SHENLIN 发表于 2025-7-31 13:48 diag(i)是什么，i是nocc*vir这个维度吗 |
SHENLIN 发表于 2025-7-31 16:11 讲道理不需要设定max space。或者说设定max space不能大于A矩阵大小 |
SHENLIN 发表于 2025-7-31 16:11 我不清楚你的程序有没有trial vector的space，也就是个数的概念，如果没有的话，大概是求n个根就只有n个trial vector？那效率应该是比较低的。 如果有space的概念，每一步会扩大space，但是没有max space（超过了就重来），也可能会有收敛问题，但也不一定。 |
本帖最后由 SHENLIN 于 2025-7-31 16:16 编辑 hebrewsnabla 发表于 2025-7-31 12:21 好的，谢谢。一定要设定max space吗？直接用最大迭代圈数控制可以吗？ |
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do j = 1, lowest do i=1,nocc do a=1,nvir ia=(i-1)*nvir+a denom = -eorb(a+nocc)+eorb(i)+eigenvalues(j) ! 处理分母过小的情况 if (abs(denom) < t) then denom = sign(t, denom) end if ! 计算修正项 correction(ia, j) = residues(ia, j) / denom end do end do end do 我这样写preconditioner就是正确的，能正常收敛 do j = 1, size(residues, 2) do i = 1, size(correction, 1) D = eigenvalues(j) - diag(i) ! 处理分母过小的情况 if (abs(D) < t) then D = sign(t, D) end if ! 计算修正项 correction(i, j) = residues(i, j) / D end do end do这样写就是错误的，一直收敛不了。这两者不是等价的吗？好奇怪 |
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本帖最后由 hebrewsnabla 于 2025-7-31 12:23 编辑 可以参考一下这个实现 https://github.com/pyscf/pyscf/b ... nalg_helper.py#L291 你的max space是多少？ |
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本帖最后由 SHENLIN 于 2025-7-31 10:44 编辑 谢谢老师指导，确实是diag的原因，因为我如果把矩阵元都求出来，然后取对角线元素，上面的例子16步左右能收敛。但是我在写CIS的过程中，为了节约存储，不是不求出H(ia,jb),而是直接求sigma向量HV吗？所以我的diag取的都是HF轨道能级差项，忽略了后面电子积分项（我看很多程序好像都是这么做的）。初猜和preconditioner用的都是这个，需要怎么调整呢？ do i=1,nocc do a=1,nvir ia=(i-1)*nvir+a diag(ia)=eorb(a+nocc)-eorb(i) enddo enddo |
SHENLIN 发表于 2025-7-7 09:36 感觉大体还是有收敛趋势的，可能preconditioner实现得有问题？可以对角化一个对角矩阵，看是不是一步收敛，这样验证preconditioner有没有实现对 |
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和上面一样的,nstate=5需要迭代43圈才收敛，nstate=10需要22圈才收敛。到底是啥问题？？ Number of occupied orbitals : 5 Number of virtual orbitals : 44 r-norm 0.0859670869 0.0961734206 0.0961779972 0.0823855538 0.0823923430 Elap time for1 iteration: 0.07 min r-norm 0.0939422432 0.1136267943 0.1133913454 0.0932864648 0.0919924146 Elap time for2 iteration: 0.10 min r-norm 0.1104706139 0.1402461731 0.1362228944 0.1047233933 0.0992314979 Elap time for3 iteration: 0.10 min r-norm 0.0839918056 0.1276662383 0.1345923188 0.1114826929 0.1167705100 Elap time for4 iteration: 0.10 min r-norm 0.0879364097 0.1367220350 0.1345198104 0.0817144452 0.1023588033 Elap time for5 iteration: 0.12 min r-norm 0.1333545255 0.1256084830 0.1509244491 0.0733161709 0.0816386380 Elap time for6 iteration: 0.12 min r-norm 0.0918918996 0.1194373967 0.1129820572 0.0778894700 0.0745357280 Elap time for7 iteration: 0.13 min r-norm 0.0945563448 0.1496321715 0.1360978203 0.0954277892 0.1042596870 Elap time for8 iteration: 0.13 min r-norm 0.1382295514 0.1113698975 0.1474383490 0.0743684072 0.0854812935 Elap time for9 iteration: 0.13 min r-norm 0.1025797830 0.1000518348 0.0937715458 0.0662613920 0.0638135975 Elap time for10 iteration: 0.15 min r-norm 0.0931504528 0.0922992344 