From 2f63f5f6af2b5d9d612d2512c5cd9122a0148e5b Mon Sep 17 00:00:00 2001 From: "github-actions[bot]" Date: Tue, 28 Jul 2020 00:23:21 +0000 Subject: [PATCH] Rebuild introduction/01-ode_introduction.jmd --- html/introduction/01-ode_introduction.html | 472 +++++++++--------- markdown/introduction/01-ode_introduction.md | 413 ++++++++------- .../figures/01-ode_introduction_13_1.png | Bin 15321 -> 15606 bytes .../figures/01-ode_introduction_29_1.png | Bin 114812 -> 114817 bytes .../figures/01-ode_introduction_30_1.png | Bin 149639 -> 149811 bytes .../figures/01-ode_introduction_31_1.png | Bin 148181 -> 148203 bytes .../figures/01-ode_introduction_32_1.png | Bin 59340 -> 59349 bytes .../figures/01-ode_introduction_4_1.png | Bin 12423 -> 12526 bytes .../figures/01-ode_introduction_5_1.png | Bin 23795 -> 23948 bytes .../figures/01-ode_introduction_6_1.png | Bin 27233 -> 27413 bytes pdf/introduction/01-ode_introduction.pdf | Bin 532037 -> 532361 bytes script/introduction/01-ode_introduction.jl | 4 +- 12 files changed, 445 insertions(+), 444 deletions(-) diff --git a/html/introduction/01-ode_introduction.html b/html/introduction/01-ode_introduction.html index 8145f699..84af8649 100644 --- a/html/introduction/01-ode_introduction.html +++ b/html/introduction/01-ode_introduction.html @@ -725,7 +725,7 @@

First Model: Exponential Growth

 retcode: Success
-Interpolation: Automatic order switching interpolation
+Interpolation: automatic order switching interpolation
 t: 5-element Array{Float64,1}:
  0.0
  0.10042494449239292
@@ -752,7 +752,7 @@ 

Analyzing the Solution

- +

From the picture we see that the solution is an exponential curve, which matches our intuition. As a plot recipe, we can annotate the result using any of the Plots.jl attributes. For example:

@@ -763,7 +763,7 @@

Analyzing the Solution

- +

Using the mutating plot! command we can add other pieces to our plot. For this ODE we know that the true solution is $u(t) = u_0 exp(at)$, so let's add some of the true solution to our plot:

@@ -773,7 +773,7 @@

Analyzing the Solution

- +

In the previous command I demonstrated sol.t, which grabs the array of time points that the solution was saved at:

@@ -839,7 +839,7 @@

Analyzing the Solution

 retcode: Success
-Interpolation: Automatic order switching interpolation
+Interpolation: automatic order switching interpolation
 t: 5-element Array{Float64,1}:
  0.0
  0.10042494449239292
@@ -880,7 +880,7 @@ 

Controlling the Solver

 retcode: Success
-Interpolation: Automatic order switching interpolation
+Interpolation: automatic order switching interpolation
 t: 9-element Array{Float64,1}:
  0.0
  0.04127492324135852
@@ -913,7 +913,7 @@ 

Controlling the Solver

- +

Notice that by decreasing the tolerance, the number of steps the solver had to take was 9 instead of the previous 5. There is a trade off between accuracy and speed, and it is up to you to determine what is the right balance for your problem.

Another common option is to use saveat to make the solver save at specific time points. For example, if we want the solution at an even grid of t=0.1k for integers k, we would use the command:

@@ -1195,7 +1195,7 @@

Systems of ODEs: The Lorenz Equation

 retcode: Success
-Interpolation: Automatic order switching interpolation
+Interpolation: automatic order switching interpolation
 t: 1294-element Array{Float64,1}:
    0.0
    3.5678604836301404e-5
@@ -1293,7 +1293,7 @@ 

Systems of ODEs: The Lorenz Equation

- +

If we instead want to plot values against each other, we can use the vars command. Let's plot variable 1 against variable 2 against variable 3:

@@ -1303,7 +1303,7 @@

Systems of ODEs: The Lorenz Equation

- +

This is the classic Lorenz attractor plot, where the x axis is u[1], the y axis is u[2], and the z axis is u[3]. Note that the plot recipe by default uses the interpolation, but we can turn this off:

@@ -1313,7 +1313,7 @@

Systems of ODEs: The Lorenz Equation

- +

Yikes! This shows how calculating the continuous solution has saved a lot of computational effort by computing only a sparse solution and filling in the values! Note that in vars, 0=time, and thus we can plot the time series of a single component like:

@@ -1323,7 +1323,7 @@

Systems of ODEs: The Lorenz Equation

- +

Internal Types

The last basic user-interface feature to explore is the choice of types. DifferentialEquations.jl respects your input types to determine the internal types that are used. Thus since in the previous cases, when we used Float64 values for the initial condition, this meant that the internal values would be solved using Float64. We made sure that time was specified via Float64 values, meaning that time steps would utilize 64-bit floats as well. But, by simply changing these types we can change what is used internally.

@@ -1345,49 +1345,53 @@

Internal Types

 retcode: Success
-Interpolation: Automatic order switching interpolation
-t: 10-element Array{Float64,1}:
+Interpolation: automatic order switching interpolation
+t: 11-element Array{Float64,1}:
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@@ -1401,10 +1405,10 @@

Internal Types

 4×2 Array{Float64,2}:
- -0.42416    0.618257
-  0.0370802  0.828585
-  0.453646   0.487887
-  1.11215    1.10741
+ 0.44732   -0.217635
+ 0.713033   0.00026306
+ 0.730249   0.119802
+ 1.51383    1.17964
 
@@ -1418,10 +1422,10 @@

Internal Types

 4×2 Array{BigFloat,2}:
- 0.137254  0.958207
- 0.30834   0.61675
- 0.288282  0.771294
- 0.818406  0.421275
+ 0.907369  0.234926
+ 0.633932  0.269101
+ 0.869287  0.0363703
+ 0.884096  0.91222
 
@@ -1436,66 +1440,66 @@

Internal Types

 retcode: Success
-Interpolation: Automatic order switching interpolation
+Interpolation: automatic order switching interpolation
 t: 6-element Array{Float64,1}:
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@@ -1506,8 +1510,8 @@

Internal Types

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+-2.833767611872948157911473208307873819373486758358471462262186914056376438
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@@ -1522,70 +1526,70 @@

Internal Types

 retcode: Success
-Interpolation: Automatic order switching interpolation
+Interpolation: automatic order switching interpolation
 t: 6-element Array{BigFloat,1}:
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+ [-5.8727779018395179458298006830444536779478457050140742913573188357890539
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@@ -1608,49 +1612,49 @@

