mehdibgh

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6 years, 26 days

MaplePrimes Activity


These are replies submitted by mehdibgh

@JohnS Thanks John, vv,

Here I post my recent findings about my problem.

 The idea is to replace

[M11 0] 
[  0 0]

with

[M11     0] 
[ 0  eps*I]

for some small value eps, small enough to perturb the problem only a small amount. Let N = M^(-1/2), multiply the equation on the left by

[N  0]
[ 0 c*I] 

and insert the identity matrix in the form

[N  0 ]   [N^-1      0]
[0 c*I]   [ 0  (1/c)*I]

between the matrices and the eigenvector

[X     ]
[lambda].

Multiply it all out blockwise and we get what they got, with

I22 = c^2*eps*I. 

You want I22 to be the identity matrix, so

c = 1/sqrt(eps).

c is what they called LV. So how small do we have to make eps to not affect the problem too much? Having no direct experience with this I don't know, but I would hazard a guess of least 10 times smaller than the smallest eigenvalue of M11. Here the smallest eigenvalue is 3e-11 so we can plan accordingly. It does lead to some pretty big LV numbers. (The largest eigenvalue is 4e-3, so scaling could be a problem).

There are spurious eigenvalues for the problem I have. Note that the original problem has a number of eigenvalues "at infinity", which correspond to large negative eigenvalues for the approximating problem. Those eigenvalues have size of order LV. The number of these eigenvalues "at infinity" is the dimension of lambda. So these eigenvalues should be ignored -- only the "small" eigenvalues should be kept. The trouble is that if LV becomes large, the smaller eigenvalues are subject to numerical (roundoff) "noise" of size LV.u, u = unit round-off. So taking LV = 10200 would likely destroy any accuracy the small eigenvalues have left. (I could be wrong; it will depend on the exact algorithm used.).

I am noticed these kinds of problems are solved very easily using Eigenvalues(K,M) command in Maple, because this command accepts both K and M matrices as its inputs, regardless how the K and M are.

But does anybody knows how this command compute the eigenvalues of generalized eigenvalue problem?

@vv Ok let prepare data you need.

M=5(I+1)(J+1),  N=10(I+1)+10(J+1)

For M=500 and N=200, here are the five known omegas:

The related matrices are as below:



Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/K21.mw .
 

K21.mw

K22.mw

K11.mw

K22.mw

M21.mw

M22.mw

M11.mw

M12.mw

Waiting your comments.

@vv Dont you have any comment how to choose LV in this method?

What other ways you know to find eigenvalues of problem in maple, that dont have the form of standard eigenvalue problem like mentioned problem?

@vv This Method are presented in some authentic papers, so I trusted them. Now I am using this method for my own problem.

for example:

http://www.sciencedirect.com/science/article/pii/S0045794916306113

@vv thanks. As you see my matrices are inconsistent (A matrix have very big and very small elements at the same time) . What do you recommend in such conditions?

 

@mehdibaghaee It seems the problem is because of matrix inconsistency(A matrix have very big and very small elements at the same time).

How cope with this problem?

@vv  when I use my own matrices, the results do not converge and increse.

But whats the problem with my matrices??

@vv any comment yet???

@vv I re arranged my question as above, please help.

Acer deleted my question, guide me to pose my question here.

Let me ask my question in another way. Here are a little introduction:

Doing above method on my problem in Maple, I got several omegas for several LVs(the omegas continuesly increase when LV increases). While I expect my results converge to specific omegas when LV increases.


 

``

restart; with(LinearAlgebra)

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received shareman

 

N := 200:

K11 := ImportMatrix("C:/K11.mw"):

K12 := ImportMatrix("C:/K12.mw"):

K21 := LinearAlgebra:-HermitianTranspose(K12):

K22 := ImportMatrix("C:/K22.mw"):

M11 := ImportMatrix("C:/M11.mw"):

M12 := ImportMatrix("C:/M12.mw"):

M21 := LinearAlgebra:-HermitianTranspose(M12):

M22 := ImportMatrix("C:/M22.mw"):

V, Q := Eigenvectors(M11):

MV := DiagonalMatrix(`~`[sqrt](Vector(V, datatype = complex))):

M1 := Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Q, MV), LinearAlgebra:-HermitianTranspose(Q)):

M11t := MatrixInverse(M1):

M11t := Matrix(`~`[convert](M11t, float[8]), datatype = float[8]):

LV := 5.6*10^11:

A12 := Typesetting:-delayDotProduct(LV*M11t, K12):

A21 := Typesetting:-delayDotProduct(LV*K21, M11t):

A11 := Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(M11t, K11), M11t):

A22 := Matrix(N, datatype = float[8]):

AA := Matrix([[A11, A12], [A21, A22]]):

ss := Eigenvalues(AA):

SS := `~`[sqrt](Vector(ss, datatype = complex))

