch.empty((N,) + dimensions, dtype=dtype)
+    for i, dim in enumerate(dimensions):
+        idx = torch.arange(dim, dtype=dtype).reshape(
+            shape[:i] + (dim,) + shape[i + 1 :]
+        )
+        if sparse:
+            res = res + (idx,)
+        else:
+            res[i] = idx
+    return res
+
+
+# ### tri*-something ###
+
+
+def tril(m: ArrayLike, k=0):
+    return torch.tril(m, k)
+
+
+def triu(m: ArrayLike, k=0):
+    return torch.triu(m, k)
+
+
+def tril_indices(n, k=0, m=None):
+    if m is None:
+        m = n
+    return torch.tril_indices(n, m, offset=k)
+
+
+def triu_indices(n, k=0, m=None):
+    if m is None:
+        m = n
+    return torch.triu_indices(n, m, offset=k)
+
+
+def tril_indices_from(arr: ArrayLike, k=0):
+    if arr.ndim != 2:
+        raise ValueError("input array must be 2-d")
+    # Return a tensor rather than a tuple to avoid a graphbreak
+    return torch.tril_indices(arr.shape[0], arr.shape[1], offset=k)
+
+
+def triu_indices_from(arr: ArrayLike, k=0):
+    if arr.ndim != 2:
+        raise ValueError("input array must be 2-d")
+    # Return a tensor rather than a tuple to avoid a graphbreak
+    return torch.triu_indices(arr.shape[0], arr.shape[1], offset=k)
+
+
+def tri(
+    N,
+    M=None,
+    k=0,
+    dtype: Optional[DTypeLike] = None,
+    *,
+    like: NotImplementedType = None,
+):
+    if M is None:
+        M = N
+    tensor = torch.ones((N, M), dtype=dtype)
+    return torch.tril(tensor, diagonal=k)
+
+
+# ### equality, equivalence, allclose ###
+
+
+def isclose(a: ArrayLike, b: ArrayLike, rtol=1.0e-5, atol=1.0e-8, equal_nan=False):
+    dtype = _dtypes_impl.result_type_impl(a, b)
+    a = _util.cast_if_needed(a, dtype)
+    b = _util.cast_if_needed(b, dtype)
+    return torch.isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)
+
+
+def allclose(a: ArrayLike, b: ArrayLike, rtol=1e-05, atol=1e-08, equal_nan=False):
+    dtype = _dtypes_impl.result_type_impl(a, b)
+    a = _util.cast_if_needed(a, dtype)
+    b = _util.cast_if_needed(b, dtype)
+    return torch.allclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)
+
+
+def _tensor_equal(a1, a2, equal_nan=False):
+    # Implementation of array_equal/array_equiv.
+    if a1.shape != a2.shape:
+        return False
+    cond = a1 == a2
+    if equal_nan:
+        cond = cond | (torch.isnan(a1) & torch.isnan(a2))
+    return cond.all().item()
+
+
+def array_equal(a1: ArrayLike, a2: ArrayLike, equal_nan=False):
+    return _tensor_equal(a1, a2, equal_nan=equal_nan)
+
+
+def array_equiv(a1: ArrayLike, a2: ArrayLike):
+    # *almost* the same as array_equal: _equiv tries to broadcast, _equal does not
+    try:
+        a1_t, a2_t = torch.broadcast_tensors(a1, a2)
+    except RuntimeError:
+        # failed to broadcast => not equivalent
+        return False
+    return _tensor_equal(a1_t, a2_t)
+
+
+def nan_to_num(
+    x: ArrayLike, copy: NotImplementedType = True, nan=0.0, posinf=None, neginf=None
+):
+    # work around RuntimeError: "nan_to_num" not implemented for 'ComplexDouble'
+    if x.is_complex():
+        re = torch.nan_to_num(x.real, nan=nan, posinf=posinf, neginf=neginf)
+        im = torch.nan_to_num(x.imag, nan=nan, posinf=posinf, neginf=neginf)
+        return re + 1j * im
+    else:
+        return torch.nan_to_num(x, nan=nan, posinf=posinf, neginf=neginf)
+
+
+# ### put/take_along_axis ###
+
+
+def take(
+    a: ArrayLike,
+    indices: ArrayLike,
+    axis=None,
+    out: Optional[OutArray] = None,
+    mode: NotImplementedType = "raise",
+):
+    (a,), axis = _util.axis_none_flatten(a, axis=axis)
+    axis = _util.normalize_axis_index(axis, a.ndim)
+    idx = (slice(None),) * axis + (indices, ...)
+    result = a[idx]
+    return result
+
+
+def take_along_axis(arr: ArrayLike, indices: ArrayLike, axis):
+    (arr,), axis = _util.axis_none_flatten(arr, axis=axis)
+    axis = _util.normalize_axis_index(axis, arr.ndim)
+    return torch.take_along_dim(arr, indices, axis)
+
+
+def put(
+    a: NDArray,
+    indices: ArrayLike,
+    values: ArrayLike,
+    mode: NotImplementedType = "raise",
+):
+    v = values.type(a.dtype)
+    # If indices is larger than v, expand v to at least the size of indices. Any
+    # unnecessary trailing elements are then trimmed.
+    if indices.numel() > v.numel():
+        ratio = (indices.numel() + v.numel() - 1) // v.numel()
+        v = v.unsqueeze(0).expand((ratio,) + v.shape)
+    # Trim unnecessary elements, regardless if v was expanded or not. Note
+    # np.put() trims v to match indices by default too.
+    if indices.numel() < v.numel():
+        v = v.flatten()
+        v = v[: indices.numel()]
+    a.put_(indices, v)
+    return None
+
+
+def put_along_axis(arr: ArrayLike, indices: ArrayLike, values: ArrayLike, axis):
+    (arr,), axis = _util.axis_none_flatten(arr, axis=axis)
+    axis = _util.normalize_axis_index(axis, arr.ndim)
+
+    indices, values = torch.broadcast_tensors(indices, values)
+    values = _util.cast_if_needed(values, arr.dtype)
+    result = torch.scatter(arr, axis, indices, values)
+    arr.copy_(result.reshape(arr.shape))
+    return None
+
+
+def choose(
+    a: ArrayLike,
+    choices: Sequence[ArrayLike],
+    out: Optional[OutArray] = None,
+    mode: NotImplementedType = "raise",
+):
+    # First, broadcast elements of `choices`
+    choices = torch.stack(torch.broadcast_tensors(*choices))
+
+    # Use an analog of `gather(choices, 0, a)` which broadcasts `choices` vs `a`:
+    # (taken from https://github.com/pytorch/pytorch/issues/9407#issuecomment-1427907939)
+    idx_list = [
+        torch.arange(dim).view((1,) * i + (dim,) + (1,) * (choices.ndim - i - 1))
+        for i, dim in enumerate(choices.shape)
+    ]
+
+    idx_list[0] = a
+    return choices[idx_list].squeeze(0)
+
+
+# ### unique et al ###
+
+
+def unique(
+    ar: ArrayLike,
+    return_index: NotImplementedType = False,
+    return_inverse=False,
+    return_counts=False,
+    axis=None,
+    *,
+    equal_nan: NotImplementedType = True,
+):
+    (ar,), axis = _util.axis_none_flatten(ar, axis=axis)
+    axis = _util.normalize_axis_index(axis, ar.ndim)
+
+    result = torch.unique(
+        ar, return_inverse=return_inverse, return_counts=return_counts, dim=axis
+    )
+
+    return result
+
+
+def nonzero(a: ArrayLike):
+    return torch.nonzero(a, as_tuple=True)
+
+
+def argwhere(a: ArrayLike):
+    return torch.argwhere(a)
+
+
+def flatnonzero(a: ArrayLike):
+    return torch.flatten(a).nonzero(as_tuple=True)[0]
+
+
+def clip(
+    a: ArrayLike,
+    min: Optional[ArrayLike] = None,
+    max: Optional[ArrayLike] = None,
+    out: Optional[OutArray] = None,
+):
+    return torch.clamp(a, min, max)
+
+
+def repeat(a: ArrayLike, repeats: ArrayLikeOrScalar, axis=None):
+    return torch.repeat_interleave(a, repeats, axis)
+
+
+def tile(A: ArrayLike, reps):
+    if isinstance(reps, int):
+        reps = (reps,)
+    return torch.tile(A, reps)
+
+
+def resize(a: ArrayLike, new_shape=None):
+    # implementation vendored from
+    # https://github.com/numpy/numpy/blob/v1.24.0/numpy/core/fromnumeric.py#L1420-L1497
+    if new_shape is None:
+        return a
+
+    if isinstance(new_shape, int):
+        new_shape = (new_shape,)
+
+    a = a.flatten()
+
+    new_size = 1
+    for dim_length in new_shape:
+        new_size *= dim_length
+        if dim_length < 0:
+            raise ValueError("all elements of `new_shape` must be non-negative")
+
+    if a.numel() == 0 or new_size == 0:
+        # First case must zero fill. The second would have repeats == 0.
+        return torch.zeros(new_shape, dtype=a.dtype)
+
+    repeats = -(-new_size // a.numel())  # ceil division
+    a = concatenate((a,) * repeats)[:new_size]
+
+    return reshape(a, new_shape)
+
+
+# ### diag et al ###
+
+
+def diagonal(a: ArrayLike, offset=0, axis1=0, axis2=1):
+    axis1 = _util.normalize_axis_index(axis1, a.ndim)
+    axis2 = _util.normalize_axis_index(axis2, a.ndim)
+    return torch.diagonal(a, offset, axis1, axis2)
+
+
+def trace(
+    a: ArrayLike,
+    offset=0,
+    axis1=0,
+    axis2=1,
+    dtype: Optional[DTypeLike] = None,
+    out: Optional[OutArray] = None,
+):
+    result = torch.diagonal(a, offset, dim1=axis1, dim2=axis2).sum(-1, dtype=dtype)
+    return result
+
+
+def eye(
+    N,
+    M=None,
+    k=0,
+    dtype: Optional[DTypeLike] = None,
+    order: NotImplementedType = "C",
+    *,
+    like: NotImplementedType = None,
+):
+    if dtype is None:
+        dtype = _dtypes_impl.default_dtypes().float_dtype
+    if M is None:
+        M = N
+    z = torch.zeros(N, M, dtype=dtype)
+    z.diagonal(k).fill_(1)
+    return z
+
+
+def identity(n, dtype: Optional[DTypeLike] = None, *, like: NotImplementedType = None):
+    return torch.eye(n, dtype=dtype)
+
+
+def diag(v: ArrayLike, k=0):
+    return torch.diag(v, k)
+
+
+def diagflat(v: ArrayLike, k=0):
+    return torch.diagflat(v, k)
+
+
+def diag_indices(n, ndim=2):
+    idx = torch.arange(n)
+    return (idx,) * ndim
+
+
+def diag_indices_from(arr: ArrayLike):
+    if not arr.ndim >= 2:
+        raise ValueError("input array must be at least 2-d")
+    # For more than d=2, the strided formula is only valid for arrays with
+    # all dimensions equal, so we check first.
+    s = arr.shape
+    if s[1:] != s[:-1]:
+        raise ValueError("All dimensions of input must be of equal length")
+    return diag_indices(s[0], arr.ndim)
+
+
+def fill_diagonal(a: ArrayLike, val: ArrayLike, wrap=False):
+    if a.ndim < 2:
+        raise ValueError("array must be at least 2-d")
+    if val.numel() == 0 and not wrap:
+        a.fill_diagonal_(val)
+        return a
+
+    if val.ndim == 0:
+        val = val.unsqueeze(0)
+
+    # torch.Tensor.fill_diagonal_ only accepts scalars
+    # If the size of val is too large, then val is trimmed
+    if a.ndim == 2:
+        tall = a.shape[0] > a.shape[1]
+        # wrap does nothing for wide matrices...
+        if not wrap or not tall:
+            # Never wraps
+            diag = a.diagonal()
+            diag.copy_(val[: diag.numel()])
+        else:
+            # wraps and tall... leaving one empty line between diagonals?!
+            max_, min_ = a.shape
+            idx = torch.arange(max_ - max_ // (min_ + 1))
+            mod = idx % min_
+            div = idx // min_
+            a[(div * (min_ + 1) + mod, mod)] = val[: idx.numel()]
+    else:
+        idx = diag_indices_from(a)
+        # a.shape = (n, n, ..., n)
+        a[idx] = val[: a.shape[0]]
+
+    return a
+
+
+def vdot(a: ArrayLike, b: ArrayLike, /):
+    # 1. torch only accepts 1D arrays, numpy flattens
+    # 2. torch requires matching dtype, while numpy casts (?)
+    t_a, t_b = torch.atleast_1d(a, b)
+    if t_a.ndim > 1:
+        t_a = t_a.flatten()
+    if t_b.ndim > 1:
+        t_b = t_b.flatten()
+
+    dtype = _dtypes_impl.result_type_impl(t_a, t_b)
+    is_half = dtype == torch.float16 and (t_a.is_cpu or t_b.is_cpu)
+    is_bool = dtype == torch.bool
+
+    # work around torch's "dot" not implemented for 'Half', 'Bool'
+    if is_half:
+        dtype = torch.float32
+    elif is_bool:
+        dtype = torch.uint8
+
+    t_a = _util.cast_if_needed(t_a, dtype)
+    t_b = _util.cast_if_needed(t_b, dtype)
+
+    result = torch.vdot(t_a, t_b)
+
+    if is_half:
+        result = result.to(torch.float16)
+    elif is_bool:
+        result = result.to(torch.bool)
+
+    return result
+
+
+def tensordot(a: ArrayLike, b: ArrayLike, axes=2):
+    if isinstance(axes, (list, tuple)):
+        axes = [[ax] if isinstance(ax, int) else ax for ax in axes]
+
+    target_dtype = _dtypes_impl.result_type_impl(a, b)
+    a = _util.cast_if_needed(a, target_dtype)
+    b = _util.cast_if_needed(b, target_dtype)
+
+    return torch.tensordot(a, b, dims=axes)
+
+
+def dot(a: ArrayLike, b: ArrayLike, out: Optional[OutArray] = None):
+    dtype = _dtypes_impl.result_type_impl(a, b)
+    is_bool = dtype == torch.bool
+    if is_bool:
+        dtype = torch.uint8
+
+    a = _util.cast_if_needed(a, dtype)
+    b = _util.cast_if_needed(b, dtype)
+
+    if a.ndim == 0 or b.ndim == 0:
+        result = a * b
+    else:
+        result = torch.matmul(a, b)
+
+    if is_bool:
+        result = result.to(torch.bool)
+
+    return result
+
+
+def inner(a: ArrayLike, b: ArrayLike, /):
+    dtype = _dtypes_impl.result_type_impl(a, b)
+    is_half = dtype == torch.float16 and (a.is_cpu or b.is_cpu)
+    is_bool = dtype == torch.bool
+
+    if is_half:
+        # work around torch's "addmm_impl_cpu_" not implemented for 'Half'"
+        dtype = torch.float32
+    elif is_bool:
+        dtype = torch.uint8
+
+    a = _util.cast_if_needed(a, dtype)
+    b = _util.cast_if_needed(b, dtype)
+
+    result = torch.inner(a, b)
+
+    if is_half:
+        result = result.to(torch.float16)
+    elif is_bool:
+        result = result.to(torch.bool)
+    return result
+
+
+def outer(a: ArrayLike, b: ArrayLike, out: Optional[OutArray] = None):
+    return torch.outer(a, b)
+
+
+def cross(a: ArrayLike, b: ArrayLike, axisa=-1, axisb=-1, axisc=-1, axis=None):
+    # implementation vendored from
+    # https://github.com/numpy/numpy/blob/v1.24.0/numpy/core/numeric.py#L1486-L1685
+    if axis is not None:
+        axisa, axisb, axisc = (axis,) * 3
+
+    # Check axisa and axisb are within bounds
+    axisa = _util.normalize_axis_index(axisa, a.ndim)
