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taps.apps.cholesky

taps/apps/cholesky.py

Cholesky decomposition application.

CholeskyApp 

CholeskyApp(matrix_size: int, block_size: int)

Cholesky decomposition application.

Computes the tiled Cholesky decomposition of a random positive-definite square matrix.

Parameters:

  • matrix_size (int) –

    Matrix side length.

  • block_size (int) –

    Block size length.

Source code in taps/apps/cholesky.py 
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def __init__(self, matrix_size: int, block_size: int) -> None:
    self.matrix_size = matrix_size
    self.block_size = block_size

close() 

close() -> None

Close the application.

Source code in taps/apps/cholesky.py 
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def close(self) -> None:
    """Close the application."""
    pass

run() 

run(engine: Engine, run_dir: Path) -> None

Run the application.

Parameters:

  • engine (Engine) –

    Application execution engine.

  • run_dir (Path) –

    Run directory.

Source code in taps/apps/cholesky.py 
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def run(self, engine: Engine, run_dir: pathlib.Path) -> None:
    """Run the application.

    Args:
        engine: Application execution engine.
        run_dir: Run directory.
    """
    max_print_size = 8

    matrix = create_psd_matrix(self.matrix_size)
    lower = numpy.zeros_like(matrix)

    n = matrix.shape[0]
    block_size = min(self.block_size, n)

    if matrix.shape[0] <= max_print_size:
        logger.log(
            APP_LOG_LEVEL,
            f'Generated input matrix: {matrix.shape}\n{matrix}',
        )
    else:
        logger.log(
            APP_LOG_LEVEL,
            f'Generated input matrix: {matrix.shape}',
        )
    logger.log(APP_LOG_LEVEL, f'Block size: {block_size}')

    for k in range(0, n, block_size):
        end_k = min(k + block_size, n)
        lower_tasks: dict[tuple[int, int], TaskFuture[Array]] = {}

        lower_tasks[(k, k)] = engine.submit(
            potrf,
            matrix[k:end_k, k:end_k],
        )

        for i in range(k + block_size, n, block_size):
            end_i = min(i + block_size, n)

            lower_tasks[(i, k)] = engine.submit(
                trsm,
                lower_tasks[(k, k)],
                matrix[i:end_i, k:end_k],
            )

        gemm_tasks: dict[tuple[int, int], TaskFuture[Array]] = {}

        for i in range(k + block_size, n, block_size):
            end_i = min(i + block_size, n)
            for j in range(i, n, block_size):
                end_j = min(j + block_size, n)

                syrk_task = engine.submit(
                    syrk,
                    matrix[i:end_i, j:end_j],
                    lower_tasks[(i, k)],
                )

                gemm_tasks[(i, j)] = engine.submit(
                    gemm,
                    syrk_task,
                    lower_tasks[(i, k)],
                    lower_tasks[(j, k)],
                )

        for (i, j), tile in lower_tasks.items():
            end_i = min(i + block_size, n)
            end_j = min(j + block_size, n)
            lower[i:end_i, j:end_j] = tile.result()

        for (i, j), tile in gemm_tasks.items():
            end_i = min(i + block_size, n)
            end_j = min(j + block_size, n)
            matrix[i:end_i, j:end_j] = tile.result()

    if matrix.shape[0] <= max_print_size:
        logger.log(APP_LOG_LEVEL, f'Output matrix:\n{lower}')
    else:
        logger.log(APP_LOG_LEVEL, f'Output matrix: {lower.shape}')

potrf() 

potrf(tile: Array) -> Array

POTRF task.

Source code in taps/apps/cholesky.py 
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def potrf(tile: Array) -> Array:
    """POTRF task."""
    return numpy.linalg.cholesky(tile)

trsm() 

trsm(lower: Array, block: Array) -> Array

TRSM task.

Source code in taps/apps/cholesky.py 
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def trsm(lower: Array, block: Array) -> Array:
    """TRSM task."""
    return numpy.linalg.solve(lower, block.T).T

syrk() 

syrk(tile: Array, lower: Array) -> Array

SYRK task.

Source code in taps/apps/cholesky.py 
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def syrk(tile: Array, lower: Array) -> Array:
    """SYRK task."""
    return tile - numpy.dot(lower, lower.T)

gemm() 

gemm(a: Array, b: Array, c: Array) -> Array

GEMM task.

Source code in taps/apps/cholesky.py 
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def gemm(a: Array, b: Array, c: Array) -> Array:
    """GEMM task."""
    return a - numpy.dot(b, c)

create_psd_matrix() 

create_psd_matrix(n: int) -> Array

Create a positive semi-definite matrix.

Parameters:

  • n (int) –

    Create an n x n square matrix.

Returns:

  • Array –

    Random matrix that is positive semi-definite.

Source code in taps/apps/cholesky.py 
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def create_psd_matrix(n: int) -> Array:
    """Create a positive semi-definite matrix.

    Args:
        n: Create an `n` x `n` square matrix.

    Returns:
        Random matrix that is positive semi-definite.
    """
    psd = numpy.random.randn(n, n)
    psd = numpy.dot(psd, psd.T)
    psd += n * numpy.eye(n)
    return psd