SS := Vector(700, {(1) = HFloat(0.0)+HFloat(3.128326066829099e11)*I, (2) = HFloat(0.0)+HFloat(3.1283241310372235e11)*I, (3) = HFloat(3.1283260668392816e11)+HFloat(0.0)*I, (4) = HFloat(3.1283241310389746e11)+HFloat(0.0)*I, (5) = HFloat(0.0)+HFloat(3.128323607078121e11)*I, (6) = HFloat(3.128323607084089e11)+HFloat(0.0)*I, (7) = HFloat(0.0)+HFloat(2.899899150143945e11)*I, (8) = HFloat(0.0)+HFloat(2.89989768973818e11)*I, (9) = HFloat(2.899899150152933e11)+HFloat(0.0)*I, (10) = HFloat(2.899897689739713e11)+HFloat(0.0)*I, (11) = HFloat(0.0)+HFloat(3.0132477781996533e11)*I, (12) = HFloat(0.0)+HFloat(3.0132464181003406e11)*I, (13) = HFloat(0.0)+HFloat(3.013245359405702e11)*I, (14) = HFloat(0.0)+HFloat(3.013245162395782e11)*I, (15) = HFloat(3.013247778209111e11)+HFloat(0.0)*I, (16) = HFloat(3.0132464181092865e11)+HFloat(0.0)*I, (17) = HFloat(3.013245359407637e11)+HFloat(0.0)*I, (18) = HFloat(3.013245162397984e11)+HFloat(0.0)*I, (19) = HFloat(2.899897294123467e11)+HFloat(0.0)*I, (20) = HFloat(0.0)+HFloat(2.899897294118204e11)*I, (21) = HFloat(3.01324487729064e11)+HFloat(0.0)*I, (22) = HFloat(0.0)+HFloat(3.013244877285015e11)*I, (23) = HFloat(0.0)+HFloat(3.0132448605751965e11)*I, (24) = HFloat(3.0132448605808295e11)+HFloat(0.0)*I, (25) = HFloat(0.0)+HFloat(2.7088980401265292e11)*I, (26) = HFloat(0.0)+HFloat(2.708899442312293e11)*I, (27) = HFloat(2.7088980401276068e11)+HFloat(0.0)*I, (28) = HFloat(2.7088994423185822e11)+HFloat(0.0)*I, (29) = HFloat(0.0)+HFloat(2.6802509484694894e11)*I, (30) = HFloat(0.0)+HFloat(2.6802495369041138e11)*I, (31) = HFloat(2.6802509484760828e11)+HFloat(0.0)*I, (32) = HFloat(2.6802495369052472e11)+HFloat(0.0)*I, (33) = HFloat(2.708897660571933e11)+HFloat(0.0)*I, (34) = HFloat(2.5053821391446387e11)+HFloat(0.0)*I, (35) = HFloat(2.5053834141894263e11)+HFloat(0.0)*I, (36) = HFloat(0.0)+HFloat(2.5053821391434824e11)*I, (37) = HFloat(0.0)+HFloat(2.5053834141826294e11)*I, (38) = HFloat(0.0)+HFloat(2.4631151277794217e11)*I, (39) = HFloat(0.0)+HFloat(2.4631140769997647e11)*I, (40) = HFloat(0.0)+HFloat(2.466647840875788e11)*I, (41) = HFloat(0.0)+HFloat(2.4666465490404684e11)*I, (42) = HFloat(2.4666478408829504e11)+HFloat(0.0)*I, (43) = HFloat(2.466646549041693e11)+HFloat(0.0)*I, (44) = HFloat(2.4943042673834863e11)+HFloat(0.0)*I, (45) = HFloat(2.494303225201663e11)+HFloat(0.0)*I, (46) = HFloat(2.4631151277853293e11)+HFloat(0.0)*I, (47) = HFloat(0.0)+HFloat(2.463113792327248e11)*I, (48) = HFloat(2.4631140770007767e11)+HFloat(0.0)*I, (49) = HFloat(0.0)+HFloat(2.4943042673779074e11)*I, (50) = HFloat(0.0)+HFloat(2.4943032252007117e11)*I, (51) = HFloat(0.0)+HFloat(2.6091794945520062e11)*I, (52) = HFloat(0.0)+HFloat(2.609178136157797e11)*I, (53) = HFloat(2.6091794945575122e11)+HFloat(0.0)*I, (54) = HFloat(2.6091781361636e11)+HFloat(0.0)*I, (55) = HFloat(2.6091774484281158e11)+HFloat(0.0)*I, (56) = HFloat(2.4631137923307056e11)+HFloat(0.0)*I, (57) = HFloat(0.0)+HFloat(2.4943029428565695e11)*I, (58) = HFloat(0.0)+HFloat(2.609177448429035e11)*I, (59) = HFloat(0.0)+HFloat(2.6091771912453253e11)*I, (60) = HFloat(0.0)+HFloat(2.6091770539798422e11)*I, (61) = HFloat(2.609177191250094e11)+HFloat(0.0)*I, (62) = HFloat(2.6091770539836234e11)+HFloat(0.0)*I, (63) = HFloat(2.609177037209371e11)+HFloat(0.0)*I, (64) = HFloat(0.0)+HFloat(2.6091770372055933e11)*I, (65) = HFloat(2.4943029428598468e11)+HFloat(0.0)*I, (66) = HFloat(0.0)+HFloat(2.5593859551842896e11)*I, (67) = HFloat(0.0)+HFloat(2.5593848989782724e11)*I, (68) = HFloat(0.0)+HFloat(2.5593840993238315e11)*I, (69) = HFloat(0.0)+HFloat(2.559383957382152e11)*I, (70) = HFloat(2.5593848989835553e11)+HFloat(0.0)*I, (71) = HFloat(2.559385955189302e11)+HFloat(0.0)*I, (72) = HFloat(2.5593842884314923e11)+HFloat(0.0)*I, (73) = HFloat(2.5593840993276413e11)+HFloat(0.0)*I, (74) = HFloat(2.5593839573855112e11)+HFloat(0.0)*I, (75) = HFloat(2.5593839444756073e11)+HFloat(0.0)*I, (76) = HFloat(0.0)+HFloat(2.559384288432106e11)*I, (77) = HFloat(0.0)+HFloat(2.5593839444722495e11)*I, (78) = HFloat(0.0)+HFloat(2.7088976605682397e11)*I, (79) = HFloat(0.0)+HFloat(2.6802491548068143e11)*I, (80) = HFloat(2.6802491548106735e11)+HFloat(0.0)*I, (81) = HFloat(2.232303813943803e11)+HFloat(0.0)*I, (82) = HFloat(2.2323028661359e11)+HFloat(0.0)*I, (83) = HFloat(0.0)+HFloat(2.2323038139373105e11)*I, (84) = HFloat(0.0)+HFloat(2.232302866134791e11)*I, (85) = HFloat(0.0)+HFloat(2.274837647789468e11)*I, (86) = HFloat(0.0)+HFloat(2.2748367162007117e11)*I, (87) = HFloat(2.274837647795595e11)+HFloat(0.0)*I, (88) = HFloat(2.274836716201763e11)+HFloat(0.0)*I, (89) = HFloat(0.0)+HFloat(2.4666461993502917e11)*I, (90) = HFloat(2.4666461993544873e11)+HFloat(0.0)*I, (91) = HFloat(0.0)+HFloat(2.387111199987827e11)*I, (92) = HFloat(0.0)+HFloat(2.3871109684632574e11)*I, (93) = HFloat(0.0)+HFloat(2.3465172372993524e11)*I, (94) = HFloat(0.0)+HFloat(2.3465171379391534e11)*I, (95) = HFloat(0.0)+HFloat(2.3871099921826184e11)*I, (96) = HFloat(2.3465172373061508e11)+HFloat(0.0)*I, (97) = HFloat(2.3465171379459656e11)+HFloat(0.0)*I, (98) = HFloat(2.3871111999942426e11)+HFloat(0.0)*I, (99) = HFloat(2.387110968469832e11)+HFloat(0.0)*I, (100) = HFloat(2.3871099624893436e11)+HFloat(0.0)*I, (101) = HFloat(2.3871096827922003e11)+HFloat(0.0)*I, (102) = HFloat(2.3871099921833105e11)+HFloat(0.0)*I, (103) = HFloat(2.387109680024763e11)+HFloat(0.0)*I, (104) = HFloat(0.0)+HFloat(2.3871096827883865e11)*I, (105) = HFloat(0.0)+HFloat(2.387109962487736e11)*I, (106) = HFloat(0.0)+HFloat(2.3871096800209564e11)*I, (107) = HFloat(2.3465160886982687e11)+HFloat(0.0)*I, (108) = HFloat(2.3465160766752405e11)+HFloat(0.0)*I, (109) = HFloat(2.34651578362555e11)+HFloat(0.0)*I, (110) = HFloat(2.3465157848134668e11)+HFloat(0.0)*I, (111) = HFloat(0.0)+HFloat(2.3465160886971375e11)*I, (112) = HFloat(0.0)+HFloat(2.346515783621563e11)*I, (113) = HFloat(0.0)+HFloat(2.346515784809475e11)*I, (114) = HFloat(0.0)+HFloat(2.3465160766740347e11)*I, (115) = HFloat(0.0)+HFloat(1.9156909819178485e11)*I, (116) = HFloat(0.0)+HFloat(1.9156901620078577e11)*I, (117) = HFloat(1.9156909819253604e11)+HFloat(0.0)*I, (118) = HFloat(0.0)+HFloat(1.969708162000865e11)*I, (119) = HFloat(1.9156901620091528e11)+HFloat(0.0)*I, (120) = HFloat(1.9697081620079388e11)+HFloat(0.0)*I, (121) = HFloat(1.9697073696584824e11)+HFloat(0.0)*I, (122) = HFloat(0.0)+HFloat(2.192799838017134e11)*I, (123) = HFloat(0.0)+HFloat(2.1927986859513544e11)*I, (124) = HFloat(0.0)+HFloat(2.5053817939971887e11)*I, (125) = HFloat(2.1927998380251593e11)+HFloat(0.0)*I, (126) = HFloat(2.192798685952728e11)+HFloat(0.0)*I, (127) = HFloat(2.5053817940011743e11)+HFloat(0.0)*I, (128) = HFloat(0.0)+HFloat(2.2413950710506677e11