+    axisb = _util.normalize_axis_index(axisb, b.ndim)
+
+    # Move working axis to the end of the shape
+    a = torch.moveaxis(a, axisa, -1)
+    b = torch.moveaxis(b, axisb, -1)
+    msg = "incompatible dimensions for cross product\n(dimension must be 2 or 3)"
+    if a.shape[-1] not in (2, 3) or b.shape[-1] not in (2, 3):
+        raise ValueError(msg)
+
+    # Create the output array
+    shape = broadcast_shapes(a[..., 0].shape, b[..., 0].shape)
+    if a.shape[-1] == 3 or b.shape[-1] == 3:
+        shape += (3,)
+        # Check axisc is within bounds
+        axisc = _util.normalize_axis_index(axisc, len(shape))
+    dtype = _dtypes_impl.result_type_impl(a, b)
+    cp = torch.empty(shape, dtype=dtype)
+
+    # recast arrays as dtype
+    a = _util.cast_if_needed(a, dtype)
+    b = _util.cast_if_needed(b, dtype)
+
+    # create local aliases for readability
+    a0 = a[..., 0]
+    a1 = a[..., 1]
+    if a.shape[-1] == 3:
+        a2 = a[..., 2]
+    b0 = b[..., 0]
+    b1 = b[..., 1]
+    if b.shape[-1] == 3:
+        b2 = b[..., 2]
+    if cp.ndim != 0 and cp.shape[-1] == 3:
+        cp0 = cp[..., 0]
+        cp1 = cp[..., 1]
+        cp2 = cp[..., 2]
+
+    if a.shape[-1] == 2:
+        if b.shape[-1] == 2:
+            # a0 * b1 - a1 * b0
+            cp[...] = a0 * b1 - a1 * b0
+            return cp
+        else:
+            assert b.shape[-1] == 3
+            # cp0 = a1 * b2 - 0  (a2 = 0)
+            # cp1 = 0 - a0 * b2  (a2 = 0)
+            # cp2 = a0 * b1 - a1 * b0
+            cp0[...] = a1 * b2
+            cp1[...] = -a0 * b2
+            cp2[...] = a0 * b1 - a1 * b0
+    else:
+        assert a.shape[-1] == 3
+        if b.shape[-1] == 3:
+            cp0[...] = a1 * b2 - a2 * b1
+            cp1[...] = a2 * b0 - a0 * b2
+            cp2[...] = a0 * b1 - a1 * b0
+        else:
+            assert b.shape[-1] == 2
+            cp0[...] = -a2 * b1
+            cp1[...] = a2 * b0
+            cp2[...] = a0 * b1 - a1 * b0
+
+    return torch.moveaxis(cp, -1, axisc)
+
+
+def einsum(*operands, out=None, dtype=None, order="K", casting="safe", optimize=False):
+    # Have to manually normalize *operands and **kwargs, following the NumPy signature
+    # We have a local import to avoid poluting the global space, as it will be then
+    # exported in funcs.py
+    from ._ndarray import ndarray
+    from ._normalizations import (
+        maybe_copy_to,
+        normalize_array_like,
+        normalize_casting,
+        normalize_dtype,
+        wrap_tensors,
+    )
+
+    dtype = normalize_dtype(dtype)
+    casting = normalize_casting(casting)
+    if out is not None and not isinstance(out, ndarray):
+        raise TypeError("'out' must be an array")
+    if order != "K":
+        raise NotImplementedError("'order' parameter is not supported.")
+
+    # parse arrays and normalize them
+    sublist_format = not isinstance(operands[0], str)
+    if sublist_format:
+        # op, str, op, str ... [sublistout] format: normalize every other argument
+
+        # - if sublistout is not given, the length of operands is even, and we pick
+        #   odd-numbered elements, which are arrays.
+        # - if sublistout is given, the length of operands is odd, we peel off
+        #   the last one, and pick odd-numbered elements, which are arrays.
+        #   Without [:-1], we would have picked sublistout, too.
+        array_operands = operands[:-1][::2]
+    else:
+        # ("ij->", arrays) format
+        subscripts, array_operands = operands[0], operands[1:]
+
+    tensors = [normalize_array_like(op) for op in array_operands]
+    target_dtype = _dtypes_impl.result_type_impl(*tensors) if dtype is None else dtype
+
+    # work around 'bmm' not implemented for 'Half' etc
+    is_half = target_dtype == torch.float16 and all(t.is_cpu for t in tensors)
+    if is_half:
+        target_dtype = torch.float32
+
+    is_short_int = target_dtype in [torch.uint8, torch.int8, torch.int16, torch.int32]
+    if is_short_int:
+        target_dtype = torch.int64
+
+    tensors = _util.typecast_tensors(tensors, target_dtype, casting)
+
+    from torch.backends import opt_einsum
+
+    try:
+        # set the global state to handle the optimize=... argument, restore on exit
+        if opt_einsum.is_available():
+            old_strategy = torch.backends.opt_einsum.strategy
+            old_enabled = torch.backends.opt_einsum.enabled
+
+            # torch.einsum calls opt_einsum.contract_path, which runs into
+            # https://github.com/dgasmith/opt_einsum/issues/219
+            # for strategy={True, False}
+            if optimize is True:
+                optimize = "auto"
+            elif optimize is False:
+                torch.backends.opt_einsum.enabled = False
+
+            torch.backends.opt_einsum.strategy = optimize
+
+        if sublist_format:
+            # recombine operands
+            sublists = operands[1::2]
+            has_sublistout = len(operands) % 2 == 1
+            if has_sublistout:
+                sublistout = operands[-1]
+            operands = list(itertools.chain.from_iterable(zip(tensors, sublists)))
+            if has_sublistout:
+                operands.append(sublistout)
+
+            result = torch.einsum(*operands)
+        else:
+            result = torch.einsum(subscripts, *tensors)
+
+    finally:
+        if opt_einsum.is_available():
+            torch.backends.opt_einsum.strategy = old_strategy
+            torch.backends.opt_einsum.enabled = old_enabled
+
+    result = maybe_copy_to(out, result)
+    return wrap_tensors(result)
+
+
+# ### sort and partition ###
+
+
+def _sort_helper(tensor, axis, kind, order):
+    if tensor.dtype.is_complex:
+        raise NotImplementedError(f"sorting {tensor.dtype} is not supported")
+    (tensor,), axis = _util.axis_none_flatten(tensor, axis=axis)
+    axis = _util.normalize_axis_index(axis, tensor.ndim)
+
+    stable = kind == "stable"
+
+    return tensor, axis, stable
+
+
+def sort(a: ArrayLike, axis=-1, kind=None, order: NotImplementedType = None):
+    # `order` keyword arg is only relevant for structured dtypes; so not supported here.
+    a, axis, stable = _sort_helper(a, axis, kind, order)
+    result = torch.sort(a, dim=axis, stable=stable)
+    return result.values
+
+
+def argsort(a: ArrayLike, axis=-1, kind=None, order: NotImplementedType = None):
+    a, axis, stable = _sort_helper(a, axis, kind, order)
+    return torch.argsort(a, dim=axis, stable=stable)
+
+
+def searchsorted(
+    a: ArrayLike, v: ArrayLike, side="left", sorter: Optional[ArrayLike] = None
+):
+    if a.dtype.is_complex:
+        raise NotImplementedError(f"searchsorted with dtype={a.dtype}")
+
+    return torch.searchsorted(a, v, side=side, sorter=sorter)
+
+
+# ### swap/move/roll axis ###
+
+
+def moveaxis(a: ArrayLike, source, destination):
+    source = _util.normalize_axis_tuple(source, a.ndim, "source")
+    destination = _util.normalize_axis_tuple(destination, a.ndim, "destination")
+    return torch.moveaxis(a, source, destination)
+
+
+def swapaxes(a: ArrayLike, axis1, axis2):
+    axis1 = _util.normalize_axis_index(axis1, a.ndim)
+    axis2 = _util.normalize_axis_index(axis2, a.ndim)
+    return torch.swapaxes(a, axis1, axis2)
+
+
+def rollaxis(a: ArrayLike, axis, start=0):
+    # Straight vendor from:
+    # https://github.com/numpy/numpy/blob/v1.24.0/numpy/core/numeric.py#L1259
+    #
+    # Also note this function in NumPy is mostly retained for backwards compat
+    # (https://stackoverflow.com/questions/29891583/reason-why-numpy-rollaxis-is-so-confusing)
+    # so let's not touch it unless hard pressed.
+    n = a.ndim
+    axis = _util.normalize_axis_index(axis, n)
+    if start < 0:
+        start += n
+    msg = "'%s' arg requires %d <= %s < %d, but %d was passed in"
+    if not (0 <= start < n + 1):
+        raise _util.AxisError(msg % ("start", -n, "start", n + 1, start))
+    if axis < start:
+        # it's been removed
+        start -= 1
+    if axis == start:
+        # numpy returns a view, here we try returning the tensor itself
+        # return tensor[...]
+        return a
+    axes = list(range(0, n))
+    axes.remove(axis)
+    axes.insert(start, axis)
+    return a.view(axes)
+
+
+def roll(a: ArrayLike, shift, axis=None):
+    if axis is not None:
+        axis = _util.normalize_axis_tuple(axis, a.ndim, allow_duplicate=True)
+        if not isinstance(shift, tuple):
+            shift = (shift,) * len(axis)
+    return torch.roll(a, shift, axis)
+
+
+# ### shape manipulations ###
+
+
+def squeeze(a: ArrayLike, axis=None):
+    if axis == ():
+        result = a
+    elif axis is None:
+        result = a.squeeze()
+    else:
+        if isinstance(axis, tuple):
+            result = a
+            for ax in axis:
+                result = a.squeeze(ax)
+        else:
+            result = a.squeeze(axis)
+    return result
+
+
+def reshape(a: ArrayLike, newshape, order: NotImplementedType = "C"):
+    # if sh = (1, 2, 3), numpy allows both .reshape(sh) and .reshape(*sh)
+    newshape = newshape[0] if len(newshape) == 1 else newshape
+    return a.reshape(newshape)
+
+
+# NB: cannot use torch.reshape(a, newshape) above, because of
+# (Pdb) torch.reshape(torch.as_tensor([1]), 1)
+# *** TypeError: reshape(): argument 'shape' (position 2) must be tuple of SymInts, not int
+
+
+def transpose(a: ArrayLike, axes=None):
+    # numpy allows both .transpose(sh) and .transpose(*sh)
+    # also older code uses axes being a list
+    if axes in [(), None, (None,)]:
+        axes = tuple(reversed(range(a.ndim)))
+    elif len(axes) == 1:
+        axes = axes[0]
+    return a.permute(axes)
+
+
+def ravel(a: ArrayLike, order: NotImplementedType = "C"):
+    return torch.flatten(a)
+
+
+def diff(
+    a: ArrayLike,
+    n=1,
+    axis=-1,
+    prepend: Optional[ArrayLike] = None,
+    append: Optional[ArrayLike] = None,
+):
+    axis = _util.normalize_axis_index(axis, a.ndim)
+
+    if n < 0:
+        raise ValueError(f"order must be non-negative but got {n}")
+
+    if n == 0:
+        # match numpy and return the input immediately
+        return a
+
+    if prepend is not None:
+        shape = list(a.shape)
+        shape[axis] = prepend.shape[axis] if prepend.ndim > 0 else 1
+        prepend = torch.broadcast_to(prepend, shape)
+
+    if append is not None:
+        shape = list(a.shape)
+        shape[axis] = append.shape[axis] if append.ndim > 0 else 1
+        append = torch.broadcast_to(append, shape)
+
+    return torch.diff(a, n, axis=axis, prepend=prepend, append=append)
+
+
+# ### math functions ###
+
+
+def angle(z: ArrayLike, deg=False):
+    result = torch.angle(z)
+    if deg:
+        result = result * (180 / torch.pi)
+    return result
+
+
+def sinc(x: ArrayLike):
+    return torch.sinc(x)
+
+
+# NB: have to normalize *varargs manually
+def gradient(f: ArrayLike, *varargs, axis=None, edge_order=1):
+    N = f.ndim  # number of dimensions
+
+    varargs = _util.ndarrays_to_tensors(varargs)
+
+    if axis is None:
+        axes = tuple(range(N))
+    else:
+        axes = _util.normalize_axis_tuple(axis, N)
+
+    len_axes = len(axes)
+    n = len(varargs)
+    if n == 0:
+        # no spacing argument - use 1 in all axes
+        dx = [1.0] * len_axes
+    elif n == 1 and (_dtypes_impl.is_scalar(varargs[0]) or varargs[0].ndim == 0):
+        # single scalar or 0D tensor for all axes (np.ndim(varargs[0]) == 0)
+        dx = varargs * len_axes
+    elif n == len_axes:
+        # scalar or 1d array for each axis
+        dx = list(varargs)
+        for i, distances in enumerate(dx):
+            distances = torch.as_tensor(distances)
+            if distances.ndim == 0:
+                continue
+            elif distances.ndim != 1:
+                raise ValueError("distances must be either scalars or 1d")
+            if len(distances) != f.shape[axes[i]]:
+                raise ValueError(
+                    "when 1d, distances must match "
+                    "the length of the corresponding dimension"
+                )
+            if not (distances.dtype.is_floating_point or distances.dtype.is_complex):
+                distances = distances.double()
+
+            diffx = torch.diff(distances)
+            # if distances are constant reduce to the scalar case
+            # since it brings a consistent speedup
+            if (diffx == diffx[0]).all():
+                diffx = diffx[0]
+            dx[i] = diffx
+    else:
+        raise TypeError("invalid number of arguments")
+
+    if edge_order > 2:
+        raise ValueError("'edge_order' greater than 2 not supported")
+
+    # use central differences on interior and one-sided differences on the
+    # endpoints. This preserves second order-accuracy over the full domain.
+
+    outvals = []
+
+    # create slice objects --- initially all are [:, :, ..., :]
+    slice1 = [slice(None)] * N
+    slice2 = [slice(None)] * N
+    slice3 = [slice(None)] * N
+    slice4 = [slice(None)] * N
+
+    otype = f.dtype
+    if _dtypes_impl.python_type_for_torch(otype) in (int, bool):
+        # Convert to floating point.
+        # First check if f is a numpy integer type; if so, convert f to float64
+        # to avoid modular arithmetic when computing the changes in f.
+        f = f.double()
+        otype = torch.float64
+
+    for axis, ax_dx in zip(axes, dx):
