rapid_models.gp_diagnostics.utils.linalg

Module Contents

Functions

triang_solve(...)	Wrapper for lapack dtrtrs function
mulinv_solve(...)	Solve A*X = B where A = F*F^{T}
mulinv_solve_rev(...)	Reversed version of mulinv_solve
symmetrify(A, *], nptyping.Float], upper)	Create symmetric matrix from triangular matrix
chol_inv(→ nptyping.NDArray[nptyping.Shape[N, N], ...)	Return inverse of matrix A = L*L.T where L is lower triangular
traceprod(→ float)	Calculate trace(A*B) for two matrices A and B
try_chol(→ Union[nptyping.NDArray[nptyping.Shape[N, ...)	Try to compute the Cholesky decomposition of (K + noise_variance*I), and print an error message if it does not work

rapid_models.gp_diagnostics.utils.linalg.triang_solve(A: nptyping.NDArray[nptyping.Shape[N, N], nptyping.Float], B: Union[nptyping.NDArray[nptyping.Shape[N], nptyping.Float], nptyping.NDArray[nptyping.Shape[N, M], nptyping.Float]], lower: bool = True, trans: bool = False) → Union[nptyping.NDArray[nptyping.Shape[N], nptyping.Float], nptyping.NDArray[nptyping.Shape[N, M], nptyping.Float]]

Wrapper for lapack dtrtrs function DTRTRS solves a triangular system of the form

A * X = B or A**T * X = B,

where A is a triangular matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular. :param A: Matrix A(triangular) :param B: Matrix B :param lower: is matrix lower (true) or upper (false) :param trans: calculate A**T * X = B (true) or A * X = B (false)

Returns:

Solution to A * X = B or A**T * X = B

rapid_models.gp_diagnostics.utils.linalg.mulinv_solve(F: nptyping.NDArray[nptyping.Shape[N, N], nptyping.Float], B: Union[nptyping.NDArray[nptyping.Shape[N], nptyping.Float], nptyping.NDArray[nptyping.Shape[N, M], nptyping.Float]], lower: bool = True) → Union[nptyping.NDArray[nptyping.Shape[N], nptyping.Float], nptyping.NDArray[nptyping.Shape[N, M], nptyping.Float]]

Solve A*X = B where A = F*F^{T}

lower = True -> when F is LOWER triangular. This gives faster calculation

rapid_models.gp_diagnostics.utils.linalg.mulinv_solve_rev(F: nptyping.NDArray[nptyping.Shape[N, N], nptyping.Float], B: Union[nptyping.NDArray[nptyping.Shape[N], nptyping.Float], nptyping.NDArray[nptyping.Shape[M, N], nptyping.Float]], lower: bool = True) → Union[nptyping.NDArray[nptyping.Shape[N], nptyping.Float], nptyping.NDArray[nptyping.Shape[M, N], nptyping.Float]]

Reversed version of mulinv_solve

Solves X*A = B where A = F*F^{T}

lower = True -> when F is LOWER triangular. This gives faster calculation

rapid_models.gp_diagnostics.utils.linalg.symmetrify(A: nptyping.NDArray[nptyping.Shape[*, *], nptyping.Float], upper: bool = False)

Create symmetric matrix from triangular matrix

rapid_models.gp_diagnostics.utils.linalg.chol_inv(L: nptyping.NDArray[nptyping.Shape[N, N], nptyping.Float]) → nptyping.NDArray[nptyping.Shape[N, N], nptyping.Float]

Return inverse of matrix A = L*L.T where L is lower triangular Uses LAPACK function dpotri

rapid_models.gp_diagnostics.utils.linalg.traceprod(A: nptyping.NDArray[nptyping.Shape[N, M], nptyping.Float], B: nptyping.NDArray[nptyping.Shape[M, N], nptyping.Float]) → float

Calculate trace(A*B) for two matrices A and B

rapid_models.gp_diagnostics.utils.linalg.try_chol(K: nptyping.NDArray[nptyping.Shape[N, N], nptyping.Float], noise_variance: float = 0.0, func_name: str = '') → Union[nptyping.NDArray[nptyping.Shape[N, N], nptyping.Float], None]

Try to compute the Cholesky decomposition of (K + noise_variance*I), and print an error message if it does not work