)*I, (129) = HFloat(0.0)+HFloat(2.2413939460242706e11)*I, (130) = HFloat(2.241395071058268e11)+HFloat(0.0)*I, (131) = HFloat(2.2413939460255786e11)+HFloat(0.0)*I, (132) = HFloat(0.0)+HFloat(2.232302609347356e11)*I, (133) = HFloat(2.2323026093511636e11)+HFloat(0.0)*I, (134) = HFloat(0.0)+HFloat(1.969707369657277e11)*I, (135) = HFloat(1.8225214175973798e11)+HFloat(0.0)*I, (136) = HFloat(1.8225205205123245e11)+HFloat(0.0)*I, (137) = HFloat(1.7640802230881586e11)+HFloat(0.0)*I, (138) = HFloat(1.764079282261956e11)+HFloat(0.0)*I, (139) = HFloat(0.0)+HFloat(1.822521417588039e11)*I, (140) = HFloat(0.0)+HFloat(1.8225205205107245e11)*I, (141) = HFloat(0.0)+HFloat(1.7640802230783014e11)*I, (142) = HFloat(0.0)+HFloat(1.7640792822602704e11)*I, (143) = HFloat(1.2706167103097461e11)+HFloat(0.0)*I, (144) = HFloat(1.2706161514440456e11)+HFloat(0.0)*I, (145) = HFloat(0.0)+HFloat(1.2706167102986774e11)*I, (146) = HFloat(0.0)+HFloat(1.2706161514421452e11)*I, (147) = HFloat(1.9156899398821234e11)+HFloat(0.0)*I, (148) = HFloat(0.0)+HFloat(1.9156899398777277e11)*I, (149) = HFloat(0.0)+HFloat(2.2748364637960687e11)*I, (150) = HFloat(2.274836463799643e11)+HFloat(0.0)*I, (151) = HFloat(0.0)+HFloat(1.3303948034784596e11)*I, (152) = HFloat(1.3303948034889293e11)+HFloat(0.0)*I, (153) = HFloat(0.0)+HFloat(1.3303942887861894e11)*I, (154) = HFloat(1.3303942887879909e11)+HFloat(0.0)*I, (155) = HFloat(0.0)+HFloat(2.241393641500681e11)*I, (156) = HFloat(2.2413936415051294e11)+HFloat(0.0)*I, (157) = HFloat(0.0)+HFloat(2.192798374104621e11)*I, (158) = HFloat(2.192798374109319e11)+HFloat(0.0)*I, (159) = HFloat(0.0)+HFloat(1.9697071549925784e11)*I, (160) = HFloat(1.9697071549967142e11)+HFloat(0.0)*I, (161) = HFloat(0.0)+HFloat(1.822520277672099e11)*I, (162) = HFloat(1.8225202776775684e11)+HFloat(0.0)*I, (163) = HFloat(0.0)+HFloat(1.764079027591712e11)*I, (164) = HFloat(1.7640790275974774e11)+HFloat(0.0)*I, (165) = HFloat(0.0)+HFloat(1.2706160000374927e11)*I, (166) = HFloat(1.270616000043979e11)+HFloat(0.0)*I, (167) = HFloat(2.1175928623654297e11)+HFloat(0.0)*I, (168) = HFloat(0.0)+HFloat(2.1175928623595453e11)*I, (169) = HFloat(0.0)+HFloat(2.117591988256723e11)*I, (170) = HFloat(2.1175919882628998e11)+HFloat(0.0)*I, (171) = HFloat(2.1175915158501758e11)+HFloat(0.0)*I, (172) = HFloat(2.117591355081302e11)+HFloat(0.0)*I, (173) = HFloat(0.0)+HFloat(2.1175912415386282e11)*I, (174) = HFloat(0.0)+HFloat(2.1175913550766733e11)*I, (175) = HFloat(0.0)+HFloat(2.1175915158509436e11)*I, (176) = HFloat(2.1175912415426007e11)+HFloat(0.0)*I, (177) = HFloat(0.0)+HFloat(2.1175912522341992e11)*I, (178) = HFloat(0.0)+HFloat(2.033888314431657e11)*I, (179) = HFloat(0.0)+HFloat(2.0338872624463266e11)*I, (180) = HFloat(2.0338883144388217e11)+HFloat(0.0)*I, (181) = HFloat(2.0338872624538675e11)+HFloat(0.0)*I, (182) = HFloat(2.117591252238183e11)+HFloat(0.0)*I, (183) = HFloat(0.0)+HFloat(2.0338867229379703e11)*I, (184) = HFloat(2.0338867229368115e11)+HFloat(0.0)*I, (185) = HFloat(0.0)+HFloat(2.033886402221415e11)*I, (186) = HFloat(2.0338865248281454e11)+HFloat(0.0)*I, (187) = HFloat(2.0338864022263254e11)+HFloat(0.0)*I, (188) = HFloat(2.0338864152544495e11)+HFloat(0.0)*I, (189) = HFloat(0.0)+HFloat(2.0338864152495322e11)*I, (190) = HFloat(0.0)+HFloat(2.033886524822031e11)*I, (191) = HFloat(1.3303941493570714e11)+HFloat(0.0)*I, (192) = HFloat(0.0)+HFloat(1.3303941493509389e11)*I, (193) = HFloat(1.7082734929457407e11)+HFloat(0.0)*I, (194) = HFloat(1.708272620301303e11)+HFloat(0.0)*I, (195) = HFloat(0.0)+HFloat(1.7082734929390433e11)*I, (196) = HFloat(0.0)+HFloat(1.70827262029443e11)*I, (197) = HFloat(0.0)+HFloat(1.7082723036287708e11)*I, (198) = HFloat(0.0)+HFloat(1.7082720830627515e11)*I, (199) = HFloat(0.0)+HFloat(1.708272094130585e11)*I, (200) = HFloat(1.7082723036272018e11)+HFloat(0.0)*I, (201) = HFloat(1.7082721111738504e11)+HFloat(0.0)*I, (202) = HFloat(1.7082720830675983e11)+HFloat(0.0)*I, (203) = HFloat(0.0)+HFloat(1.7082721111664755e11)*I, (204) = HFloat(1.7082720941354276e11)+HFloat(0.0)*I, (205) = HFloat(0.0)+HFloat(1.3642989987007164e11)*I, (206) = HFloat(0.0)+HFloat(1.3642981451180106e11)*I, (207) = HFloat(0.0)+HFloat(1.3642978260480458e11)*I, (208) = HFloat(0.0)+HFloat(1.3642976181220717e11)*I, (209) = HFloat(1.3642989987108083e11)+HFloat(0.0)*I, (210) = HFloat(1.3642981451284912e11)+HFloat(0.0)*I, (211) = HFloat(1.3642978260454892e11)+HFloat(0.0)*I, (212) = HFloat(1.3642976181294104e11)+HFloat(0.0)*I, (213) = HFloat(0.0)+HFloat(1.364297640754042e11)*I, (214) = HFloat(0.0)+HFloat(1.3642976073100073e11)*I, (215) = HFloat(1.3642976073173477e11)+HFloat(0.0)*I, (216) = HFloat(1.3642976407653857e11)+HFloat(0.0)*I, (217) = HFloat(0.0)+HFloat(2.6038861983556423e10)*I, (218) = HFloat(0.0)+HFloat(2.6038860477904953e10)*I, (219) = HFloat(2.603886206952868e10)+HFloat(0.0)*I, (220) = HFloat(2.6038860563877136e10)+HFloat(0.0)*I, (221) = HFloat(0.0)+HFloat(2.413753521799753e10)*I, (222) = HFloat(0.0)+HFloat(2.413753634560689e10)*I, (223) = HFloat(0.0)+HFloat(2.508099482952617e10)*I, (224) = HFloat(0.0)+HFloat(2.508099406967429e10)*I, (225) = HFloat(0.0)+HFloat(2.508099303223387e10)*I, (226) = HFloat(0.0)+HFloat(2.5080993127182796e10)*I, (227) = HFloat(2.4137535293949432e10)+HFloat(0.0)*I, (228) = HFloat(2.413753642155885e10)+HFloat(0.0)*I, (229) = HFloat(2.508099491074228e10)+HFloat(0.0)*I, (230) = HFloat(2.5080994150890423e10)+HFloat(0.0)*I, (231) = HFloat(2.5080993113449974e10)+HFloat(0.0)*I, (232) = HFloat(2.5080993208398945e10)+HFloat(0.0)*I, (233) = HFloat(0.0)+HFloat(2.254773395793503e10)*I, (234) = HFloat(0.0)+HFloat(2.2547735018068146e10)*I, (235) = HFloat(0.0)+HFloat(2.230927680486148e10)*I, (236) = HFloat(0.0)+HFloat(2.2309275739654957e10)*I, (237) = HFloat(2.2547734011017384e10)+HFloat(0.0)*I, (238) = HFloat(2.2547735071150463e10)+HFloat(0.0)*I, (239) = HFloat(2.2309275795346184e10)+HFloat(0.0)*I, (240) = HFloat(2.230927686055267e10)+HFloat(0.0)*I, (241) = HFloat(0.0)+HFloat(2.0761537893235756e10)*I, (242) = HFloat(0.0)+HFloat(2.076153710533164e10)*I, (243) = HFloat(0.0)+HFloat(2.085375279279756e10)*I, (244) = HFloat(0.0)+HFloat(2.0853753757117336e10)*I, (245) = HFloat(0.0)+HFloat(2.053133482753444e10)*I, (246) = HFloat(0.0)+HFloat(2.0531333852717827e10)*I, (247) = HFloat(0.0)+HFloat(2.0501931620813725e10)*I, (248) = HFloat(0.0)+HFloat(2.050193241384371e10)*I, (249) = HFloat(0.0)+HFloat(1.9869305833505894e10)*I, (250) = HFloat(2.0761537940403336e10)+HFloat(0.0)*I, (251) = HFloat(2.0761537152499157e10)+HFloat(0.0)*I, (252) = HFloat(2.085375285019185e10)+HFloat(0.0)*I, (253) = HFloat(2.0853753814511616e10)+HFloat(0.0)*I, (254) = HFloat(2.0531334888025898e10)+HFloat(0