+        if f.shape[axis] < edge_order + 1:
+            raise ValueError(
+                "Shape of array too small to calculate a numerical gradient, "
+                "at least (edge_order + 1) elements are required."
+            )
+        # result allocation
+        out = torch.empty_like(f, dtype=otype)
+
+        # spacing for the current axis (NB: np.ndim(ax_dx) == 0)
+        uniform_spacing = _dtypes_impl.is_scalar(ax_dx) or ax_dx.ndim == 0
+
+        # Numerical differentiation: 2nd order interior
+        slice1[axis] = slice(1, -1)
+        slice2[axis] = slice(None, -2)
+        slice3[axis] = slice(1, -1)
+        slice4[axis] = slice(2, None)
+
+        if uniform_spacing:
+            out[tuple(slice1)] = (f[tuple(slice4)] - f[tuple(slice2)]) / (2.0 * ax_dx)
+        else:
+            dx1 = ax_dx[0:-1]
+            dx2 = ax_dx[1:]
+            a = -(dx2) / (dx1 * (dx1 + dx2))
+            b = (dx2 - dx1) / (dx1 * dx2)
+            c = dx1 / (dx2 * (dx1 + dx2))
+            # fix the shape for broadcasting
+            shape = [1] * N
+            shape[axis] = -1
+            a = a.reshape(shape)
+            b = b.reshape(shape)
+            c = c.reshape(shape)
+            # 1D equivalent -- out[1:-1] = a * f[:-2] + b * f[1:-1] + c * f[2:]
+            out[tuple(slice1)] = (
+                a * f[tuple(slice2)] + b * f[tuple(slice3)] + c * f[tuple(slice4)]
+            )
+
+        # Numerical differentiation: 1st order edges
+        if edge_order == 1:
+            slice1[axis] = 0
+            slice2[axis] = 1
+            slice3[axis] = 0
+            dx_0 = ax_dx if uniform_spacing else ax_dx[0]
+            # 1D equivalent -- out[0] = (f[1] - f[0]) / (x[1] - x[0])
+            out[tuple(slice1)] = (f[tuple(slice2)] - f[tuple(slice3)]) / dx_0
+
+            slice1[axis] = -1
+            slice2[axis] = -1
+            slice3[axis] = -2
+            dx_n = ax_dx if uniform_spacing else ax_dx[-1]
+            # 1D equivalent -- out[-1] = (f[-1] - f[-2]) / (x[-1] - x[-2])
+            out[tuple(slice1)] = (f[tuple(slice2)] - f[tuple(slice3)]) / dx_n
+
+        # Numerical differentiation: 2nd order edges
+        else:
+            slice1[axis] = 0
+            slice2[axis] = 0
+            slice3[axis] = 1
+            slice4[axis] = 2
+            if uniform_spacing:
+                a = -1.5 / ax_dx
+                b = 2.0 / ax_dx
+                c = -0.5 / ax_dx
+            else:
+                dx1 = ax_dx[0]
+                dx2 = ax_dx[1]
+                a = -(2.0 * dx1 + dx2) / (dx1 * (dx1 + dx2))
+                b = (dx1 + dx2) / (dx1 * dx2)
+                c = -dx1 / (dx2 * (dx1 + dx2))
+            # 1D equivalent -- out[0] = a * f[0] + b * f[1] + c * f[2]
+            out[tuple(slice1)] = (
+                a * f[tuple(slice2)] + b * f[tuple(slice3)] + c * f[tuple(slice4)]
+            )
+
+            slice1[axis] = -1
+            slice2[axis] = -3
+            slice3[axis] = -2
+            slice4[axis] = -1
+            if uniform_spacing:
+                a = 0.5 / ax_dx
+                b = -2.0 / ax_dx
+                c = 1.5 / ax_dx
+            else:
+                dx1 = ax_dx[-2]
+                dx2 = ax_dx[-1]
+                a = (dx2) / (dx1 * (dx1 + dx2))
+                b = -(dx2 + dx1) / (dx1 * dx2)
+                c = (2.0 * dx2 + dx1) / (dx2 * (dx1 + dx2))
+            # 1D equivalent -- out[-1] = a * f[-3] + b * f[-2] + c * f[-1]
+            out[tuple(slice1)] = (
+                a * f[tuple(slice2)] + b * f[tuple(slice3)] + c * f[tuple(slice4)]
+            )
+
+        outvals.append(out)
+
+        # reset the slice object in this dimension to ":"
+        slice1[axis] = slice(None)
+        slice2[axis] = slice(None)
+        slice3[axis] = slice(None)
+        slice4[axis] = slice(None)
+
+    if len_axes == 1:
+        return outvals[0]
+    else:
+        return outvals
+
+
+# ### Type/shape etc queries ###
+
+
+def round(a: ArrayLike, decimals=0, out: Optional[OutArray] = None):
+    if a.is_floating_point():
+        result = torch.round(a, decimals=decimals)
+    elif a.is_complex():
+        # RuntimeError: "round_cpu" not implemented for 'ComplexFloat'
+        result = torch.complex(
+            torch.round(a.real, decimals=decimals),
+            torch.round(a.imag, decimals=decimals),
+        )
+    else:
+        # RuntimeError: "round_cpu" not implemented for 'int'
+        result = a
+    return result
+
+
+around = round
+round_ = round
+
+
+def real_if_close(a: ArrayLike, tol=100):
+    if not torch.is_complex(a):
+        return a
+    if tol > 1:
+        # Undocumented in numpy: if tol < 1, it's an absolute tolerance!
+        # Otherwise, tol > 1 is relative tolerance, in units of the dtype epsilon
+        # https://github.com/numpy/numpy/blob/v1.24.0/numpy/lib/type_check.py#L577
+        tol = tol * torch.finfo(a.dtype).eps
+
+    mask = torch.abs(a.imag) < tol
+    return a.real if mask.all() else a
+
+
+def real(a: ArrayLike):
+    return torch.real(a)
+
+
+def imag(a: ArrayLike):
+    if a.is_complex():
+        return a.imag
+    return torch.zeros_like(a)
+
+
+def iscomplex(x: ArrayLike):
+    if torch.is_complex(x):
+        return x.imag != 0
+    return torch.zeros_like(x, dtype=torch.bool)
+
+
+def isreal(x: ArrayLike):
+    if torch.is_complex(x):
+        return x.imag == 0
+    return torch.ones_like(x, dtype=torch.bool)
+
+
+def iscomplexobj(x: ArrayLike):
+    return torch.is_complex(x)
+
+
+def isrealobj(x: ArrayLike):
+    return not torch.is_complex(x)
+
+
+def isneginf(x: ArrayLike, out: Optional[OutArray] = None):
+    return torch.isneginf(x)
+
+
+def isposinf(x: ArrayLike, out: Optional[OutArray] = None):
+    return torch.isposinf(x)
+
+
+def i0(x: ArrayLike):
+    return torch.special.i0(x)
+
+
+def isscalar(a):
+    # We need to use normalize_array_like, but we don't want to export it in funcs.py
+    from ._normalizations import normalize_array_like
+
+    try:
+        t = normalize_array_like(a)
+        return t.numel() == 1
+    except Exception:
+        return False
+
+
+# ### Filter windows ###
+
+
+def hamming(M):
+    dtype = _dtypes_impl.default_dtypes().float_dtype
+    return torch.hamming_window(M, periodic=False, dtype=dtype)
+
+
+def hanning(M):
+    dtype = _dtypes_impl.default_dtypes().float_dtype
+    return torch.hann_window(M, periodic=False, dtype=dtype)
+
+
+def kaiser(M, beta):
+    dtype = _dtypes_impl.default_dtypes().float_dtype
+    return torch.kaiser_window(M, beta=beta, periodic=False, dtype=dtype)
+
+
+def blackman(M):
+    dtype = _dtypes_impl.default_dtypes().float_dtype
+    return torch.blackman_window(M, periodic=False, dtype=dtype)
+
+
+def bartlett(M):
+    dtype = _dtypes_impl.default_dtypes().float_dtype
+    return torch.bartlett_window(M, periodic=False, dtype=dtype)
+
+
+# ### Dtype routines ###
+
+# vendored from https://github.com/numpy/numpy/blob/v1.24.0/numpy/lib/type_check.py#L666
+
+
+array_type = [
+    [torch.float16, torch.float32, torch.float64],
+    [None, torch.complex64, torch.complex128],
+]
+array_precision = {
+    torch.float16: 0,
+    torch.float32: 1,
+    torch.float64: 2,
+    torch.complex64: 1,
+    torch.complex128: 2,
+}
+
+
+def common_type(*tensors: ArrayLike):
+    is_complex = False
+    precision = 0
+    for a in tensors:
+        t = a.dtype
+        if iscomplexobj(a):
+            is_complex = True
+        if not (t.is_floating_point or t.is_complex):
+            p = 2  # array_precision[_nx.double]
+        else:
+            p = array_precision.get(t, None)
+            if p is None:
+                raise TypeError("can't get common type for non-numeric array")
+        precision = builtins.max(precision, p)
+    if is_complex:
+        return array_type[1][precision]
+    else:
+        return array_type[0][precision]
+
+
+# ### histograms ###
+
+
+def histogram(
+    a: ArrayLike,
+    bins: ArrayLike = 10,
+    range=None,
+    normed=None,
+    weights: Optional[ArrayLike] = None,
+    density=None,
+):
+    if normed is not None:
+        raise ValueError("normed argument is deprecated, use density= instead")
+
+    if weights is not None and weights.dtype.is_complex:
+        raise NotImplementedError("complex weights histogram.")
+
+    is_a_int = not (a.dtype.is_floating_point or a.dtype.is_complex)
+    is_w_int = weights is None or not weights.dtype.is_floating_point
+    if is_a_int:
+        a = a.double()
+
+    if weights is not None:
+        weights = _util.cast_if_needed(weights, a.dtype)
+
+    if isinstance(bins, torch.Tensor):
+        if bins.ndim == 0:
+            # bins was a single int
+            bins = operator.index(bins)
+        else:
+            bins = _util.cast_if_needed(bins, a.dtype)
+
+    if range is None:
+        h, b = torch.histogram(a, bins, weight=weights, density=bool(density))
+    else:
+        h, b = torch.histogram(
+            a, bins, range=range, weight=weights, density=bool(density)
+        )
+
+    if not density and is_w_int:
+        h = h.long()
+    if is_a_int:
+        b = b.long()
+
+    return h, b
+
+
+def histogram2d(
+    x,
+    y,
+    bins=10,
+    range: Optional[ArrayLike] = None,
+    normed=None,
+    weights: Optional[ArrayLike] = None,
+    density=None,
+):
+    # vendored from https://github.com/numpy/numpy/blob/v1.24.0/numpy/lib/twodim_base.py#L655-L821
+    if len(x) != len(y):
+        raise ValueError("x and y must have the same length.")
+
+    try:
+        N = len(bins)
+    except TypeError:
+        N = 1
+
+    if N != 1 and N != 2:
+        bins = [bins, bins]
+
+    h, e = histogramdd((x, y), bins, range, normed, weights, density)
+
+    return h, e[0], e[1]
+
+
+def histogramdd(
+    sample,
+    bins=10,
+    range: Optional[ArrayLike] = None,
+    normed=None,
+    weights: Optional[ArrayLike] = None,
+    density=None,
+):
+    # have to normalize manually because `sample` interpretation differs
+    # for a list of lists and a 2D array
+    if normed is not None:
+        raise ValueError("normed argument is deprecated, use density= instead")
+
+    from ._normalizations import normalize_array_like, normalize_seq_array_like
+
+    if isinstance(sample, (list, tuple)):
+        sample = normalize_array_like(sample).T
+    else:
+        sample = normalize_array_like(sample)
+
+    sample = torch.atleast_2d(sample)
+
+    if not (sample.dtype.is_floating_point or sample.dtype.is_complex):
+        sample = sample.double()
+
+    # bins is either an int, or a sequence of ints or a sequence of arrays
+    bins_is_array = not (
+        isinstance(bins, int) or builtins.all(isinstance(b, int) for b in bins)
+    )
+    if bins_is_array:
+        bins = normalize_seq_array_like(bins)
+        bins_dtypes = [b.dtype for b in bins]
+        bins = [_util.cast_if_needed(b, sample.dtype) for b in bins]
+
+    if range is not None:
+        range = range.flatten().tolist()
+
+    if weights is not None:
+        # range=... is required : interleave min and max values per dimension
+        mm = sample.aminmax(dim=0)
+        range = torch.cat(mm).reshape(2, -1).T.flatten()
+        range = tuple(range.tolist())
+        weights = _util.cast_if_needed(weights, sample.dtype)
+        w_kwd = {"weight": weights}
+    else:
+        w_kwd = {}
+
+    h, b = torch.histogramdd(sample, bins, range, density=bool(density), **w_kwd)
+
+    if bins_is_array:
+        b = [_util.cast_if_needed(bb, dtyp) for bb, dtyp in zip(b, bins_dtypes)]
+
+    return h, b
+
+
+# ### odds and ends
+
+
+def min_scalar_type(a: ArrayLike, /):
+    # https://github.com/numpy/numpy/blob/maintenance/1.24.x/numpy/core/src/multiarray/convert_datatype.c#L1288
+
+    from ._dtypes import DType
+
+    if a.numel() > 1:
+        # numpy docs: "For non-scalar array a, returns the vector’s dtype unmodified."
+        return DType(a.dtype)
+
+    if a.dtype == torch.bool:
+        dtype = torch.bool
+
+    elif a.dtype.is_complex:
+        fi = torch.finfo(torch.float32)
+        fits_in_single = a.dtype == torch.complex64 or (
+            fi.min <= a.real <= fi.max and fi.min <= a.imag <= fi.max
+        )
+        dtype = torch.complex64 if fits_in_single else torch.complex128
+
+    elif a.dtype.is_floating_point:
+        for dt in [torch.float16, torch.float32, torch.float64]:
+            fi = torch.finfo(dt)
+            if fi.min <= a <= fi.max:
+                dtype = dt
+                break
+    else:
+        # must be integer
+        for dt in [torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64]:
+            # Prefer unsigned int where possible, as numpy does.
+            ii = torch.iinfo(dt)
+            if ii.min <= a <= ii.max:
+                dtype = dt
+                break
+
+    return DType(dtype)
+
+
+def pad(array: ArrayLike, pad_width: ArrayLike, mode="constant", **kwargs):
+    if mode != "constant":
+        raise NotImplementedError
+    value = kwargs.get("constant_values", 0)
+    # `value` must be a python scalar for torch.nn.functional.pad
+    typ = _dtypes_impl.python_type_for_torch(array.dtype)
+    value = typ(value)
+
+    pad_width = torch.broadcast_to(pad_width, (array.ndim, 2))
+    pad_width = torch.flip(pad_width, (0,)).flatten()
+
+    return torch.nn.functional.pad(array, tuple(pad_width), value=value)

