Created
December 5, 2016 11:53
-
-
Save kvchen/2f57229897038073adbb76bc2ee0a6be to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
@ray.remote | |
def lu_decomp_invert(lu_decomp): | |
"""Takes the inverse of each of the components in the P, L, U | |
decomposition. Needed as a helper function for the block-level LU decomp. | |
""" | |
return tuple(np.linalg.inv(x) for x in lu_decomp) | |
@ray.remote(num_return_vals=3) | |
def block_lu(a, block_size=100): | |
"""Returns the LU decomposition of a square matrix. | |
Parameters | |
---------- | |
a : array_like | |
Returns | |
------- | |
p : array_like | |
l : array_like | |
u : array_like | |
""" | |
if a.shape[0] <= block_size or a.shape[1] <= block_size: | |
return ray.get(ra.linalg.lu.remote(a)) | |
p, l, u = np.zeros(a.shape), np.zeros(a.shape), np.zeros(a.shape) | |
num_blocks = int(np.ceil(float(a.shape[0]) / block_size)) | |
# Compute all single-node LU decompositions in parallel | |
block_decomps_remote = [] | |
for idx in range(num_blocks): | |
block_low = block_size * idx | |
block_high = block_low + block_size | |
a11 = a[block_low:block_high, block_low:block_high] | |
block_decomps_remote.append(ra.linalg.lu.remote(a11)) | |
a12 = a[block_low:block_high, block_high:] | |
a21 = a[block_high:, block_low:block_high] | |
# Modify a with the Schur complements as we go along so we don't have | |
# to repeat the computations later | |
schur_complement = np.dot(a21, np.dot(np.linalg.inv(a11), a12)) | |
a[block_high:, block_high:] -= schur_complement | |
block_decomps = ray.get(block_decomps_remote) | |
# Compute the inverses for each of the LU components in parallel | |
block_decomp_inverses = ray.get([lu_decomp_invert.remote(decomp) | |
for decomp in block_decomps_remote]) | |
for idx, (p11, _, _) in enumerate(block_decomps): | |
block_low = block_size * idx | |
block_high = block_low + block_size | |
p[block_low:block_high, block_low:block_high] = p11 | |
# Perform coalescing. | |
# TODO(kvchen): Modify most of this code to use distributed routines. | |
for idx, (plu, plu_inverse) in enumerate(zip(block_decomps, | |
block_decomp_inverses)): | |
p11, l11, u11 = plu | |
p11_inverse, l11_inverse, u11_inverse = plu_inverse | |
block_low = block_size * idx | |
block_high = block_low + block_size | |
if idx < num_blocks - 1: | |
a12 = a[block_low:block_high, block_high:] | |
a21 = a[block_high:, block_low:block_high] | |
# Inverse of the permutation matrix is just its transpose | |
p22_inverse = p[block_high:, block_high:].T | |
u12, l21 = ray.get([ | |
ra.dot.remote(l11_inverse, ra.dot.remote(p11_inverse, a12)), | |
ra.dot.remote(p22_inverse, ra.dot.remote(a21, u11_inverse)), | |
]) | |
l[block_high:, block_low:block_high] = l21 | |
u[block_low:block_high, block_high:] = u12 | |
l[block_low:block_high, block_low:block_high] = l11 | |
u[block_low:block_high, block_low:block_high] = u11 | |
return p, l, u |
ray.get(ra.linalg.lu.remote(a))?
what is the work?
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
what s the meaning of ra.dot.remote?