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Hutch++ #52

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Hutch++ #52

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a4741f4
hutch++
Fr0do Sep 10, 2023
7791a1c
Merge branch 'wilson-labs:main' into hutch++
Fr0do Sep 10, 2023
0f8262d
Merge branch 'main' into hutch++
Fr0do Sep 10, 2023
8014329
Merge branch 'main' into hutch++
Fr0do Sep 11, 2023
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29 changes: 27 additions & 2 deletions cola/algorithms/diagonal_estimation.py
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Original file line number Diff line number Diff line change
Expand Up @@ -98,7 +98,7 @@ def exact_diag(A: LinearOperator, k=0, bs=100, tol=3e-2, max_iters=10000, pbar=F


@export
def approx_diag(A: LinearOperator, k=0, bs=100, tol=3e-2, max_iters=10000, pbar=False):
def approx_diag(A: LinearOperator, k=0, bs=100, tol=3e-2, max_iters=10000, hutchpp_dist="rademacher", pbar=False):
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Maybe lets separate this kwarg into
hutchpp=False
probe_dist='normal' or 'rademacher'
to keep things more straightforward

""" Extract the (kth) diagonal of a linear operator using stochastic estimation

Args:
Expand All @@ -107,6 +107,7 @@ def approx_diag(A: LinearOperator, k=0, bs=100, tol=3e-2, max_iters=10000, pbar=
bs (int, optional): Chunk size (default 100).
tol (float, optional): Tolerance (default 3e-2).
max_iters (int, optional): Maximum number of iterations (default 10000).
hutchpp_dist (str, optional): whether to use Hutch++ and what distribution should basis be sampled from.
pbar (bool, optional): Flag for showing progress bar.

Returns:
Expand All @@ -124,6 +125,10 @@ def body(state):
i, diag_sum, diag_sumsq, key = state
key = xnp.next_key(key)
z = xnp.randn(A.shape[0], bs, dtype=A.dtype, key=key, device=A.device)
if hutchpp_dist == "rademacher":
z = xnp.sign(z)
if Q is not None:
z = z - Q @ (Q.T @ z)
z2 = xnp.roll(z, -k, 0)
z2 = xnp.update_array(z2, 0, slice(0, abs(k)) if k <= 0 else slice(-abs(k), None))
slc = slice(abs(k), None) if -k > 0 else slice(None, -abs(k) or None)
Expand All @@ -139,9 +144,29 @@ def err(state):
def cond(state):
return (state[0] == 0) | ((state[0] < max_iters) & (err(state) > tol))

@xnp.jit
def hutchpp(key):
m = max_iters // 3 if hutchpp_dist == "rademacher" else (max_iters + 2) // 4
key = xnp.next_key(key)
S = xnp.randn(A.shape[0], m, dtype=A.dtype, key=key, device=A.device)
if hutchpp_dist == "rademacher":
S = xnp.sign(S)
Q, _ = xnp.qr(A @ S)
Q2 = xnp.roll(Q, -k, 0)
Q2 = xnp.update_array(Q2, 0, slice(0, abs(k)) if k <= 0 else slice(-abs(k), None))
slc = slice(abs(k), None) if -k > 0 else slice(None, -abs(k) or None)
diag_sum = ((A @ Q) * Q2)[slc].sum(-1)
new_max_iters = max_iters - m
return Q, diag_sum, new_max_iters

key = xnp.PRNGKey(42)
if hutchpp_dist:
Q, hutch_sum, max_iters = hutchpp(key)
while_loop, infos = xnp.while_loop_winfo(err, tol, max_iters, pbar=pbar)
# while_loop = xnp.while_loop
zeros = xnp.zeros((A.shape[0] - abs(k), ), dtype=A.dtype, device=A.device)
n, diag_sum, *_ = while_loop(cond, body, (0, zeros, zeros, xnp.PRNGKey(42)))
n, diag_sum, *_ = while_loop(cond, body, (0, zeros, zeros, key))
mean = diag_sum / (n * bs)
if hutchpp_dist:
mean += hutch_sum
return mean, infos
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