Internal Types

 retcode: Success
-Interpolation: Automatic order switching interpolation
+Interpolation: automatic order switching interpolation
 t: 10-element Array{Float64,1}:
  0.0
- 0.044019433880129626
- 0.11340860061700495
- 0.18686809681314331
- 0.28967976392584077
- 0.4103974859085485
- 0.5450064975363861
- 0.682854838188347
- 0.8416413227647191
+ 0.04787147906142052
+ 0.12539802723603002
+ 0.21507571783207402
+ 0.325846259176126
+ 0.4460780571742323
+ 0.5872688137412091
+ 0.7254883852950837
+ 0.8746888396672391
  1.0
 u: 10-element Array{StaticArrays.SArray{Tuple{4,2},Float64,2,8},1}:
- [0.7806589547275609 0.1281076049030141; 0.7585836578597696 0.4889402884546
-9184; 0.9886332384589747 0.022050397374959063; 0.7427563334758511 0.1849924
-2291853557]
- [0.6167614249185218 0.09110541219263482; 0.8597661654739824 0.444855553353
-33243; 0.903567388578723 0.01106449229040158; 1.0258517221892927 0.19454824
-791425282]
- [0.21849243321286121 0.026250356400060307; 0.8448626060063068 0.3658366318
-902835; 0.8693848079819948 0.008413146945199113; 1.4333586944916195 0.20126
-212498293825]
- [-0.3812384847867338 -0.04796471658686899; 0.6287231165301572 0.2760512250
-903074; 1.0079636023486183 0.026200123096339616; 1.790680478627126 0.196550
-7568863395]
- [-1.4881542753538775 -0.1532474585103542; 0.08552376808745832 0.1553380544
-570292; 1.5854192805254699 0.08667893565913648; 2.111381417291435 0.1684421
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- [-3.062878335935082 -0.2621706447709511; -0.6553213685775562 0.04882482214
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- [-4.881067233541826 -0.3362373881794372; -1.1274207288602511 0.01396018170
-8591028; 5.337427307948131 0.37545937793620204; 1.5667253588759675 -0.01117
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- [-6.6340242655457855 -0.15279063031789797; 2.2279645600664937 0.3922566980
-039255; 12.665050680590905 0.6698726684547723; -2.300815788450243 -0.370543
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-706; 15.69819158543608 0.5841267355426283; -5.753940514510894 -0.5678591328
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+ [0.4874233029564281 0.3982867450807297; 0.6772478849572932 0.6959236614196
+576; 0.6085330252525174 0.9374145300523831; 0.23536295170345212 0.995082846
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+ [0.43638242256861465 0.14301977844655916; 0.7621138510001858 0.69894050777
+71581; 0.5341686470849878 0.9381431319946251; 0.37586987888505197 1.2442550
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+ [0.27779815214551834 -0.4174290891948917; 0.793141527335821 0.540624562039
+3191; 0.45840817411154205 1.086355879293604; 0.5833150951434182 1.583199145
+06541]
+ [-0.016829347389339444 -1.2653846282178236; 0.6870445133418367 0.174608873
+34331776; 0.46964627496784694 1.53721689113887; 0.7769949328810547 1.841512
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+ [-0.5206740041543536 -2.524411407968275; 0.40969849906855377 -0.3753253293
+3379414; 0.6788138558288686 2.5806036031435466; 0.9187098123407041 1.898433
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+ [-1.1815959989375062 -3.974778988372509; 0.051100745340523335 -0.786059412
+6151734; 1.1970019209323275 4.356707097792163; 0.9105784263360842 1.5469023
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+ [-1.9680054748106561 -5.402860864133682; -0.20940321655428795 -0.482147548
+12639904; 2.20298262314218 7.182542513561056; 0.6319484020283754 0.48019898
+98343846]
+ [-2.5327620620005526 -5.9585953516559895; -0.005926578426302509 1.24124998
+10927173; 3.5124964485205914 10.327992534124597; 0.035749747961268175 -1.30
+498695854531]
+ [-2.596994248611811 -4.859412994319518; 1.0430262489490545 5.2527113808371
+89; 5.014706361397094 13.277481617574193; -0.9754492789048056 -3.9954590891
+753945]
+ [-1.9434568050318903 -1.9782594583345565; 2.759616135186503 10.52423871589
+5834; 5.995676470583454 14.410346738576262; -2.0761188513245865 -6.67750766
+9090453]
 
@@ -1663,10 +1667,10 @@

Internal Types

 4×2 StaticArrays.SArray{Tuple{4,2},Float64,2,8} with indices SOneTo(4)×SOne
 To(2):
- 0.218492  0.0262504
- 0.844863  0.365837
- 0.869385  0.00841315
- 1.43336   0.201262
+ 0.277798  -0.417429
+ 0.793142   0.540625
+ 0.458408   1.08636
+ 0.583315   1.5832
 
@@ -1675,11 +1679,11 @@

Conclusion

Appendix

-

This tutorial is part of the DiffEqTutorials.jl repository, found at: https://github.com/JuliaDiffEq/DiffEqTutorials.jl

+

This tutorial is part of the SciMLTutorials.jl repository, found at: https://github.com/SciMLTutorials/SciMLTutorials.jl. For more information on doing scientific machine learning (SciML) with open source software, check out https://sciml.ai/.

