解一个代数矩阵方程
3个观点(过去30天)
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文森特·艾克
2021年7月13日
请我需要帮助获得变量(U, V, W, Th)作为下面矩阵代数方程的解,说
信谊U V W Th
a24 = 0:0.2:5;%是阶跃强制函数(及时)
F =兰德(4,4)* (U;V;W;Th] - [zero (4,2), rand(4,2)]*[0;0;W ^ 2;Th ^ 2] - [0 (26);a24;a24];
错误使用symengine(第59行)
数组大小必须匹配。
错误在sym/privBinaryOp(第903行)
Csym = mupadmex (op, args{1}。年代,args{2}。年代,变长度输入宗量{:});
错误在-(7)行
X = privBinaryOp(A, B,“symobj:邮政”,“_subtract”);
我被困住了,试图从一个双4 × 26矩阵中按列减去一个4 × 1符号关联的矩阵,这样我就可以使用
FF = solve(F == 0,[U,V,W,Th])
在这个问题上我需要帮助。由于预期。
5个评论
沃尔特·罗伯森
2021年7月13日
为了这个目的,涉及到象征性的表达是略微重要的。
MATLAB在R2016b中增加了数值的隐式展开。
然而,直到R2017b,符号表达式才加入隐式展开。
我们可以推断用户正在使用R2017a或之前。
接受的答案
沃尔特·罗伯森
2021年7月13日
该操作在当前版本中是允许的:
信谊U V W Th
a24 = 0:0.2:5;%是阶跃强制函数(及时)
F =兰德(4,4)* (U;V;W;Th] - [zero (4,2), rand(4,2)]*[0;0;W ^ 2;Th ^ 2] - [0 (26);a24;a24]
F =
您没有标记您的版本,也没有提及您的版本,因此志愿者有权期望您使用最新版本。
然而,我碰巧认识到一个问题:在足够老的MATLAB版本中,隐式展开并不存在。此外,在足够老的版本中,bsxfun()不能用于符号表达式。
在那么老的版本中,您必须repmat()
F = repmat(兰德(4,4)* (U;V;W;Th] - [zero (4,2), rand(4,2)]*[0;0;W ^ 2;Th^2], 1,26) - [0 (2,26);a24;a24]
F =
7评论
沃尔特·罗伯森
2021年7月15日
信谊U V W Th
a24 = 0:0.2:5;%是阶跃强制函数(及时)
F = repmat(兰德(4,4)* (U;V;W;Th] - [zero (4,2), rand(4,2)]*[0;0;W ^ 2;Th^2], 1,26) - [0 (2,26);a24;a24]
F =
大小(F)
ans =
1×2
4 26
sol = cell2mat(arrayfun(@(COL) solve(F(:,COL),“maxdegree”4) 1:尺寸(F, 2),“统一”, 0))
索尔=1×26带字段的struct数组:
Th U V W
索尔(1)。Th,索尔(1)。U,索尔(1)。V,索尔(1)。W)
ans =
有精确解,但它们看起来没什么用。万博 尤文图斯
文森特·艾克
2021年7月15日
不,考虑到我的目标,这不是无用的,你实际上给了我进展。下图是我的目标。我现在注意到的唯一一个问题是,我在每一列(而不是一列)中都有两个根(U,V,W,Th),如果它必须与步骤(1到26)相对应,这并不能得到很好的结果。
沃尔特·罗伯森
2021年7月15日
如果算上复解,每列有4根,不是2根。万博 尤文图斯这是一个四次元。
想要过滤到实际值是很常见的。
格式长
信谊U V W Th
a24 = 0:0.2:5;%是阶跃强制函数(及时)
F = repmat(兰德(4,4)* (U;V;W;Th] - [zero (4,2), rand(4,2)]*[0;0;W ^ 2;Th^2], 1,26) - [0 (2,26);a24;a24]
F =
大小(F)
ans =
1×2
4 26
[solTh, solU, solV, solW] = arrayfun(@(COL) solve(F(:,COL), [Th, U, V, W],“MaxDegree”4) 1:尺寸(F, 2),“统一”, 0);
Thvals = cell2mat(cellfun(@double, solTh,“统一”, 0))
Thvals =
-0.094682841308648 - 1.169458034215385我2.086480594346070 + 0.000000000000000 2.077784406966989 + 0.000000000000000 2.066795882117770 2.053794533719276 + 0.000000000000000 + 0.000000000000000我2.038985728582344 + 0.000000000000000我2.022522049377702 + 0.000000000000000 2.004516987533478 + 0.000000000000000 1.985053995067856 1.964192590106933 + 0.000000000000000 + 0.000000000000000我1.941972506033464 + 0.000000000000000我1.893532051138880 + 1.918416480745901 + 0.0000000000000000.000000000000000我1.867312574149251 + 0.000000000000000 1.839737600058620 1.780368421188653 1.810772653755723 + 0.000000000000000 + 0.000000000000000我我1.748459280706609 + 0.000000000000000 + 0.000000000000000 1.714961052314520 1.679767749597541 + 0.000000000000000 + 0.000000000000000我1.642746990646218 + 0.000000000000000我1.603733524609510 + 0.000000000000000 1.562520003400327 + 0.000000000000000 1.518843566340973 1.472365792402213 + 0.000000000000000 + 0.000000000000000我1.422641643933716 + 0.000000000000000我-0.094682841308648 + 1.169458034215385 -0.191588462920180 -0.383827289614846 -0.308693627863736 + 0.000000000000000 + 0.000000000000000我我-0.434142419854720 + 0.000000000000000 + 0.000000000000000 -0.468377862190450 -0.491368986603327 + 0.000000000000000 + 