Concepts#

MatX uses numerous concepts that are given names to help understand how the library works. This document compiles a list of the terms and definitions that will be useful when reading other documents and code.

Operator#

The most important concept in MatX is the Operator. An Operator is any type that adheres to the Operator interface. Specifically, any operator must implement the following functions:

Size
Shape
Stride
Rank
operator() (For rvalues at a minimum, and optionally lvalues)

These functions provide a minimum set of functionality that can be used on both the host and device.

The API definition above is simple, but very powerful. Any class/type that implements these functions can be used anywhere an operator is accepted. This includes: arithmetic expressions, transforms, assignments, etc. Operators are a superset containing other types, including generators and tensors.

As an example:

// Create a tensor. "t" is an operator
auto t    = make_tensor<float>({10);

// Create a sin operator that operates on "t" and name it "op"
auto op   = sin(t);

// Create a Hamming window generator and assign it to the variable "win"
auto win  = hamming({10});

// Launch a kernel where "win" is copied into "t"
(t = win).run();

The first three lines have a single operator created. In order, they create a tensor, operator, and generator, respectively. As mentioned above, t, sin(t), and hamming({10}) all have the operator interface above implemented.

The last line more nuanced in where the operator is used. In t = win the operator is the assignment operator (=), which in this case produces a lazily-evaluated assignment of win into t. = implements the entire operator interface above and is used as an operator in the assignment expression.

Tensor#

Tensors are memory-backed operators providing several initialization methods for different use cases. Tensors implement the entire operator interface above, plus many more helper functions specific to a tensor type. Tensors can be used as both lvalues and rvalues in every place an operator is expected.

For more information on creating tensors, see Creating Tensors.

Generator#

Generators are a type of operator that can generate values without another tensor or operator as input. For example, windowing functions, such as a Hamming window, can generate values by only taking a length as input. Generators are efficient since they require no memory.

Transform#

Transforms are operators that take one or more inputs and call a backend library or kernel. Transforms usually changes one or more properties of the input, but that is not always the case. An fft may change the input type or shape, but a sort transform does not. Depending on the context used, a transform may asynchronously allocate temporary memory if the expression requires it.

For example:

(b = fft(A)).run();

The expression above performs an out-of-place FFT by taking the input A and storing in output B. Transforms may also be used in larger expressions:

(C = B * fft(A)).run();

In this case fft(A) may need somewhere to store the output of the FFT, and could asynchronously allocate memory to do so. However, MatX may also perform fusion on the expression if possible.

Since some transforms rely on CUDA math library backends not all of them are available with different executors. Please see the documentation for the individual function to check compatibility.

Executor#

Executors are types that describe how to execute an operator expression or transform. They are similar to C++’s execution policy, and may even use C++ execution policies behind the scenes. Executors are designed so that the code can remain unchanged while executing on a variety of different targets. Currently the following executors are defined:

cudaExecutor - Execute on a CUDA-supported device
HostExecutor - Execute on one or more host (CPU) threads

More executor types will be added in future releases.

Shape#

Shape is used to describe the size of each dimension of an operator.

Stride#

Stride is used to describe the spacing between elements in each dimension of an operator

Concepts

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