To locally run this tutorial, do the following commands:

-
using DiffEqTutorials
-DiffEqTutorials.weave_file("introduction","01-ode_introduction.jmd")
+
using SciMLTutorials
+SciMLTutorials.weave_file("introduction","01-ode_introduction.jmd")

Computer Information:

@@ -1692,21 +1696,21 @@

Conclusion

LIBM: libopenlibm LLVM: libLLVM-8.0.1 (ORCJIT, skylake) Environment: + JULIA_LOAD_PATH = /builds/JuliaGPU/DiffEqTutorials.jl: JULIA_DEPOT_PATH = /builds/JuliaGPU/DiffEqTutorials.jl/.julia - JULIA_CUDA_MEMORY_LIMIT = 536870912 - JULIA_PROJECT = @. - JULIA_NUM_THREADS = 4 + JULIA_CUDA_MEMORY_LIMIT = 2147483648 + JULIA_NUM_THREADS = 8

Package Information:

Status `/builds/JuliaGPU/DiffEqTutorials.jl/tutorials/introduction/Project.toml`
 [6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf] BenchmarkTools 0.5.0
-[0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.14.0
-[65888b18-ceab-5e60-b2b9-181511a3b968] ParameterizedFunctions 5.3.0
-[91a5bcdd-55d7-5caf-9e0b-520d859cae80] Plots 1.4.3
-[90137ffa-7385-5640-81b9-e52037218182] StaticArrays 0.12.3
-[c3572dad-4567-51f8-b174-8c6c989267f4] Sundials 4.2.3
+[0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.15.0
+[65888b18-ceab-5e60-b2b9-181511a3b968] ParameterizedFunctions 5.4.0
+[91a5bcdd-55d7-5caf-9e0b-520d859cae80] Plots 1.5.6
+[90137ffa-7385-5640-81b9-e52037218182] StaticArrays 0.12.4
+[c3572dad-4567-51f8-b174-8c6c989267f4] Sundials 4.2.5
 [37e2e46d-f89d-539d-b4ee-838fcccc9c8e] LinearAlgebra
@@ -1715,7 +1719,7 @@