0.000000000000000我-0.506014476764549 -0.517068833132778我-0.514166684625613 + 0.000000000000000 + 0.000000000000000 + 0.000000000000000我-0.510339554292225 + -0.515586704069267 + 0.0000000000000000.000000000000000我-0.501778068300653 + 0.000000000000000 -0.490232746397509 -0.459086817629438 -0.475944888940360 + 0.000000000000000 + 0.000000000000000我我-0.439775100856340 + 0.000000000000000 + 0.000000000000000 -0.418078966958619 -0.394025160701052 + 0.000000000000000 + 0.000000000000000我-0.367599905080814 + 0.000000000000000我-0.338748196592134 + 0.000000000000000 -0.307370272150378 + 0.000000000000000 -0.273314637267979 -0.236366403929786 + 0.000000000000000 + 0.000000000000000我-0.196228620500677 + 0.000000000000000我0.000000000000000 + -0.152492309223418 + 0.000000000000000 0.000000000000000我0.004119107756266 - 1.296399624887958 0.067019783917584 - 1.418624948607412 0.110080877217749 - 1.529559144442854 0.141739116536933 - 1.630183653277971 0.166261240273264 - 1.722318188701896我我0.185988642082023 - 1.807515406888357 0.202313918084746 - 1.886977745764290 0.216121518248089 - 1.961626965218137我0.238372272487112 - 0.228003294982134 - 2.032177207998635我0.247526710242373 - 2.163116664678125 0.255688182050097 - 2.224320763805330 2.099190557970499 0.263025259593340 - 2.283103665714060 0.269668817910081 - 2.339716222355765 0.275722255406068 - 2.394369966943788我我0.281268513303054 - 2.447245064241453 0.286375016595215 - 2.498496341645928 0.291097227662477 - 2.548257929195656我0.295481251210847 - 2.596646876044579 0.299565776442169 - 2.643766003083962 0.303383547239644 - 2.689706177909450 0.306962490403037 - 2.734548147533245我我0.310326592263617 - 2.778364028616950 0.313496587518443 - 2.821218529669286 0.316490506114062 - 2.863169961402136 0.067019783917584我2.092496029555718 + 0.000000000000000 0.004119107756266 + 1.296399624887958 + 1.418624948607412我0.110080877217749 + 1.529559144442854 0.141739116536933 + 1.630183653277971 0.166261240273264 0.185988642082023 + 1.807515406888357 + 1.722318188701896我0.202313918084746 + 1.886977745764290我0.228003294982134 + 0.216121518248089 + 1.9616269652181372.032177207998635我0.238372272487112 + 2.099190557970499 0.247526710242373 0.263025259593340 0.255688182050097 + 2.224320763805330 + 2.163116664678125我我0.269668817910081 + 2.339716222355765 + 2.283103665714060 0.275722255406068 0.281268513303054 + 2.447245064241453 + 2.394369966943788我0.286375016595215 + 2.498496341645928我0.291097227662477 + 2.548257929195656 0.295481251210847 + 2.596646876044579 0.299565776442169 0.303383547239644 + 2.689706177909450 + 2.643766003083962我0.306962490403037 + 2.734548147533245i 0.310326592263617 + 2.778364028616950i 0.313496587518443 + 2.821218529669286i 0.316490506114062 + 2.863169961402136i
Uvals = cell2mat(cellfun(@double, solU,“统一”, 0))
Uvals =