0.1080575882 0.0620406054 0.0748651619 Elap time for11 iteration: 0.17 min r-norm 0.0926317499 0.0772896051 0.0809489506 0.0613332612 0.0641595639 Elap time for12 iteration: 0.15 min r-norm 0.0665347374 0.0629086255 0.0770907103 0.0425396491 0.0594336014 Elap time for13 iteration: 0.18 min r-norm 0.0523427534 0.0622265817 0.0625065519 0.0356882962 0.0386663151 Elap time for14 iteration: 0.17 min r-norm 0.0499933112 0.0456126482 0.0626748593 0.0299150655 0.0414691036 Elap time for15 iteration: 0.18 min r-norm 0.0278982335 0.0292917812 0.0391304847 0.0252510147 0.0324943526 Elap time for16 iteration: 0.20 min r-norm 0.0221077037 0.0167310702 0.0230958364 0.0192126420 0.0215620310 Elap time for17 iteration: 0.22 min r-norm 0.0137119275 0.0121285101 0.0149942035 0.0181570962 0.0159096701 Elap time for18 iteration: 0.20 min r-norm 0.0101229064 0.0065642979 0.0114052417 0.0246803063 0.0145937636 Elap time for19 iteration: 0.22 min r-norm 0.0053748381 0.0045956244 0.0060060404 0.0340680875 0.0173046677 Elap time for20 iteration: 0.23 min r-norm 0.0032055613 0.0030581182 0.0037756580 0.1187479188 0.0225333528 Elap time for21 iteration: 0.23 min r-norm 0.0019937965 0.0019969316 0.0021297509 0.1485934236 0.0355366962 Elap time for22 iteration: 0.23 min r-norm 0.0015196083 0.0011215612 0.0015955654 0.0864943371 0.0502523481 Elap time for23 iteration: 0.25 min r-norm 0.0011999264 0.0007936677 0.0009122443 0.0704919186 0.0892320727 Elap time for24 iteration: 0.25 min r-norm 0.0008931291 0.0005064775 0.0006463799 0.0716211999 0.1176367125 Elap time for25 iteration: 0.27 min r-norm 0.0006871657 0.0002780361 0.0004348996 0.0506645645 0.1007364757 Elap time for26 iteration: 0.27 min r-norm 0.0005234747 0.0001451260 0.0003245010 0.0397565107 0.0870168418 Elap time for27 iteration: 0.27 min r-norm 0.0003975630 0.0000903843 0.0002054682 0.0370669757 0.0694277818 Elap time for28 iteration: 0.32 min r-norm 0.0003009416 0.0000650028 0.0001465787 0.0258479447 0.0710442528 Elap time for29 iteration: 0.32 min r-norm 0.0001913904 0.0000389681 0.0001114010 0.0177343223 0.0602410773 Elap time for30 iteration: 0.35 min r-norm 0.0001331266 0.0000345184 0.0000624007 0.0101300747 0.0347834598 Elap time for31 iteration: 0.30 min r-norm 0.0000798987 0.0000438127 0.0000215644 0.0083319747 0.0251518196 Elap time for32 iteration: 0.32 min r-norm 0.0000452280 0.0000222379 0.0000115394 0.0077254885 0.0145465833 Elap time for33 iteration: 0.32 min r-norm 0.0000248855 0.0000115116 0.0000058604 0.0059863711 0.0076289659 Elap time for34 iteration: 0.33 min r-norm 0.0000072587 0.0000049618 0.0000030861 0.0035746366 0.0040836744 Elap time for35 iteration: 0.33 min r-norm 0.0000037596 0.0000030474 0.0000014237 0.0014577607 0.0024615593 Elap time for36 iteration: 0.35 min r-norm 0.0000020340 0.0000008507 0.0000005975 0.0006395652 0.0010532152 Elap time for37 iteration: 0.47 min r-norm 