exercises:2015_pitt:ls
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exercises:2015_pitt:ls [2015/03/05 14:09] – vondele | exercises:2015_pitt:ls [2020/08/21 10:15] (current) – external edit 127.0.0.1 | ||
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===== 1. Task: Scaling Behavior ===== | ===== 1. Task: Scaling Behavior ===== | ||
- | Calculate the energy of the 2D-polymer for various different system sizes, by using '' | + | Calculate the energy of the 2D-polymer for various different system sizes, by using '' |
The number of seconds required of each SCF cycle is printed as part of the regular output. | The number of seconds required of each SCF cycle is printed as part of the regular output. | ||
Line 33: | Line 33: | ||
===== 2. Task: Filter Threshold ===== | ===== 2. Task: Filter Threshold ===== | ||
- | Calculate the energy of the single unit-cell with the linear scaling method at different filter thresholds, by changing '' | + | Calculate the energy of the single unit-cell with the linear scaling method at different filter thresholds, by changing '' |
+ | |||
+ | ===== 3. Task: LS algorithm ===== | ||
+ | |||
+ | Finally, compare the efficiency of three different algorithms (using NREP 2x2). The following three options can be tried: | ||
+ | |||
+ | sign matrix iterations [[doi> | ||
+ | < | ||
+ | ! linear scaling SCF | ||
+ | & | ||
+ | ! SIGN_MATRIX, | ||
+ | PURIFICATION_METHOD SIGN_MATRIX | ||
+ | ! threshold used to determine sparsity and thus speed and accuracy | ||
+ | EPS_FILTER 1E-7 | ||
+ | ! convergence for the SCF | ||
+ | EPS_SCF | ||
+ | ! chemical potential, an energy from within in the HOMO-LUMO gap | ||
+ | MU | ||
+ | S_PRECONDITIONER ATOMIC | ||
+ | &END | ||
+ | </ | ||
+ | |||
+ | trs4 iterations [[doi> | ||
+ | < | ||
+ | ! linear scaling SCF | ||
+ | & | ||
+ | ! TRS4, does not need an estimate for the chemical potential | ||
+ | PURIFICATION_METHOD TRS4 | ||
+ | ! threshold used to determine sparsity and thus speed and accuracy | ||
+ | EPS_FILTER 1E-7 | ||
+ | ! convergence for the SCF | ||
+ | EPS_SCF | ||
+ | ! chemical potential, an energy from within in the HOMO-LUMO gap | ||
+ | MU | ||
+ | S_PRECONDITIONER ATOMIC | ||
+ | &END | ||
+ | </ | ||
+ | |||
+ | curvy steps [[doi> | ||
+ | < | ||
+ | ! linear scaling SCF | ||
+ | & | ||
+ | ! TRS4, does not need an estimate for the chemical potential | ||
+ | PURIFICATION_METHOD TRS4 | ||
+ | ! threshold used to determine sparsity and thus speed and accuracy | ||
+ | EPS_FILTER 1E-7 | ||
+ | ! convergence for the SCF | ||
+ | EPS_SCF | ||
+ | ! chemical potential, an energy from within in the HOMO-LUMO gap | ||
+ | MU | ||
+ | S_PRECONDITIONER NONE | ||
+ | & | ||
+ | &END CURVY_STEPS | ||
+ | &END | ||
+ | </ | ||
+ | |||
+ | In making your judgement, consider the fact that the rate of convergence might not be the same for all algorithms. | ||
+ | |||
+ | From a practical point of view, the curvy_steps algorithm seems very robust in converging the SCF of electronically difficult systems, while the sign matrix algorithm is only worthwhile considering if the chemical potential is known (or fixed). | ||
===== Input File ===== | ===== Input File ===== |
exercises/2015_pitt/ls.1425564576.txt.gz · Last modified: 2020/08/21 10:15 (external edit)