-1.337768754800854 + 0.370281008481964我4.147886744121340 + 0.000000000000000 4.203560186062389 4.289236671744841 4.250258520665525 + 0.000000000000000 + 0.000000000000000我我4.321456315964071 + 0.000000000000000 + 0.000000000000000 4.347670628085559 4.368479501435571 + 0.000000000000000 + 0.000000000000000我4.384366836852620 4.402880479358474我4.395726450913830 + 0.000000000000000 + 0.000000000000000 + 0.000000000000000我4.405577976024064 + 4.406092656438100 + 0.0000000000000000.000000000000000我4.401509706214511 + 0.000000000000000 4.394024388753237 4.369184096585521 4.383225226296037 + 0.000000000000000 + 0.000000000000000我我4.351942302360433 + 0.000000000000000 + 0.000000000000000 4.331510046834908 4.307864496160035 + 0.000000000000000 + 0.000000000000000我4.280946127701744 + 0.000000000000000我4.250652829464192 + 0.000000000000000 4.216830848578836 + 0.000000000000000 4.179261067482686 4.137637978360862 + 0.000000000000000 + 0.000000000000000我我4.091536621178077 + 0.000000000000000 -1.337768754800854 - 0.370281008481964 0.151621657240662 0.467299478476283 0.315412697274949 + 0.000000000000000 + 0.000000000000000我我0.605192159902538 + 0.000000000000000 + 0.000000000000000 0.730826828987543 0.846241109011629 + 0.000000000000000 + 0.000000000000000我0.953172616120265 1.146902914347910我1.053019876536729 + 0.000000000000000 + 0.000000000000000 + 0.000000000000000我1.320242309412003 + 1.235728419650252 + 0.0000000000000000.000000000000000我1.401069436339662 + 0.000000000000000 1.478743274374451 1.626437574596235 1.553728349607752 + 0.000000000000000 + 0.000000000000000我我1.697246082881442 + 0.000000000000000 + 0.000000000000000 1.766502754777867 1.834540366915902 + 0.000000000000000 + 0.000000000000000我1.901685163978232 + 0.000000000000000我1.968266631030993 + 0.000000000000000 2.034628350384807 + 0.000000000000000 2.101141103746500 2.168219934876123 + 0.000000000000000 + 0.000000000000000我2.236347949055212 + 0.000000000000000我2.306111696526823 + 0.000000000000000 0.000000000000000 -1.579824069165484 + 0.155947166774068 + 0.000000000000000我我-1.822634446669780 - 0.006667761087284 -2.055005141088642 - 0.138071360027912 -2.276518693858056 - 0.249708586776252 -2.488523987026801 - 0.347748394596868 -2.692416419616214 - 0.435807057388301我我-2.889364746362167 - 0.516180905531849 -3.080310180795550 - 0.590423624507290 -3.266009643248373 - 0.659639629270387 -3.447077546638494 -我-3.624018716575809 - 0.786062149931840 -3.797253076349249 - 0.844377379631293 0.724645073425437 -3.967133996978494 - 0.899979289566606 -4.133962012381135 - 0.953183699362246 -4.297995180163404 - 1.004251238526169我我-4.459457005967377 - 1.053399815600127 -4.618542581319673 - 1.100813704462502 -4.775423396142555 - 1.146650302181526我-4.930251155852911 - 1.191045246118383 -5.083160841666774 - 1.234116350680520 -5.234273188741532 - 1.275966679170814 -5.383696711496329 - 1.316686971368663我我-5.531529373029692 - 1.356357584047785 -5.677859972074953 - 1.395050058324667 -5.822769303735992 - 1.432828397609563我4.081554045665995 + 0.000000000000000 -1.579824069165484 - 0.155947166774068 -1.822634446669780 -2.055005141088642 + 0.138071360027912 + 0.006667761087284我-2.276518693858056 0.249708586776252 -2.692416419616214我-2.488523987026801 + 0.347748394596868 + 0.435807057388301 + -2.889364746362167 + 0.516180905531849我我-3.266009643248373 + -3.080310180795550 + 0.5904236245072900.659639629270387我-3.447077546638494 + 0.724645073425437 -3.624018716575809 -3.967133996978494 -3.797253076349249 + 0.844377379631293 + 0.786062149931840我我-4.133962012381135 + 0.953183699362246 + 0.899979289566606 -4.297995180163404 -4.459457005967377 + 1.053399815600127 + 1.004251238526169我-4.618542581319673 + 1.100813704462502我-4.775423396142555 + 1.146650302181526 -4.930251155852911 + 1.191045246118383 -5.083160841666774 -5.234273188741532 + 1.275966679170814 + 1.234116350680520我-5.383696711496329 + 1.316686971368663i -5.531529373029692 + 1.356357584047785i -5.677859972074953 + 1.395050058324667i -5.822769303735992 + 1.432828397609563i