.0)*I, (255) = HFloat(2.0531333913209225e10)+HFloat(0.0)*I, (256) = HFloat(2.050193167063531e10)+HFloat(0.0)*I, (257) = HFloat(2.0501932463665325e10)+HFloat(0.0)*I, (258) = HFloat(1.9869305888579845e10)+HFloat(0.0)*I, (259) = HFloat(2.1717702815612522e10)+HFloat(0.0)*I, (260) = HFloat(2.1717701057705227e10)+HFloat(0.0)*I, (261) = HFloat(2.1717701633259586e10)+HFloat(0.0)*I, (262) = HFloat(2.171770137583627e10)+HFloat(0.0)*I, (263) = HFloat(0.0)+HFloat(2.1717702761003273e10)*I, (264) = HFloat(0.0)+HFloat(2.1717701003096096e10)*I, (265) = HFloat(0.0)+HFloat(2.1717701578650383e10)*I, (266) = HFloat(0.0)+HFloat(2.171770132122715e10)*I, (267) = HFloat(2.130324560303247e10)+HFloat(0.0)*I, (268) = HFloat(2.1303244424315723e10)+HFloat(0.0)*I, (269) = HFloat(2.1303244691356113e10)+HFloat(0.0)*I, (270) = HFloat(2.1303244179601917e10)+HFloat(0.0)*I, (271) = HFloat(0.0)+HFloat(2.1303245554459557e10)*I, (272) = HFloat(0.0)+HFloat(2.130324413102906e10)*I, (273) = HFloat(0.0)+HFloat(2.130324437574282e10)*I, (274) = HFloat(0.0)+HFloat(2.1303244642783173e10)*I, (275) = HFloat(1.8934790447487556e10)+HFloat(0.0)*I, (276) = HFloat(1.893478974304374e10)+HFloat(0.0)*I, (277) = HFloat(1.8251939736631622e10)+HFloat(0.0)*I, (278) = HFloat(1.8251938867225483e10)+HFloat(0.0)*I, (279) = HFloat(1.85807556761978e10)+HFloat(0.0)*I, (280) = HFloat(1.8580756391490364e10)+HFloat(0.0)*I, (281) = HFloat(1.9869305122626663e10)+HFloat(0.0)*I, (282) = HFloat(1.986930607387114e10)+HFloat(0.0)*I, (283) = HFloat(0.0)+HFloat(1.893479039576956e10)*I, (284) = HFloat(0.0)+HFloat(1.8934789691325684e10)*I, (285) = HFloat(1.8656425610070457e10)+HFloat(0.0)*I, (286) = HFloat(0.0)+HFloat(1.825193879947602e10)*I, (287) = HFloat(0.0)+HFloat(1.8251939668882156e10)*I, (288) = HFloat(0.0)+HFloat(1.98693060187972e10)*I, (289) = HFloat(0.0)+HFloat(1.9869305067552723e10)*I, (290) = HFloat(1.986930517045466e10)+HFloat(0.0)*I, (291) = HFloat(1.8656426460994114e10)+HFloat(0.0)*I, (292) = HFloat(1.639502127486311e10)+HFloat(0.0)*I, (293) = HFloat(0.0)+HFloat(1.858075562131689e10)*I, (294) = HFloat(0.0)+HFloat(1.8580756336609447e10)*I, (295) = HFloat(0.0)+HFloat(1.986930511538064e10)*I, (296) = HFloat(1.6395020675736088e10)+HFloat(0.0)*I, (297) = HFloat(0.0)+HFloat(1.865642554591631e10)*I, (298) = HFloat(0.0)+HFloat(1.8656426396839977e10)*I, (299) = HFloat(1.4683457892845684e10)+HFloat(0.0)*I, (300) = HFloat(1.4683458602877178e10)+HFloat(0.0)*I, (301) = HFloat(0.0)+HFloat(1.6395021215133423e10)*I, (302) = HFloat(0.0)+HFloat(1.6395020616006275e10)*I, (303) = HFloat(1.5945404521691875e10)+HFloat(0.0)*I, (304) = HFloat(1.5945403902865656e10)+HFloat(0.0)*I, (305) = HFloat(1.9531419281936604e10)+HFloat(0.0)*I, (306) = HFloat(1.9531419339353558e10)+HFloat(0.0)*I, (307) = HFloat(1.9531418472287304e10)+HFloat(0.0)*I, (308) = HFloat(1.5169898491084602e10)+HFloat(0.0)*I, (309) = HFloat(0.0)+HFloat(1.5945403839402935e10)*I, (310) = HFloat(0.0)+HFloat(1.5945404458229103e10)*I, (311) = HFloat(0.0)+HFloat(1.468345780964035e10)*I, (312) = HFloat(0.0)+HFloat(1.4683458519671782e10)*I, (313) = HFloat(1.516989916958359e10)+HFloat(0.0)*I, (314) = HFloat(0.0)+HFloat(1.5169898412185799e10)*I, (315) = HFloat(0.0)+HFloat(1.9531419224439438e10)*I, (316) = HFloat(0.0)+HFloat(1.953141928185636e10)*I, (317) = HFloat(0.0)+HFloat(1.9531418414790207e10)*I, (318) = HFloat(0.0)+HFloat(1.953141842321525e10)*I, (319) = HFloat(1.9531418480712383e10)+HFloat(0.0)*I, (320) = HFloat(0.0)+HFloat(1.516989909068478e10)*I, (321) = HFloat(1.421894435250693e10)+HFloat(0.0)*I, (322) = HFloat(0.0)+HFloat(1.762594714877531e10)*I, (323) = HFloat(1.762594720615669e10)+HFloat(0.0)*I, (324) = HFloat(1.762594625557114e10)+HFloat(0.0)*I, (325) = HFloat(1.4218944395568945e10)+HFloat(0.0)*I, (326) = HFloat(0.0)+HFloat(1.7625946198189728e10)*I, (327) = HFloat(0.0)+HFloat(1.7625946392556114e10)*I, (328) = HFloat(1.4218945173568743e10)+HFloat(0.0)*I, (329) = HFloat(1.7625946449937515e10)+HFloat(0.0)*I, (330) = HFloat(0.0)+HFloat(1.4218944282659203e10)*I, (331) = HFloat(0.0)+HFloat(1.4218944325721243e10)*I, (332) = HFloat(1.6929221848326664e10)+HFloat(0.0)*I, (333) = HFloat(0.0)+HFloat(1.6929221777470102e10)*I, (334) = HFloat(0.0)+HFloat(1.692922222890502e10)*I, (335) = HFloat(1.6929222299761642e10)+HFloat(0.0)*I, (336) = HFloat(1.7625946052695076e10)+HFloat(0.0)*I, (337) = HFloat(0.0)+HFloat(1.7625945995313744e10)*I, (338) = HFloat(0.0)+HFloat(1.4218945103721035e10)*I, (339) = HFloat(0.0)+HFloat(1.4218944072280153e10)*I, (340) = HFloat(0.0)+HFloat(1.69292231426306e10)*I, (341) = HFloat(1.6929223213487133e10)+HFloat(0.0)*I, (342) = HFloat(1.6929222093359928e10)+HFloat(0.0)*I, (343) = HFloat(0.0)+HFloat(1.6929222022503328e10)*I, (344) = HFloat(1.4218944142127888e10)+HFloat(0.0)*I, (345) = HFloat(0.0)+HFloat(1.0576077458919355e10)*I, (346) = HFloat(0.0)+HFloat(1.0576077880751673e10)*I, (347) = HFloat(1.0576077552453472e10)+HFloat(0.0)*I, (348) = HFloat(1.0576077974285769e10)+HFloat(0.0)*I, (349) = HFloat(1.1073646330185757e10)+HFloat(0.0)*I, (350) = HFloat(1.107364594098155e10)+HFloat(0.0)*I, (351) = HFloat(0.0)+HFloat(1.1073646241753101e10)*I, (352) = HFloat(0.0)+HFloat(1.1073645852548988e10)*I, (353) = HFloat(1.1355844353035913e10)+HFloat(0.0)*I, (354) = HFloat(1.135584409634208e10)+HFloat(0.0)*I, (355) = HFloat(1.1355845112286394e10)+HFloat(0.0)*I, (356) = HFloat(0.0)+HFloat(1.135584399052271e10)*I, (357) = HFloat(0.0)+HFloat(1.135584424721655e10)*I, (358) = HFloat(0.0)+HFloat(1.135584419570144e10)*I, (359) = HFloat(0.0)+HFloat(1.1355845006467022e10)*I, (360) = HFloat(1.1355844301520813e10)+HFloat(0.0)*I, (361) = HFloat(157268.9213451579)+HFloat(0.0)*I, (362) = HFloat(0.0)+HFloat(157270.52875477463)*I, (363) = HFloat(150335.7684143892)+HFloat(0.0)*I, (364) = HFloat(0.0)+HFloat(150340.8069231008)*I, (365) = HFloat(115846.71170264334)+HFloat(0.0)*I, (366) = HFloat(0.0)+HFloat(115851.6422137592)*I, (367) = HFloat(104148.64677560228)+HFloat(0.0)*I, (368) = HFloat(0.0)+HFloat(104136.15012836785)*I, (369) = HFloat(93701.32780671051)+HFloat(0.0)*I, (370) = HFloat(0.0)+HFloat(93692.87817642518)*I, (371) = HFloat(0.0)+HFloat(84157.4870840474)*I, (372) = HFloat(84154.5515166927)+HFloat(0.0)*I, (373) = HFloat(36701.614343789326)+HFloat(0.0)*I, (374) = HFloat(35194.9338957977)+HFloat(0.0)*I, (375) = HFloat(0.0)+HFloat(36683.501949820005)*I, (376) = HFloat(0.0)+HFloat(35145.457757574695)*I, (377) = HFloat(5073.8265778605)+HFloat(395.0924175629166)*I, (378) = HFloat(5073.8265778605)-HFloat(395.0924175629166)*I, (379) = HFloat(3991.1137883584174)+HFloat(3232.391839564931)*I, (380) = HFloat(3991.1137883584174)-HFloat(3232.391839564931)*I, (381) = HFloat(0.0)+HFloat(4923.096904553619)*I, (382) = HFloat(355.80868305084465)+HFloat(4954.797275187767)*I, (383) = HFloat(355.80868305084465)-HFloat(4954.797275187767)*I, (384) = HFloat(3108.7167955663663)+HFloat(4007.9983282364115)*I, (385) = HFloat(3108.7167955663663)-HFloat(4007.9983282364115)*I, (386) = HFloat(2416.344994259764)+HFloat(4398.3820153204915)*I, (387) = HFloat(2416.344994259764)-HFloat(4398.3820153204915)*I, (388) = HFloat(2635.447630648785)+HFloat(4205.131523204462)*I, (389) = HFloat(2635.447630648785)-HFloat(4205.131523204462)*I, (390) = HFloat(1038.855157456167)+HFloat(4733.048324558123)*I, (391) = HFloat(1038.855157456167)-HFloat(4733.048324558123)*I, (392) = HFloat(4553.0284761167095)+HFloat(1991.436172455588)*I, (393) = HFloat(4553.0284761167095)-HFloat(1991.436172455588)*I, (394) = HFloat(4835.858736537255)+HFloat(0.0)*I, (395) = HFloat(4633.983488537295)+HFloat(1368.4525082531752)*I, (396) = HFloat(4633.983488537295)-HFloat(1368.4525082531752)*I, (397) = HFloat(4132.304437641948)+HFloat(2439.344248057234)*I, (398) = HFloat(4132.304437641948)-HFloat(2439.344248057234)*I, (399) = HFloat(4556.380077206366)+HFloat(379.72564207637186)*I, (400) = HFloat(4556.380077206366)-HFloat(379.72564207637186)*I, (401) = HFloat(4338.602358934595)+HFloat(1122.1021571247475)*I, (402) = HFloat(4338.602358934595)-HFloat(1122.1021571247475)*I, (403) = HFloat(3626.8896345501826)+HFloat(3017.8679547957786)*I, (404) = HFloat(3626.8896345501826)-HFloat(3017.8679547957786)*I, (405) = HFloat(4070.09420801911)+HFloat(2006.312983133468)*I, (406) = HFloat(4070.09420801911)-HFloat(2006.312983133468)*I, (407) = HFloat(4010.7449397162272)+HFloat(1767.1259453512364)*I, (408) = HFloat(4010.7449397162272)-HFloat(1767.1259453512364)*I, (409) = HFloat(3087.6916230609518)+HFloat(3490.892536870371)*I, (410) = HFloat(3087.6916230609518)-HFloat(3490.892536870371)*I, (411) = HFloat(3343.3299270980983)+HFloat(3152.9423211769345)*I, (412) = HFloat(3343.3299270980983)-HFloat(3152.9423211769345)*I, (413) = HFloat(2300.342911992544)+HFloat(3921.866743501259)*I, (414) = HFloat(2300.342911992544)-HFloat(3921.866743501259)*I, (415) = HFloat(1156.1752107574623)+HFloat(4439.017473593972)*I, (416) = HFloat(1156.1752107574623)-HFloat(4439.017473593972)*I, (417) = HFloat(1647.68967965322)+HFloat(4009.0938965063765)*I, (418) = HFloat(1647.68967965322)-HFloat(4009.0938965063765)*I, (419) = HFloat(1020.4471636506946)+HFloat(4227.870941986736)*I, (420) = HFloat(1020.4471636506946)-HFloat(4227.870941986736)*I, (421) = HFloat(4450.0447829538425)+HFloat(0.0)*I, (422) = HFloat(228.1322861359352)+HFloat(4395.535528591593)*I, (423) = HFloat(228.1322861359352)-HFloat(4395.535528591593)*I, (424) = HFloat(362.7500102576454)+HFloat(4324.148561246249)*I, (425) = HFloat(362.7500102576454)-HFloat(4324.148561246249)*I, (426) = HFloat(1757.496404705381)+HFloat(3841.313598245525)*I, (427) = HFloat(1757.496404705381)-HFloat(3841.313598245525)*I, (428) = HFloat(3610.098968038375)+HFloat(2330.216934377035)*I, (429) = HFloat(3610.098968038375)-HFloat(2330.216934377035)*I, (430) = HFloat(3242.441567199116)+HFloat(2734.3477296634514)*I, (431) = HFloat(3242.441567199116)-HFloat(2734.3477296634514)*I, (432) = HFloat(0.0)+HFloat(4225.264731846452)*I, (433) = HFloat(4282.753619818499)+HFloat(0.0)*I, (434) = HFloat(2222.5000301951177)+HFloat(3521.5342038416575)*I, (435) = HFloat(2222.5000301951177)-HFloat(3521.5342038416575)*I, (436) = HFloat(4025.609846953705)+HFloat(950.365786933205)*I, (437) = HFloat(4025.609846953705)-HFloat(950.365786933205)*I, (438) = HFloat(3280.0293154722463)+HFloat(2611.9650199569587)*I, (439) = HFloat(3280.0293154722463)-HFloat(2611.9650199569587)*I, (440) = HFloat(3754.0578090642325)+HFloat(1709.2234368238223)*I, (441) = HFloat(3754.0578090642325)-HFloat(1709.2234368238223)*I, (442) = HFloat(4046.3099426027875)+HFloat(495.1493844071691)*I, (443) = HFloat(4046.3099426027875)-HFloat(495.1493844071691)*I, (444) = HFloat(2386.3600801732573)+HFloat(3321.13134381449)*I, (445) = HFloat(2386.3600801732573)-HFloat(3321.13134381449)*I, (446) = HFloat(3289.3225475298595)+HFloat(2314.830001390338)*I, (447) = HFloat(3289.3225475298595)-HFloat(2314.830001390338)*I, (448) = HFloat(3431.263898604786)+HFloat(2038.1802332946731)*I, (449) = HFloat(3431.263898604786)-HFloat(2038.1802332946731)*I, (450) = HFloat(3966.5888505731396)+HFloat(0.0)*I, (451) = HFloat(3487.70371887116)+HFloat(1633.3028862799958)*I, (452) = HFloat(3487.70371887116)-HFloat(1633.3028862799958)*I, (453) = HFloat(1243.0134798638835)+HFloat(3762.4167676499296)*I, (454) = HFloat(1243.0134798638835)-HFloat(3762.4167676499296)*I, (455) = HFloat(0.0)+HFloat(3972.352295438696)*I, (456) = HFloat(933.7439310353159)+HFloat(3776.417887778737)*I, (457) = HFloat(933.7439310353159)-HFloat(3776.417887778737)*I, (458) = HFloat(747.7745393119857)+HFloat(3780.3184500310563)*I, (459) = HFloat(747.7745393119857)-HFloat(3780.3184500310563)*I, (460) = HFloat(2780.2073203704713)+HFloat(2611.3265944784243)*I, (461) = HFloat(2780.2073203704713)-HFloat(2611.3265944784243)*I, (462) = HFloat(2455.9271867130683)+HFloat(2881.3593147645406)*I, (463) = HFloat(2455.9271867130683)-HFloat(2881.3593147645406)*I, (464) = HFloat(3681.410406409821)+HFloat(676.7469424387995)*I, (465) = HFloat(3681.410406409821)-HFloat(676.7469424387995)*I, (466) = HFloat(2053.521036386661)+HFloat(3035.572464253596)*I, (467) = HFloat(2053.521036386661)-HFloat(3035.572464253596)*I, (468) = HFloat(0.0)+HFloat(3523.2148801369844)*I, (469) = HFloat(2174.33008180766)+HFloat(2912.054070699819)*I, (470) = HFloat(2174.33008180766)-HFloat(2912.054070699819)*I, (471) = HFloat(3462.7893226009555)+HFloat(333.3265818814259)*I, (472) = HFloat(3462.7893226009555)-HFloat(333.3265818814259)*I, (473) = HFloat(3153.383640435064)+HFloat(1108.9482431782105)*I, (474) = HFloat(3153.383640435064)-HFloat(1108.9482431782105)*I, (475) = HFloat(1203.9959984742147)+HFloat(3225.964612418773)*I, (476) = HFloat(1203.9959984742147)-HFloat(3225.964612418773)*I, (477) = HFloat(541.8285285380863)+HFloat(3444.0118354930796)*I, (478) = HFloat(541.8285285380863)-HFloat(3444.0118354930796)*I, (479) = HFloat(0.0)+HFloat(3068.3147370619226)*I, (480) = HFloat(1713.3166863699173)+HFloat(2828.027657018556)*I, (481) = HFloat(1713.3166863699173)-HFloat(2828.027657018556)*I, (482) = HFloat(2789.1856861524493)+HFloat(1601.7548090625685)*I, (483) = HFloat(2789.1856861524493)-HFloat(1601.7548090625685)*I, (484) = HFloat(2538.252285537942)+HFloat(1960.6853822775988)*I, (485) = HFloat(2538.252285537942)-HFloat(1960.6853822775988)*I, (486) = HFloat(1874.2993920835124)+HFloat(2577.9935016860545)*I, (487) = HFloat(1874.2993920835124)-HFloat(2577.9935016860545)*I, (488) = HFloat(1473.3096791692888)+HFloat(2785.7040716467513)*I, (489) = HFloat(1473.3096791692888)-HFloat(2785.7040716467513)*I, (490) = HFloat(2943.9279710449214)+HFloat(929.2808311170284)*I, (491) = HFloat(2943.9279710449214)-HFloat(929.2808311170284)*I, (492) = HFloat(1091.6475468635854)+HFloat(2797.1464981369654)*I, (493) = HFloat(1091.6475468635854)-HFloat(2797.1464981369654)*I, (494) = HFloat(2728.949129898927)+HFloat(1422.1091574777863)*I, (495) = HFloat(2728.949129898927)-HFloat(1422.1091574777863)*I, (496) = HFloat(618.8836526876327)+HFloat(2788.929420257734)*I, (497) = HFloat(618.8836526876327)-HFloat(2788.929420257734)*I, (498) = HFloat(2976.789820772417)+HFloat(0.0)*I, (499) = HFloat(2343.9646463549316)+HFloat(1692.0337727258377)*I, (500) = HFloat(2343.9646463549316)-HFloat(1692.0337727258377)*I, (501) = HFloat(2937.9546706503697)+HFloat(108.74155556901977)*I, (502) = HFloat(2937.9546706503697)-HFloat(108.74155556901977)*I, (503) = HFloat(2205.3959827011095)+HFloat(1849.8713880100152)*I, (504) = HFloat(2205.3959827011095)-HFloat(1849.8713880100152)*I, (505) = HFloat(19.42597957546096)+HFloat(2791.882688642894)*I, (506) = HFloat(19.42597957546096)-HFloat(2791.882688642894)*I, (507) = HFloat(1988.4965421387772)+HFloat(1950.837812600771)*I, (508) = HFloat(1988.4965421387772)-HFloat(1950.837812600771)*I, (509) = HFloat(1181.1655923596695)+HFloat(2456.5828203467945)*I, (510) = HFloat(1181.1655923596695)-HFloat(2456.5828203467945)*I, (511) = HFloat(2431.9837147221674)+HFloat(1054.689280989327)*I, (512) = HFloat(2431.9837147221674)-HFloat(1054.689280989327)*I, (513) = HFloat(2679.5151803131603)+HFloat(505.3943314095876)*I, (514) = HFloat(2679.5151803131603)-HFloat(505.3943314095876)*I, (515) = HFloat(2732.699700484979)+HFloat(0.0)*I, (516) = HFloat(2581.634074301646)+HFloat(197.67860682658815)*I, (517) = HFloat(2581.634074301646)-HFloat(197.67860682658815)*I, (518) = HFloat(715.9949192622356)+HFloat(2455.91830021026)*I, (519) = HFloat(715.9949192622356)-HFloat(2455.91830021026)*I, (520) = HFloat(0.0)+HFloat(2298.0182716792606)*I, (521) = HFloat(2370.422847079266)+HFloat(596.6035654954509)*I, (522) = HFloat(2370.422847079266)-HFloat(596.6035654954509)*I, (523) = HFloat(2137.6994791918514)+HFloat(1195.963358101822)*I, (524) = HFloat(2137.6994791918514)-HFloat(1195.963358101822)*I, (525) = HFloat(1145.6659831679592)+HFloat(2112.6317613306664)*I, (526) = HFloat(1145.6659831679592)-HFloat(2112.6317613306664)*I, (527) = HFloat(1543.7095216824873)+HFloat(1783.8369460474664)*I, (528) = HFloat(1543.7095216824873)-HFloat(1783.8369460474664)*I, (529) = HFloat(847.2297591993063)+HFloat(2057.7489075087537)*I, (530) = HFloat(847.2297591993063)-HFloat(2057.7489075087537)*I, (531) = HFloat(1980.380244530765)+HFloat(926.8093671122932)*I, (532) = HFloat(1980.380244530765)-HFloat(926.8093671122932)*I, (533) = HFloat(155.97751025688646)+HFloat(2145.2865214782873)*I, (534) = HFloat(155.97751025688646)-HFloat(2145.2865214782873)*I, (535) = HFloat(1696.7183497840067)+HFloat(1186.6702878569909)*I, (536) = HFloat(1696.7183497840067)-HFloat(1186.6702878569909)*I, (537) = HFloat(1647.985252475415)+HFloat(984.4502126238178)*I, (538) = HFloat(1647.985252475415)-HFloat(984.4502126238178)*I, (539) = HFloat(1727.1332698494728)+HFloat(0.0)*I, (540) = HFloat(439.6329861007922)+HFloat(1811.4511290525832)*I, (541) = HFloat(439.6329861007922)-HFloat(1811.4511290525832)*I, (542) = HFloat(1145.1549097128852)+HFloat(1409.3588688826112)*I, (543) = HFloat(1145.1549097128852)-HFloat(1409.3588688826112)*I, (544) = HFloat(1774.1579667918497)+HFloat(297.7477509790167)*I, (545) = HFloat(1774.1579667918497)-HFloat(297.7477509790167)*I, (546) = HFloat(96.6553001600956)+HFloat(1801.4083139354948)*I, (547) = HFloat(96.6553001600956)-HFloat(1801.4083139354948)*I, (548) = HFloat(1284.4523624949716)+HFloat(1155.2557865459814)*I, (549) = HFloat(1284.4523624949716)-HFloat(1155.2557865459814)*I, (550) = HFloat(989.9771278760578)+HFloat(1201.6037141012368)*I, (551) = HFloat(989.9771278760578)-HFloat(1201.6037141012368)*I, (552) = HFloat(537.5005507844425)+HFloat(1422.229297945499)*I, (553) = HFloat(537.5005507844425)-HFloat(1422.229297945499)*I, (554) = HFloat(734.0865169866943)+HFloat(1289.4909134145266)*I, (555) = HFloat(734.0865169866943)-HFloat(1289.4909134145266)*I, (556) = HFloat(1378.2418299901674)+HFloat(419.34780362425306)*I, (557) = HFloat(1378.2418299901674)-HFloat(419.34780362425306)*I, (558) = HFloat(1190.5520975540664)+HFloat(814.3296962480478)*I, (559) = HFloat(1190.5520975540664)-HFloat(814.3296962480478)*I, (560) = HFloat(358.7197927857897)+HFloat(1268.2489469868483)*I, (561) = HFloat(358.7197927857897)-HFloat(1268.2489469868483)*I, (562) = HFloat(1253.3465566002963)+HFloat(342.7424779456501)*I, (563) = HFloat(1253.3465566002963)-HFloat(342.7424779456501)*I, (564) = HFloat(1292.616523945355)+HFloat(94.10041261296668)*I, (565) = HFloat(1292.616523945355)-HFloat(94.10041261296668)*I, (566) = HFloat(442.8787335933938)+HFloat(964.4946652533554)*I, (567) = HFloat(442.8787335933938)-HFloat(964.4946652533554)*I, (568) = HFloat(605.6435728556866)+HFloat(831.0110757882934)*I, (569) = HFloat(605.6435728556866)-HFloat(831.0110757882934)*I, (570) = HFloat(0.0)+HFloat(944.881916513597)*I, (571) = HFloat(948.3480433828403)+HFloat(293.8225956963345)*I, (572) = HFloat(948.3480433828403)-HFloat(293.8225956963345)*I, (573) = HFloat(311.14132266138506)+HFloat(907.2544394894344)*I, (574) = HFloat(311.14132266138506)-HFloat(907.2544394894344)*I, (575) = HFloat(745.4573264155493)+HFloat(594.0959707662935)*I, (576) = HFloat(745.4573264155493)-HFloat(594.0959707662935)*I, (577) = HFloat(854.6028251957603)+HFloat(0.0)*I, (578) = HFloat(100.97519696456763)+HFloat(625.4033656613652)*I, (579) = HFloat(100.97519696456763)-HFloat(625.4033656613652)*I, (580) = HFloat(452.5695597766738)+HFloat(450.6831100080505)*I, (581) = HFloat(452.5695597766738)-HFloat(450.6831100080505)*I, (582) = HFloat(667.3887784319786)+HFloat(0.0)*I, (583) = HFloat(648.9597576972654)+HFloat(45.286538820066895)*I, (584) = HFloat(648.9597576972654)-HFloat(45.286538820066895)*I, (585) = HFloat(572.6104418533254)+HFloat(170.1748298871424)*I, (586) = HFloat(572.6104418533254)-HFloat(170.1748298871424)*I, (587) = HFloat(0.0)+HFloat(531.8354647182015)*I, (588) = HFloat(0.0)+HFloat(494.35495734846137)*I, (589) = HFloat(460.44563507486964)+HFloat(210.35776258139362)*I, (590) = HFloat(460.44563507486964)-HFloat(210.35776258139362)*I, (591) = HFloat(484.4865054952113)+HFloat(139.87143530089264)*I, (592) = HFloat(484.4865054952113)-HFloat(139.87143530089264)*I, (593) = HFloat(143.71766125792124)+HFloat(432.5703758936112)*I, (594) = HFloat(143.71766125792124)-HFloat(432.5703758936112)*I, (595) = HFloat(498.4254421995683)+HFloat(19.079628094815952)*I, (596) = HFloat(498.4254421995683)-HFloat(19.079628094815952)*I, (597) = HFloat(0.0)+HFloat(415.3419512056688)*I, (598) = HFloat(176.87198782032308)+HFloat(386.31618217025806)*I, (599) = HFloat(176.87198782032308)-HFloat(386.31618217025806)*I, (600) = HFloat(313.9217077529305)+HFloat(285.9187171739824)*I, (601) = HFloat(313.9217077529305)-HFloat(285.9187171739824)*I, (602) = HFloat(428.8026206025167)+HFloat(67.01209682607151)*I, (603) = HFloat(428.8026206025167)-HFloat(67.01209682607151)*I, (604) = HFloat(181.13319045135995)+HFloat(329.5863909195456)*I, (605) = HFloat(181.13319045135995)-HFloat(329.5863909195456)*I, (606) = HFloat(389.467597836227)+HFloat(0.0)*I, (607) = HFloat(414.5243343092878)+HFloat(14.395636340403849)*I, (608) = HFloat(414.5243343092878)-HFloat(14.395636340403849)*I, (609) = HFloat(288.98555438843096)+HFloat(211.40519710976307)*I, (610) = HFloat(288.98555438843096)-HFloat(211.40519710976307)*I, (611) = HFloat(0.0)+HFloat(347.99645263745407)*I, (612) = HFloat(94.74405433446864)+HFloat(288.8285560951835)*I, (613) = HFloat(94.74405433446864)-HFloat(288.8285560951835)*I, (614) = HFloat(316.73945539942054)+HFloat(127.01428774559801)*I, (615) = HFloat(316.73945539942054)-HFloat(127.01428774559801)*I, (616) = HFloat(372.1264469884495)+HFloat(0.0)*I, (617) = HFloat(335.94342862084363)+HFloat(102.14506790115607)*I, (618) = HFloat(335.94342862084363)-HFloat(102.14506790115607)*I, (619) = HFloat(21.85480715472142)+HFloat(300.0810677033566)*I, (620) = HFloat(21.85480715472142)-HFloat(300.0810677033566)*I, (621) = HFloat(0.0)+HFloat(305.407565586851)*I, (622) = HFloat(329.2247671357515)+HFloat(45.44537095486625)*I, (623) = HFloat(329.2247671357515)-HFloat(45.44537095486625)*I, (624) = HFloat(281.8805115419692)+HFloat(128.52504210433688)*I, (625) = HFloat(281.8805115419692)-HFloat(128.52504210433688)*I, (626) = HFloat(318.1558256200091)+HFloat(27.57016845099467)*I, (627) = HFloat(318.1558256200091)-HFloat(27.57016845099467)*I, (628) = HFloat(315.028989408211)+HFloat(0.0)*I, (629) = HFloat(138.16025266404273)+HFloat(242.27669793646984)*I, (630) = HFloat(138.16025266404273)-HFloat(242.27669793646984)*I, (631) = HFloat(244.4910485997406)+HFloat(155.1871674068116)*I, (632) = HFloat(244.4910485997406)-HFloat(155.1871674068116)*I, (633) = HFloat(0.0)+HFloat(257.14825436881654)*I, (634) = HFloat(177.264471450038)+HFloat(190.40131053176344)*I, (635) = HFloat(177.264471450038)-HFloat(190.40131053176344)*I, (636) = HFloat(20.4840674693217)+HFloat(248.54855708352528)*I, (637) = HFloat(20.4840674693217)-HFloat(248.54855708352528)*I, (638) = HFloat(291.04451877859833)+HFloat(31.131450431697)*I, (639) = HFloat(291.04451877859833)-HFloat(31.131450431697)*I, (640) = HFloat(127.273671694846)+HFloat(199.23163768017224)*I, (641) = HFloat(127.273671694846)-HFloat(199.23163768017224)*I, (642) = HFloat(61.541807926604776)+HFloat(219.50235079392817)*I, (643) = HFloat(61.541807926604776)-HFloat(219.50235079392817)*I, (644) = HFloat(194.98746614322494)+HFloat(129.1444742192117)*I, (645) = HFloat(194.98746614322494)-HFloat(129.1444742192117)*I, (646) = HFloat(263.59767767264447)+HFloat(0.0)*I, (647) = HFloat(54.4096618026861)+HFloat(183.18392988705773)*I, (648) = HFloat(54.4096618026861)-HFloat(183.18392988705773)*I, (649) = HFloat(218.71735515259255)+HFloat(86.77422279627609)*I, (650) = HFloat(218.71735515259255)-HFloat(86.77422279627609)*I, (651) = HFloat(238.35304719252278)+HFloat(53.92116454439134)*I, (652) = HFloat(238.35304719252278)-HFloat(53.92116454439134)*I, (653) = HFloat(244.75619904436508)+HFloat(28.424040595524865)*I, (654) = HFloat(244.75619904436508)-HFloat(28.424040595524865)*I, (655) = HFloat(78.8624665872682)+HFloat(170.59575769553194)*I, (656) = HFloat(78.8624665872682)-HFloat(170.59575769553194)*I, (657) = HFloat(0.0)+HFloat(169.57063059966518)*I, (658) = HFloat(226.39524956530474)+HFloat(56.112210269562645)*I, (659) = HFloat(226.39524956530474)-HFloat(56.112210269562645)*I, (660) = HFloat(0.0)+HFloat(155.8567246128773)*I, (661) = HFloat(221.89079676962075)+HFloat(0.0)*I, (662) = HFloat(108.44983903820278)+HFloat(114.42302416975811)*I, (663) = HFloat(108.44983903820278)-HFloat(114.42302416975811)*I, (664) = HFloat(141.45968871405472)+HFloat(96.64451960916871)*I, (665) = HFloat(141.45968871405472)-HFloat(96.64451960916871)*I, (666) = HFloat(0.0)+HFloat(129.5316717600758)*I, (667) = HFloat(200.34841297314202)+HFloat(21.34523086237802)*I, (668) = HFloat(200.34841297314202)-HFloat(21.34523086237802)*I, (669) = HFloat(51.63893015965976)+HFloat(99.34021524831148)*I, (670) = HFloat(51.63893015965976)-HFloat(99.34021524831148)*I, (671) = HFloat(85.30796334137827)+HFloat(95.28456986799658)*I, (672) = HFloat(85.30796334137827)-HFloat(95.28456986799658)*I, (673) = HFloat(185.09768069311085)+HFloat(33.37459691767084)*I, (674) = HFloat(185.09768069311085)-HFloat(33.37459691767084)*I, (675) = HFloat(154.96613054284643)+HFloat(62.393960374438045)*I, (676) = HFloat(154.96613054284643)-HFloat(62.393960374438045)*I, (677) = HFloat(185.0873485756328)+HFloat(5.146568966190643)*I, (678) = HFloat(185.0873485756328)-HFloat(5.146568966190643)*I, (679) = HFloat(26.762393098541235)+HFloat(63.997485574915416)*I, (680) = HFloat(26.762393098541235)-HFloat(63.997485574915416)*I, (681) = HFloat(173.45273892971673)+HFloat(0.0)*I, (682) = HFloat(0.0)+HFloat(32.225442512504415)*I, (683) = HFloat(155.79871429380535)+HFloat(11.324324009801945)*I, (684) = HFloat(155.79871429380535)-HFloat(11.324324009801945)*I, (685) = HFloat(60.35729737833421)+HFloat(9.102324921805549)*I, (686) = HFloat(60.35729737833421)-HFloat(9.102324921805549)*I, (687) = HFloat(107.42131836835468)+HFloat(28.34681598809886)*I, (688) = HFloat(107.42131836835468)-HFloat(28.34681598809886)*I, (689) = HFloat(131.05911452058245)+HFloat(20.74750591603703)*I, (690) = HFloat(131.05911452058245)-HFloat(20.74750591603703)*I, (691) = HFloat(73.52858173880192)+HFloat(0.0)*I, (692) = HFloat(118.6798234542339)+HFloat(0.0)*I, (693) = HFloat(87.58775101224597)+HFloat(9.449453952276484)*I, (694) = HFloat(87.58775101224597)-HFloat(9.449453952276484)*I, (695) = HFloat(146.91702760856268)+HFloat(0.7528794054578921)*I, (696) = HFloat(146.91702760856268)-HFloat(0.7528794054578921)*I, (697) = HFloat(97.85814784762381)+HFloat(12.385872121093305)*I, (698) = HFloat(97.85814784762381)-HFloat(12.385872121093305)*I, (699) = HFloat(83.29796557761745)+HFloat(0.0)*I, (700) = HFloat(97.67168583950388)+HFloat(0.0)*I})

