python/pyfaasm/pyfaasm/matrix.py at bump-cpp · faasm/python · GitHub

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import numpy as np

from numpy import int32

from pyfaasm.config import (

MATRIX_CONF_STATE_KEY,

SUBMATRICES_KEY_A,

SUBMATRICES_KEY_B,

MatrixConf,

RESULT_MATRIX_KEY,

)

from pyfaasm.core import (

write_state,

read_state,

chain,

await_call,

)

from pyfaasm.matrix_data import do_subdivide_matrix, do_reconstruct_matrix

def write_matrix_params_to_state(matrix_size, n_splits):

params = np.array((matrix_size, n_splits), dtype=int32)

write_state(MATRIX_CONF_STATE_KEY, params.tobytes())

def load_matrix_conf_from_state():

# Params are ints so need to work out what size they are

dummy = np.array((1, 2), dtype=int32)

param_len = len(dummy.tobytes())

param_bytes = read_state(MATRIX_CONF_STATE_KEY, param_len)

params = np.frombuffer(param_bytes, dtype=int32)

matrix_size = params[0]

n_splits = params[1]

conf = MatrixConf(matrix_size, n_splits)

return conf

def random_matrix(size):

return np.random.rand(size, size).astype(np.float32)

# Split up the original matrix into square submatrices and write to state

def subdivide_matrix_into_state(conf, mat, key_prefix):

def _write_submatrix_to_state(sm_bytes, row_idx, col_idx):

full_key = conf.get_submatrix_key(

key_prefix, conf.n_splits, row_idx, col_idx

)

write_state(full_key, sm_bytes)

do_subdivide_matrix(conf, mat, _write_submatrix_to_state)

# Reads a given submatrix from the input

def read_input_submatrix(conf, key_prefix, row_idx, col_idx):

sm_bytes = conf.get_bytes_per_submatrix(conf.n_splits)

sm_size = conf.get_submatrix_size(conf.n_splits)

full_key = conf.get_submatrix_key(

key_prefix, conf.n_splits, row_idx, col_idx

)

sub_mat_data = read_state(full_key, sm_bytes)

return np.frombuffer(sub_mat_data, dtype=np.float32).reshape(

sm_size, sm_size

)

# Rebuilds a matrix from its submatrices in state

def reconstruct_matrix_from_submatrices(conf, key_prefix):

def _read_submatrix_from_state(row_idx, col_idx):

full_key = conf.get_submatrix_key(

key_prefix, conf.n_splits, row_idx, col_idx

)

sm_bytes = conf.get_bytes_per_submatrix(conf.n_splits)

return read_state(full_key, sm_bytes)

return do_reconstruct_matrix(conf, _read_submatrix_from_state)

# This is the distributed worker that will be invoked by faasm

def distributed_divide_and_conquer(input_bytes):

conf = load_matrix_conf_from_state()

input_args = np.frombuffer(input_bytes, dtype=int32)

split_level = input_args[0]

row_a = input_args[1]

col_a = input_args[2]

row_b = input_args[3]

col_b = input_args[4]

# If we're at the target number of splits, do the work

if split_level == conf.n_splits:

# Read in the relevant submatrices of each input matrix

mat_a = read_input_submatrix(conf, SUBMATRICES_KEY_A, row_a, col_a)

mat_b = read_input_submatrix(conf, SUBMATRICES_KEY_B, row_b, col_b)

# Do the multiplication in memory

result = np.dot(mat_a, mat_b)

else:

# Recursively kick off more divide and conquer

result = chain_multiplications(

conf, split_level, row_a, col_a, row_b, col_b

)

# Write the result

result_key = conf.get_intermediate_result_key(

split_level, row_a, col_a, row_b, col_b

)

write_state(result_key, result.tobytes())

def divide_and_conquer():

conf = load_matrix_conf_from_state()

print(

"Running divide and conquer for {}x{} matrix with {} splits".format(

conf.matrix_size, conf.matrix_size, conf.n_splits

)

# Short-cut for no splits

if conf.n_splits == 0:

