nvmath.linalg.advanced.matmul

nvmath.linalg.advanced.matmul(a, b, /, c=None, *, alpha=None, beta=None, epilog=None, epilog_inputs=None, qualifiers=None, options=None, preferences=None, algorithm=None, stream=None)[source]

Perform the specified matrix multiplication computation \(F(\alpha a @ b + \beta c)\), where \(F\) is the epilog. This function-form is a wrapper around the stateful Matmul object APIs and is meant for single use (the user needs to perform just one matrix multiplication, for example), in which case there is no possibility of amortizing preparatory costs.

Detailed information on what’s happening within this function can be obtained by passing in a logging.Logger object to MatmulOptions or by setting the appropriate options in the root logger object, which is used by default:

>>> import logging
>>> logging.basicConfig(level=logging.INFO, format='%(asctime)s %(levelname)-8s %(message)s', datefmt='%m-%d %H:%M:%S')

A user can select the desired logging level and, in general, take advantage of all of the functionality offered by the Python logging module.

Parameters:

  • a – A tensor representing the first operand to the matrix multiplication (see Semantics). The currently supported types are numpy.ndarray, cupy.ndarray, and torch.Tensor.

  • b – A tensor representing the second operand to the matrix multiplication (see Semantics). The currently supported types are numpy.ndarray, cupy.ndarray, and torch.Tensor.

  • c – (Optional) A tensor representing the operand to add to the matrix multiplication result (see Semantics). The currently supported types are numpy.ndarray, cupy.ndarray, and torch.Tensor.

  • alpha – The scale factor for the matrix multiplication term as a real or complex number. The default is \(1.0\).

  • beta – The scale factor for the matrix addition term as a real or complex number. A value for beta must be provided if operand c is specified. from a previously planned and autotuned matrix multiplication.

  • epilog – Specify an epilog \(F\) as an object of type MatmulEpilog to apply to the result of the matrix multiplication: \(F(\alpha A @ B + \beta C\)). The default is no epilog.

  • epilog_inputs – Specify the additional inputs needed for the selected epilog as a dictionary, where the key is the epilog input name and the value is the epilog input. The epilog input must be a tensor with the same package and in the same memory space as the operands (see the constructor for more information on the operands). If the required epilog inputs are not provided, an exception is raised that lists the required epilog inputs.

  • qualifiers – If desired, specify the matrix qualifiers as a numpy.ndarray of matrix_qualifiers_dtype objects of length 3 corresponding to the operands a, b, and c.

  • options – Specify options for the matrix multiplication as a MatmulOptions object. Alternatively, a dict containing the parameters for the MatmulOptions constructor can also be provided. If not specified, the value will be set to the default-constructed MatmulOptions object.

  • preferences – This parameter specifies the preferences for planning as a MatmulPlanPreferences object. Alternatively, a dictionary containing the parameters for the MatmulPlanPreferences constructor can also be provided. If not specified, the value will be set to the default-constructed MatmulPlanPreferences object.

  • algorithm – An object of type Algorithm objects can be directly provided to bypass planning, if desired. The algorithm object must be compatible with the matrix multiplication. A typical use for this option is to provide an algorithm that has been serialized (pickled) from a previously planned and autotuned matrix multiplication.

  • stream – Provide the CUDA stream to use for executing the operation. Acceptable inputs include cudaStream_t (as Python int), cupy.cuda.Stream, and torch.cuda.Stream. If a stream is not provided, the current stream from the operand package will be used.

Semantics:

The semantics of the matrix multiplication follows numpy.matmul() semantics, with some restrictions on broadcasting. In addition, the semantics for the fused matrix addition are described below:

  • If arguments a and b are matrices, they are multiplied according to the rules of matrix multiplication.

  • If argument a is 1-D, it is promoted to a matrix by prefixing 1 to its dimensions. After matrix multiplication, the prefixed 1 is removed from the result’s dimensions.

  • If argument b is 1-D, it is promoted to a matrix by appending 1 to its dimensions. After matrix multiplication, the appended 1 is removed from the result’s dimensions.

  • If a or b is N-D (N > 2), then the operand is treated as a batch of matrices. If both a and b are N-D, their batch dimensions must match. If exactly one of a or b is N-D, the other operand is broadcast.

  • The operand for the matrix addition c may be a vector of length M, a matrix of shape (M, 1) or (M, N), or batched versions of the latter (…, M, 1) or (…, M, N). Here M and N are the dimensions of the result of the matrix multiplication. If a vector is provided or N = 1, the columns of c are broadcast for the addition. If batch dimensions are not present, c is broadcast across batches as needed.

See also

Matmul, MatmulOptions, MatmulEpilog, MatmulPlanPreferences

Examples

>>> import cupy as cp
>>> import nvmath

Create three float64 ndarrays on the GPU:

>>> M, N, K = 128, 64, 256
>>> a = cp.random.rand(M, K)
>>> b = cp.random.rand(K, N)
>>> c = cp.random.rand(M, N)

Perform the operation \(\alpha A @ B + \beta C\) using matmul(). The result r is also a CuPy float64 ndarray:

>>> r = nvmath.linalg.advanced.matmul(a, b, c, alpha=1.23, beta=0.74)

An epilog can be used as well. Here we perform \(RELU(\alpha A @ B + \beta C)\):

>>> epilog = nvmath.linalg.advanced.MatmulEpilog.RELU
>>> r = nvmath.linalg.advanced.matmul(a, b, c, alpha=1.23, beta=0.74, epilog=epilog)

Options can be provided to customize the operation:

>>> compute_type = nvmath.linalg.advanced.MatmulComputeType.COMPUTE_32F_FAST_TF32
>>> o = nvmath.linalg.advanced.MatmulOptions(compute_type=compute_type)
>>> r = nvmath.linalg.advanced.matmul(a, b, options=o)

See MatmulOptions for the complete list of available options.

The package current stream is used by default, but a stream can be explicitly provided to the Matmul operation. This can be done if the operands are computed on a different stream, for example:

>>> s = cp.cuda.Stream()
>>> with s:
...    a = cp.random.rand(M, K)
...    b = cp.random.rand(K, N)
>>> nvmath.linalg.advanced.matmul(a, b, stream=s)

The operation above runs on stream s and is ordered with respect to the input computation.

Create NumPy ndarrays on the CPU.

>>> import numpy as np
>>> a = np.random.rand(M, K)
>>> b = np.random.rand(K, N)

Provide the NumPy ndarrays to matmul(), with the result also being a NumPy ndarray:

>>> r = nvmath.linalg.advanced.matmul(a, b)

Notes

  • This function is a convenience wrapper around Matmul and and is specifically meant for single use.

Further examples can be found in the nvmath/examples/linalg/advanced/matmul directory.