0.0000009556 0.0000002606 0.0000003213 0.0004556286 0.0002249363 Elap time for38 iteration: 0.47 min r-norm 0.0000002619 0.0000001297 0.0000000842 0.0001885796 0.0001356042 Elap time for39 iteration: 0.37 min r-norm 0.0000000769 0.0000000345 0.0000000754 0.0000684111 0.0000568973 Elap time for40 iteration: 0.37 min r-norm 0.0000000686 0.0000000138 0.0000000510 0.0000336428 0.0000179266 Elap time for41 iteration: 0.37 min r-norm 0.0000000663 0.0000000107 0.0000000477 0.0000185220 0.0000102552 Elap time for42 iteration: 0.50 min r-norm 0.0000000432 0.0000000099 0.0000000336 0.0000037480 0.0000024045 Converged in 43 iterations. |
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占据轨道5，虚轨道44，nstate=3，为啥我写得程序一直收敛不了？ Number of occupied orbitals : 5 Number of virtual orbitals : 44 r-norm 0.0904215215 0.0954082545 0.0955254642 Elap time for1 iteration: 0.05 min r-norm 0.1020421580 0.1005147596 0.3195436706 Elap time for2 iteration: 0.07 min r-norm 0.1147001275 0.1182726230 0.4759256149 Elap time for3 iteration: 0.07 min r-norm 0.0912756888 0.1447432953 1.6792727450 Elap time for4 iteration: 0.08 min r-norm 0.0847314365 0.1083200385 1.3451540912 Elap time for5 iteration: 0.10 min r-norm 0.1017993397 0.1161335163 0.9611721320 Elap time for6 iteration: 0.08 min r-norm 0.0977623559 0.1457940707 1.1992824782 Elap time for7 iteration: 0.10 min r-norm 0.0845577392 0.1163889397 0.7997297814 Elap time for8 iteration: 0.12 min r-norm 0.0913815993 0.1284229977 0.7724938236 Elap time for9 iteration: 0.12 min r-norm 0.1473733525 0.1621629793 0.9306342023 Elap time for10 iteration: 0.10 min r-norm 0.1022261208 0.1520397934 0.8568445039 Elap time for11 iteration: 0.13 min r-norm 0.0747816170 0.1215488567 0.5824591344 Elap time for12 iteration: 0.12 min r-norm 0.1038876657 0.1438944762 0.6743080739 Elap time for13 iteration: 0.13 min r-norm 0.1119399114 0.1492259623 0.7073477389 Elap time for14 iteration: 0.12 min r-norm 0.0716162756 0.0678459788 0.4724069512 Elap time for15 iteration: 0.13 min r-norm 0.0685578300 0.0721142019 0.4848637315 Elap time for16 iteration: 0.15 min r-norm 0.0506047135 0.0770437986 0.3580719103 Elap time for17 iteration: 0.15 min r-norm 0.0332001995 0.0589313271 0.2426525056 Elap time for18 iteration: 0.15 min r-norm 0.0356365333 0.0585605558 0.2491546503 Elap time for19 iteration: 0.15 min r-norm 0.0235190389 0.0403184234 0.1662902469 Elap time for20 iteration: 0.15 min r-norm 0.0168157222 0.0429556733 0.1319907180 Elap time for21 iteration: 0.17 min r-norm 0.0153743840 0.0338096331 0.1234901048 Elap time for22 iteration: 0.15 min r-norm 0.0123653356 0.0204147965 0.1167310930 Elap time for23 iteration: 0.18 min r-norm 0.0085262483 0.0162310911 0.2834981384 Elap time for24 iteration: 0.17 min r-norm 0.0063609159 0.0122873015 0.2248542586 Elap time for25 iteration: 0.18 min r-norm 0.0034141409 0.0105203632 0.1803029904 Elap time