venv/lib/python3.10/site-packages/torch/_numpy/_getlimits.py

@@ -0,0 +1,15 @@
+# mypy: ignore-errors
+
+import torch
+
+from . import _dtypes
+
+
+def finfo(dtyp):
+    torch_dtype = _dtypes.dtype(dtyp).torch_dtype
+    return torch.finfo(torch_dtype)
+
+
+def iinfo(dtyp):
+    torch_dtype = _dtypes.dtype(dtyp).torch_dtype
+    return torch.iinfo(torch_dtype)

venv/lib/python3.10/site-packages/torch/_numpy/_ndarray.py

@@ -0,0 +1,591 @@
+# mypy: ignore-errors
+
+from __future__ import annotations
+
+import builtins
+import math
+import operator
+from typing import Sequence
+
+import torch
+
+from . import _dtypes, _dtypes_impl, _funcs, _ufuncs, _util
+from ._normalizations import (
+    ArrayLike,
+    normalize_array_like,
+    normalizer,
+    NotImplementedType,
+)
+
+newaxis = None
+
+FLAGS = [
+    "C_CONTIGUOUS",
+    "F_CONTIGUOUS",
+    "OWNDATA",
+    "WRITEABLE",
+    "ALIGNED",
+    "WRITEBACKIFCOPY",
+    "FNC",
+    "FORC",
+    "BEHAVED",
+    "CARRAY",
+    "FARRAY",
+]
+
+SHORTHAND_TO_FLAGS = {
+    "C": "C_CONTIGUOUS",
+    "F": "F_CONTIGUOUS",
+    "O": "OWNDATA",
+    "W": "WRITEABLE",
+    "A": "ALIGNED",
+    "X": "WRITEBACKIFCOPY",
+    "B": "BEHAVED",
+    "CA": "CARRAY",
+    "FA": "FARRAY",
+}
+
+
+class Flags:
+    def __init__(self, flag_to_value: dict):
+        assert all(k in FLAGS for k in flag_to_value.keys())  # sanity check
+        self._flag_to_value = flag_to_value
+
+    def __getattr__(self, attr: str):
+        if attr.islower() and attr.upper() in FLAGS:
+            return self[attr.upper()]
+        else:
+            raise AttributeError(f"No flag attribute '{attr}'")
+
+    def __getitem__(self, key):
+        if key in SHORTHAND_TO_FLAGS.keys():
+            key = SHORTHAND_TO_FLAGS[key]
+        if key in FLAGS:
+            try:
+                return self._flag_to_value[key]
+            except KeyError as e:
+                raise NotImplementedError(f"{key=}") from e
+        else:
+            raise KeyError(f"No flag key '{key}'")
+
+    def __setattr__(self, attr, value):
+        if attr.islower() and attr.upper() in FLAGS:
+            self[attr.upper()] = value
+        else:
+            super().__setattr__(attr, value)
+
+    def __setitem__(self, key, value):
+        if key in FLAGS or key in SHORTHAND_TO_FLAGS.keys():
+            raise NotImplementedError("Modifying flags is not implemented")
+        else:
+            raise KeyError(f"No flag key '{key}'")
+
+
+def create_method(fn, name=None):
+    name = name or fn.__name__
+
+    def f(*args, **kwargs):
+        return fn(*args, **kwargs)
+
+    f.__name__ = name
+    f.__qualname__ = f"ndarray.{name}"
+    return f
+
+
+# Map ndarray.name_method -> np.name_func
+# If name_func == None, it means that name_method == name_func
+methods = {
+    "clip": None,
+    "nonzero": None,
+    "repeat": None,
+    "round": None,
+    "squeeze": None,
+    "swapaxes": None,
+    "ravel": None,
+    # linalg
+    "diagonal": None,
+    "dot": None,
+    "trace": None,
+    # sorting
+    "argsort": None,
+    "searchsorted": None,
+    # reductions
+    "argmax": None,
+    "argmin": None,
+    "any": None,
+    "all": None,
+    "max": None,
+    "min": None,
+    "ptp": None,
+    "sum": None,
+    "prod": None,
+    "mean": None,
+    "var": None,
+    "std": None,
+    # scans
+    "cumsum": None,
+    "cumprod": None,
+    # advanced indexing
+    "take": None,
+    "choose": None,
+}
+
+dunder = {
+    "abs": "absolute",
+    "invert": None,
+    "pos": "positive",
+    "neg": "negative",
+    "gt": "greater",
+    "lt": "less",
+    "ge": "greater_equal",
+    "le": "less_equal",
+}
+
+# dunder methods with right-looking and in-place variants
+ri_dunder = {
+    "add": None,
+    "sub": "subtract",
+    "mul": "multiply",
+    "truediv": "divide",
+    "floordiv": "floor_divide",
+    "pow": "power",
+    "mod": "remainder",
+    "and": "bitwise_and",
+    "or": "bitwise_or",
+    "xor": "bitwise_xor",
+    "lshift": "left_shift",
+    "rshift": "right_shift",
+    "matmul": None,
+}
+
+
+def _upcast_int_indices(index):
+    if isinstance(index, torch.Tensor):
+        if index.dtype in (torch.int8, torch.int16, torch.int32, torch.uint8):
+            return index.to(torch.int64)
+    elif isinstance(index, tuple):
+        return tuple(_upcast_int_indices(i) for i in index)
+    return index
+
+
+# Used to indicate that a parameter is unspecified (as opposed to explicitly
+# `None`)
+class _Unspecified:
+    pass
+
+
+_Unspecified.unspecified = _Unspecified()
+
+###############################################################
+#                      ndarray class                          #
+###############################################################
+
+
+class ndarray:
+    def __init__(self, t=None):
+        if t is None:
+            self.tensor = torch.Tensor()
+        elif isinstance(t, torch.Tensor):
+            self.tensor = t
+        else:
+            raise ValueError(
+                "ndarray constructor is not recommended; prefer"
+                "either array(...) or zeros/empty(...)"
+            )
+
+    # Register NumPy functions as methods
+    for method, name in methods.items():
+        fn = getattr(_funcs, name or method)
+        vars()[method] = create_method(fn, method)
+
+    # Regular methods but coming from ufuncs
+    conj = create_method(_ufuncs.conjugate, "conj")
+    conjugate = create_method(_ufuncs.conjugate)
+
+    for method, name in dunder.items():
+        fn = getattr(_ufuncs, name or method)
+        method = f"__{method}__"
+        vars()[method] = create_method(fn, method)
+
+    for method, name in ri_dunder.items():
+        fn = getattr(_ufuncs, name or method)
+        plain = f"__{method}__"
+        vars()[plain] = create_method(fn, plain)
+        rvar = f"__r{method}__"
+        vars()[rvar] = create_method(lambda self, other, fn=fn: fn(other, self), rvar)
+        ivar = f"__i{method}__"
+        vars()[ivar] = create_method(
+            lambda self, other, fn=fn: fn(self, other, out=self), ivar
+        )
+
+    # There's no __idivmod__
+    __divmod__ = create_method(_ufuncs.divmod, "__divmod__")
+    __rdivmod__ = create_method(
+        lambda self, other: _ufuncs.divmod(other, self), "__rdivmod__"
+    )
+
+    # prevent loop variables leaking into the ndarray class namespace
+    del ivar, rvar, name, plain, fn, method
+
+    @property
+    def shape(self):
+        return tuple(self.tensor.shape)
+
+    @property
+    def size(self):
+        return self.tensor.numel()
+
+    @property
+    def ndim(self):
+        return self.tensor.ndim
+
+    @property
+    def dtype(self):
+        return _dtypes.dtype(self.tensor.dtype)
+
+    @property
+    def strides(self):
+        elsize = self.tensor.element_size()
+        return tuple(stride * elsize for stride in self.tensor.stride())
+
+    @property
+    def itemsize(self):
+        return self.tensor.element_size()
+
+    @property
+    def flags(self):
+        # Note contiguous in torch is assumed C-style
+        return Flags(
+            {
+                "C_CONTIGUOUS": self.tensor.is_contiguous(),
+                "F_CONTIGUOUS": self.T.tensor.is_contiguous(),
+                "OWNDATA": self.tensor._base is None,
+                "WRITEABLE": True,  # pytorch does not have readonly tensors
+            }
+        )
+
+    @property
+    def data(self):
+        return self.tensor.data_ptr()
+
+    @property
+    def nbytes(self):
+        return self.tensor.storage().nbytes()
+
+    @property
+    def T(self):
+        return self.transpose()
+
+    @property
+    def real(self):
+        return _funcs.real(self)
+
+    @real.setter
+    def real(self, value):
+        self.tensor.real = asarray(value).tensor
+
+    @property
+    def imag(self):
+        return _funcs.imag(self)
+
+    @imag.setter
+    def imag(self, value):
+        self.tensor.imag = asarray(value).tensor
+
+    # ctors
+    def astype(self, dtype, order="K", casting="unsafe", subok=True, copy=True):
+        if order != "K":
+            raise NotImplementedError(f"astype(..., order={order} is not implemented.")
+        if casting != "unsafe":
+            raise NotImplementedError(
+                f"astype(..., casting={casting} is not implemented."
+            )
+        if not subok:
+            raise NotImplementedError(f"astype(..., subok={subok} is not implemented.")
+        if not copy:
+            raise NotImplementedError(f"astype(..., copy={copy} is not implemented.")
+        torch_dtype = _dtypes.dtype(dtype).torch_dtype
+        t = self.tensor.to(torch_dtype)
+        return ndarray(t)
+
+    @normalizer
+    def copy(self: ArrayLike, order: NotImplementedType = "C"):
+        return self.clone()
+
+    @normalizer
+    def flatten(self: ArrayLike, order: NotImplementedType = "C"):
+        return torch.flatten(self)
+
+    def resize(self, *new_shape, refcheck=False):
+        # NB: differs from np.resize: fills with zeros instead of making repeated copies of input.
+        if refcheck:
+            raise NotImplementedError(
+                f"resize(..., refcheck={refcheck} is not implemented."
+            )
+        if new_shape in [(), (None,)]:
+            return
+
+        # support both x.resize((2, 2)) and x.resize(2, 2)
+        if len(new_shape) == 1:
+            new_shape = new_shape[0]
+        if isinstance(new_shape, int):
+            new_shape = (new_shape,)
+
+        if builtins.any(x < 0 for x in new_shape):
+            raise ValueError("all elements of `new_shape` must be non-negative")
+
+        new_numel, old_numel = math.prod(new_shape), self.tensor.numel()
+
+        self.tensor.resize_(new_shape)
+
+        if new_numel >= old_numel:
+            # zero-fill new elements
+            assert self.tensor.is_contiguous()
+            b = self.tensor.flatten()  # does not copy
+            b[old_numel:].zero_()
+
+    def view(self, dtype=_Unspecified.unspecified, type=_Unspecified.unspecified):
+        if dtype is _Unspecified.unspecified:
+            dtype = self.dtype
+        if type is not _Unspecified.unspecified:
+            raise NotImplementedError(f"view(..., type={type} is not implemented.")
+        torch_dtype = _dtypes.dtype(dtype).torch_dtype
+        tview = self.tensor.view(torch_dtype)
+        return ndarray(tview)
+
+    @normalizer
+    def fill(self, value: ArrayLike):
+        # Both Pytorch and NumPy accept 0D arrays/tensors and scalars, and
+        # error out on D > 0 arrays
+        self.tensor.fill_(value)
+
+    def tolist(self):
+        return self.tensor.tolist()
+
+    def __iter__(self):
+        return (ndarray(x) for x in self.tensor.__iter__())
+
+    def __str__(self):
+        return (
+            str(self.tensor)
+            .replace("tensor", "torch.ndarray")
+            .replace("dtype=torch.", "dtype=")
+        )
+
+    __repr__ = create_method(__str__)
+
+    def __eq__(self, other):
+        try:
+            return _ufuncs.equal(self, other)
+        except (RuntimeError, TypeError):
+            # Failed to convert other to array: definitely not equal.
+            falsy = torch.full(self.shape, fill_value=False, dtype=bool)
+            return asarray(falsy)
+
+    def __ne__(self, other):
+        return ~(self == other)
+
+    def __index__(self):
+        try:
+            return operator.index(self.tensor.item())
+        except Exception as exc:
+            raise TypeError(
+                "only integer scalar arrays can be converted to a scalar index"
+            ) from exc
+
+    def __bool__(self):
+        return bool(self.tensor)
+
+    def __int__(self):
+        return int(self.tensor)
+
+    def __float__(self):
+        return float(self.tensor)
+
+    def __complex__(self):
+        return complex(self.tensor)
+
+    def is_integer(self):
+        try:
+            v = self.tensor.item()
+            result = int(v) == v
+        except Exception:
+            result = False
+        return result
+
+    def __len__(self):
+        return self.tensor.shape[0]
+
+    def __contains__(self, x):
+        return self.tensor.__contains__(x)
+
+    def transpose(self, *axes):
+        # np.transpose(arr, axis=None) but arr.transpose(*axes)
+        return _funcs.transpose(self, axes)
+
+    def reshape(self, *shape, order="C"):
+        # arr.reshape(shape) and arr.reshape(*shape)
+        return _funcs.reshape(self, shape, order=order)
+
+    def sort(self, axis=-1, kind=None, order=None):
+        # ndarray.sort works in-place
+        _funcs.copyto(self, _funcs.sort(self, axis, kind, order))
+
+    def item(self, *args):
+        # Mimic NumPy's implementation with three special cases (no arguments,
+        # a flat index and a multi-index):
+        # https://github.com/numpy/numpy/blob/main/numpy/core/src/multiarray/methods.c#L702
+        if args == ():
+            return self.tensor.item()
+        elif len(args) == 1:
+            # int argument
+            return self.ravel()[args[0]]
+        else:
+            return self.__getitem__(args)
+
+    def __getitem__(self, index):
+        tensor = self.tensor
+
+        def neg_step(i, s):
+            if not (isinstance(s, slice) and s.step is not None and s.step < 0):
+                return s
+
+            nonlocal tensor
+            tensor = torch.flip(tensor, (i,))
+
+            # Account for the fact that a slice includes the start but not the end
+            assert isinstance(s.start, int) or s.start is None
+            assert isinstance(s.stop, int) or s.stop is None
+            start = s.stop + 1 if s.stop else None
+            stop = s.start + 1 if s.start else None
+
+            return slice(start, stop, -s.step)
+
+        if isinstance(index, Sequence):
+            index = type(index)(neg_step(i, s) for i, s in enumerate(index))
+        else:
+            index = neg_step(0, index)
+        index = _util.ndarrays_to_tensors(index)
+        index = _upcast_int_indices(index)
+        return ndarray(tensor.__getitem__(index))
+
+    def __setitem__(self, index, value):
+        index = _util.ndarrays_to_tensors(index)
+        index = _upcast_int_indices(index)
+
+        if not _dtypes_impl.is_scalar(value):
+            value = normalize_array_like(value)
+            value = _util.cast_if_needed(value, self.tensor.dtype)
+
+        return self.tensor.__setitem__(index, value)
+
+    take = _funcs.take
+    put = _funcs.put
+
+    def __dlpack__(self, *, stream=None):
+        return self.tensor.__dlpack__(stream=stream)
+
+    def __dlpack_device__(self):
+        return self.tensor.__dlpack_device__()
+
+
+def _tolist(obj):
+    """Recursively convert tensors into lists."""
+    a1 = []
+    for elem in obj:
+        if isinstance(elem, (list, tuple)):
+            elem = _tolist(elem)
+        if isinstance(elem, ndarray):
+            a1.append(elem.tensor.tolist())
+        else:
+            a1.append(elem)
+    return a1
+
+
+# This is the ideally the only place which talks to ndarray directly.
+# The rest goes through asarray (preferred) or array.
+
+
+def array(obj, dtype=None, *, copy=True, order="K", subok=False, ndmin=0, like=None):
+    if subok is not False:
+        raise NotImplementedError("'subok' parameter is not supported.")
+    if like is not None:
+        raise NotImplementedError("'like' parameter is not supported.")
+    if order != "K":
+        raise NotImplementedError()
+
+    # a happy path
+    if (
+        isinstance(obj, ndarray)
+        and copy is False
+        and dtype is None
+        and ndmin <= obj.ndim
+    ):
+        return obj
+
+    if isinstance(obj, (list, tuple)):
+        # FIXME and they have the same dtype, device, etc
+        if obj and all(isinstance(x, torch.Tensor) for x in obj):
+            # list of arrays: *under torch.Dynamo* these are FakeTensors
+            obj = torch.stack(obj)
+        else:
+            # XXX: remove tolist
+            # lists of ndarrays: [1, [2, 3], ndarray(4)] convert to lists of lists
+            obj = _tolist(obj)
+
+    # is obj an ndarray already?
+    if isinstance(obj, ndarray):
+        obj = obj.tensor
+
+    # is a specific dtype requested?
+    torch_dtype = None
+    if dtype is not None:
+        torch_dtype = _dtypes.dtype(dtype).torch_dtype
+
+    tensor = _util._coerce_to_tensor(obj, torch_dtype, copy, ndmin)
+    return ndarray(tensor)
+
+
+def asarray(a, dtype=None, order="K", *, like=None):
+    return array(a, dtype=dtype, order=order, like=like, copy=False, ndmin=0)
+
+
+def ascontiguousarray(a, dtype=None, *, like=None):
+    arr = asarray(a, dtype=dtype, like=like)
+    if not arr.tensor.is_contiguous():
+        arr.tensor = arr.tensor.contiguous()
+    return arr
+
+
+def from_dlpack(x, /):
+    t = torch.from_dlpack(x)
+    return ndarray(t)
+
+
+def _extract_dtype(entry):
+    try:
+        dty = _dtypes.dtype(entry)
+    except Exception:
+        dty = asarray(entry).dtype
+    return dty
+
+
+def can_cast(from_, to, casting="safe"):
+    from_ = _extract_dtype(from_)
+    to_ = _extract_dtype(to)
+
+    return _dtypes_impl.can_cast_impl(from_.torch_dtype, to_.torch_dtype, casting)
+
+
+def result_type(*arrays_and_dtypes):
+    tensors = []
+    for entry in arrays_and_dtypes:
+        try:
+            t = asarray(entry).tensor
+        except (RuntimeError, ValueError, TypeError):
+            dty = _dtypes.dtype(entry)
+            t = torch.empty(1, dtype=dty.torch_dtype)
+        tensors.append(t)
+
+    torch_dtype = _dtypes_impl.result_type_impl(*tensors)
+    return _dtypes.dtype(torch_dtype)

venv/lib/python3.10/site-packages/torch/_numpy/_normalizations.py

@@ -0,0 +1,258 @@
+# mypy: ignore-errors
+
+""" "Normalize" arguments: convert array_likes to tensors, dtypes to torch dtypes and so on.
+"""
+from __future__ import annotations
+
+import functools
+import inspect
+import operator
+import typing
+
+import torch
+
+from . import _dtypes, _dtypes_impl, _util
+
+ArrayLike = typing.TypeVar("ArrayLike")
+Scalar = typing.Union[int, float, complex, bool]
+ArrayLikeOrScalar = typing.Union[ArrayLike, Scalar]
+
+DTypeLike = typing.TypeVar("DTypeLike")
+AxisLike = typing.TypeVar("AxisLike")
+NDArray = typing.TypeVar("NDArray")
+CastingModes = typing.TypeVar("CastingModes")
+KeepDims = typing.TypeVar("KeepDims")
+
+# OutArray is to annotate the out= array argument.
+#
+# This one is special is several respects:
+# First, It needs to be an NDArray, and we need to preserve the `result is out`
+# semantics. Therefore, we cannot just extract the Tensor from the out array.
+# So we never pass the out array to implementer functions and handle it in the
+# `normalizer` below.
+# Second, the out= argument can be either keyword or positional argument, and
+# as a positional arg, it can be anywhere in the signature.
+# To handle all this, we define a special `OutArray` annotation and dispatch on it.
+#
+OutArray = typing.TypeVar("OutArray")
+
+try:
+    from typing import NotImplementedType
+except ImportError:
+    NotImplementedType = typing.TypeVar("NotImplementedType")
+
+
+def normalize_array_like(x, parm=None):
+    from ._ndarray import asarray
+
+    return asarray(x).tensor
+
+
+def normalize_array_like_or_scalar(x, parm=None):
+    if _dtypes_impl.is_scalar_or_symbolic(x):
+        return x
+    return normalize_array_like(x, parm)
+
+
+def normalize_optional_array_like_or_scalar(x, parm=None):
+    if x is None:
+        return None
+    return normalize_array_like_or_scalar(x, parm)
+
+
+def normalize_optional_array_like(x, parm=None):
+    # This explicit normalizer is needed because otherwise normalize_array_like
+    # does not run for a parameter annotated as Optional[ArrayLike]
+    return None if x is None else normalize_array_like(x, parm)
+
+
+def normalize_seq_array_like(x, parm=None):
+    return tuple(normalize_array_like(value) for value in x)
+
+
+def normalize_dtype(dtype, parm=None):
+    # cf _decorators.dtype_to_torch
+    torch_dtype = None
+    if dtype is not None:
+        dtype = _dtypes.dtype(dtype)
+        torch_dtype = dtype.torch_dtype
+    return torch_dtype
+
+
+def normalize_not_implemented(arg, parm):
+    if arg != parm.default:
+        raise NotImplementedError(f"'{parm.name}' parameter is not supported.")
+
+
+def normalize_axis_like(arg, parm=None):
+    from ._ndarray import ndarray
+
+    if isinstance(arg, ndarray):
+        arg = operator.index(arg)
+    return arg
+
+
+def normalize_ndarray(arg, parm=None):
+    # check the arg is an ndarray, extract its tensor attribute
+    if arg is None:
+        return arg
+
+    from ._ndarray import ndarray
+
+    if not isinstance(arg, ndarray):
+        raise TypeError(f"'{parm.name}' must be an array")
+    return arg.tensor
+
+
+def normalize_outarray(arg, parm=None):
+    # almost normalize_ndarray, only return the array, not its tensor
+    if arg is None:
+        return arg
+    from ._ndarray import ndarray
+
+    # Dynamo can pass torch tensors as out arguments,
+    # wrap it in an ndarray before processing
+    if isinstance(arg, torch.Tensor):
+        arg = ndarray(arg)
+
+    if not isinstance(arg, ndarray):
+        raise TypeError(f"'{parm.name}' must be an array")
+    return arg
+
+
+def normalize_casting(arg, parm=None):
+    if arg not in ["no", "equiv", "safe", "same_kind", "unsafe"]:
+        raise ValueError(
+            f"casting must be one of 'no', 'equiv', 'safe', 'same_kind', or 'unsafe' (got '{arg}')"
+        )
+    return arg
+
+
+normalizers = {
+    "ArrayLike": normalize_array_like,
+    "ArrayLikeOrScalar": normalize_array_like_or_scalar,
+    "Optional[ArrayLike]": normalize_optional_array_like,
+    "Sequence[ArrayLike]": normalize_seq_array_like,
+    "Optional[ArrayLikeOrScalar]": normalize_optional_array_like_or_scalar,
+    "Optional[NDArray]": normalize_ndarray,
+    "Optional[OutArray]": normalize_outarray,
+    "NDArray": normalize_ndarray,
+    "Optional[DTypeLike]": normalize_dtype,
+    "AxisLike": normalize_axis_like,
+    "NotImplementedType": normalize_not_implemented,
+    "Optional[CastingModes]": normalize_casting,
+}
+
+
+def maybe_normalize(arg, parm):
+    """Normalize arg if a normalizer is registered."""
+    normalizer = normalizers.get(parm.annotation, None)
+    return normalizer(arg, parm) if normalizer else arg
+
+
+# ### Return value helpers ###
+
+
+def maybe_copy_to(out, result, promote_scalar_result=False):
+    # NB: here out is either an ndarray or None
+    if out is None:
+        return result
+    elif isinstance(result, torch.Tensor):
+        if result.shape != out.shape:
+            can_fit = result.numel() == 1 and out.ndim == 0
+            if promote_scalar_result and can_fit:
+                result = result.squeeze()
+            else:
+                raise ValueError(
+                    f"Bad size of the out array: out.shape = {out.shape}"
+                    f" while result.shape = {result.shape}."
+                )
+        out.tensor.copy_(result)
+        return out
+    elif isinstance(result, (tuple, list)):
+        return type(result)(
+            maybe_copy_to(o, r, promote_scalar_result) for o, r in zip(out, result)
+        )
+    else:
+        raise AssertionError()  # We should never hit this path
+
+
+def wrap_tensors(result):
+    from ._ndarray import ndarray
+
+    if isinstance(result, torch.Tensor):
+        return ndarray(result)
+    elif isinstance(result, (tuple, list)):
+        result = type(result)(wrap_tensors(x) for x in result)
+    return result
+
+
+def array_or_scalar(values, py_type=float, return_scalar=False):
+    if return_scalar:
+        return py_type(values.item())
+    else:
+        from ._ndarray import ndarray
+
+        return ndarray(values)
+
+
+# ### The main decorator to normalize arguments / postprocess the output ###
+
+
+def normalizer(_func=None, *, promote_scalar_result=False):
+    def normalizer_inner(func):
+        @functools.wraps(func)
+        def wrapped(*args, **kwds):
+            sig = inspect.signature(func)
+            params = sig.parameters
+            first_param = next(iter(params.values()))
+
+            # NumPy's API does not have positional args before variadic positional args
+            if first_param.kind == inspect.Parameter.VAR_POSITIONAL:
+                args = [maybe_normalize(arg, first_param) for arg in args]
+            else:
+                # NB: extra unknown arguments: pass through, will raise in func(*args) below
+                args = (
+                    tuple(
+                        maybe_normalize(arg, parm)
+                        for arg, parm in zip(args, params.values())
+                    )
+                    + args[len(params.values()) :]
+                )
+
+            kwds = {
+                name: maybe_normalize(arg, params[name]) if name in params else arg
+                for name, arg in kwds.items()
+            }
+
+            result = func(*args, **kwds)
+
+            # keepdims
+            bound_args = None
+            if "keepdims" in params and params["keepdims"].annotation == "KeepDims":
+                # keepdims can be in any position so we need sig.bind
+                bound_args = sig.bind(*args, **kwds).arguments
+                if bound_args.get("keepdims", False):
+                    # In this case the first arg is the initial tensor and
+                    # the second arg is (optionally) the axis
+                    tensor = args[0]
+                    axis = bound_args.get("axis")
+                    result = _util.apply_keepdims(result, axis, tensor.ndim)
+
+            # out
+            if "out" in params:
+                # out can be in any position so we need sig.bind
+                if bound_args is None:
+                    bound_args = sig.bind(*args, **kwds).arguments
+                out = bound_args.get("out")
+                result = maybe_copy_to(out, result, promote_scalar_result)
+            result = wrap_tensors(result)
+
+            return result
+
+        return wrapped
+
+    if _func is None:
+        return normalizer_inner
+    else:
+        return normalizer_inner(_func)