(1)

``

sort(Re(SS))

RTABLE(18446744074183923702, anything, Vector[column], rectangular, Fortran_order, [], 1, 1 .. 700)

(2)

``

``

``

``

``

``

``

``

``


 

Download Suals.mw

K21.mw

K22.mw

K11.mw

K12.mw

M21.mw

M22.mw

M11.mw

M12.mw

 

Where is the problem in my matrices?

 

Please guide and help me.

 

@taro using CodeGeneration is tedious for worksheet including 3000 lines of commands. Is there a fast method to translate a Maple worksheet into Matlab?

@taro yes this post was for four years ago. I wanted to know if there is new activity to develope more complete new tools in this case.

Anyway thanks

@tomleslie Ok, lets do the same process for some of my matrices.


 

restart;with(LinearAlgebra):

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received shareman

 

 

B:=RandomVector(20)*f

B := Vector(20, {(1) = -98*f, (2) = -77*f, (3) = 57*f, (4) = 27*f, (5) = -93*f, (6) = -76*f, (7) = -72*f, (8) = -2*f, (9) = -32*f, (10) = -74*f, (11) = -4*f, (12) = 27*f, (13) = 8*f, (14) = 69*f, (15) = 99*f, (16) = 29*f, (17) = 44*f, (18) = 92*f, (19) = -31*f, (20) = 67*f})

(1)

A:=Vector([U[0, 0], U[0, 1], U[1, 0], U[1, 1], V[0, 0], V[0, 1], V[1, 0], V[1, 1], W[0, 0], W[0, 1], W[1, 0], W[1, 1], Phi[0, 0], Phi[0, 1], Phi[1, 0], Phi[1, 1], Xi[0, 0], Xi[0, 1], Xi[1, 0], Xi[1, 1]]):

varList := "Phi[0,0]", "Phi[0,1]", "Phi[1,0]", "Phi[1,1]", "U[0,0]", "U[0,1]", "U[1,0]", "U[1,1]", "V[0,0]", "V[0,1]", "V[1,0]", "V[1,1]", "W[0,0]", "W[0,1]", "W[1,0]", "W[1,1]", "Xi[0,0]", "Xi[0,1]", "Xi[1,0]", "Xi[1,1]":

``

``

``

for f to 11 do
    assign~(A=~B):
    seq( unassign( convert(j,name)), j in varList);
 end do;:

RTABLE(18446744074184893230, anything, Vector[column], rectangular, Fortran_order, [], 1, 1 .. 20)

 

Error, invalid left hand side in assignment

 

 

``


 

Download unassign2-1.mw

But error persists

@vv Let me explain more.

Let the A be a square matrix of function of omega and b is vector function of  y1,y2,y3,...,yi, and X be X := [seq(seq(U[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(V[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(W[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(Phi[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(Xi[i, j], j = 0 .. JJ), i = 0 .. II)]

I initialize omega with for loop, then solve the  AX=b by X=inv(A)*b. So, X will be function of yi. Now I want to put them(Solved X) into series of equations(functions of X) and build the new CY=0 equation. Then determinant of C will be calculated. The omega that makes the determinant of C zero will be my output.

Note II and JJ are are 50.

It seems if there was a way to unassign X[i], the problem will be solved. But I dont know How is it pussible to unassign X[i].

@vv 

May matrix have the variables as below.

var1 := [seq(seq(U[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(V[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(W[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(Phi[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(Xi[i, j], j = 0 .. JJ), i = 0 .. II)]

How to unassign them?

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