Vvals = cell2mat(cellfun(@double, solV,“统一”, 0))
Vvals =
-0.504055209573428 + 0.375368805056658我1.538127719112909 + 0.000000000000000 1.890511678779503 2.586550305531252 2.239840799349641 + 0.000000000000000 + 0.000000000000000我我2.930975461892485 + 0.000000000000000 + 0.000000000000000 3.273380473029579 3.613977359915537 + 0.000000000000000 + 0.000000000000000我3.952938744999917 4.626499475971578我4.290406771478357 + 0.000000000000000 + 0.000000000000000 + 0.000000000000000我5.294937147196451 + 4.961315427222944 + 0.0000000000000000.000000000000000我5.627433650621144 + 0.000000000000000 5.958862324873501 6.618695379709691 6.289270296695796 + 0.000000000000000 + 0.000000000000000我我6.947166657143294 + 0.000000000000000 + 0.000000000000000 7.274704720846710 7.601321554900924 + 0.000000000000000 + 0.000000000000000我7.927020013930278 + 0.000000000000000我8.251792794379593 + 0.000000000000000 8.575620717975008 + 0.000000000000000 8.898470015403628 9.220288065124281 + 0.000000000000000 + 0.000000000000000我我9.540996600448889 + 0.000000000000000 -0.504055209573428 - 0.375368805056658 0.425952114310920 1.245051555178251 0.841967175397670 + 0.000000000000000 + 0.000000000000000我我1.637772165506094 + 0.000000000000000 + 0.000000000000000 2.022531164515393 2.401078554174221 + 0.000000000000000 + 0.000000000000000我2.774665087221919 3.510374041664118我3.144202622804048 + 0.000000000000000 + 0.000000000000000 + 0.000000000000000我4.234607352502596 + 3.873704412200672 + 0.0000000000000000.000000000000000我4.593415923112354 + 0.000000000000000 4.950403771429729 5.659799970539773 5.305800008380226 + 0.000000000000000 + 0.000000000000000我我6.012573234731134 + 0.000000000000000 + 0.000000000000000 6.364269781274358 6.715024917878184 + 0.000000000000000 + 0.000000000000000我7.064963406763741 + 0.000000000000000我7.414203144181120 + 0.000000000000000 7.762858705799702 + 0.000000000000000 8.111045091132313 8.458882090336328 + 0.000000000000000 + 0.000000000000000我8.806499901058485 + 0.000000000000000我9.154047044217846 + 0.000000000000000 0.000000000000000 -0.067584248920351 -0.289213068042489 + 0.316657961026758 + 0.000000000000000我我0.162037330403100 + 0.247762453617693 + 0.277225925982538 0.398150601647183 0.639386853460727 + 0.203854096904311 + 0.223989032114299我0.884738982561576 1.385054471259112我1.133475602093557 + 0.170519225798469 + 0.186250862023458 + 0.156233909123522我1.895179870072590 + 1.639063078088668 + 0.1431042313455940.130922155241616我2.153148753794755 + 0.119533255261260 2.412761938001932 2.936263965527091 2.673848091629708 + 0.098688314897300 + 0.108819468524092我我3.199888328034980 + 0.079892019272787 + 0.089065870041373 3.464617483931162 3.730361901441559 + 0.062699808381617 + 0.071117153491821我3.997043630786747 + 0.054604939049523我4.264594298815672 + 0.046802633892629 