opencl_fdfd/opencl_fdfd/csr.py

"""
Sparse matrix solvers

This file holds the sparse matrix solvers, as well as the
CSRMatrix sparse matrix representation.

The FDFD solver (fdfd_cg_solver()) solves an FDFD problem by
creating a sparse matrix representing the problem (using
fdfd_tools) and then passing it to cg(), which performs a
conjugate gradient solve.

cg() is capable of solving arbitrary sparse matrices which
satisfy the constraints for the 'conjugate gradient' algorithm
(positive definite, symmetric) and some that don't.
"""

from typing import Dict, Any
import time

import numpy
from numpy.linalg import norm
import pyopencl
import pyopencl.array

import fdfd_tools.solvers

from . import ops


class CSRMatrix(object):
    """
    Matrix stored in Compressed Sparse Row format, in GPU RAM.
    """
    row_ptr = None      # type: pyopencl.array.Array
    col_ind = None      # type: pyopencl.array.Array
    data = None         # type: pyopencl.array.Array

    def __init__(self,
                 queue: pyopencl.CommandQueue,
                 m: 'scipy.sparse.csr_matrix'):
        self.row_ptr = pyopencl.array.to_device(queue, m.indptr)
        self.col_ind = pyopencl.array.to_device(queue, m.indices)
        self.data = pyopencl.array.to_device(queue, m.data.astype(numpy.complex128))


def cg(A: 'scipy.sparse.csr_matrix',
       b: numpy.ndarray,
       max_iters: int = 10000,
       err_threshold: float = 1e-6,
       context: pyopencl.Context = None,
       queue: pyopencl.CommandQueue = None,
       verbose: bool = False,
       ) -> numpy.ndarray:
    """
    General conjugate-gradient solver for sparse matrices, where A @ x = b.

    :param A: Matrix to solve (CSR format)
    :param b: Right-hand side vector (dense ndarray)
    :param max_iters: Maximum number of iterations
    :param err_threshold: Error threshold for successful solve, relative to norm(b)
    :param context: PyOpenCL context. Will be created if not given.
    :param queue: PyOpenCL command queue. Will be created if not given.
    :param verbose: Whether to print statistics to screen.
    :return: Solution vector x; returned even if solve doesn't converge.
    """

    start_time = time.perf_counter()

    if context is None:
        context = pyopencl.create_some_context(False)

    if queue is None:
        queue = pyopencl.CommandQueue(context)

    def load_field(v, dtype=numpy.complex128):
        return pyopencl.array.to_device(queue, v.astype(dtype))

    r = load_field(b)
    x = pyopencl.array.zeros_like(r)
    v = pyopencl.array.zeros_like(r)
    p = pyopencl.array.zeros_like(r)

    alpha = 1.0 + 0j
    rho = 1.0 + 0j
    errs = []

    m = CSRMatrix(queue, A)

    '''
    Generate OpenCL kernels
    '''
    a_step = ops.create_a_csr(context)
    xr_step = ops.create_xr_step(context)
    rhoerr_step = ops.create_rhoerr_step(context)
    p_step = ops.create_p_step(context)
    dot = ops.create_dot(context)

    '''
    Start the solve
    '''
    start_time2 = time.perf_counter()

    _, err2 = rhoerr_step(r, [])
    b_norm = numpy.sqrt(err2)
    if verbose:
        print('b_norm check: ', b_norm)

    success = False
    for k in range(max_iters):
        if verbose:
            print('[{:06d}] rho {:.4} alpha {:4.4}'.format(k, rho, alpha), end=' ')

        rho_prev = rho
        e = xr_step(x, p, r, v, alpha, [])
        rho, err2 = rhoerr_step(r, e)

        errs += [numpy.sqrt(err2) / b_norm]

        if verbose:
            print('err', errs[-1])

        if errs[-1] < err_threshold:
            success = True
            break

        e = p_step(p, r, rho/rho_prev, [])
        e = a_step(v, m, p, e)
        alpha = rho / dot(p, v, e)

        if verbose and k % 1000 == 0:
            print(k)

    '''
    Done solving
    '''
    time_elapsed = time.perf_counter() - start_time

    x = x.get()

    if verbose:
        if success:
            print('Success', end='')
        else:
            print('Failure', end=', ')
        print(', {} iterations in {} sec: {} iterations/sec \
                      '.format(k, time_elapsed, k / time_elapsed))
        print('final error', errs[-1])
        print('overhead {} sec'.format(start_time2 - start_time))

        print('Final residual:', norm(A @ x - b) / norm(b))
    return x


def fdfd_cg_solver(solver_opts: Dict[str, Any] = None,
                   **fdfd_args
                   ) -> numpy.ndarray:
    """
    Conjugate gradient FDFD solver using CSR sparse matrices, mainly for
     testing and development since it's much slower than the solver in main.py.

    Calls fdfd_tools.solvers.generic(**fdfd_args,
                                     matrix_solver=opencl_fdfd.csr.cg,
                                     matrix_solver_opts=solver_opts)

    :param solver_opts: Passed as matrix_solver_opts to fdfd_tools.solver.generic(...).
        Default {}.
    :param fdfd_args: Passed as **fdfd_args to fdfd_tools.solver.generic(...).
        Should include all of the arguments **except** matrix_solver and matrix_solver_opts
    :return: E-field which solves the system.
    """

    if solver_opts is None:
        solver_opts = dict()

    x = fdfd_tools.solvers.generic(matrix_solver=cg,
                                   matrix_solver_opts=solver_opts,
                                   **fdfd_args)

    return x