4. Parameters and Configurations

4.1. General Parameters

Parameter	Description	Suggested value	Default value
N_	Rank of the matrix \(A\).		N/A
nev_	Number of desired eigenpairs	No more than 20% of the total number of eigenvalues (or rank of \(A\))	N/A
nex_	Search space increment such that the overall size of the search space is nev_ + nex_.	In most cases 20% of the value of nev_. Best case scenario for optimal convergence is when there is a large spectrum gap between nev_ and nex_.	N/A
approx_	An optional flag indicating whether the user provides ChASE with approximate eigenvectors or uses ChASE in isolation as a traditional black-box solver	When approx_ is set to true, ChASE expects to receive in input two arrays holding approximate vectors and values, respectively	false (black-box solver)
tol_	An optional parameter indicating the minimal value for the residual such that the corresponding eigenpair is declared converged.	As a rule of thumb a minimum value of 1e-08 and 1e-04 are suggested for DP and SP, respectively.	1e-10 in DP. 1e-05 in SP.
max_iter_	An optional parameter set as to avoid that ChASE internal while loop runs unchecked in the rare cases where convergence of the desired eigenpairs cannot be secured. Once reached the max_iter_, ChASE stops execution and returns.	Typically ChASE does not need more than 10 iterations even in the most complex cases and averages 4-5 iterations to convergence.	25

4.2. Chebyshev Filter

Parameter	Description	Suggested value	Default value
deg_	Polynomial degree for the Chebyshev filter. When the value of optimization_ = true, this is the initial polynomial degree used in only the first subspace iteration. Otherwise the same value deg_ is used for every vector for each filter call.	When optimization_ = true, it is advisable to set to a value not larger than 10. If optimization_ = false, then it is advised to select a value not smaller than 15 but not larger than 30.	20 in DP, 10 in SP
optimization_	An optional flag indicating that the filter uses a vector of degrees optimized for each single filtered vector.	Despite the fact that the default value is set to false, it is advisable to set this flag to true often as possible in order to avoid wasting extra FLOPs.	false
deg_extra_	A small value used only in combination with optimization_ = true.	Usually a small number never larger than 5. Apart for rare cases, avoid changing the default value.	2
max_deg_	A parameter which avoids that vectors with a rather small convergence ratio get overfiltered entering in a regime of numerical instability.	This value is a result of practice and experience. We suggest to avoid setting it below 30 and be quite careful to set it too high (> 50).	36 in DP, 18 in SP.

4.3. Lanczos DoS (Spectral Estimator)

Parameter	Description	Suggested value	Default value
lanczos_iter_	In order to estimate the spectral bounds, ChASE executes a limited number of Lanczos steps. These steps are then used to compute an estimate of \(\lambda_1\), \(\lambda_{nev+nex}\), and \(\lambda_N\) based on the Density of State (DoS) algorithm.	ChASE does not need very precise spectral estimates because at each iteration such estimates are automatically improved by the approximate spectrum computed. For the DoS algorithm to work effectively without overburdening the eigensolver, the number of Lanczos iteration should be not less than 10 but also no more than 100.	25
num_lanczos_	After having executed a number of Lanczos steps, ChASE uses a cheap and efficient estimator to calculate the value of the upper extremum of the search space. Such an estimator uses a small number of stochastic vectors indicated by the variable num_lanczos_.	Because ChASE does not need precise estimates of the upper extremum of the search space, the number of vectors used is quite small. The expert user can can change the value to a larger number than the default value (it is not suggested to use a smaller value) and pay a higher computing cost. It is suggested to not set a value for num_lanczos_ higher than 20.	4