├── .github └── workflows │ └── Deploy.yml ├── .gitignore ├── README.md ├── courseworks ├── .vscode │ └── settings.json ├── exercise_lesson │ └── lesson1 │ │ └── lesson1.ipynb ├── week1 │ ├── Tinho_WHU │ │ ├── hw1.docx │ │ ├── hw1.md │ │ └── readme.md │ ├── XU,Chengzhen │ │ ├── Coursework 1 XU,Chengzhen.md │ │ ├── XCZ_1.pdf │ │ ├── lscpu.res │ │ ├── lsmem.res │ │ ├── number-of-failed-tests.txt │ │ └── versions.txt │ ├── XU_Shiqinrui │ │ ├── Assignment 1.md │ │ ├── latest-chage.txt │ │ ├── lscpu.res │ │ ├── lsmem.res │ │ ├── number-of-failed-tests.txt │ │ └── versions.txt │ ├── XuanzhaoGao │ │ ├── HW1.md │ │ ├── latest-change.txt │ │ ├── lscpu.res │ │ ├── lsmem.res │ │ └── versions.txt │ ├── ZhigaoXIE │ │ ├── Q1.md │ │ ├── latest-change.txt │ │ ├── lscpu.res │ │ ├── lsmem.res │ │ ├── number-of-failed-tests.txt │ │ └── versions.txt │ ├── yanyuduan │ │ ├── note.md │ │ └── week1_yanyuduan.pdf │ └── yushengzhao │ │ ├── hw1 │ │ ├── ans.org │ │ ├── ans.pdf │ │ ├── ans.tex │ │ ├── cpu.txt │ │ └── mem.txt │ │ ├── latest-change.txt │ │ ├── lscpu.res │ │ ├── lsmem.res │ │ ├── number-of-failed-tests.txt │ │ └── versions.txt ├── week10 │ ├── tianhaohu │ │ ├── flowchart.jpeg │ │ ├── hw10.ipynb │ │ └── hw10.md │ ├── xuanzhaogao │ │ └── hw10.ipynb │ └── yushengzhao │ │ ├── answer.org │ │ └── tensor_train.jpeg ├── week11 │ ├── tianhaohu │ │ ├── week11.ipynb │ │ └── week11.md │ └── yushengzhao │ │ ├── assignment11.jl │ │ ├── assignment11.jl.html │ │ └── last_deriv.pdf ├── week2 │ ├── Shiqinrui_Xu │ │ ├── 2D_brown_motion.jl │ │ └── result.png │ ├── Tinho_WHU │ │ ├── Brownian_Motion.jl │ │ ├── hw2_2_a.jl │ │ ├── hw2_revised │ │ │ ├── hw3_revised.ipynb │ │ │ └── week2_1_reviesed.md │ │ └── week2_1.md │ ├── XU,Chengzhen │ │ ├── Assignment 2.md │ │ └── repl_history.jl │ ├── Xuanzhao_Gao │ │ ├── 3x+1.ipynb │ │ ├── HW2.ipynb │ │ └── HW2.md │ ├── ZhigaoXIE │ │ ├── Q1.jl │ │ ├── Q1.md │ │ └── repl_history.jl │ ├── yanyu Duan │ │ ├── Q1andQ2.md │ │ ├── Q1andQ2yanyuduan.pdf │ │ ├── Q3yanyuduan.jl │ │ └── Week2_hw.md │ └── yanyuduan │ │ ├── repl_history.jl │ │ └── week2.md ├── week3 │ ├── ChengzhenXU │ │ └── Week3.md │ ├── TianhaoHu │ │ ├── hw3.ipynb │ │ └── hw_3.md │ ├── ZhigaoXIE │ │ ├── AS3.md │ │ ├── Q1.txt │ │ ├── Q1_revised.md │ │ └── Q3.jl │ ├── shiqinruixu │ │ └── week3.ipynb │ ├── xuanzhaogao │ │ ├── hw.md │ │ └── hw3.ipynb │ └── yushengzhao │ │ ├── ans.md │ │ ├── ans.org │ │ ├── brownian.jl │ │ └── period.jl ├── week4 │ ├── ChengzhenXU │ │ └── Week4.md │ ├── TianhaoHu │ │ ├── hw4.md │ │ └── hw_week4.ipynb │ ├── ZhigaoXIE │ │ ├── Q1.md │ │ └── code.jl │ ├── shiqinruixu │ │ └── week4.ipynb │ ├── xuanzhaogao │ │ └── hw4.ipynb │ ├── yanyu duan │ │ ├── Q1yanyuduan.md │ │ └── Q2yanyuduan.jl │ └── yushengzhao │ │ ├── gauss_jordan.jl │ │ ├── hw.org │ │ └── hw.tex ├── week5 │ ├── ChengzhenXU │ │ └── week5.md │ ├── TianhaoHu │ │ ├── hw5.md │ │ └── sparse_vector_mul.ipynb │ ├── ZhigaoXIE │ │ ├── Q1.jl │ │ ├── Q2.jl │ │ └── Q2_revised.jl │ ├── shiqinruixu │ │ └── week5.ipynb │ ├── xuanzhaogao │ │ └── hw5.ipynb │ ├── yuanyu Duan │ │ ├── Q1.jl │ │ └── Q2.jl │ └── yushengzhao │ │ ├── given_trisym.jl │ │ └── hw5.org ├── week6 │ ├── TianhaoHu │ │ └── hw6.ipynb │ ├── ZhigaoXIE │ │ ├── HW_FFTW.jl │ │ ├── wavelet-2.png │ │ └── wavelet.png │ ├── shiqinruixu │ │ ├── wavelet.png │ │ └── week6.ipynb │ ├── xuanzhaogao │ │ ├── hw6.ipynb │ │ └── wavelet.png │ └── yushengzhao │ │ ├── ans.org │ │ ├── csc.jl │ │ └── lanczos.jl ├── week7 │ ├── ChengzhenXU │ │ └── week7.md │ ├── ZhigaoXIE │ │ ├── HW7.jl │ │ └── unit_disk_embedding.png │ ├── shiqinruixu │ │ └── week7.ipynb │ ├── xuanzhaogao │ │ ├── HW7.pdf │ │ ├── hw7.jl │ │ ├── plot.py │ │ └── unit_disk_py.png │ └── yushengzhao │ │ ├── 7.fft.jl │ │ └── heatmap.png ├── week8 │ ├── ChengzhenXU │ │ └── week8.md │ ├── TianhaoHU │ │ └── hw8.ipynb │ ├── XuanzhaoGao │ │ └── hw8.ipynb │ ├── shiqinruixu │ │ └── week8.ipynb │ └── yushengzhao │ │ ├── make_plot.py │ │ ├── unit_disk_py.png │ │ └── unitdisk.jl └── week9 │ ├── ChengzhenXU │ ├── 1.png │ └── week9.md │ ├── shiqinruixu │ ├── digram.jpg │ ├── digram2.jpg │ └── week9.ipynb │ ├── tianhaohu │ ├── HW9.ipynb │ └── HW9.md │ ├── xuanzhaogao │ ├── hw_9_tensor.ipynb │ └── tensors.jpg │ └── yushengzhao │ ├── hw9.md │ └── hw9.org ├── lib ├── CUDATutorial │ ├── Manifest.toml │ ├── Project.toml │ ├── kernelprog.jl │ └── libraries.jl ├── CompressedSensingTutorial │ ├── .github │ │ └── workflows │ │ │ ├── CI.yml │ │ │ ├── CompatHelper.yml │ │ │ └── TagBot.yml │ ├── .gitignore │ ├── LICENSE │ ├── Project.toml │ ├── README.md │ ├── src │ │ ├── CompressedSensingTutorial.jl │ │ ├── compressed_sensing_2d.jl │ │ └── owlqn.jl │ └── test │ │ ├── compressed_sensing_2d.jl │ │ ├── owlqn.jl │ │ ├── runtests.jl │ │ └── waterfall.jpeg ├── KernelPCA │ ├── .github │ │ └── workflows │ │ │ ├── CI.yml │ │ │ ├── CompatHelper.yml │ │ │ └── TagBot.yml │ ├── .gitignore │ ├── LICENSE │ ├── Project.toml │ ├── README.md │ ├── project │ │ └── kernelf.jl │ ├── src │ │ ├── KernelPCA.jl │ │ ├── dataset.jl │ │ ├── kernels.jl │ │ └── kpca.jl │ └── test │ │ ├── kernels.jl │ │ ├── kpca.jl │ │ └── runtests.jl ├── LatticeGasCA │ ├── .github │ │ └── workflows │ │ │ ├── CI.yml │ │ │ ├── CompatHelper.yml │ │ │ └── TagBot.yml │ ├── .gitignore │ ├── LICENSE │ ├── Project.toml │ ├── README.md │ ├── docs │ │ ├── Manifest.toml │ │ ├── Project.toml │ │ ├── make.jl │ │ └── src │ │ │ └── index.md │ ├── project │ │ └── visualize.jl │ ├── src │ │ ├── LatticeGasCA.jl │ │ ├── cuda.jl │ │ └── hpp.jl │ └── test │ │ ├── cuda.jl │ │ ├── hpp.jl │ │ └── runtests.jl └── PlutoLecturing │ ├── .gitignore │ ├── LICENSE │ ├── Project.toml │ ├── README.md │ ├── src │ ├── PlutoLecturing.jl │ ├── functions.jl │ ├── trees.jl │ └── xbind.jl │ └── test │ └── runtests.jl ├── notebooks ├── 1.understanding-our-computing-devices.jl ├── 1.understanding-our-computing-devices.pdf ├── 10.inference.jl ├── 10.inference.pdf ├── 