venv/lib/python3.10/site-packages/torch/_numpy/_reductions_impl.py

@@ -0,0 +1,456 @@
+# mypy: ignore-errors
+
+""" Implementation of reduction operations, to be wrapped into arrays, dtypes etc
+in the 'public' layer.
+
+Anything here only deals with torch objects, e.g. "dtype" is a torch.dtype instance etc
+"""
+from __future__ import annotations
+
+import functools
+from typing import Optional
+
+import torch
+
+from . import _dtypes_impl, _util
+from ._normalizations import (
+    ArrayLike,
+    AxisLike,
+    DTypeLike,
+    KeepDims,
+    NotImplementedType,
+    OutArray,
+)
+
+
+def _deco_axis_expand(func):
+    """
+    Generically handle axis arguments in reductions.
+    axis is *always* the 2nd arg in the function so no need to have a look at its signature
+    """
+
+    @functools.wraps(func)
+    def wrapped(a, axis=None, *args, **kwds):
+        if axis is not None:
+            axis = _util.normalize_axis_tuple(axis, a.ndim)
+
+        if axis == ():
+            # So we insert a length-one axis and run the reduction along it.
+            # We cannot return a.clone() as this would sidestep the checks inside the function
+            newshape = _util.expand_shape(a.shape, axis=0)
+            a = a.reshape(newshape)
+            axis = (0,)
+
+        return func(a, axis, *args, **kwds)
+
+    return wrapped
+
+
+def _atleast_float(dtype, other_dtype):
+    """Return a dtype that is real or complex floating-point.
+
+    For inputs that are boolean or integer dtypes, this returns the default
+    float dtype; inputs that are complex get converted to the default complex
+    dtype; real floating-point dtypes (`float*`) get passed through unchanged
+    """
+    if dtype is None:
+        dtype = other_dtype
+    if not (dtype.is_floating_point or dtype.is_complex):
+        return _dtypes_impl.default_dtypes().float_dtype
+    return dtype
+
+
+@_deco_axis_expand
+def count_nonzero(a: ArrayLike, axis: AxisLike = None, *, keepdims: KeepDims = False):
+    return a.count_nonzero(axis)
+
+
+@_deco_axis_expand
+def argmax(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    out: Optional[OutArray] = None,
+    *,
+    keepdims: KeepDims = False,
+):
+    if a.is_complex():
+        raise NotImplementedError(f"argmax with dtype={a.dtype}.")
+
+    axis = _util.allow_only_single_axis(axis)
+
+    if a.dtype == torch.bool:
+        # RuntimeError: "argmax_cpu" not implemented for 'Bool'
+        a = a.to(torch.uint8)
+
+    return torch.argmax(a, axis)
+
+
+@_deco_axis_expand
+def argmin(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    out: Optional[OutArray] = None,
+    *,
+    keepdims: KeepDims = False,
+):
+    if a.is_complex():
+        raise NotImplementedError(f"argmin with dtype={a.dtype}.")
+
+    axis = _util.allow_only_single_axis(axis)
+
+    if a.dtype == torch.bool:
+        # RuntimeError: "argmin_cpu" not implemented for 'Bool'
+        a = a.to(torch.uint8)
+
+    return torch.argmin(a, axis)
+
+
+@_deco_axis_expand
+def any(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    out: Optional[OutArray] = None,
+    keepdims: KeepDims = False,
+    *,
+    where: NotImplementedType = None,
+):
+    axis = _util.allow_only_single_axis(axis)
+    axis_kw = {} if axis is None else {"dim": axis}
+    return torch.any(a, **axis_kw)
+
+
+@_deco_axis_expand
+def all(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    out: Optional[OutArray] = None,
+    keepdims: KeepDims = False,
+    *,
+    where: NotImplementedType = None,
+):
+    axis = _util.allow_only_single_axis(axis)
+    axis_kw = {} if axis is None else {"dim": axis}
+    return torch.all(a, **axis_kw)
+
+
+@_deco_axis_expand
+def amax(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    out: Optional[OutArray] = None,
+    keepdims: KeepDims = False,
+    initial: NotImplementedType = None,
+    where: NotImplementedType = None,
+):
+    if a.is_complex():
+        raise NotImplementedError(f"amax with dtype={a.dtype}")
+
+    return a.amax(axis)
+
+
+max = amax
+
+
+@_deco_axis_expand
+def amin(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    out: Optional[OutArray] = None,
+    keepdims: KeepDims = False,
+    initial: NotImplementedType = None,
+    where: NotImplementedType = None,
+):
+    if a.is_complex():
+        raise NotImplementedError(f"amin with dtype={a.dtype}")
+
+    return a.amin(axis)
+
+
+min = amin
+
+
+@_deco_axis_expand
+def ptp(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    out: Optional[OutArray] = None,
+    keepdims: KeepDims = False,
+):
+    return a.amax(axis) - a.amin(axis)
+
+
+@_deco_axis_expand
+def sum(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    dtype: Optional[DTypeLike] = None,
+    out: Optional[OutArray] = None,
+    keepdims: KeepDims = False,
+    initial: NotImplementedType = None,
+    where: NotImplementedType = None,
+):
+    assert dtype is None or isinstance(dtype, torch.dtype)
+
+    if dtype == torch.bool:
+        dtype = _dtypes_impl.default_dtypes().int_dtype
+
+    axis_kw = {} if axis is None else {"dim": axis}
+    return a.sum(dtype=dtype, **axis_kw)
+
+
+@_deco_axis_expand
+def prod(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    dtype: Optional[DTypeLike] = None,
+    out: Optional[OutArray] = None,
+    keepdims: KeepDims = False,
+    initial: NotImplementedType = None,
+    where: NotImplementedType = None,
+):
+    axis = _util.allow_only_single_axis(axis)
+
+    if dtype == torch.bool:
+        dtype = _dtypes_impl.default_dtypes().int_dtype
+
+    axis_kw = {} if axis is None else {"dim": axis}
+    return a.prod(dtype=dtype, **axis_kw)
+
+
+product = prod
+
+
+@_deco_axis_expand
+def mean(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    dtype: Optional[DTypeLike] = None,
+    out: Optional[OutArray] = None,
+    keepdims: KeepDims = False,
+    *,
+    where: NotImplementedType = None,
+):
+    dtype = _atleast_float(dtype, a.dtype)
+
+    axis_kw = {} if axis is None else {"dim": axis}
+    result = a.mean(dtype=dtype, **axis_kw)
+
+    return result
+
+
+@_deco_axis_expand
+def std(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    dtype: Optional[DTypeLike] = None,
+    out: Optional[OutArray] = None,
+    ddof=0,
+    keepdims: KeepDims = False,
+    *,
+    where: NotImplementedType = None,
+):
+    in_dtype = dtype
+    dtype = _atleast_float(dtype, a.dtype)
+    tensor = _util.cast_if_needed(a, dtype)
+    result = tensor.std(dim=axis, correction=ddof)
+    return _util.cast_if_needed(result, in_dtype)
+
+
+@_deco_axis_expand
+def var(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    dtype: Optional[DTypeLike] = None,
+    out: Optional[OutArray] = None,
+    ddof=0,
+    keepdims: KeepDims = False,
+    *,
+    where: NotImplementedType = None,
+):
+    in_dtype = dtype
+    dtype = _atleast_float(dtype, a.dtype)
+    tensor = _util.cast_if_needed(a, dtype)
+    result = tensor.var(dim=axis, correction=ddof)
+    return _util.cast_if_needed(result, in_dtype)
+
+
+# cumsum / cumprod are almost reductions:
+#   1. no keepdims
+#   2. axis=None flattens
+
+
+def cumsum(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    dtype: Optional[DTypeLike] = None,
+    out: Optional[OutArray] = None,
+):
+    if dtype == torch.bool:
+        dtype = _dtypes_impl.default_dtypes().int_dtype
+    if dtype is None:
+        dtype = a.dtype
+
+    (a,), axis = _util.axis_none_flatten(a, axis=axis)
+    axis = _util.normalize_axis_index(axis, a.ndim)
+
+    return a.cumsum(axis=axis, dtype=dtype)
+
+
+def cumprod(
+    a: ArrayLike,
+    axis: AxisLike = None,
+    dtype: Optional[DTypeLike] = None,
+    out: Optional[OutArray] = None,
+):
+    if dtype == torch.bool:
+        dtype = _dtypes_impl.default_dtypes().int_dtype
+    if dtype is None:
+        dtype = a.dtype
+
+    (a,), axis = _util.axis_none_flatten(a, axis=axis)
+    axis = _util.normalize_axis_index(axis, a.ndim)
+
+    return a.cumprod(axis=axis, dtype=dtype)
+
+
+cumproduct = cumprod
+
+
+def average(
+    a: ArrayLike,
+    axis=None,
+    weights: ArrayLike = None,
+    returned=False,
+    *,
+    keepdims=False,
+):
+    if weights is None:
+        result = mean(a, axis=axis)
+        wsum = torch.as_tensor(a.numel() / result.numel(), dtype=result.dtype)
+    else:
+        if not a.dtype.is_floating_point:
+            a = a.double()
+
+        # axis & weights
+        if a.shape != weights.shape:
+            if axis is None:
+                raise TypeError(
+                    "Axis must be specified when shapes of a and weights differ."
+                )
+            if weights.ndim != 1:
+                raise TypeError(
+                    "1D weights expected when shapes of a and weights differ."
+                )
+            if weights.shape[0] != a.shape[axis]:
+                raise ValueError(
+                    "Length of weights not compatible with specified axis."
+                )
+
+            # setup weight to broadcast along axis
+            weights = torch.broadcast_to(weights, (a.ndim - 1) * (1,) + weights.shape)
+            weights = weights.swapaxes(-1, axis)
+
+        # do the work
+        result_dtype = _dtypes_impl.result_type_impl(a, weights)
+        numerator = sum(a * weights, axis, dtype=result_dtype)
+        wsum = sum(weights, axis, dtype=result_dtype)
+        result = numerator / wsum
+
+    # We process keepdims manually because the decorator does not deal with variadic returns
+    if keepdims:
+        result = _util.apply_keepdims(result, axis, a.ndim)
+
+    if returned:
+        if wsum.shape != result.shape:
+            wsum = torch.broadcast_to(wsum, result.shape).clone()
+        return result, wsum
+    else:
+        return result
+
+
+# Not using deco_axis_expand as it assumes that axis is the second arg
+def quantile(
+    a: ArrayLike,
+    q: ArrayLike,
+    axis: AxisLike = None,
+    out: Optional[OutArray] = None,
+    overwrite_input=False,
+    method="linear",
+    keepdims: KeepDims = False,
+    *,
+    interpolation: NotImplementedType = None,
+):
+    if overwrite_input:
+        # raise NotImplementedError("overwrite_input in quantile not implemented.")
+        # NumPy documents that `overwrite_input` MAY modify inputs:
+        # https://numpy.org/doc/stable/reference/generated/numpy.percentile.html#numpy-percentile
+        # Here we choose to work out-of-place because why not.
+        pass
+
+    if not a.dtype.is_floating_point:
+        dtype = _dtypes_impl.default_dtypes().float_dtype
+        a = a.to(dtype)
+
+    # edge case: torch.quantile only supports float32 and float64
+    if a.dtype == torch.float16:
+        a = a.to(torch.float32)
+
+    if axis is None:
+        a = a.flatten()
+        q = q.flatten()
+        axis = (0,)
+    else:
+        axis = _util.normalize_axis_tuple(axis, a.ndim)
+
+    # FIXME(Mario) Doesn't np.quantile accept a tuple?
+    # torch.quantile does accept a number. If we don't want to implement the tuple behaviour
+    # (it's deffo low prio) change `normalize_axis_tuple` into a normalize_axis index above.
+    axis = _util.allow_only_single_axis(axis)
+
+    q = _util.cast_if_needed(q, a.dtype)
+
+    return torch.quantile(a, q, axis=axis, interpolation=method)
+
+
+def percentile(
+    a: ArrayLike,
+    q: ArrayLike,
+    axis: AxisLike = None,
+    out: Optional[OutArray] = None,
+    overwrite_input=False,
+    method="linear",
+    keepdims: KeepDims = False,
+    *,
+    interpolation: NotImplementedType = None,
+):
+    # np.percentile(float_tensor, 30) : q.dtype is int64 => q / 100.0 is float32
+    if _dtypes_impl.python_type_for_torch(q.dtype) == int:
+        q = q.to(_dtypes_impl.default_dtypes().float_dtype)
+    qq = q / 100.0
+
+    return quantile(
+        a,
+        qq,
+        axis=axis,
+        overwrite_input=overwrite_input,
+        method=method,
+        keepdims=keepdims,
+        interpolation=interpolation,
+    )
+
+
+def median(
+    a: ArrayLike,
+    axis=None,
+    out: Optional[OutArray] = None,
+    overwrite_input=False,
+    keepdims: KeepDims = False,
+):
+    return quantile(
+        a,
+        torch.as_tensor(0.5),
+        axis=axis,
+        overwrite_input=overwrite_input,
+        out=out,
+        keepdims=keepdims,
+    )

