Notebooks · lib/randla/repro

randla's results to 17 digits, for the three-engine comparison

Each line is a sum over one operator or one driver's result, printed with every digit a double has. tools/three-engines.sh requires the interpreter, C and wasm to print these bytes identically, so a sketch or a driver that depended on evaluation order, a platform libm or an engine's summation would show up here as a differing digit.

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[1]lines 12–50

from randla.sketch import gaussian, rademacher, saso_dense, srht_apply
from randla.lowrank import rsvd, nystrom, rpcholesky, with_spectrum, poly_decay
from randla.lstsq import sap_lstsq
from randla.trace import hutchpp

G = gaussian(40, 30, 2026, 0)
R = rademacher(40, 30, 2026, 1)
S = saso_dense(12, 40, 3, 2026, 2)
H = srht_apply(G, 16, 2026, 3)
print("gaussian  ", fmt(sum(G * G), 17), fmt(G[39, 29], 17))
print("rademacher", fmt(sum(R), 17))
print("saso      ", fmt(sum(S * S), 17), fmt(sum(S @ G), 17))
print("srht      ", fmt(sum(H * H), 17))

s = poly_decay(30, 1.5)
A = with_spectrum(50, 35, s, 7)
U, sk, Vt = rsvd(A, 6)
print("rsvd      ", fmt(sum(sk), 17), fmt(norm(A - (U * sk) @ Vt), 17))
P = transpose(A) @ A
Un, lam = nystrom(P, 8, 7, 1)
print("nystrom   ", fmt(sum(lam), 17))
F, piv = rpcholesky(P, 8, 7, 2)
print("rpchol    ", fmt(sum(F * F), 17), piv[0], piv[7])
# least squares needs full column rank: a tall 120-by-12 problem
T = with_spectrum(120, 12, poly_decay(12, 1.0), 8)
b = T @ ones(12) + 0.01 * gaussian(120, 1, 7, 9)[:, 0]
x, it = sap_lstsq(T, b, kind="saso")
print("sap_lstsq ", fmt(sum(x), 17), it)
print("hutchpp   ", fmt(hutchpp(P, 12, 7, 4), 17), fmt(trace(P), 17))

test "the printed results are what the drivers claim" {
    assert_near(sum(R * R), 1200.0, 0.0)
    assert_lt(norm(A - (U * sk) @ Vt), 1.05 * norm(s[6:]))
    assert_true(len(piv) == 8)
    assert_lt(float(it), 60.0)
}

# SPDX-License-Identifier: MIT OR Apache-2.0
# SPDX-FileCopyrightText: 2026 The Viv authors

from randla.sketch import gaussian, rademacher, saso_dense, srht_apply
from randla.lowrank import rsvd, nystrom, rpcholesky, with_spectrum, poly_decay
from randla.lstsq import sap_lstsq
from randla.trace import hutchpp

G = gaussian(40, 30, 2026, 0)
R = rademacher(40, 30, 2026, 1)
S = saso_dense(12, 40, 3, 2026, 2)
H = srht_apply(G, 16, 2026, 3)
print("gaussian  ", fmt(sum(G * G), 17), fmt(G[39, 29], 17))
print("rademacher", fmt(sum(R), 17))
print("saso      ", fmt(sum(S * S), 17), fmt(sum(S @ G), 17))
print("srht      ", fmt(sum(H * H), 17))

s = poly_decay(30, 1.5)
A = with_spectrum(50, 35, s, 7)
U, sk, Vt = rsvd(A, 6)
print("rsvd      ", fmt(sum(sk), 17), fmt(norm(A - (U * sk) @ Vt), 17))
P = transpose(A) @ A
Un, lam = nystrom(P, 8, 7, 1)
print("nystrom   ", fmt(sum(lam), 17))
F, piv = rpcholesky(P, 8, 7, 2)
print("rpchol    ", fmt(sum(F * F), 17), piv[0], piv[7])
# least squares needs full column rank: a tall 120-by-12 problem
T = with_spectrum(120, 12, poly_decay(12, 1.0), 8)
b = T @ ones(12) + 0.01 * gaussian(120, 1, 7, 9)[:, 0]
x, it = sap_lstsq(T, b, kind="saso")
print("sap_lstsq ", fmt(sum(x), 17), it)
print("hutchpp   ", fmt(hutchpp(P, 12, 7, 4), 17), fmt(trace(P), 17))

test "the printed results are what the drivers claim" {
    assert_near(sum(R * R), 1200.0, 0.0)
    assert_lt(norm(A - (U * sk) @ Vt), 1.05 * norm(s[6:]))
    assert_true(len(piv) == 8)
    assert_lt(float(it), 60.0)
}

# SPDX-License-Identifier: MIT OR Apache-2.0
# SPDX-FileCopyrightText: 2026 The Viv authors