4.532953530091115 + 0.039267139009943 4.802067688555977 5.071888863590774 + 0.024910008045871 + 0.031976106629563我5.342374044773266 + 0.018051669320386我5.613484444050670 + 0.011385899926830 5.885184934307497 1.182107457488089 + 0.000000000000000 + 0.004899192691078我我-0.289213068042489 - 0.316657961026758 -0.067584248920351 - 0.277225925982538 0.162037330403100 - 0.247762453617693 0.398150601647183 - 0.223989032114299 0.639386853460727 - 0.203854096904311我我0.884738982561576 - 0.186250862023458 1.133475602093557 - 0.170519225798469 1.385054471259112 - 0.156233909123522 1.639063078088668 -我1.895179870072590 - 0.130922155241616 2.153148753794755 - 0.119533255261260 0.143104231345594 2.412761938001932 - 0.108819468524092 2.673848091629708 - 0.098688314897300 2.936263965527091 - 0.089065870041373我我3.199888328034980 - 0.079892019272787 3.464617483931162 - 0.071117153491821 3.730361901441559 - 0.062699808381617我3.997043630786747 - 0.054604939049523 4.264594298815672 - 0.046802633892629 4.532953530091115 - 0.039267139009943 4.802067688555977 - 0.031976106629563我5.071888863590774 - 0.024910008045871i 5.342374044773266 - 0.018051669320386i 5.613484444050670 - 0.011385899926830i 5.885184934307497 - 0.004899192691078i
Wvals = cell2mat(cellfun(@double, solW,“统一”, 0))
Wvals =
0.799679476330780 - 0.841095593907892我-1.592380803469869 + 0.000000000000000 -1.674426897140375 + 0.000000000000000 -1.751966864870528 -1.825652020612525 + 0.000000000000000 + 0.000000000000000我-1.895986058491776 + 0.000000000000000我-1.963367746894912 + 0.000000000000000 -2.028118866002349 + 0.000000000000000 -2.090503174160550 -2.150739680847249 + 0.000000000000000 + 0.000000000000000我-2.209012172212263 + 0.000000000000000我-2.320264233416095 + -2.265476190489518 + 0.0000000000000000.000000000000000我-2.373489675456903 + 0.000000000000000 -2.425249746225831 -2.524694980011617 -2.475627792939262 + 0.000000000000000 + 0.000000000000000我我-2.572511526093993 + 0.000000000000000 + 0.000000000000000 -2.619127537923073 -2.664583464619840 + 0.000000000000000 + 0.000000000000000我-2.708910159496266 + 0.000000000000000我-2.752128491792144 + 0.000000000000000 -2.794248387207062 + 0.000000000000000 -2.835267074342088 -2.875166136297033 + 0.000000000000000 + 0.000000000000000我-2.913906631752097 + 0.000000000000000我0.799679476330780 + 0.841095593907892 -0.237720136058116 -0.622080124030598 -0.444554099309726 + 0.000000000000000 + 0.000000000000000我我-0.777863240702378 + 0.000000000000000 + 0.000000000000000 -0.917534549677085 -1.044893165145636 + 0.000000000000000 + 0.000000000000000我-1.162544012017425 -1.375619727331622我-1.272334529393337 + 0.000000000000000 + 0.000000000000000 + 0.000000000000000我-1.566540454409061 + -1.473423624594866 + 0.0000000000000000.000000000000000我-1.655600263387808 + 0.000000000000000 -1.741112826864168 -1.903106899457258 -1.823497940488323 + 0.000000000000000 + 0.000000000000000我我-1.980238131051339 + 0.000000000000000 + 0.000000000000000 -2.055148868114853 -2.128064105776656 + 0.000000000000000 + 0.000000000000000我-2.199183691172421 + 0.000000000000000我-2.268688158280731 + 0.000000000000000 -2.336743784825519 + 0.000000000000000 -2.403507291303494 -2.469130621645908 + 