venv/lib/python3.10/site-packages/torch/_numpy/_ufuncs.py

@@ -0,0 +1,334 @@
+# mypy: ignore-errors
+
+from __future__ import annotations
+
+from typing import Optional
+
+import torch
+
+from . import _binary_ufuncs_impl, _dtypes_impl, _unary_ufuncs_impl, _util
+from ._normalizations import (
+    ArrayLike,
+    ArrayLikeOrScalar,
+    CastingModes,
+    DTypeLike,
+    normalizer,
+    NotImplementedType,
+    OutArray,
+)
+
+
+def _ufunc_postprocess(result, out, casting):
+    if out is not None:
+        result = _util.typecast_tensor(result, out.dtype.torch_dtype, casting)
+        result = torch.broadcast_to(result, out.shape)
+    return result
+
+
+# ############# Binary ufuncs ######################
+
+_binary = [
+    name
+    for name in dir(_binary_ufuncs_impl)
+    if not name.startswith("_") and name not in ["torch", "matmul", "divmod", "ldexp"]
+]
+
+
+NEP50_FUNCS = (
+    "add",
+    "subtract",
+    "multiply",
+    "floor_divide",
+    "true_divide",
+    "divide",
+    "remainder",
+    "bitwise_and",
+    "bitwise_or",
+    "bitwise_xor",
+    "bitwise_left_shift",
+    "bitwise_right_shift",
+    "hypot",
+    "arctan2",
+    "logaddexp",
+    "logaddexp2",
+    "heaviside",
+    "copysign",
+    "fmax",
+    "minimum",
+    "fmin",
+    "maximum",
+    "fmod",
+    "gcd",
+    "lcm",
+    "pow",
+)
+
+
+def deco_binary_ufunc(torch_func):
+    """Common infra for binary ufuncs.
+
+    Normalize arguments, sort out type casting, broadcasting and delegate to
+    the pytorch functions for the actual work.
+    """
+
+    @normalizer
+    def wrapped(
+        x1: ArrayLikeOrScalar,
+        x2: ArrayLikeOrScalar,
+        /,
+        out: Optional[OutArray] = None,
+        *,
+        where: NotImplementedType = True,
+        casting: Optional[CastingModes] = "same_kind",
+        order: NotImplementedType = "K",
+        dtype: Optional[DTypeLike] = None,
+        subok: NotImplementedType = False,
+        signature: NotImplementedType = None,
+        extobj: NotImplementedType = None,
+    ):
+        if dtype is not None:
+
+            def cast(x, dtype):
+                if isinstance(x, torch.Tensor):
+                    return _util.typecast_tensor(x, dtype, casting)
+                else:
+                    return torch.as_tensor(x, dtype=dtype)
+
+            x1 = cast(x1, dtype)
+            x2 = cast(x2, dtype)
+        elif isinstance(x1, torch.Tensor) and isinstance(x2, torch.Tensor):
+            dtype = _dtypes_impl.result_type_impl(x1, x2)
+            x1, x2 = _util.typecast_tensors((x1, x2), dtype, casting)
+        else:
+            x1, x2 = _dtypes_impl.nep50_to_tensors(
+                x1, x2, torch_func.__name__ in NEP50_FUNCS, torch_func.__name__
+            )
+
+        result = torch_func(x1, x2)
+
+        return _ufunc_postprocess(result, out, casting)
+
+    wrapped.__qualname__ = torch_func.__name__
+    wrapped.__name__ = torch_func.__name__
+
+    return wrapped
+
+
+# matmul's signature is _slightly_ different from other ufuncs:
+# - no where=...
+# - additional axis=..., axes=...
+# - no NEP50 scalars in or out
+@normalizer
+def matmul(
+    x1: ArrayLike,
+    x2: ArrayLike,
+    /,
+    out: Optional[OutArray] = None,
+    *,
+    casting: Optional[CastingModes] = "same_kind",
+    order: NotImplementedType = "K",
+    dtype: Optional[DTypeLike] = None,
+    subok: NotImplementedType = False,
+    signature: NotImplementedType = None,
+    extobj: NotImplementedType = None,
+    axes: NotImplementedType = None,
+    axis: NotImplementedType = None,
+):
+    if dtype is None:
+        dtype = _dtypes_impl.result_type_impl(x1, x2)
+    x1, x2 = _util.typecast_tensors((x1, x2), dtype, casting)
+
+    result = _binary_ufuncs_impl.matmul(x1, x2)
+
+    result = _ufunc_postprocess(result, out, casting)
+    return result
+
+
+# ldexp casting is special : the dtype of the result == dtype of the 1st arg
+@normalizer
+def ldexp(
+    x1: ArrayLikeOrScalar,
+    x2: ArrayLikeOrScalar,
+    /,
+    out: Optional[OutArray] = None,
+    *,
+    where: NotImplementedType = True,
+    casting: Optional[CastingModes] = "same_kind",
+    order: NotImplementedType = "K",
+    dtype: Optional[DTypeLike] = None,
+    subok: NotImplementedType = False,
+    signature: NotImplementedType = None,
+    extobj: NotImplementedType = None,
+):
+    if dtype is not None:
+        if isinstance(x1, torch.Tensor):
+            x1 = _util.typecast_tensor(x1, dtype, casting)
+        else:
+            x1 = torch.as_tensor(x1, dtype=dtype)
+    else:
+        if not isinstance(x1, torch.Tensor):
+            x1 = torch.as_tensor(x1)
+            x1 = _util.cast_int_to_float(x1)
+
+    x2 = torch.as_tensor(x2)
+    # the second arg must be integer
+    if _dtypes_impl._category(x2.dtype) != 1:
+        raise ValueError("ldexp 2nd arg must be integer")
+
+    result = _binary_ufuncs_impl.ldexp(x1, x2)
+
+    if x1.dtype == torch.float16:
+        # torch.ldexp(f16, int) -> f32, undo it
+        result = result.to(torch.float16)
+
+    return _ufunc_postprocess(result, out, casting)
+
+
+# nin=2, nout=2
+@normalizer
+def divmod(
+    x1: ArrayLike,
+    x2: ArrayLike,
+    out1: Optional[OutArray] = None,
+    out2: Optional[OutArray] = None,
+    /,
+    out: tuple[Optional[OutArray], Optional[OutArray]] = (None, None),
+    *,
+    where: NotImplementedType = True,
+    casting: Optional[CastingModes] = "same_kind",
+    order: NotImplementedType = "K",
+    dtype: Optional[DTypeLike] = None,
+    subok: NotImplementedType = False,
+    signature: NotImplementedType = None,
+    extobj: NotImplementedType = None,
+):
+    # make sure we either have no out arrays at all, or there is either
+    # out1, out2, or out=tuple, but not both
+    num_outs = sum(x is not None for x in [out1, out2])
+    if num_outs == 1:
+        raise ValueError("both out1 and out2 need to be provided")
+    elif num_outs == 2:
+        o1, o2 = out
+        if o1 is not None or o2 is not None:
+            raise TypeError(
+                "cannot specify 'out' as both a positional and keyword argument"
+            )
+    else:
+        out1, out2 = out
+
+    if dtype is None:
+        dtype = _dtypes_impl.result_type_impl(x1, x2)
+    x1, x2 = _util.typecast_tensors((x1, x2), dtype, casting)
+
+    quot, rem = _binary_ufuncs_impl.divmod(x1, x2)
+
+    quot = _ufunc_postprocess(quot, out1, casting)
+    rem = _ufunc_postprocess(rem, out2, casting)
+    return quot, rem
+
+
+#
+# Attach ufuncs to this module, for a further export to the public namespace in __init__.py
+#
+for name in _binary:
+    ufunc = getattr(_binary_ufuncs_impl, name)
+    vars()[name] = deco_binary_ufunc(ufunc)
+
+
+def modf(x, /, *args, **kwds):
+    quot, rem = divmod(x, 1, *args, **kwds)
+    return rem, quot
+
+
+_binary = _binary + ["divmod", "modf", "matmul", "ldexp"]
+
+
+# ############# Unary ufuncs ######################
+
+
+_unary = [
+    name
+    for name in dir(_unary_ufuncs_impl)
+    if not name.startswith("_") and name != "torch"
+]
+
+
+# these are ufunc(int) -> float
+_fp_unary = [
+    "arccos",
+    "arccosh",
+    "arcsin",
+    "arcsinh",
+    "arctan",
+    "arctanh",
+    "cbrt",
+    "cos",
+    "cosh",
+    "deg2rad",
+    "degrees",
+    "exp",
+    "exp2",
+    "expm1",
+    "log",
+    "log10",
+    "log1p",
+    "log2",
+    "rad2deg",
+    "radians",
+    "reciprocal",
+    "sin",
+    "sinh",
+    "sqrt",
+    "square",
+    "tan",
+    "tanh",
+    "trunc",
+]
+
+
+def deco_unary_ufunc(torch_func):
+    """Common infra for unary ufuncs.
+
+    Normalize arguments, sort out type casting, broadcasting and delegate to
+    the pytorch functions for the actual work.
+    """
+
+    @normalizer
+    def wrapped(
+        x: ArrayLike,
+        /,
+        out: Optional[OutArray] = None,
+        *,
+        where=True,
+        casting: Optional[CastingModes] = "same_kind",
+        order="K",
+        dtype: Optional[DTypeLike] = None,
+        subok: NotImplementedType = False,
+        signature=None,
+        extobj=None,
+    ):
+        if dtype is not None:
+            x = _util.typecast_tensor(x, dtype, casting)
+
+        if torch_func.__name__ in _fp_unary:
+            x = _util.cast_int_to_float(x)
+
+        result = torch_func(x)
+        result = _ufunc_postprocess(result, out, casting)
+        return result
+
+    wrapped.__qualname__ = torch_func.__name__
+    wrapped.__name__ = torch_func.__name__
+
+    return wrapped
+
+
+#
+# Attach ufuncs to this module, for a further export to the public namespace in __init__.py
+#
+for name in _unary:
+    ufunc = getattr(_unary_ufuncs_impl, name)
+    vars()[name] = deco_unary_ufunc(ufunc)
+
+
+__all__ = _binary + _unary  # noqa: PLE0605

venv/lib/python3.10/site-packages/torch/_numpy/_unary_ufuncs_impl.py

@@ -0,0 +1,73 @@
+# mypy: ignore-errors
+
+"""Export torch work functions for unary ufuncs, rename/tweak to match numpy.
+This listing is further exported to public symbols in the `_numpy/_ufuncs.py` module.
+"""
+
+import torch
+
+from torch import (  # noqa: F401
+    absolute as fabs,  # noqa: F401
+    arccos,  # noqa: F401
+    arccosh,  # noqa: F401
+    arcsin,  # noqa: F401
+    arcsinh,  # noqa: F401
+    arctan,  # noqa: F401
+    arctanh,  # noqa: F401
+    bitwise_not,  # noqa: F401
+    bitwise_not as invert,  # noqa: F401
+    ceil,  # noqa: F401
+    conj_physical as conjugate,  # noqa: F401
+    cos,  # noqa: F401
+    cosh,  # noqa: F401
+    deg2rad,  # noqa: F401
+    deg2rad as radians,  # noqa: F401
+    exp,  # noqa: F401
+    exp2,  # noqa: F401
+    expm1,  # noqa: F401
+    floor,  # noqa: F401
+    isfinite,  # noqa: F401
+    isinf,  # noqa: F401
+    isnan,  # noqa: F401
+    log,  # noqa: F401
+    log10,  # noqa: F401
+    log1p,  # noqa: F401
+    log2,  # noqa: F401
+    logical_not,  # noqa: F401
+    negative,  # noqa: F401
+    rad2deg,  # noqa: F401
+    rad2deg as degrees,  # noqa: F401
+    reciprocal,  # noqa: F401
+    round as fix,  # noqa: F401
+    round as rint,  # noqa: F401
+    sign,  # noqa: F401
+    signbit,  # noqa: F401
+    sin,  # noqa: F401
+    sinh,  # noqa: F401
+    sqrt,  # noqa: F401
+    square,  # noqa: F401
+    tan,  # noqa: F401
+    tanh,  # noqa: F401
+    trunc,  # noqa: F401
+)
+
+
+# special cases: torch does not export these names
+def cbrt(x):
+    return torch.pow(x, 1 / 3)
+
+
+def positive(x):
+    return +x
+
+
+def absolute(x):
+    # work around torch.absolute not impl for bools
+    if x.dtype == torch.bool:
+        return x
+    return torch.absolute(x)
+
+
+# TODO set __name__ and __qualname__
+abs = absolute
+conj = conjugate

venv/lib/python3.10/site-packages/torch/_numpy/_util.py

@@ -0,0 +1,261 @@
+# mypy: ignore-errors
+
+"""Assorted utilities, which do not need anything other then torch and stdlib.
+"""
+
+import operator
+
+import torch
+
+from . import _dtypes_impl
+
+
+# https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/misc_util.py#L497-L504
+def is_sequence(seq):
+    if isinstance(seq, str):
+        return False
+    try:
+        len(seq)
+    except Exception:
+        return False
+    return True
+
+
+class AxisError(ValueError, IndexError):
+    pass
+
+
+class UFuncTypeError(TypeError, RuntimeError):
+    pass
+
+
+def cast_if_needed(tensor, dtype):
+    # NB: no casting if dtype=None
+    if dtype is not None and tensor.dtype != dtype:
+        tensor = tensor.to(dtype)
+    return tensor
+
+
+def cast_int_to_float(x):
+    # cast integers and bools to the default float dtype
+    if _dtypes_impl._category(x.dtype) < 2:
+        x = x.to(_dtypes_impl.default_dtypes().float_dtype)
+    return x
+
+
+# a replica of the version in ./numpy/numpy/core/src/multiarray/common.h
+def normalize_axis_index(ax, ndim, argname=None):
+    if not (-ndim <= ax < ndim):
+        raise AxisError(f"axis {ax} is out of bounds for array of dimension {ndim}")
+    if ax < 0:
+        ax += ndim
+    return ax
+
+
+# from https://github.com/numpy/numpy/blob/main/numpy/core/numeric.py#L1378
+def normalize_axis_tuple(axis, ndim, argname=None, allow_duplicate=False):
+    """
+    Normalizes an axis argument into a tuple of non-negative integer axes.
+
+    This handles shorthands such as ``1`` and converts them to ``(1,)``,
+    as well as performing the handling of negative indices covered by
+    `normalize_axis_index`.
+
+    By default, this forbids axes from being specified multiple times.
+    Used internally by multi-axis-checking logic.
+
+    Parameters
+    ----------
+    axis : int, iterable of int
+        The un-normalized index or indices of the axis.
+    ndim : int
+        The number of dimensions of the array that `axis` should be normalized
+        against.
+    argname : str, optional
+        A prefix to put before the error message, typically the name of the
+        argument.
+    allow_duplicate : bool, optional
+        If False, the default, disallow an axis from being specified twice.
+
+    Returns
+    -------
+    normalized_axes : tuple of int
+        The normalized axis index, such that `0 <= normalized_axis < ndim`
+    """
+    # Optimization to speed-up the most common cases.
+    if type(axis) not in (tuple, list):
+        try:
+            axis = [operator.index(axis)]
+        except TypeError:
+            pass
+    # Going via an iterator directly is slower than via list comprehension.
+    axis = tuple([normalize_axis_index(ax, ndim, argname) for ax in axis])
+    if not allow_duplicate and len(set(axis)) != len(axis):
+        if argname:
+            raise ValueError(f"repeated axis in `{argname}` argument")
+        else:
+            raise ValueError("repeated axis")
+    return axis
+
+
+def allow_only_single_axis(axis):
+    if axis is None:
+        return axis
+    if len(axis) != 1:
+        raise NotImplementedError("does not handle tuple axis")
+    return axis[0]
+
+
+def expand_shape(arr_shape, axis):
+    # taken from numpy 1.23.x, expand_dims function
+    if type(axis) not in (list, tuple):
+        axis = (axis,)
+    out_ndim = len(axis) + len(arr_shape)
+    axis = normalize_axis_tuple(axis, out_ndim)
+    shape_it = iter(arr_shape)
+    shape = [1 if ax in axis else next(shape_it) for ax in range(out_ndim)]
+    return shape
+
+
+def apply_keepdims(tensor, axis, ndim):
+    if axis is None:
+        # tensor was a scalar
+        shape = (1,) * ndim
+        tensor = tensor.expand(shape).contiguous()
+    else:
+        shape = expand_shape(tensor.shape, axis)
+        tensor = tensor.reshape(shape)
+    return tensor
+
+
+def axis_none_flatten(*tensors, axis=None):
+    """Flatten the arrays if axis is None."""
+    if axis is None:
+        tensors = tuple(ar.flatten() for ar in tensors)
+        return tensors, 0
+    else:
+        return tensors, axis
+
+
+def typecast_tensor(t, target_dtype, casting):
+    """Dtype-cast tensor to target_dtype.
+
+    Parameters
+    ----------
+    t : torch.Tensor
+        The tensor to cast
+    target_dtype : torch dtype object
+        The array dtype to cast all tensors to
+    casting : str
+        The casting mode, see `np.can_cast`
+
+     Returns
+     -------
+    `torch.Tensor` of the `target_dtype` dtype
+
+     Raises
+     ------
+     ValueError
+        if the argument cannot be cast according to the `casting` rule
+
+    """
+    can_cast = _dtypes_impl.can_cast_impl
+
+    if not can_cast(t.dtype, target_dtype, casting=casting):
+        raise TypeError(
+            f"Cannot cast array data from {t.dtype} to"
+            f" {target_dtype} according to the rule '{casting}'"
+        )
+    return cast_if_needed(t, target_dtype)
+
+
+def typecast_tensors(tensors, target_dtype, casting):
+    return tuple(typecast_tensor(t, target_dtype, casting) for t in tensors)
+
+
+def _try_convert_to_tensor(obj):
+    try:
+        tensor = torch.as_tensor(obj)
+    except Exception as e:
+        mesg = f"failed to convert {obj} to ndarray. \nInternal error is: {str(e)}."
+        raise NotImplementedError(mesg)  # noqa: TRY200
+    return tensor
+
+
+def _coerce_to_tensor(obj, dtype=None, copy=False, ndmin=0):
+    """The core logic of the array(...) function.
+
+    Parameters
+    ----------
+    obj : tensor_like
+        The thing to coerce
+    dtype : torch.dtype object or None
+        Coerce to this torch dtype
+    copy : bool
+        Copy or not
+    ndmin : int
+        The results as least this many dimensions
+    is_weak : bool
+        Whether obj is a weakly typed python scalar.
+
+    Returns
+    -------
+    tensor : torch.Tensor
+        a tensor object with requested dtype, ndim and copy semantics.
+
+    Notes
+    -----
+    This is almost a "tensor_like" coersion function. Does not handle wrapper
+    ndarrays (those should be handled in the ndarray-aware layer prior to
+    invoking this function).
+    """
+    if isinstance(obj, torch.Tensor):
+        tensor = obj
+    else:
+        # tensor.dtype is the pytorch default, typically float32. If obj's elements
+        # are not exactly representable in float32, we've lost precision:
+        # >>> torch.as_tensor(1e12).item() - 1e12
+        # -4096.0
+        default_dtype = torch.get_default_dtype()
+        torch.set_default_dtype(_dtypes_impl.get_default_dtype_for(torch.float32))
+        try:
+            tensor = _try_convert_to_tensor(obj)
+        finally:
+            torch.set_default_dtype(default_dtype)
+
+    # type cast if requested
+    tensor = cast_if_needed(tensor, dtype)
+
+    # adjust ndim if needed
+    ndim_extra = ndmin - tensor.ndim
+    if ndim_extra > 0:
+        tensor = tensor.view((1,) * ndim_extra + tensor.shape)
+
+    # copy if requested
+    if copy:
+        tensor = tensor.clone()
+
+    return tensor
+
+
+def ndarrays_to_tensors(*inputs):
+    """Convert all ndarrays from `inputs` to tensors. (other things are intact)"""
+    from ._ndarray import ndarray
+
+    if len(inputs) == 0:
+        return ValueError()
+    elif len(inputs) == 1:
+        input_ = inputs[0]
+        if isinstance(input_, ndarray):
+            return input_.tensor
+        elif isinstance(input_, tuple):
+            result = []
+            for sub_input in input_:
+                sub_result = ndarrays_to_tensors(sub_input)
+                result.append(sub_result)
+            return tuple(result)
+        else:
+            return input_
+    else:
+        assert isinstance(inputs, tuple)  # sanity check
+        return ndarrays_to_tensors(inputs)

