def test_mat(self):
n = 8
perms = sn(n)
g = random.choice(perms)
mat = g.mat()
for j in range(1, n + 1):
i = g[j]
self.assertEqual(mat[i-1, j-1], 1)
def raw_ft(f, _lambda):
n = sum(_lambda)
_sn = sn(n)
rho = SnIrrep(_lambda, fmt='dense')
fhat = 0
for p in _sn:
fhat += rho(p) * f(p)
return fhat
def test_yor_inv(self):
partition = (4, 3, 1)
s8 = sn(8)
rho = SnIrrep(partition, 'dense')
g = random.choice(s8)
gmat = rho(g)
mat_inv = np.linalg.inv(gmat)
ginv_mat = rho(g.inv())
self.assertTrue(np.allclose(mat_inv, ginv_mat))
def main():
n = 6
_sn = sn(n)
_lambda = (n - 2, 1, 1)
distr = sn_distr(n)
sn_func = make_sn_func(distr, _sn)
irreps, _ = qap_decompose(_lambda)
all_tups = ordered_tups(n)
fhat_perm = ft(sn_func, perm_rep, _sn)
fhat_perm_tup = ft(sn_func, lambda p: perm_tup(p, all_tups), _sn)
block_diag = gen_fhat_blocks(sn_func, irreps, _sn)
c_mat = c_lambda(_lambda)
print(np.allclose(
np.linalg.inv(c_mat) @ block_diag @ c_mat, fhat_perm_tup))
def test_yor_dense(self):
partition = (4, 2, 1, 1)
s8 = sn(8)
g = random.choice(s8)
h = random.choice(s8)
gh = g * h
rho = SnIrrep(partition, 'dense')
gd = rho(g)
hd = rho(h)
ghd = rho(gh)
self.assertTrue(np.allclose(gd.dot(hd), ghd))
rho_sp = SnIrrep(partition, 'sparse')
gsp = rho_sp(g)
hsp = rho_sp(h)
ghsp = rho_sp(gh)
self.assertTrue(np.allclose(gd, gsp.toarray()))
self.assertTrue(np.allclose(hd, hsp.toarray()))
self.assertTrue(np.allclose(ghd, ghsp.toarray()))
self.assertTrue(np.allclose(gsp.dot(hsp).toarray(), ghsp.toarray()))
perm_tup = c_lambdas_inv[(n-2, 1, 1)] @ block_diags[(n - 2, 1, 1)].value @c_lambdas[(n-2, 1, 1)]
res = ((perm @ amat @ perm.T)@ bmat).sum()
print('Perm tup sums:', perm_tup.sum(axis=1), perm_tup.sum(axis=0), perm_tup.sum(), perm_tup.shape)
print(f'Lower bound: {res} | result: {result}')
pdb.set_trace()
if __name__ == '__main__':
#fname = '../data/rou12.mat'
#mat = scipy.io.loadmat(fname)
np.random.seed(0)
n = 6
mat = {}
mat['A'] = np.random.randint(0, 10, (n,n))
mat['B'] = np.random.randint(0, 100, (n,n))
best = (mat['A'] * mat['B']).sum()
best_p = Perm.eye(n)
avg = 0
for p in sn(mat['A'].shape[0]):
obj = ((p.mat() @ mat['A'] @ p.mat().T) @ mat['B']).sum()
avg += obj
if obj > best:
best = obj
best_p = p
avg = avg / math.factorial(n)
print('Opt value: {} | Avg value: {:.2f} | Opt perm: {}'.format(best, avg, best_p))
start = time.time()
main(mat)
print('Elapsed: {:.2f}s'.format(time.time() - start))