matrix_operations.md

Matrix Operations

LD matrix operations are centered on PrecisionOperator, which subclasses SciPy's LinearOperator. It represents an LDGM precision matrix or its Schur complement.

If you need correlation_matrix[indices, indices] @ vector, use ldgm[indices].solve(vector). If you need inv(correlation_matrix[indices, indices]) @ vector, use ldgm[indices] @ vector. Do not index the dense matrix manually: the submatrix of an inverse is not the inverse of a submatrix.

import numpy as np
import graphld as gld

ldgm = gld.load_ldgm(
    filepath="data/test/1kg_chr1_16103_2888443.EAS.edgelist",
    snplist_path="data/test/1kg_chr1_16103_2888443.snplist",
)

vector = np.random.randn(ldgm.shape[0])
precision_times_vector = ldgm @ vector
correlation_times_vector = ldgm.solve(precision_times_vector)
assert np.allclose(correlation_times_vector, vector)

See also:

• I/O and Merging
• graphld.precision API Reference
• graphld package overview