venv/lib/python3.10/site-packages/torch/_numpy/fft.py

@@ -0,0 +1,130 @@
+# mypy: ignore-errors
+
+from __future__ import annotations
+
+import functools
+
+import torch
+
+from . import _dtypes_impl, _util
+from ._normalizations import ArrayLike, normalizer
+
+
+def upcast(func):
+    """NumPy fft casts inputs to 64 bit and *returns 64-bit results*."""
+
+    @functools.wraps(func)
+    def wrapped(tensor, *args, **kwds):
+        target_dtype = (
+            _dtypes_impl.default_dtypes().complex_dtype
+            if tensor.is_complex()
+            else _dtypes_impl.default_dtypes().float_dtype
+        )
+        tensor = _util.cast_if_needed(tensor, target_dtype)
+        return func(tensor, *args, **kwds)
+
+    return wrapped
+
+
+@normalizer
+@upcast
+def fft(a: ArrayLike, n=None, axis=-1, norm=None):
+    return torch.fft.fft(a, n, dim=axis, norm=norm)
+
+
+@normalizer
+@upcast
+def ifft(a: ArrayLike, n=None, axis=-1, norm=None):
+    return torch.fft.ifft(a, n, dim=axis, norm=norm)
+
+
+@normalizer
+@upcast
+def rfft(a: ArrayLike, n=None, axis=-1, norm=None):
+    return torch.fft.rfft(a, n, dim=axis, norm=norm)
+
+
+@normalizer
+@upcast
+def irfft(a: ArrayLike, n=None, axis=-1, norm=None):
+    return torch.fft.irfft(a, n, dim=axis, norm=norm)
+
+
+@normalizer
+@upcast
+def fftn(a: ArrayLike, s=None, axes=None, norm=None):
+    return torch.fft.fftn(a, s, dim=axes, norm=norm)
+
+
+@normalizer
+@upcast
+def ifftn(a: ArrayLike, s=None, axes=None, norm=None):
+    return torch.fft.ifftn(a, s, dim=axes, norm=norm)
+
+
+@normalizer
+@upcast
+def rfftn(a: ArrayLike, s=None, axes=None, norm=None):
+    return torch.fft.rfftn(a, s, dim=axes, norm=norm)
+
+
+@normalizer
+@upcast
+def irfftn(a: ArrayLike, s=None, axes=None, norm=None):
+    return torch.fft.irfftn(a, s, dim=axes, norm=norm)
+
+
+@normalizer
+@upcast
+def fft2(a: ArrayLike, s=None, axes=(-2, -1), norm=None):
+    return torch.fft.fft2(a, s, dim=axes, norm=norm)
+
+
+@normalizer
+@upcast
+def ifft2(a: ArrayLike, s=None, axes=(-2, -1), norm=None):
+    return torch.fft.ifft2(a, s, dim=axes, norm=norm)
+
+
+@normalizer
+@upcast
+def rfft2(a: ArrayLike, s=None, axes=(-2, -1), norm=None):
+    return torch.fft.rfft2(a, s, dim=axes, norm=norm)
+
+
+@normalizer
+@upcast
+def irfft2(a: ArrayLike, s=None, axes=(-2, -1), norm=None):
+    return torch.fft.irfft2(a, s, dim=axes, norm=norm)
+
+
+@normalizer
+@upcast
+def hfft(a: ArrayLike, n=None, axis=-1, norm=None):
+    return torch.fft.hfft(a, n, dim=axis, norm=norm)
+
+
+@normalizer
+@upcast
+def ihfft(a: ArrayLike, n=None, axis=-1, norm=None):
+    return torch.fft.ihfft(a, n, dim=axis, norm=norm)
+
+
+@normalizer
+def fftfreq(n, d=1.0):
+    return torch.fft.fftfreq(n, d)
+
+
+@normalizer
+def rfftfreq(n, d=1.0):
+    return torch.fft.rfftfreq(n, d)
+
+
+@normalizer
+def fftshift(x: ArrayLike, axes=None):
+    return torch.fft.fftshift(x, axes)
+
+
+@normalizer
+def ifftshift(x: ArrayLike, axes=None):
+    return torch.fft.ifftshift(x, axes)

venv/lib/python3.10/site-packages/torch/_numpy/linalg.py

@@ -0,0 +1,239 @@
+# mypy: ignore-errors
+
+from __future__ import annotations
+
+import functools
+import math
+from typing import Sequence
+
+import torch
+
+from . import _dtypes_impl, _util
+from ._normalizations import ArrayLike, KeepDims, normalizer
+
+
+class LinAlgError(Exception):
+    pass
+
+
+def _atleast_float_1(a):
+    if not (a.dtype.is_floating_point or a.dtype.is_complex):
+        a = a.to(_dtypes_impl.default_dtypes().float_dtype)
+    return a
+
+
+def _atleast_float_2(a, b):
+    dtyp = _dtypes_impl.result_type_impl(a, b)
+    if not (dtyp.is_floating_point or dtyp.is_complex):
+        dtyp = _dtypes_impl.default_dtypes().float_dtype
+
+    a = _util.cast_if_needed(a, dtyp)
+    b = _util.cast_if_needed(b, dtyp)
+    return a, b
+
+
+def linalg_errors(func):
+    @functools.wraps(func)
+    def wrapped(*args, **kwds):
+        try:
+            return func(*args, **kwds)
+        except torch._C._LinAlgError as e:
+            raise LinAlgError(*e.args)  # noqa: TRY200
+
+    return wrapped
+
+
+# ### Matrix and vector products ###
+
+
+@normalizer
+@linalg_errors
+def matrix_power(a: ArrayLike, n):
+    a = _atleast_float_1(a)
+    return torch.linalg.matrix_power(a, n)
+
+
+@normalizer
+@linalg_errors
+def multi_dot(inputs: Sequence[ArrayLike], *, out=None):
+    return torch.linalg.multi_dot(inputs)
+
+
+# ### Solving equations and inverting matrices ###
+
+
+@normalizer
+@linalg_errors
+def solve(a: ArrayLike, b: ArrayLike):
+    a, b = _atleast_float_2(a, b)
+    return torch.linalg.solve(a, b)
+
+
+@normalizer
+@linalg_errors
+def lstsq(a: ArrayLike, b: ArrayLike, rcond=None):
+    a, b = _atleast_float_2(a, b)
+    # NumPy is using gelsd: https://github.com/numpy/numpy/blob/v1.24.0/numpy/linalg/umath_linalg.cpp#L3991
+    # on CUDA, only `gels` is available though, so use it instead
+    driver = "gels" if a.is_cuda or b.is_cuda else "gelsd"
+    return torch.linalg.lstsq(a, b, rcond=rcond, driver=driver)
+
+
+@normalizer
+@linalg_errors
+def inv(a: ArrayLike):
+    a = _atleast_float_1(a)
+    result = torch.linalg.inv(a)
+    return result
+
+
+@normalizer
+@linalg_errors
+def pinv(a: ArrayLike, rcond=1e-15, hermitian=False):
+    a = _atleast_float_1(a)
+    return torch.linalg.pinv(a, rtol=rcond, hermitian=hermitian)
+
+
+@normalizer
+@linalg_errors
+def tensorsolve(a: ArrayLike, b: ArrayLike, axes=None):
+    a, b = _atleast_float_2(a, b)
+    return torch.linalg.tensorsolve(a, b, dims=axes)
+
+
+@normalizer
+@linalg_errors
+def tensorinv(a: ArrayLike, ind=2):
+    a = _atleast_float_1(a)
+    return torch.linalg.tensorinv(a, ind=ind)
+
+
+# ### Norms and other numbers ###
+
+
+@normalizer
+@linalg_errors
+def det(a: ArrayLike):
+    a = _atleast_float_1(a)
+    return torch.linalg.det(a)
+
+
+@normalizer
+@linalg_errors
+def slogdet(a: ArrayLike):
+    a = _atleast_float_1(a)
+    return torch.linalg.slogdet(a)
+
+
+@normalizer
+@linalg_errors
+def cond(x: ArrayLike, p=None):
+    x = _atleast_float_1(x)
+
+    # check if empty
+    # cf: https://github.com/numpy/numpy/blob/v1.24.0/numpy/linalg/linalg.py#L1744
+    if x.numel() == 0 and math.prod(x.shape[-2:]) == 0:
+        raise LinAlgError("cond is not defined on empty arrays")
+
+    result = torch.linalg.cond(x, p=p)
+
+    # Convert nans to infs (numpy does it in a data-dependent way, depending on
+    # whether the input array has nans or not)
+    # XXX: NumPy does this: https://github.com/numpy/numpy/blob/v1.24.0/numpy/linalg/linalg.py#L1744
+    return torch.where(torch.isnan(result), float("inf"), result)
+
+
+@normalizer
+@linalg_errors
+def matrix_rank(a: ArrayLike, tol=None, hermitian=False):
+    a = _atleast_float_1(a)
+
+    if a.ndim < 2:
+        return int((a != 0).any())
+
+    if tol is None:
+        # follow https://github.com/numpy/numpy/blob/v1.24.0/numpy/linalg/linalg.py#L1885
+        atol = 0
+        rtol = max(a.shape[-2:]) * torch.finfo(a.dtype).eps
+    else:
+        atol, rtol = tol, 0
+    return torch.linalg.matrix_rank(a, atol=atol, rtol=rtol, hermitian=hermitian)
+
+
+@normalizer
+@linalg_errors
+def norm(x: ArrayLike, ord=None, axis=None, keepdims: KeepDims = False):
+    x = _atleast_float_1(x)
+    return torch.linalg.norm(x, ord=ord, dim=axis)
+
+
+# ### Decompositions ###
+
+
+@normalizer
+@linalg_errors
+def cholesky(a: ArrayLike):
+    a = _atleast_float_1(a)
+    return torch.linalg.cholesky(a)
+
+
+@normalizer
+@linalg_errors
+def qr(a: ArrayLike, mode="reduced"):
+    a = _atleast_float_1(a)
+    result = torch.linalg.qr(a, mode=mode)
+    if mode == "r":
+        # match NumPy
+        result = result.R
+    return result
+
+
+@normalizer
+@linalg_errors
+def svd(a: ArrayLike, full_matrices=True, compute_uv=True, hermitian=False):
+    a = _atleast_float_1(a)
+    if not compute_uv:
+        return torch.linalg.svdvals(a)
+
+    # NB: ignore the hermitian= argument (no pytorch equivalent)
+    result = torch.linalg.svd(a, full_matrices=full_matrices)
+    return result
+
+
+# ### Eigenvalues and eigenvectors ###
+
+
+@normalizer
+@linalg_errors
+def eig(a: ArrayLike):
+    a = _atleast_float_1(a)
+    w, vt = torch.linalg.eig(a)
+
+    if not a.is_complex() and w.is_complex() and (w.imag == 0).all():
+        w = w.real
+        vt = vt.real
+    return w, vt
+
+
+@normalizer
+@linalg_errors
+def eigh(a: ArrayLike, UPLO="L"):
+    a = _atleast_float_1(a)
+    return torch.linalg.eigh(a, UPLO=UPLO)
+
+
+@normalizer
+@linalg_errors
+def eigvals(a: ArrayLike):
+    a = _atleast_float_1(a)
+    result = torch.linalg.eigvals(a)
+    if not a.is_complex() and result.is_complex() and (result.imag == 0).all():
+        result = result.real
+    return result
+
+
+@normalizer
+@linalg_errors
+def eigvalsh(a: ArrayLike, UPLO="L"):
+    a = _atleast_float_1(a)
+    return torch.linalg.eigvalsh(a, UPLO=UPLO)

venv/lib/python3.10/site-packages/torch/_numpy/random.py

@@ -0,0 +1,191 @@
+# mypy: ignore-errors
+
+"""Wrapper to mimic (parts of) np.random API surface.
+
+NumPy has strict guarantees on reproducibility etc; here we don't give any.
+
+Q: default dtype is float64 in numpy
+
+"""
+from __future__ import annotations
+
+import functools
+from math import sqrt
+from typing import Optional
+
+import torch
+
+from . import _dtypes_impl, _util
+from ._normalizations import array_or_scalar, ArrayLike, normalizer
+
+
+__all__ = [
+    "seed",
+    "random_sample",
+    "sample",
+    "random",
+    "rand",
+    "randn",
+    "normal",
+    "choice",
+    "randint",
+    "shuffle",
+    "uniform",
+]
+
+
+def use_numpy_random():
+    # local import to avoid ref cycles
+    import torch._dynamo.config as config
+
+    return config.use_numpy_random_stream
+
+
+def deco_stream(func):
+    @functools.wraps(func)
+    def inner(*args, **kwds):
+        if not use_numpy_random():
+            return func(*args, **kwds)
+        else:
+            import numpy
+
+            from ._ndarray import ndarray
+
+            f = getattr(numpy.random, func.__name__)
+
+            # numpy funcs accept numpy ndarrays, unwrap
+            args = tuple(
+                arg.tensor.numpy() if isinstance(arg, ndarray) else arg for arg in args
+            )
+            kwds = {
+                key: val.tensor.numpy() if isinstance(val, ndarray) else val
+                for key, val in kwds.items()
+            }
+
+            value = f(*args, **kwds)
+
+            # `value` can be either numpy.ndarray or python scalar (or None)
+            if isinstance(value, numpy.ndarray):
+                value = ndarray(torch.as_tensor(value))
+
+            return value
+
+    return inner
+
+
+@deco_stream
+def seed(seed=None):
+    if seed is not None:
+        torch.random.manual_seed(seed)
+
+
+@deco_stream
+def random_sample(size=None):
+    if size is None:
+        size = ()
+    dtype = _dtypes_impl.default_dtypes().float_dtype
+    values = torch.empty(size, dtype=dtype).uniform_()
+    return array_or_scalar(values, return_scalar=size == ())
+
+
+def rand(*size):
+    if size == ():
+        size = None
+    return random_sample(size)
+
+
+sample = random_sample
+random = random_sample
+
+
+@deco_stream
+def uniform(low=0.0, high=1.0, size=None):
+    if size is None:
+        size = ()
+    dtype = _dtypes_impl.default_dtypes().float_dtype
+    values = torch.empty(size, dtype=dtype).uniform_(low, high)
+    return array_or_scalar(values, return_scalar=size == ())
+
+
+@deco_stream
+def randn(*size):
+    dtype = _dtypes_impl.default_dtypes().float_dtype
+    values = torch.randn(size, dtype=dtype)
+    return array_or_scalar(values, return_scalar=size == ())
+
+
+@deco_stream
+def normal(loc=0.0, scale=1.0, size=None):
+    if size is None:
+        size = ()
+    dtype = _dtypes_impl.default_dtypes().float_dtype
+    values = torch.empty(size, dtype=dtype).normal_(loc, scale)
+    return array_or_scalar(values, return_scalar=size == ())
+
+
+@deco_stream
+def shuffle(x):
+    # no @normalizer because we do not cast e.g. lists to tensors
+    from ._ndarray import ndarray
+
+    if isinstance(x, torch.Tensor):
+        tensor = x
+    elif isinstance(x, ndarray):
+        tensor = x.tensor
+    else:
+        raise NotImplementedError("We do not random.shuffle lists in-place")
+
+    perm = torch.randperm(tensor.shape[0])
+    xp = tensor[perm]
+    tensor.copy_(xp)
+
+
+@deco_stream
+def randint(low, high=None, size=None):
+    if size is None:
+        size = ()
+    if not isinstance(size, (tuple, list)):
+        size = (size,)
+    if high is None:
+        low, high = 0, low
+    values = torch.randint(low, high, size=size)
+    return array_or_scalar(values, int, return_scalar=size == ())
+
+
+@deco_stream
+@normalizer
+def choice(a: ArrayLike, size=None, replace=True, p: Optional[ArrayLike] = None):
+    # https://stackoverflow.com/questions/59461811/random-choice-with-pytorch
+    if a.numel() == 1:
+        a = torch.arange(a)
+
+    # TODO: check a.dtype is integer -- cf np.random.choice(3.4) which raises
+
+    # number of draws
+    if size is None:
+        num_el = 1
+    elif _util.is_sequence(size):
+        num_el = 1
+        for el in size:
+            num_el *= el
+    else:
+        num_el = size
+
+    # prepare the probabilities
+    if p is None:
+        p = torch.ones_like(a) / a.shape[0]
+
+    # cf https://github.com/numpy/numpy/blob/main/numpy/random/mtrand.pyx#L973
+    atol = sqrt(torch.finfo(p.dtype).eps)
+    if abs(p.sum() - 1.0) > atol:
+        raise ValueError("probabilities do not sum to 1.")
+
+    # actually sample
+    indices = torch.multinomial(p, num_el, replacement=replace)
+
+    if _util.is_sequence(size):
+        indices = indices.reshape(size)
+
+    samples = a[indices]
+
+    return samples

