Module: tfp.experimental.fastgp.preconditioners.tfp_math

Functions for common linear algebra operations.

Functions

cholesky_concat(...): Concatenates chol @ chol.T with additional rows and columns.

cholesky_update(...): Returns cholesky of chol @ chol.T + multiplier * u @ u.T.

fill_triangular(...): Creates a (batch of) triangular matrix from a vector of inputs.

fill_triangular_inverse(...): Creates a vector from a (batch of) triangular matrix.

hpsd_logdet(...): Computes log|det(matrix)|, where matrix is a HPSD matrix.

hpsd_quadratic_form_solve(...): Computes rhs^T matrix^-1 rhs, where matrix is HPSD.

hpsd_quadratic_form_solvevec(...): Computes rhs^T matrix^-1 rhs, where matrix is HPSD.

hpsd_solve(...): Computes matrix^-1 rhs, where matrix is HPSD.

hpsd_solvevec(...): Computes matrix^-1 rhs, where matrix is HPSD.

low_rank_cholesky(...): Computes a low-rank approximation to the Cholesky decomposition.

lu_matrix_inverse(...): Computes a matrix inverse given the matrix's LU decomposition.

lu_reconstruct(...): The inverse LU decomposition, X == lu_reconstruct(*tf.linalg.lu(X)).

lu_reconstruct_assertions(...): Returns list of assertions related to lu_reconstruct assumptions.

lu_solve(...): Solves systems of linear eqns A X = RHS, given LU factorizations.

pivoted_cholesky(...): Computes the (partial) pivoted cholesky decomposition of matrix.

sparse_or_dense_matmul(...): Returns (batched) matmul of a SparseTensor (or Tensor) with a Tensor.

sparse_or_dense_matvecmul(...): Returns (batched) matmul of a (sparse) matrix with a column vector.