Conclusion

diff --git a/markdown/introduction/01-ode_introduction.md b/markdown/introduction/01-ode_introduction.md index 39e88495..51fba6c4 100644 --- a/markdown/introduction/01-ode_introduction.md +++ b/markdown/introduction/01-ode_introduction.md @@ -75,7 +75,7 @@ sol = solve(prob) ```` retcode: Success -Interpolation: Automatic order switching interpolation +Interpolation: automatic order switching interpolation t: 5-element Array{Float64,1}: 0.0 0.10042494449239292 @@ -202,7 +202,7 @@ sol ```` retcode: Success -Interpolation: Automatic order switching interpolation +Interpolation: automatic order switching interpolation t: 5-element Array{Float64,1}: 0.0 0.10042494449239292 @@ -249,7 +249,7 @@ sol = solve(prob,abstol=1e-8,reltol=1e-8) ```` retcode: Success -Interpolation: Automatic order switching interpolation +Interpolation: automatic order switching interpolation t: 9-element Array{Float64,1}: 0.0 0.04127492324135852 @@ -599,7 +599,7 @@ sol = solve(prob) ```` retcode: Success -Interpolation: Automatic order switching interpolation +Interpolation: automatic order switching interpolation t: 1294-element Array{Float64,1}: 0.0 3.5678604836301404e-5 @@ -764,53 +764,49 @@ sol = solve(prob) ```` retcode: Success -Interpolation: Automatic order switching interpolation -t: 11-element Array{Float64,1}: +Interpolation: automatic order switching interpolation +t: 10-element Array{Float64,1}: 0.0 - 0.04607057407067815 - 0.1124668145681987 - 0.1821322854968907 - 0.27290665707088113 - 0.38822018198766434 - 0.5208308076580936 - 0.643747804384864 - 0.785728049362553 - 0.9551021713322809 + 0.04391849892224981 + 0.11616653082165809 + 0.19658120398062442 + 0.2952629698711988 + 0.41733702034155395 + 0.5506712825781492 + 0.7166461355644652 + 0.8883937134768247 1.0 -u: 11-element Array{Array{Float64,2},1}: - [0.7941532891032377 0.4907734093293066; 0.5862181620470468 0.9455968500164 -746; 0.17738770304358664 0.9271748093737235; 0.7438330652698997 0.572531308 -0506806] - [0.6276311358533029 0.35722914295528574; 0.5682531316110733 1.007931562807 -279; 0.08530979883863311 0.8789494696303977; 0.9865032644617893 0.755546676 -9971214] - [0.2761469047001174 0.08190797533615646; 0.40922861319528 0.99122315447337 -52; 0.03884261294722911 0.876614598527304; 1.3098877852101074 0.98687156123 -89992] - [-0.23000099518297468 -0.30374667127066973; 0.09681577222203658 0.86120757 -85832805; 0.13095282834491492 0.9810622182569285; 1.6001764982037967 1.1758 -123515847376] - [-1.0812281457148751 -0.9292729041735204; -0.4708810435794842 0.5764610956 -11605; 0.5215662579937026 1.315360996510325; 1.872193503717329 1.3157626303 -991383] - [-2.4056927920844453 -1.8487150076708467; -1.2871104494811305 0.1703590781 -570687; 1.5425064471823777 2.104828641997566; 1.981603611173861 1.276084917 -6482931] - [-4.0765400335903 -2.898116140145526; -2.0014967755905984 -0.0699032475790 -351; 3.5090556510040787 3.51626244563223; 1.6760471818246647 0.865211473707 -7802] - [-5.480917797680895 -3.6159027799712002; -2.01896531971339 0.2480010846624 -4825; 6.034180566884379 5.196215933802348; 0.8837186347882154 0.08938142426 -766538] - [-6.441027631393474 -3.753997249725007; -0.6945994516424794 1.649670784879 -0688; 9.487396518871714 7.255076106962838; -0.7239426815081805 -1.289723982 -4006614] - [-5.744628878475986 -2.303742281673544; 3.512929443628275 5.17072862725652 -6; 13.406839080073667 9.028167314944797; -3.606276777438641 -3.499456119340 -925] - [-5.07730655915073 -1.5322359772549357; 5.177298567770851 6.45719382049693 -5; 14.199891218877683 9.203665415216822; -4.51978430231523 -4.1495596973658 -03] +u: 10-element Array{Array{Float64,2},1}: + [0.19547760575940165 0.47247399507044374; 0.9947932470272081 0.15631428237 +218148; 0.3573489500076166 0.23763371724112692; 0.03808030495696069 0.31982 +31726743066] + [0.1967588904438102 0.4049692637996855; 0.9971930547885663 0.2018872361416 +5527; 0.32439425488809615 0.17741325228186972; 0.02792721637674083 0.470989 +78156002314] + [0.20539607624568004 0.21469182945001108; 0.9933207532448118 