def test_tril_triu():
A = np.random.randn(20, 20)
for chk in [5, 4]:
dA = da.from_array(A, (chk, chk))
assert np.allclose(da.triu(dA).compute(), np.triu(A))
assert np.allclose(da.tril(dA).compute(), np.tril(A))
for k in [
-25,
-20,
-19,
-15,
-14,
-9,
-8,
-6,
-5,
-1,
1,
4,
5,
6,
8,
10,
11,
15,
16,
19,
20,
21,
]:
assert np.allclose(da.triu(dA, k).compute(), np.triu(A, k))
assert np.allclose(da.tril(dA, k).compute(), np.tril(A, k))
def test_tril_triu():
A = cupy.random.randn(20, 20)
for chk in [5, 4]:
dA = da.from_array(A, (chk, chk), asarray=False)
assert_eq(da.triu(dA), np.triu(A))
assert_eq(da.tril(dA), np.tril(A))
for k in [-25, -20, -9, -1, 1, 8, 19, 21]:
assert_eq(da.triu(dA, k), np.triu(A, k))
assert_eq(da.tril(dA, k), np.tril(A, k))
def test_tril_triu():
A = np.random.randn(20, 20)
for chk in [5, 4]:
dA = da.from_array(A, (chk, chk))
assert np.allclose(da.triu(dA).compute(), np.triu(A))
assert np.allclose(da.tril(dA).compute(), np.tril(A))
for k in [-25, -20, -19, -15, -14, -9, -8, -6, -5, -1,
1, 4, 5, 6, 8, 10, 11, 15, 16, 19, 20, 21]:
assert np.allclose(da.triu(dA, k).compute(), np.triu(A, k))
assert np.allclose(da.tril(dA, k).compute(), np.tril(A, k))
def test_tril_triu_non_square_arrays():
A = np.random.randint(0, 11, (30, 35))
dA = da.from_array(A, chunks=(5, 5))
assert_eq(da.triu(dA), np.triu(A))
assert_eq(da.tril(dA), np.tril(A))
def _check_lu_result(p, l, u, A):
assert np.allclose(p.dot(l).dot(u), A)
# check triangulars
assert_eq(l, da.tril(l), check_graph=False)
assert_eq(u, da.triu(u), check_graph=False)
def Weir_Goudet_beta(
ds: Dataset,
*,
stat_identity_by_state: Hashable = variables.stat_identity_by_state,
merge: bool = True,
) -> Dataset:
"""Estimate pairwise beta between all pairs of samples as described
in Weir and Goudet 2017 [1].
Beta is the kinship scaled by the average kinship of all pairs of
individuals in the dataset such that the non-diagonal (non-self) values
sum to zero.
Beta may be corrected to more accurately reflect pedigree based kinship
estimates using the formula
:math:`\\hat{\\beta}^c=\\frac{\\hat{\\beta}-\\hat{\\beta}_0}{1-\\hat{\\beta}_0}`
where :math:`\\hat{\\beta}_0` is the estimated beta between samples which are
known to be unrelated [1].
Parameters
----------
ds
Genotype call dataset.
stat_identity_by_state
Input variable name holding stat_identity_by_state as defined
by :data:`sgkit.variables.stat_identity_by_state_spec`.
If the variable is not present in ``ds``, it will be computed
using :func:`identity_by_state`.
merge
If True (the default), merge the input dataset and the computed
output variables into a single dataset, otherwise return only
the computed output variables.
See :ref:`dataset_merge` for more details.
Returns
-------
A dataset containing :data:`sgkit.variables.stat_Weir_Goudet_beta_spec`
which is a matrix of estimated pairwise kinship relative to the average
kinship of all pairs of individuals in the dataset.
The dimensions are named ``samples_0`` and ``samples_1``.
Examples
--------
>>> import sgkit as sg
>>> ds = sg.simulate_genotype_call_dataset(n_variant=3, n_sample=3, n_allele=10, seed=3)
>>> # sample 2 "inherits" alleles from samples 0 and 1
>>> ds.call_genotype.data[:, 2, 0] = ds.call_genotype.data[:, 0, 0]
>>> ds.call_genotype.data[:, 2, 1] = ds.call_genotype.data[:, 1, 0]
>>> sg.display_genotypes(ds) # doctest: +NORMALIZE_WHITESPACE
samples S0 S1 S2
variants
0 7/1 8/6 7/8
1 9/5 3/6 9/3
2 8/8 8/3 8/8
>>> # estimate beta
>>> ds = sg.Weir_Goudet_beta(ds).compute()
>>> ds.stat_Weir_Goudet_beta.values # doctest: +NORMALIZE_WHITESPACE
array([[ 0.5 , -0.25, 0.25],
[-0.25, 0.25, 0. ],
[ 0.25, 0. , 0.5 ]])
>>> # correct beta assuming least related samples are unrelated
>>> beta = ds.stat_Weir_Goudet_beta
>>> beta0 = beta.min()
>>> beta_corrected = (beta - beta0) / (1 - beta0)
>>> beta_corrected.values # doctest: +NORMALIZE_WHITESPACE
array([[0.6, 0. , 0.4],
[0. , 0.4, 0.2],
[0.4, 0.2, 0.6]])
References
----------
[1] - Bruce, S. Weir, and Jérôme Goudet 2017.
"A Unified Characterization of Population Structure and Relatedness."
Genetics 206 (4): 2085-2103.
"""
ds = define_variable_if_absent(
ds, variables.stat_identity_by_state, stat_identity_by_state, identity_by_state
)
variables.validate(
ds, {stat_identity_by_state: variables.stat_identity_by_state_spec}
)
ibs = ds[stat_identity_by_state].data
# average matching is the mean of non-diagonal elements
num = da.nansum(da.tril(ibs, -1))
denom = da.nansum(da.tril(~da.isnan(ibs), -1))
avg = num / denom
beta = (ibs - avg) / (1 - avg)
new_ds = create_dataset(
{
variables.stat_Weir_Goudet_beta: (
("samples_0", "samples_1"),
beta,
)
}
)
return conditional_merge_datasets(ds, new_ds, merge)
def _check_lu_result(p, l, u, A):
assert np.allclose(p.dot(l).dot(u), A)
# check triangulars
assert_eq(l, da.tril(l))
assert_eq(u, da.triu(u))
def test_tril_triu_non_square_arrays():
A = np.random.randint(0, 11, (30, 35))
dA = da.from_array(A, chunks=(5, 5))
assert_eq(da.triu(dA), np.triu(A))
assert_eq(da.tril(dA), np.tril(A))