for26 iteration: 0.18 min r-norm 0.0022679864 0.0097654726 0.1318347989 Elap time for27 iteration: 0.20 min r-norm 0.0018805906 0.0092926372 0.1114406811 Elap time for28 iteration: 0.20 min r-norm 0.0016178018 0.0096152892 0.1128985775 Elap time for29 iteration: 0.20 min r-norm 0.0015925451 0.0102707210 0.1566133927 Elap time for30 iteration: 0.18 min r-norm 0.0012307279 0.0092470712 0.1726686048 Elap time for31 iteration: 0.20 min r-norm 0.0011781288 0.0089239939 0.1487790273 Elap time for32 iteration: 0.22 min r-norm 0.0010114222 0.0072834724 0.1089459243 Elap time for33 iteration: 0.22 min r-norm 0.0005997315 0.0058661332 0.1400052555 Elap time for34 iteration: 0.20 min r-norm 0.0003976856 0.0042183577 0.1415724920 Elap time for35 iteration: 0.23 min r-norm 0.0002629169 0.0027596067 0.1010022602 Elap time for36 iteration: 0.23 min r-norm 0.0001700379 0.0021657765 0.1153183994 Elap time for37 iteration: 0.23 min r-norm 0.0001253134 0.0013222387 0.1614236243 Elap time for38 iteration: 0.23 min r-norm 0.0000928468 0.0008789330 0.1389585514 Elap time for39 iteration: 0.25 min r-norm 0.0000759871 0.0005949575 0.0970548157 Elap time for40 iteration: 0.25 min r-norm 0.0000435233 0.0003580981 0.1001310626 Elap time for41 iteration: 0.25 min r-norm 0.0000275080 0.0002518417 0.0915286161 Elap time for42 iteration: 0.25 min r-norm 0.0000122202 0.0001709833 0.0891311069 Elap time for43 iteration: 0.27 min r-norm 0.0000071119 0.0001243516 0.0514699726 Elap time for44 iteration: 0.27 min r-norm 0.0000055632 0.0000882621 0.0405689223 Elap time for45 iteration: 0.27 min r-norm 0.0000042761 0.0000802745 0.0215980070 Elap time for46 iteration: 0.27 min r-norm 0.0000029298 0.0000581982 0.0124480320 Elap time for47 iteration: 0.28 min r-norm 0.0000024042 0.0000446184 0.0090657784 Elap time for48 iteration: 0.28 min r-norm 0.0000020247 0.0000367220 0.0086109354 Elap time for49 iteration: 0.30 min r-norm 0.0000018733 0.0000243191 0.0080043443 Elap time for50 iteration: 0.30 min Warning: Algorithm did not converge!! |
本帖最后由 JohnCase 于 2021-8-10 09:54 编辑 wzkchem5 发表于 2021-8-10 03:16 多谢! Jacobi-Davidson方法里的较小的第二项直接扔掉后就是(D-\lambda)^-1*residual的形式 ✓但是Davidson本人推导preconditioner的时候用的瑞利商泰勒级数展啥的，一顿操作根本看不懂 （也是微扰理论？）…… 我非常好奇他原本的的详细思路是啥？毕竟Davidson在1975年就推导的，比Olsen1990要早  |
JohnCase 发表于 2021-8-9 18:16 没错，这个逻辑是这样的： 由微扰理论可以推出Jacobi-Davidson方法（又称Olsen方法），Jacobi-Davidson方法里面，当preconditioner取成(矩阵-近似本征值)的逆的时候，收敛速度是cubic的，否则一般是linear的。Davidson方法是Jacobi-Davidson方法的近似，忽略了一个比较小的项，所以Davidson方法大体继承了preconditioner接近(矩阵-近似本征值)的逆比较容易收敛这个特性，但是当特别接近的时候就不成立了。 参见Olsen, J. et al. Chem. Phys. Lett., 169, 463-472 (1990) |
wangxubo 发表于 2021-8-10 00:25 对，我就是这里不明白，这个preconditioner是为啥是近似矩阵的逆呢？如果这个近似矩阵无限近似于原矩阵的话，那么precondition这一步相当于啥也没干，只能得到当前这步的猜想解。 我正在看你推荐的书，多谢！ |
wzkchem5 发表于 2021-8-9 15:04 抱歉表意不清， 我是想问为什么preconditioner是(D-\lambda)^{-1}这个形式。 |
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