0.17931771064 +2172; 0.2676854653186985 0.12814765402639164; 0.0026932230530117354 0.70609 +82198891923] + [0.22908519743536082 -0.11156461673042634; 0.9826081603369168 0.0274918524 +95605457; 0.19700705908618227 0.17463789252360576; -0.035781566166134156 0. +9339463609707335] + [0.28559261346488707 -0.6637539057836184; 0.9671250650391829 -0.2944838280 +7270324; 0.09025850576027471 0.42558522498464146; -0.09262120131943437 1.13 +79397125539228] + [0.4060667968976291 -1.5276892713937908; 0.9493118233141383 -0.77656521243 +56482; -0.09198482510918725 1.1005046932277391; -0.16460909725367076 1.2243 +954837465991] + [0.6033391768554422 -2.57278044905076; 0.9220470903483592 -1.1706998836767 +41; -0.38443862821019276 2.3476929618145768; -0.2211142385015843 1.03543600 +71645454] + [0.9160020947639793 -3.6864769046682495; 0.8208246732749581 -0.97882022715 +92469; -0.9237891497332187 4.56751278018785; -0.21007136743282612 0.2769593 +8201657266] + [1.2214963278777484 -4.021425675138098; 0.5093406799523311 0.6643799209382 +052; -1.6874968552130294 7.215322945108149; -0.03812101279378505 -1.1961215 +559740883] + [1.327290834745476 -3.422361319155158; 0.10870253255667689 2.7861791915498 +078; -2.2531847418271047 8.702214410706276; 0.18892900683270336 -2.50756160 +184843] ```` @@ -826,10 +822,10 @@ sol[3] ```` 4×2 Array{Float64,2}: - 0.276147 0.081908 - 0.409229 0.991223 - 0.0388426 0.876615 - 1.30989 0.986872 + 0.205396 0.214692 + 0.993321 0.179318 + 0.267685 0.128148 + 0.00269322 0.706098 ```` @@ -845,10 +841,10 @@ big_u0 = big.(u0) ```` 4×2 Array{BigFloat,2}: - 0.794153 0.490773 - 0.586218 0.945597 - 0.177388 0.927175 - 0.743833 0.572531 + 0.195478 0.472474 + 0.994793 0.156314 + 0.357349 0.237634 + 0.0380803 0.319823 ```` @@ -865,56 +861,56 @@ sol = solve(prob) ```` retcode: Success -Interpolation: Automatic order switching interpolation +Interpolation: automatic order switching interpolation t: 5-element Array{Float64,1}: 0.0 - 0.15430179028206634 - 0.40356148993249996 - 0.7103297612192179 + 0.16431365291680158 + 0.42772799694479635 + 0.7429273250346953 1.0 u: 5-element Array{Array{BigFloat,2},1}: - [0.7941532891032376806350612241658382117748260498046875 0.4907734093293065 -757990234487806446850299835205078125; 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-0.19600798255877244632288902 +18995307137628399176768369382345035194959374446721225 0.0975410926106817946 +0997044065474665955596688167341843947515276845093994928158256] + [1.32729326241134006287635767311000464401606204689510237934020374199800825 +9469066 -3.4223601333714531089671639954023511016040980682317218542666375014 +39773870896201; 0.108698691255617172263659937892566078017278539155819006244 +037210103529069167236 2.786202813391037818359936976347279706879791521774288 +863680011651198991729051208; -2.2531929692789063074567968481220780504014682 +51957243224323051431841301561602982 8.7022373460083854198385569651104452783 +58232039893859938841147476377781683039161; 0.188931257809458908993136336202 +8892142683421865168275312074040879641080749853423 -2.5075752950901654872209 +05037893847063468506431249839324076778500700819963307878] ```` @@ -925,8 +921,8 @@ sol[1,3] ```` --2.595727982572591822229950276211200598644062081219682876055254086346545757 -274609 +0.4190519131376829214900992052853267706081280804459160189690813640947013103 +54188 ```` @@ -943,59 +939,59 @@ sol = solve(prob) ```` retcode: Success -Interpolation: Automatic order switching interpolation +Interpolation: automatic order switching interpolation t: 5-element Array{BigFloat,1}: 0.0 - 0.154301790282066334282984754228530361635045244524561270578218607216071593 -9716733 - 0.403561489932499970784037349339584588677311990157368071715104766286773833 -8601471 - 0.710329761219217814618631470305626707466802557043095448071604716145630073 -9301024 + 0.164313652916801585626492896583952165578411155101951286067465557611047203 +1138849 + 0.427727996944796294527843944757292385903083568773961565170119276588554755 +9741266 + 0.742927325034695136401447040365724856273947169914597190904776231270937791 +2250609 1.0 u: 5-element Array{Array{BigFloat,2},1}: - [0.7941532891032376806350612241658382117748260498046875 0.4907734093293065 -757990234487806446850299835205078125; 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-0.196007982558772479496696254 +0685288604846133832860236083107591084403132548498308 0.09754109261068218241 +424080204937089362898727370318886651500308268935613813062462] + [1.32729326241134009473729119383123162906909567782678095071089021205217968 +2879939 -3.4223601333714523499479740294823141308942481859279460784346289160 +41779415048734; 0.108698691255616798580082746990476355754390152450214892872 +3511786860842125377951 2.78620281339103973930908667389844392818958923470920 +7369001012163869895613773576; -2.253192969278906733802575017310885364302372 +826646261931733149401512713203984502 8.702237346008386350915901958643353084 +280821640119173339345533706381427717014159; 0.18893125780945911545104970108 +41252970547558183373656262026927812003675526130454 -2.507575295090166553239 +637180652369270880869599031441813099243322060728415495143] ```` @@ -1020,49 +1016,49 @@ sol = solve(prob) ```` retcode: Success -Interpolation: Automatic order switching interpolation +Interpolation: automatic order switching interpolation t: 10-element Array{Float64,1}: 0.0 - 0.05173733926519386 - 0.12968216086995493 - 0.2181507789071571 - 0.33377183039595937 - 0.45903347705795666 - 0.599523478893951 - 0.7669966844409005 - 0.9491428902520377 + 0.044869042977834686 + 0.12047218467423944 + 0.2070300915623275 + 0.31503114913992514 + 0.43779140558809754 + 0.575815544150443 + 0.7266748899317822 + 0.8810312961677973 1.0 u: 10-element Array{StaticArrays.SArray{Tuple{4,2},Float64,2,8},1}: - [0.24174231514370637 0.9588713651058418; 0.6714930389257048 0.792093961019 -5623; 0.9934337836950857 0.22231721705021368; 0.1161824600446737 0.11835856 -725928973] - [0.20916618198865156 0.9510037416277852; 0.8160929902766707 0.894604239742 -1133; 0.9551347559877428 0.035260011767177746; 0.22511190179953078 0.326297 -65025773394] - [0.10570284184988046 0.8337484301856629; 0.9505738150284061 0.893221579003 -4673; 0.9276458416039985 -0.2087975574517865; 0.3654522141473526 0.63480830 -76894289] - [-0.08140127632463262 0.5415480268328536; 1.0011668688850042 0.67766913424 -20539; 0.9591168772975129 -0.38630410321240194; 0.47822088695366133 0.96109 -5698334373] - [-0.40583827597685007 -0.09195505835799056; 0.9612263986584619 0.111067883 -27375428; 1.128585574534724 -0.3684896675387904; 0.5286896754699721 1.31144 -07836581035] - [-0.7906681231386433 -1.0626593937565882; 0.8924317438517294 -0.7250421422 -974695; 1.4907825474210916 0.09008629759693254; 0.4322439246974083 1.532707 -2838771854] - [-1.1327446348328685 -2.3864391270661436; 0.9626133966359122 -1.6512929639 -783387; 2.0804359005017963 1.2684130246537533; 0.11291985713218994 1.492569 -8001950711] - [-1.1674822889530043 -3.9716177631281235; 1.518745680102495 -2.17208675706 -43723; 2.8487978126797584 3.620423382380854; -0.557978697553646 0.904185110 -3614993] - [-0.37579837691369056 -5.036291633213437; 2.9550601185846865 -1.1464850589 -659084; 3.285465781672628 7.016116774022278; -1.5564052588686832 -0.5567971 -782024477] - [0.04941428639581352 -5.081540770528331; 3.516767773176111 -0.439809712370 -85775; 3.2335390545194254 8.005136666685008; -1.8565253332994112 -1.1272786 -856389185] + [0.4520230126339584 0.6680268714046109; 0.2368659623450058 0.7924440732034 +83; 0.7620755122991452 0.6781378044136375; 0.3435749209054344 0.69061940762 +27987] + [0.37201258585921493 0.514220246730995; 0.3567220622025925 0.8323975712094 +936; 0.70716699474354 0.6072926012645857; 0.5347450815707021 0.916571942815 +2984] + [0.13231654140001026 0.12666717046882936; 0.42658141445512027 0.7415553632 +985512; 0.6795310365018049 0.5889502442558292; 0.8323524898084189 1.2576502 +664321256] + [-0.29751254646045877 -0.5021177507444233; 0.32951655665886415 0.437385065 +69164215; 0.7883053652050243 0.7713551773106111; 1.1133248314957096 1.56100 +3336327043] + [-1.0354381534450656 -1.515623185783018; 