0.000000000000000 + 0.000000000000000我-2.533766365638827 + 0.000000000000000我0.000000000000000 + -2.597574677650533 + 0.000000000000000 0.000000000000000我0.962249250235563 - 0.770907965007232 1.106689278696621 - 0.731089165352370 1.234222274922134 - 0.705220050381949 1.348956411129022 - 0.686548000601008 1.453959084556002 - 0.672102297646812我我1.551329236491845 - 0.660393363747881 1.642530219481457 - 0.650587538929500 1.728617632248514 - 0.642176854853886我1.888416678875136 - 1.810378484561006 - 0.634830771254546我1.963207102920860 - 0.622491315078081 2.035131028873522 - 0.617216892914531 0.628322820203841 2.104500031632106 - 0.612408969851718 2.171572623828648 - 0.607997196681545 2.236566126669831 - 0.603925859764615我我2.299665336003049 - 0.600150090784758 2.361028977575994 - 0.596633227988520 2.420794602321435 - 0.593344933685396我2.479082358367701 - 0.590259822202744 2.535997939360069 - 0.587356440792213 2.591634918780402 - 0.584616499863304 2.646076619726849 - 0.582024282742178我我2.699397628465569 - 0.579566186932926 2.751665031439501 - 0.577230363207401 2.802939435172886 - 0.575006428500804 1.106689278696621我-1.504961391718419 + 0.000000000000000 0.962249250235563 + 0.770907965007232 + 0.731089165352370我1.234222274922134 + 0.705220050381949 1.348956411129022 + 0.686548000601008 1.453959084556002 1.551329236491845 + 0.660393363747881 + 0.672102297646812我1.642530219481457 + 0.650587538929500我1.810378484561006 + 1.728617632248514 + 0.6421768548538860.634830771254546我1.888416678875136 + 0.628322820203841 1.963207102920860 2.104500031632106 2.035131028873522 + 0.617216892914531 + 0.622491315078081我我2.171572623828648 + 0.607997196681545 + 0.612408969851718 2.236566126669831 2.299665336003049 + 0.600150090784758 + 0.603925859764615我2.361028977575994 + 0.596633227988520我2.420794602321435 + 0.593344933685396 2.479082358367701 + 0.590259822202744 2.535997939360069 2.591634918780402 + 0.584616499863304 + 0.587356440792213我2.646076619726849 + 0.582024282742178i 2.699397628465569 + 0.579566186932926i 2.751665031439501 + 0.57730363207401i 2.802939435172886 + 0.575006428500804i
mask = imag(Thvals) == 0 & imag(Uvals) == 0 & imag(Vvals) == 0 & imag(Wvals) == 0;
[Thvals(mask), Uvals(mask), Vvals(mask), Wvals(mask)]
ans =
52×4
0 0 0 0 2.092496029555718 4.081554045665995 1.182107457488089 -1.504961391718419 2.086480594346070 4.147886744121340 1.538127719112909 -1.592380803469869 -0.191588462920180 0.151621657240662 0.425952114310920 -0.237720136058116 2.077784406966989 4.203560186062389 1.890511678779503 -1.674426897140375 -0.308693627863736 0.315412697274949 0.841967175397670 -0.444554099309726 2.066795882117770 4.250258520665525 2.239840799349641 -1.751966864870528 -0.383827289614846 0.4672994784762831.245051555178251 -0.622080124030598 2.053794533719276 4.289236671744841 2.586550305531252 -1.825652020612525 -0.434142419854720 0.605192159902538 1.637772165506094 -0.777863240702378
解的数量是高度可变的。万博 尤文图斯我的一些测试显示只有两个解决方案,而另一些测试显示多达84个解决方案。万博 尤文图斯
文森特·艾克
2021年7月16日
谢谢你,沃尔特,我从你的回答中得到了很多启发。现在,我有一个好问题,
//www.tianjin-qmedu.com/matlabcentral/answers/879973-how-to-solve-four-sets-of-ode-having-four-variables。
我希望能从你那里学到更多。
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