11.data-sparsity.jl ├── 11.data-sparsity.pdf ├── 12.cuda.jl ├── 12.cuda.pdf ├── 3.julia.jl ├── 3.julia.pdf ├── 4.linearequation.jl ├── 4.linearequation.pdf ├── 5.linear-least-square.jl ├── 5.linear-least-square.pdf ├── 6.sparse.jl ├── 6.sparse.pdf ├── 7.fft.jl ├── 7.fft.pdf ├── 8.optimization.jl ├── 8.optimization.pdf ├── 9.autodiff.jl ├── 9.autodiff.pdf ├── clib │ └── demo.c ├── garbage.jl └── images │ ├── chatgpt.png │ ├── correct_answer.png │ ├── float-format.png │ ├── hkust-gz.png │ ├── textbook.jpg │ ├── trafalgar-square.jpg │ ├── waterfall.jpeg │ └── zulip1.png └── website ├── .gitignore ├── 404.md ├── Manifest.toml ├── Project.toml ├── README.md ├── _assets ├── favicon.jpg ├── images │ ├── arch.png │ └── gnu.png └── msc2.jpg ├── _css ├── basic.css └── franklin.css ├── _ignore ├── 2017-12-14-factorgraph.md ├── 2017-12-14-slackapp.md ├── 2017-12-28-requirements.md ├── 2017-12-7-groupleader.md ├── 2018-01-01-measurement.md ├── 2018-01-02-rbmmps.md ├── 2018-01-31-qv.md ├── 2018-06-2-HamiltonianDo.md └── diff.md ├── _layout ├── foot.html ├── foot_highlight.html ├── foot_katex.html ├── head.html ├── head_highlight.html ├── head_katex.html ├── header.html ├── page_foot.html ├── sidebar.html ├── style.html └── tag.html ├── _libs ├── asciinema │ ├── asciinema-player.css │ └── asciinema-player.min.js ├── highlight │ ├── highlight.min.js │ └── styles │ │ ├── a11y-dark.min.css │ │ ├── a11y-light.min.css │ │ ├── agate.min.css │ │ ├── an-old-hope.min.css │ │ ├── androidstudio.min.css │ │ ├── arduino-light.min.css │ │ ├── arta.min.css │ │ ├── ascetic.min.css │ │ ├── atom-one-dark-reasonable.min.css │ │ ├── atom-one-dark.min.css │ │ ├── atom-one-light.min.css │ │ ├── base16 │ │ ├── 3024.min.css │ │ ├── apathy.min.css │ │ ├── apprentice.min.css │ │ ├── ashes.min.css │ │ ├── atelier-cave-light.min.css │ │ ├── atelier-cave.min.css │ │ ├── atelier-dune-light.min.css │ │ ├── atelier-dune.min.css │ │ ├── atelier-estuary-light.min.css │ │ ├── atelier-estuary.min.css │ │ ├── atelier-forest-light.min.css │ │ ├── atelier-forest.min.css │ │ ├── atelier-heath-light.min.css │ │ ├── atelier-heath.min.css │ │ ├── atelier-lakeside-light.min.css │ │ ├── atelier-lakeside.min.css │ │ ├── atelier-plateau-light.min.css │ │ ├── atelier-plateau.min.css │ │ ├── atelier-savanna-light.min.css │ │ ├── atelier-savanna.min.css │ │ ├── atelier-seaside-light.min.css │ │ ├── atelier-seaside.min.css │ │ ├── atelier-sulphurpool-light.min.css │ │ ├── atelier-sulphurpool.min.css │ │ ├── atlas.min.css │ │ ├── bespin.min.css │ │ ├── black-metal-bathory.min.css │ │ ├── black-metal-burzum.min.css │ │ ├── black-metal-dark-funeral.min.css │ │ ├── black-metal-gorgoroth.min.css │ │ ├── black-metal-immortal.min.css │ │ ├── black-metal-khold.min.css │ │ ├── black-metal-marduk.min.css │ │ ├── black-metal-mayhem.min.css │ │ ├── black-metal-nile.min.css │ │ ├── black-metal-venom.min.css │ │ ├── black-metal.min.css │ │ ├── brewer.min.css │ │ ├── bright.min.css │ │ ├── brogrammer.min.css │ │ ├── brush-trees-dark.min.css │ │ ├── brush-trees.min.css │ │ ├── chalk.min.css │ │ ├── circus.min.css │ │ ├── classic-dark.min.css │ │ ├── classic-light.min.css │ │ ├── codeschool.min.css │ │ ├── colors.min.css │ │ ├── cupcake.min.css │ │ ├── cupertino.min.css │ │ ├── danqing.min.css │ │ ├── darcula.min.css │ │ ├── dark-violet.min.css │ │ ├── darkmoss.min.css │ │ ├── darktooth.min.css │ │ ├── decaf.min.css │ │ ├── default-dark.min.css │ │ ├── default-light.min.css │ │ ├── dirtysea.min.css │ │ ├── dracula.min.css │ │ ├── edge-dark.min.css │ │ ├── edge-light.min.css │ │ ├── eighties.min.css │ │ ├── embers.min.css │ │ ├── equilibrium-dark.min.css │ │ ├── equilibrium-gray-dark.min.css │ │ ├── equilibrium-gray-light.min.css │ │ ├── equilibrium-light.min.css │ │ ├── espresso.min.css │ │ ├── eva-dim.min.css │ │ ├── eva.min.css │ │ ├── flat.min.css │ │ ├── framer.min.css │ │ ├── fruit-soda.min.css │ │ ├── gigavolt.min.css │ │ ├── github.min.css │ │ ├── google-dark.min.css │ │ ├── google-light.min.css │ │ ├── grayscale-dark.min.css │ │ ├── grayscale-light.min.css │ │ ├── green-screen.min.css │ │ ├── gruvbox-dark-hard.min.css │ │ ├── gruvbox-dark-medium.min.css │ │ ├── gruvbox-dark-pale.min.css │ │ ├── gruvbox-dark-soft.min.css │ │ ├── gruvbox-light-hard.min.css │ │ ├── gruvbox-light-medium.min.css │ │ ├── gruvbox-light-soft.min.css │ │ ├── hardcore.min.css │ │ ├── harmonic16-dark.min.css │ │ ├── harmonic16-light.min.css │ │ ├── heetch-dark.min.css │ │ ├── heetch-light.min.css │ │ ├── helios.min.css │ │ ├── hopscotch.min.css │ │ ├── horizon-dark.min.css │ │ ├── horizon-light.min.css │ │ ├── humanoid-dark.min.css │ │ ├── humanoid-light.min.css │ │ ├── ia-dark.min.css │ │ ├── ia-light.min.css │ │ ├── icy-dark.min.css │ │ ├── ir-black.min.css │ │ ├── isotope.min.css │ │ ├── kimber.min.css │ │ ├── london-tube.min.css │ │ ├── macintosh.min.css │ │ ├── marrakesh.min.css │ │ ├── materia.min.css │ │ ├── material-darker.min.css │ │ ├── material-lighter.min.css │ │ ├── material-palenight.min.css │ │ ├── material-vivid.min.css │ │ ├── material.min.css │ │ ├── mellow-purple.min.css │ │ ├── mexico-light.min.css │ │ ├── mocha.min.css │ │ ├── monokai.min.css │ │ ├── nebula.min.css │ │ ├── nord.min.css │ │ ├── nova.min.css │ │ ├── ocean.min.css │ │ ├── oceanicnext.min.css │ │ ├── one-light.min.css │ │ ├── onedark.min.css │ │ ├── outrun-dark.min.css │ │ ├── papercolor-dark.min.css │ │ ├── papercolor-light.min.css │ │ ├── paraiso.min.css │ │ ├── pasque.min.css │ │ ├── phd.min.css │ │ ├── pico.min.css │ │ ├── pop.min.css │ │ ├── porple.min.css │ │ ├── qualia.min.css │ │ ├── railscasts.min.css │ │ ├── rebecca.min.css │ │ ├── ros-pine-dawn.min.css │ │ ├── ros-pine-moon.min.css │ │ ├── ros-pine.min.css │ │ ├── sagelight.min.css │ │ ├── sandcastle.min.css │ │ ├── seti-ui.min.css │ │ ├── shapeshifter.min.css │ │ ├── silk-dark.min.css │ │ ├── silk-light.min.css │ │ ├── snazzy.min.css │ │ ├── solar-flare-light.min.css │ │ ├── solar-flare.min.css │ │ ├── solarized-dark.min.css │ │ ├── solarized-light.min.css │ │ ├── spacemacs.min.css │ │ ├── summercamp.min.css │ │ ├── summerfruit-dark.min.css │ │ ├── summerfruit-light.min.css │ │ ├── synth-midnight-terminal-dark.min.css │ │ ├── synth-midnight-terminal-light.min.css │ │ ├── tango.min.css │ │ ├── tender.min.css │ │ ├── tomorrow-night.min.css │ │ ├── tomorrow.min.css │ │ ├── twilight.min.css │ │ ├── unikitty-dark.min.css │ │ ├── unikitty-light.min.css │ │ ├── vulcan.min.css │ │ ├── windows-10-light.min.css │ │ ├── windows-10.min.css │ │ ├── windows-95-light.min.css │ │ ├── windows-95.min.css │ │ ├── windows-high-contrast-light.min.css │ │ ├── windows-high-contrast.min.css │ │ ├── windows-nt-light.min.css │ │ ├── windows-nt.min.css │ │ ├── woodland.min.css │ │ ├── xcode-dusk.min.css │ │ └── zenburn.min.css │ │ ├── brown-paper.min.css │ │ ├── brown-papersq.png │ │ ├── codepen-embed.min.css │ │ ├── color-brewer.min.css │ │ ├── dark.min.css │ │ ├── default.min.css │ │ ├── devibeans.min.css │ │ ├── docco.min.css │ │ ├── far.min.css │ │ ├── felipec.min.css │ │ ├── foundation.min.css │ │ ├── github-dark-dimmed.min.css │ │ ├── github-dark.min.css │ │ ├── github.min.css │ │ ├── gml.min.css │ │ ├── googlecode.min.css │ │ ├── gradient-dark.min.css │ │ ├── gradient-light.min.css │ │ ├── grayscale.min.css │ │ ├── hybrid.min.css │ │ ├── idea.min.css │ │ ├── intellij-light.min.css │ │ ├── ir-black.min.css │ │ ├── isbl-editor-dark.min.css │ │ ├── isbl-editor-light.min.css │ │ ├── kimbie-dark.min.css │ │ ├── kimbie-light.min.css │ │ ├── lightfair.min.css │ │ ├── lioshi.min.css │ │ ├── magula.min.css │ │ ├── mono-blue.min.css │ │ ├── monokai-sublime.min.css │ │ ├── monokai.min.css │ │ ├── night-owl.min.css │ │ ├── nnfx-dark.min.css │ │ ├── nnfx-light.min.css │ │ ├── nord.min.css │ │ ├── obsidian.min.css │ │ ├── paraiso-dark.min.css │ │ ├── paraiso-light.min.css │ │ ├── pojoaque.jpg │ │ ├── pojoaque.min.css │ │ ├── purebasic.min.css │ │ ├── qtcreator-dark.min.css │ │ ├── qtcreator-light.min.css │ │ ├── rainbow.min.css │ │ ├── routeros.min.css │ │ ├── school-book.min.css │ │ ├── shades-of-purple.min.css │ │ ├── srcery.min.css │ │ ├── stackoverflow-dark.min.css │ │ ├── stackoverflow-light.min.css │ │ ├── sunburst.min.css │ │ ├── tokyo-night-dark.min.css │ │ ├── tokyo-night-light.min.css │ │ ├── tomorrow-night-blue.min.css │ │ ├── tomorrow-night-bright.min.css │ │ ├── vs.min.css │ │ ├── vs2015.min.css │ │ ├── xcode.min.css │ │ └── xt256.min.css └── katex │ ├── contrib │ └── auto-render.min.js │ ├── fonts │ ├── KaTeX_AMS-Regular.ttf │ ├── KaTeX_AMS-Regular.woff │ ├── KaTeX_AMS-Regular.woff2 │ ├── KaTeX_Caligraphic-Bold.ttf │ ├── KaTeX_Caligraphic-Bold.woff │ ├── KaTeX_Caligraphic-Bold.woff2 │ ├── KaTeX_Caligraphic-Regular.ttf │ ├── KaTeX_Caligraphic-Regular.woff │ ├── KaTeX_Caligraphic-Regular.woff2 │ ├── KaTeX_Fraktur-Bold.ttf │ ├── KaTeX_Fraktur-Bold.woff │ ├── KaTeX_Fraktur-Bold.woff2 │ ├── KaTeX_Fraktur-Regular.ttf │ ├── KaTeX_Fraktur-Regular.woff │ ├── KaTeX_Fraktur-Regular.woff2 │ ├── KaTeX_Main-Bold.ttf │ ├── KaTeX_Main-Bold.woff │ ├── KaTeX_Main-Bold.woff2 │ ├── KaTeX_Main-BoldItalic.ttf │ ├── KaTeX_Main-BoldItalic.woff │ ├── KaTeX_Main-BoldItalic.woff2 │ ├── KaTeX_Main-Italic.ttf │ ├── KaTeX_Main-Italic.woff │ ├── KaTeX_Main-Italic.woff2 │ ├── KaTeX_Main-Regular.ttf │ ├── KaTeX_Main-Regular.woff │ ├── KaTeX_Main-Regular.woff2 │ ├── KaTeX_Math-BoldItalic.ttf │ ├── KaTeX_Math-BoldItalic.woff │ ├── KaTeX_Math-BoldItalic.woff2 │ ├── KaTeX_Math-Italic.ttf │ ├── KaTeX_Math-Italic.woff │ ├── KaTeX_Math-Italic.woff2 │ ├── KaTeX_SansSerif-Bold.ttf │ ├── KaTeX_SansSerif-Bold.woff │ ├── KaTeX_SansSerif-Bold.woff2 │ ├── KaTeX_SansSerif-Italic.ttf │ ├── KaTeX_SansSerif-Italic.woff │ ├── KaTeX_SansSerif-Italic.woff2 │ ├── KaTeX_SansSerif-Regular.ttf │ ├── KaTeX_SansSerif-Regular.woff │ ├── KaTeX_SansSerif-Regular.woff2 │ ├── KaTeX_Script-Regular.ttf │ ├── KaTeX_Script-Regular.woff │ ├── KaTeX_Script-Regular.woff2 │ ├── KaTeX_Size1-Regular.ttf │ ├── KaTeX_Size1-Regular.woff │ ├── KaTeX_Size1-Regular.woff2 │ ├── KaTeX_Size2-Regular.ttf │ ├── KaTeX_Size2-Regular.woff │ ├── KaTeX_Size2-Regular.woff2 │ ├── KaTeX_Size3-Regular.ttf │ ├── KaTeX_Size3-Regular.woff │ ├── KaTeX_Size3-Regular.woff2 │ ├── KaTeX_Size4-Regular.ttf │ ├── KaTeX_Size4-Regular.woff │ ├── KaTeX_Size4-Regular.woff2 │ ├── KaTeX_Typewriter-Regular.ttf │ ├── KaTeX_Typewriter-Regular.woff │ └── KaTeX_Typewriter-Regular.woff2 │ ├── katex.min.css │ └── katex.min.js ├── _rss ├── head.xml └── item.xml ├── config.md ├── index.md ├── msc.md ├── msc ├── 1.devices.md ├── 2.1.opensource.md ├── 2.2.cheatsheets.md └── 3.julia.md ├── package-lock.json └── utils.jl /.gitignore: -------------------------------------------------------------------------------- 1 | __pycache__/ 2 | *.aux 3 | *.log 4 | *.out 5 | *.synctex.gz 6 | *.synctex(busy) 7 | *.synctex 8 | .DS_Store 9 | *~ 10 | *.svg 11 | *.bbl 12 | *.blg 13 | *.fdb_latexmk 14 | *.fls 15 | *.out 16 | *.dvi 17 | *.log 18 | *.aux 19 | _*.tex 20 | _*.bib 21 | _*.pdf 22 | *.auxlock 23 | *.dpth 24 | *.md5 25 | unweighted/images/gadgets/ 26 | unweighted/images/*.tex 27 | *.thm 28 | *.so 29 | website/notebooks/*.html 30 | .vscode -------------------------------------------------------------------------------- /courseworks/.vscode/settings.json: -------------------------------------------------------------------------------- 1 | {} -------------------------------------------------------------------------------- /courseworks/week1/Tinho_WHU/hw1.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week1/Tinho_WHU/hw1.docx -------------------------------------------------------------------------------- /courseworks/week1/Tinho_WHU/readme.md: -------------------------------------------------------------------------------- 1 | Sorry for the late. There is no difference between .docx & .md in their contents. But .docx highlight some information of CPU which may be important. 