venv/lib/python3.10/site-packages/torch/nn/backends/thnn.py

@@ -0,0 +1,4 @@
+# this is for historical pickle deserialization, it is not used otherwise
+
+def _get_thnn_function_backend():
+    pass

venv/lib/python3.10/site-packages/torch/nn/parallel/__init__.py

@@ -0,0 +1,14 @@
+from .parallel_apply import parallel_apply
+from .replicate import replicate
+from .data_parallel import DataParallel, data_parallel
+from .scatter_gather import gather, scatter
+from .distributed import DistributedDataParallel
+
+__all__ = ['replicate', 'scatter', 'parallel_apply', 'gather', 'data_parallel',
+           'DataParallel', 'DistributedDataParallel']
+
+def DistributedDataParallelCPU(*args, **kwargs):
+    import warnings
+    warnings.warn("torch.nn.parallel.DistributedDataParallelCPU is deprecated, "
+                  "please use torch.nn.parallel.DistributedDataParallel instead.")
+    return DistributedDataParallel(*args, **kwargs)

venv/lib/python3.10/site-packages/torch/nn/parallel/_functions.py

@@ -0,0 +1,126 @@
+import warnings
+
+import torch
+from . import comm
+from torch.autograd import Function
+from torch._utils import _get_device_index
+from typing import List, Optional
+
+
+class Broadcast(Function):
+
+    @staticmethod
+    def forward(ctx, target_gpus, *inputs):
+        assert all(i.device.type != 'cpu' for i in inputs), (
+            'Broadcast function not implemented for CPU tensors'
+        )
+        target_gpus = [_get_device_index(x, True) for x in target_gpus]
+        ctx.target_gpus = target_gpus
+        if len(inputs) == 0:
+            return tuple()
+        ctx.num_inputs = len(inputs)
+        ctx.input_device = inputs[0].get_device()
+        outputs = comm.broadcast_coalesced(inputs, ctx.target_gpus)
+        non_differentiables = []
+        for idx, input_requires_grad in enumerate(ctx.needs_input_grad[1:]):
+            if not input_requires_grad:
+                for output in outputs:
+                    non_differentiables.append(output[idx])
+        ctx.mark_non_differentiable(*non_differentiables)
+        return tuple([t for tensors in outputs for t in tensors])
+
+    @staticmethod
+    def backward(ctx, *grad_outputs):
+        return (None,) + ReduceAddCoalesced.apply(ctx.input_device, ctx.num_inputs, *grad_outputs)
+
+
+class ReduceAddCoalesced(Function):
+
+    @staticmethod
+    def forward(ctx, destination, num_inputs, *grads):
+        ctx.target_gpus = [grads[i].get_device() for i in range(0, len(grads), num_inputs)]
+
+        grads_ = [grads[i:i + num_inputs]
+                  for i in range(0, len(grads), num_inputs)]
+        return comm.reduce_add_coalesced(grads_, destination)
+
+    @staticmethod
+    def backward(ctx, *grad_outputs):
+        return (None, None,) + Broadcast.apply(ctx.target_gpus, *grad_outputs)
+
+
+class Gather(Function):
+
+    @staticmethod
+    def forward(ctx, target_device, dim, *inputs):
+        assert all(i.device.type != 'cpu' for i in inputs), (
+            'Gather function not implemented for CPU tensors'
+        )
+        if (target_device == 'cpu'):
+            ctx.target_device = 'cpu'
+        else:
+            target_device = _get_device_index(target_device, True)
+            ctx.target_device = target_device
+        ctx.dim = dim
+        ctx.input_gpus = tuple(i.get_device() for i in inputs)
+        if all(t.dim() == 0 for t in inputs) and dim == 0:
+            inputs = tuple(t.view(1) for t in inputs)
+            warnings.warn('Was asked to gather along dimension 0, but all '
+                          'input tensors were scalars; will instead unsqueeze '
+                          'and return a vector.')
+            ctx.unsqueezed_scalar = True
+        else:
+            ctx.unsqueezed_scalar = False
+        ctx.input_sizes = tuple(i.size(ctx.dim) for i in inputs)
+        return comm.gather(inputs, ctx.dim, ctx.target_device)
+
+    @staticmethod
+    def backward(ctx, grad_output):
+        scattered_grads = Scatter.apply(ctx.input_gpus, ctx.input_sizes, ctx.dim, grad_output)
+        if ctx.unsqueezed_scalar:
+            scattered_grads = tuple(g[0] for g in scattered_grads)
+        return (None, None) + scattered_grads
+
+
+class Scatter(Function):
+
+    @staticmethod
+    def forward(ctx, target_gpus, chunk_sizes, dim, input):
+        target_gpus = [_get_device_index(x, True) for x in target_gpus]
+        ctx.dim = dim
+        ctx.input_device = input.get_device() if input.device.type != "cpu" else -1
+        streams = None
+        if torch.cuda.is_available() and ctx.input_device == -1:
+            # Perform CPU to GPU copies in a background stream
+            streams = [_get_stream(torch.device("cuda", device)) for device in target_gpus]
+        outputs = comm.scatter(input, target_gpus, chunk_sizes, ctx.dim, streams)
+        # Synchronize with the copy stream
+        if streams is not None:
+            for i, output in enumerate(outputs):
+                with torch.cuda.device(target_gpus[i]):
+                    main_stream = torch.cuda.current_stream()
+                    main_stream.wait_stream(streams[i])
+                    output.record_stream(main_stream)
+        return outputs
+
+    @staticmethod
+    def backward(ctx, *grad_output):
+        return None, None, None, Gather.apply(ctx.input_device, ctx.dim, *grad_output)
+
+
+# background streams used for copying
+_streams: Optional[List[Optional[torch.Stream]]] = None
+
+def _get_stream(device: torch.device):
+    """Get a background stream for copying between CPU and target device."""
+    global _streams
+    if device.type == "cpu":
+        return None
+    device_mod = getattr(torch, device.type, None)
+    if device_mod is None:
+        return None
+    if _streams is None:
+        _streams = [None] * device_mod.device_count()
+    if _streams[device.index] is None:
+        _streams[device.index] = device_mod.Stream(device.index)
+    return _streams[device.index]

venv/lib/python3.10/site-packages/torch/nn/parallel/comm.py

@@ -0,0 +1,236 @@
+import warnings
+import torch
+from torch.cuda import nccl
+from torch._utils import _take_tensors, _flatten_dense_tensors, \
+    _unflatten_dense_tensors, _reorder_tensors_as, _get_device_index, _handle_complex
+from typing import List
+
+def broadcast(tensor, devices=None, *, out=None):
+    r"""Broadcasts a tensor to specified GPU devices.
+
+    Args:
+        tensor (Tensor): tensor to broadcast. Can be on CPU or GPU.
+        devices (Iterable[torch.device, str or int], optional): an iterable of
+          GPU devices, among which to broadcast.
+        out (Sequence[Tensor], optional, keyword-only): the GPU tensors to
+          store output results.
+
+    .. note::
+        Exactly one of :attr:`devices` and :attr:`out` must be specified.
+
+    Returns:
+        - If :attr:`devices` is specified,
+            a tuple containing copies of :attr:`tensor`, placed on
+            :attr:`devices`.
+        - If :attr:`out` is specified,
+            a tuple containing :attr:`out` tensors, each containing a copy of
+            :attr:`tensor`.
+    """
+    tensor = _handle_complex(tensor)
+    if not ((devices is None) ^ (out is None)):
+        raise RuntimeError(
+            f"Exactly one of 'devices' and 'out' must be specified, but got devices={devices} and out={out}")
+    if devices is not None:
+        devices = [_get_device_index(d) for d in devices]
+        return torch._C._broadcast(tensor, devices)
+    else:
+        return torch._C._broadcast_out(tensor, out)
+
+
+def broadcast_coalesced(tensors, devices, buffer_size=10485760):
+    """Broadcast a sequence of tensors to the specified GPUs.
+
+    Small tensors are first coalesced into a buffer to reduce the number of synchronizations.
+
+    Args:
+        tensors (sequence): tensors to broadcast. Must be on the same device,
+          either CPU or GPU.
+        devices (Iterable[torch.device, str or int]): an iterable of GPU
+          devices, among which to broadcast.
+        buffer_size (int): maximum size of the buffer used for coalescing
+
+    Returns:
+        A tuple containing copies of :attr:`tensor`, placed on :attr:`devices`.
+    """
+    devices = [_get_device_index(d) for d in devices]
+    tensors = [_handle_complex(t) for t in tensors]
+    return torch._C._broadcast_coalesced(tensors, devices, buffer_size)
+
+
+def reduce_add(inputs, destination=None):
+    """Sum tensors from multiple GPUs.
+
+    All inputs should have matching shapes, dtype, and layout. The output tensor
+    will be of the same shape, dtype, and layout.
+
+    Args:
+        inputs (Iterable[Tensor]): an iterable of tensors to add.
+        destination (int, optional): a device on which the output will be
+            placed (default: current device).
+
+    Returns:
+        A tensor containing an elementwise sum of all inputs, placed on the
+        :attr:`destination` device.
+    """
+    destination = _get_device_index(destination, optional=True)
+    input_size = inputs[0].size()
+    root_index = None  # index of input tensor that already is on the correct device
+    for i, inp in enumerate(inputs):
+        assert inp.device.type != "cpu", "reduce_add expects all inputs to be on GPUs"
+        if inp.get_device() == destination:
+            root_index = i
+        if inp.size() != input_size:
+            got = 'x'.join(str(x) for x in inp.size())
+            expected = 'x'.join(str(x) for x in input_size)
+            raise ValueError(f"input {i} has invalid size: got {got}, but expected {expected}")
+    if root_index is None:
+        raise RuntimeError("reduce_add expects destination to be on the same GPU with one of the tensors")
+
+    if len(inputs) == 1:
+        return inputs[0]
+
+    if nccl.is_available(inputs):
+        result = torch.empty_like(inputs[root_index])
+        nccl.reduce(inputs, output=result, root=root_index)
+    else:
+        destination_device = torch.device(inputs[root_index].device.type, destination)
+        nonroot = [t for i, t in enumerate(inputs) if i != root_index]
+        # make a new tensor w/o clone
+        result = inputs[root_index] + nonroot[0].to(device=destination_device, non_blocking=True)
+        for other in nonroot[1:]:
+            result.add_(other.to(device=destination_device, non_blocking=True))
+    return result
+
+
+def reduce_add_coalesced(inputs, destination=None, buffer_size=10485760):
+    """Sum tensors from multiple GPUs.
+
+    Small tensors are first coalesced into a buffer to reduce the number
+    of synchronizations.
+
+    Args:
+        inputs (Iterable[Iterable[Tensor]]): iterable of iterables that
+            contain tensors from a single device.
+        destination (int, optional): a device on which the output will be
+            placed (default: current device).
+        buffer_size (int): maximum size of the buffer used for coalescing
+
+    Returns:
+        A tuple of tensors containing an elementwise sum of each group of
+        inputs, placed on the ``destination`` device.
+    """
+    # TODO: When `len(inputs) == 1` and all inputs are on `destination`, just
+    #       return `inputs`.
+    dense_tensors: List[List] = [[] for _ in inputs]  # shape (num_gpus, num_tensors)
+    output = []
+    ref_order = []
+    # process sparse ones first since they may have different sizes on different gpus
+    for tensor_at_gpus in zip(*inputs):
+        if all(t.is_sparse for t in tensor_at_gpus):
+            result = reduce_add(tensor_at_gpus, destination)  # this will be sparse too
+            output.append(result)
+            ref_order.append(tensor_at_gpus[0])
+        else:
+            for coll, t in zip(dense_tensors, tensor_at_gpus):
+                coll.append(t.to_dense() if t.is_sparse else t)
+            ref_order.append(dense_tensors[0][-1])
+    itrs = [_take_tensors(tensors, buffer_size) for tensors in dense_tensors]
+    # now the dense ones, which have consistent sizes
+    for chunks in zip(*itrs):
+        flat_tensors = [_flatten_dense_tensors(chunk) for chunk in chunks]  # (num_gpus,)
+        flat_result = reduce_add(flat_tensors, destination)
+        for t in _unflatten_dense_tensors(flat_result, chunks[0]):
+            # The unflattened tensors do not share storage, and we don't expose
+            # base flat tensor anyways, so give them different version counters.
+            # See NOTE [ Version Counter in comm.*_coalesced ]
+            output.append(t.data)
+    return tuple(_reorder_tensors_as(output, ref_order))
+
+
+def scatter(tensor, devices=None, chunk_sizes=None, dim=0, streams=None, *, out=None):
+    """Scatters tensor across multiple GPUs.
+
+    Args:
+        tensor (Tensor): tensor to scatter. Can be on CPU or GPU.
+        devices (Iterable[torch.device, str or int], optional): an iterable of
+          GPU devices, among which to scatter.
+        chunk_sizes (Iterable[int], optional): sizes of chunks to be placed on
+          each device. It should match :attr:`devices` in length and sums to
+          ``tensor.size(dim)``. If not specified, :attr:`tensor` will be divided
+          into equal chunks.
+        dim (int, optional): A dimension along which to chunk :attr:`tensor`.
+          Default: ``0``.
+        streams (Iterable[torch.cuda.Stream], optional): an iterable of Streams, among
+          which to execute the scatter. If not specified, the default stream will
+          be utilized.
+        out (Sequence[Tensor], optional, keyword-only): the GPU tensors to
+          store output results. Sizes of these tensors must match that of
+          :attr:`tensor`, except for :attr:`dim`, where the total size must
+          sum to ``tensor.size(dim)``.
+
+    .. note::
+        Exactly one of :attr:`devices` and :attr:`out` must be specified. When
+        :attr:`out` is specified, :attr:`chunk_sizes` must not be specified and
+        will be inferred from sizes of :attr:`out`.
+
+    Returns:
+        - If :attr:`devices` is specified,
+            a tuple containing chunks of :attr:`tensor`, placed on
+            :attr:`devices`.
+        - If :attr:`out` is specified,
+            a tuple containing :attr:`out` tensors, each containing a chunk of
+            :attr:`tensor`.
+    """
+    tensor = _handle_complex(tensor)
+    if out is None:
+        devices = [_get_device_index(d) for d in devices]
+        return tuple(torch._C._scatter(tensor, devices, chunk_sizes, dim, streams))
+    else:
+        if devices is not None:
+            raise RuntimeError(
+                f"'devices' must not be specified when 'out' is specified, but got devices={devices}")
+        if chunk_sizes is not None:
+            raise RuntimeError(
+                f"'chunk_sizes' must not be specified when 'out' is specified, but got chunk_sizes={chunk_sizes}")
+        return tuple(torch._C._scatter_out(tensor, out, dim, streams))
+
+
+def gather(tensors, dim=0, destination=None, *, out=None):
+    r"""Gathers tensors from multiple GPU devices.
+
+    Args:
+        tensors (Iterable[Tensor]): an iterable of tensors to gather.
+          Tensor sizes in all dimensions other than :attr:`dim` have to match.
+        dim (int, optional): a dimension along which the tensors will be
+          concatenated. Default: ``0``.
+        destination (torch.device, str, or int, optional): the output device.
+          Can be CPU or CUDA. Default: the current CUDA device.
+        out (Tensor, optional, keyword-only): the tensor to store gather result.
+          Its sizes must match those of :attr:`tensors`, except for :attr:`dim`,
+          where the size must equal ``sum(tensor.size(dim) for tensor in tensors)``.
+          Can be on CPU or CUDA.
+
+    .. note::
+        :attr:`destination` must not be specified when :attr:`out` is specified.
+
+    Returns:
+        - If :attr:`destination` is specified,
+            a tensor located on :attr:`destination` device, that is a result of
+            concatenating :attr:`tensors` along :attr:`dim`.
+        - If :attr:`out` is specified,
+            the :attr:`out` tensor, now containing results of concatenating
+            :attr:`tensors` along :attr:`dim`.
+    """
+    tensors = [_handle_complex(t) for t in tensors]
+    if out is None:
+        if destination == -1:
+            warnings.warn(
+                'Using -1 to represent CPU tensor is deprecated. Please use a '
+                'device object or string instead, e.g., "cpu".')
+        destination = _get_device_index(destination, allow_cpu=True, optional=True)
+        return torch._C._gather(tensors, dim, destination)
+    else:
+        if destination is not None:
+            raise RuntimeError(
+                f"'destination' must not be specified when 'out' is specified, but got destination={destination}")
+        return torch._C._gather_out(tensors, out, dim)