# Read in the relevant submatrices of each input matrix

mat_a = read_input_submatrix(conf, SUBMATRICES_KEY_A, 0, 0)

mat_b = read_input_submatrix(conf, SUBMATRICES_KEY_B, 0, 0)

# Do the multiplication in memory

result = np.dot(mat_a, mat_b)

else:

# Kick off the basic multiplication jobs

result = chain_multiplications(conf, 0, 0, 0, 0, 0)

# Write final result

write_state(RESULT_MATRIX_KEY, result.tobytes())

def get_addition_result(conf, split_level, addition_def):

sm_size = conf.get_submatrix_size(split_level)

sm_byte_size = conf.get_bytes_per_submatrix(split_level)

key_a = conf.get_intermediate_result_key(

split_level,

addition_def[0][0][0],

addition_def[0][0][1],

addition_def[0][1][0],

addition_def[0][1][1],

)

key_b = conf.get_intermediate_result_key(

split_level,

addition_def[1][0][0],

addition_def[1][0][1],

addition_def[1][1][0],

addition_def[1][1][1],

)

bytes_a = read_state(key_a, sm_byte_size)

mat_a = np.frombuffer(bytes_a, dtype=np.float32).reshape(sm_size, sm_size)

bytes_b = read_state(key_b, sm_byte_size)

mat_b = np.frombuffer(bytes_b, dtype=np.float32).reshape(sm_size, sm_size)

return mat_a + mat_b

def chain_multiplications(conf, split_level, row_a, col_a, row_b, col_b):

"""

Spawns 8 workers to do the relevant multiplication in parallel.

- split level is how many times we've split the original matrix

- row_a, col_a is the chunk of matrix A

- row_b, col_b is the chunk of matrix B

The row/ col values will specify which chunk of the current split level, not

actual indices in the final input matrices. Those must only be calculated

when the final multiplication is done.

"""

call_ids = []

# Next split down we'll double the number of submatrices

next_split_level = split_level + 1

next_row_a = 2 * row_a

next_row_b = 2 * row_b

next_col_a = 2 * col_a

next_col_b = 2 * col_b

# Splitting submatrix A into four, A11, A12, A21, A22 and same with B

a11 = [next_row_a, next_col_a]

a12 = [next_row_a, next_col_a + 1]

a21 = [next_row_a + 1, next_col_a]

a22 = [next_row_a + 1, next_col_a + 1]

b11 = [next_row_b, next_col_b]

b12 = [next_row_b, next_col_b + 1]

b21 = [next_row_b + 1, next_col_b]

b22 = [next_row_b + 1, next_col_b + 1]

# Define the relevant multiplications and additions for these submatrices

additions = [

[(a11, b11), (a12, b21)],

[(a11, b12), (a12, b22)],

[(a21, b11), (a22, b21)],

[(a21, b12), (a22, b22)],

]

# Build a list of all the required multiplications

multiplications = list()

for mult_one, mult_two in additions:

multiplications.append(mult_one)

multiplications.append(mult_two)

# Kick off the multiplications in parallel

for submatrix_a, submatrix_b in multiplications:

inputs_a = np.array(

[

next_split_level,

submatrix_a[0],

submatrix_a[1],

submatrix_b[0],

submatrix_b[1],

dtype=int32,

)

call_ids.append(

chain(distributed_divide_and_conquer, inputs_a.tobytes())

)

# Await completion

for call_id in call_ids:

await_call(call_id)

# Go through and get the results

r_1 = get_addition_result(conf, next_split_level, additions[0])

r_2 = get_addition_result(conf, next_split_level, additions[1])

r_3 = get_addition_result(conf, next_split_level, additions[2])

r_4 = get_addition_result(conf, next_split_level, additions[3])

# Reconstitute the result

result = np.concatenate(

(

np.concatenate((r_1, r_2), axis=1),

np.concatenate((r_3, r_4), axis=1),

axis=0,

)

return result

python/pyfaasm/pyfaasm/matrix.py at bump-cpp · faasm/python · GitHub

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