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Tikhonov regularization¶

Tikhonov regularization is a modification of the standard least-squares problem which instead solves

\[\min_X \| \text{op}(A) X - B \|_2^2 + \| \Gamma X \|_2^2\]

C++ API¶

type TikhonovAlg¶

An enum that can take on the values:

TIKHONOV_CHOLESKY: Run a less accurate, but often faster, Cholesky-based algorithm
TIKHONOV_QR: Run a QR-based algorithm

void Tikhonov(const Matrix<F> &A, const Matrix<F> &B, const Matrix<F> &Gamma, Matrix<F> &X, TikhonovAlg alg = TIKHONOV_CHOLESKY)¶

void Tikhonov(const AbstractDistMatrix<F> &A, const AbstractDistMatrix<F> &B, const AbstractDistMatrix<F> &Gamma, AbstractDistMatrix<F> &X, TikhonovAlg alg = TIKHONOV_CHOLESKY)¶

C API¶

ElTikhonovAlg¶

An enum which can take on the values:

EL_TIKHONOV_CHOLESKY: Run a less accurate, but often faster, Cholesky-based algorithm
EL_TIKHONOV_QR: Run a QR-based algorithm

ElError ElTikhonov_s(ElConstMatrix_s A, ElConstMatrix_s B, ElConstMatrix_s Gamma, ElMatrix_s X, ElTikhonovAlg alg)¶

ElError ElTikhonov_d(ElConstMatrix_d A, ElConstMatrix_d B, ElConstMatrix_d Gamma, ElMatrix_d X, ElTikhonovAlg alg)¶

ElError ElTikhonov_c(ElConstMatrix_c A, ElConstMatrix_c B, ElConstMatrix_c Gamma, ElMatrix_c X, ElTikhonovAlg alg)¶

ElError ElTikhonov_z(ElConstMatrix_z A, ElConstMatrix_z B, ElConstMatrix_z Gamma, ElMatrix_z X, ElTikhonovAlg alg)¶

ElError ElTikhonovDist_s(ElConstDistMatrix_s A, ElConstDistMatrix_s B, ElConstDistMatrix_s Gamma, ElDistMatrix_s X, ElTikhonovAlg alg)¶

ElError ElTikhonovDist_d(ElConstDistMatrix_d A, ElConstDistMatrix_d B, ElConstDistMatrix_d Gamma, ElDistMatrix_d X, ElTikhonovAlg alg)¶

ElError ElTikhonovDist_c(ElConstDistMatrix_c A, ElConstDistMatrix_c B, ElConstDistMatrix_c Gamma, ElDistMatrix_c X, ElTikhonovAlg alg)¶

ElError ElTikhonovDist_z(ElConstDistMatrix_z A, ElConstDistMatrix_z B, ElConstDistMatrix_z Gamma, ElDistMatrix_z X, ElTikhonovAlg alg)¶