0.02489663619642557 -0.1224110615 +8104331; 1.202648044838969 1.3806948030956114; 1.330924476849903 1.75784699 +5640528] + [-2.0563188091682374 -2.850692116825032; -0.3870142281921569 -0.7539286188 +02889; 2.1230304621864518 2.662083951089823; 1.3314529882288728 1.658053699 +6231647] + [-3.229259238424727 -4.309781058826721; -0.5954576201395906 -1.01886010124 +72134; 3.7487439363241064 4.841695838848294; 0.9283975265347764 1.032035150 +0376173] + [-4.150006301664626 -5.348462541236869; -0.003884115166779778 -0.133020076 +2828313; 6.077973947112321 7.860695646513079; -0.08921447611666489 -0.36892 +328153197584] + [-4.125149934653158 -5.084176300502514; 2.045146402537434 2.70530792575870 +65; 8.563827643197406 10.95309478080606; -1.7790493688595437 -2.58548636531 +9851] + [-3.0152622751531912 -3.443740195116914; 4.873727763649718 6.4960585364530 +665; 9.998639475680433 12.608225285564842; -3.464284909772859 -4.7349967607 +28366] ```` @@ -1075,10 +1071,10 @@ sol[3] ```` 4×2 StaticArrays.SArray{Tuple{4,2},Float64,2,8} with indices SOneTo(4)×SOne To(2): - 0.105703 0.833748 - 0.950574 0.893222 - 0.927646 -0.208798 - 0.365452 0.634808 + 0.132317 0.126667 + 0.426581 0.741555 + 0.679531 0.58895 + 0.832352 1.25765 ```` @@ -1092,12 +1088,13 @@ These are the basic controls in DifferentialEquations.jl. All equations are defi ## Appendix - This tutorial is part of the DiffEqTutorials.jl repository, found at: + This tutorial is part of the SciMLTutorials.jl repository, found at: . + For more information on doing scientific machine learning (SciML) with open source software, check out . To locally run this tutorial, do the following commands: ``` -using DiffEqTutorials -DiffEqTutorials.weave_file("introduction","01-ode_introduction.jmd") +using SciMLTutorials +SciMLTutorials.weave_file("introduction","01-ode_introduction.jmd") ``` Computer Information: @@ -1111,10 +1108,10 @@ Platform Info: LIBM: libopenlibm LLVM: libLLVM-8.0.1 (ORCJIT, skylake) Environment: + JULIA_LOAD_PATH = /builds/JuliaGPU/DiffEqTutorials.jl: JULIA_DEPOT_PATH = /builds/JuliaGPU/DiffEqTutorials.jl/.julia - JULIA_CUDA_MEMORY_LIMIT = 536870912 - JULIA_PROJECT = @. - JULIA_NUM_THREADS = 4 + JULIA_CUDA_MEMORY_LIMIT = 2147483648 + JULIA_NUM_THREADS = 8 ``` @@ -1123,10 +1120,10 @@ Package Information: ``` Status `/builds/JuliaGPU/DiffEqTutorials.jl/tutorials/introduction/Project.toml` [6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf] BenchmarkTools 0.5.0 -[0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.14.0 -[65888b18-ceab-5e60-b2b9-181511a3b968] ParameterizedFunctions 5.3.0 -[91a5bcdd-55d7-5caf-9e0b-520d859cae80] Plots 1.4.3 -[90137ffa-7385-5640-81b9-e52037218182] StaticArrays 0.12.3 -[c3572dad-4567-51f8-b174-8c6c989267f4] Sundials 4.2.3 +[0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.15.0 +[65888b18-ceab-5e60-b2b9-181511a3b968] ParameterizedFunctions 5.4.0 +[91a5bcdd-55d7-5caf-9e0b-520d859cae80] Plots 1.5.6 +[90137ffa-7385-5640-81b9-e52037218182] StaticArrays 0.12.4 +[c3572dad-4567-51f8-b174-8c6c989267f4] Sundials 4.2.5 [37e2e46d-f89d-539d-b4ee-838fcccc9c8e] LinearAlgebra ``` diff --git a/markdown/introduction/figures/01-ode_introduction_13_1.png b/markdown/introduction/figures/01-ode_introduction_13_1.png index 5aa3cd6fae7c9b663f3993fcc2be86376ff6195c..48710fb1d2e625faf4ed20ac23815f603b96fe01 100644 GIT binary patch literal 15606 zcmb8WWms21*EhNe5u_UlNkJM3>6A{TJEcLoTS^J(R7#|~I|OM&x{>bghBN>BKF@W| zhxfz#;B{@en7wD#%&cC&_2r$S6#6sbXAlIT%SekWLlC?O1i|?u!-K!{U&%^?|B#I3 zq{N{|*uTt{yf_G=fMmo)Ro%buFPMwqP5nbUs;Y|23B#i&c!v##$`FRkaDnq1=Xat7 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963823de..fbbff186 100644 --- a/script/introduction/01-ode_introduction.jl +++ b/script/introduction/01-ode_introduction.jl @@ -151,6 +151,6 @@ sol = solve(prob) sol[3] -using DiffEqTutorials -DiffEqTutorials.tutorial_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file]) +using SciMLTutorials +SciMLTutorials.tutorial_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file])

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