2 | -------------------------------------------------------------------------------- /courseworks/week1/XU,Chengzhen/XCZ_1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week1/XU,Chengzhen/XCZ_1.pdf -------------------------------------------------------------------------------- /courseworks/week1/XU,Chengzhen/lsmem.res: -------------------------------------------------------------------------------- 1 | RANGE SIZE STATE REMOVABLE BLOCK 2 | 0x0000000000000000-0x00000000bfffffff 3G online yes 0-23 3 | 0x0000000100000000-0x000000013fffffff 1G online yes 32-39 4 | 5 | Memory block size: 128M 6 | Total online memory: 4G 7 | Total offline memory: 0B 8 | -------------------------------------------------------------------------------- /courseworks/week1/XU,Chengzhen/number-of-failed-tests.txt: -------------------------------------------------------------------------------- 1 | Test Summary: | Pass Total Time 2 | OMEinsum.jl | 600 600 1m32.8s 3 | Testing OMEinsum tests passed 4 | 5 | 6 | -------------------------------------------------------------------------------- /courseworks/week1/XU,Chengzhen/versions.txt: -------------------------------------------------------------------------------- 1 | v0.1.0 2 | v0.2.0 3 | v0.3.0 4 | v0.3.1 5 | v0.3.2 6 | v0.3.3 7 | v0.4.0 8 | v0.4.1 9 | v0.4.2 10 | v0.4.3 11 | v0.4.4 12 | v0.4.5 13 | v0.4.6 14 | v0.4.7 15 | v0.4.8 16 | v0.5.0 17 | v0.6.0 18 | v0.6.1 19 | v0.6.10 20 | v0.6.11 21 | v0.6.12 22 | v0.6.13 23 | v0.6.2 24 | v0.6.3 25 | v0.6.4 26 | v0.6.5 27 | v0.6.6 28 | v0.6.7 29 | v0.6.8 30 | v0.6.9 31 | v0.7.0 32 | v0.7.1 33 | v0.7.2 34 | -------------------------------------------------------------------------------- /courseworks/week1/XU_Shiqinrui/latest-chage.txt: -------------------------------------------------------------------------------- 1 | diff --git a/src/interfaces.jl b/src/interfaces.jl 2 | index cab204f..806e565 100644 3 | --- a/src/interfaces.jl 4 | +++ b/src/interfaces.jl 5 | @@ -157,7 +157,7 @@ function _ein_macro(ex; einsum=:einsum) 6 | righttuples = [ Tuple(indexin(ind, rightind)) for (A, ind) in rightpairs ] 7 | rightnames = [ esc(A) for (A, ind) in rightpairs ] 8 | 9 | - return :( $(esc(Z)) = $einsum( EinCode(($(righttuples...),), $lefttuple), ($(rightnames...),)) ) 10 | + return :( $(esc(Z)) = $einsum( StaticEinCode(($(righttuples...),), $lefttuple), ($(rightnames...),)) ) 11 | end 12 | 13 | @doc raw" 14 | -------------------------------------------------------------------------------- /courseworks/week1/XU_Shiqinrui/lsmem.res: -------------------------------------------------------------------------------- 1 | RANGE SIZE STATE REMOVABLE BLOCK 2 | 0x0000000000000000-0x00000000bfffffff 3G online yes 0-23 3 | 0x0000000100000000-0x000000013fffffff 1G online yes 32-39 4 | 5 | Memory block size: 128M 6 | Total online memory: 4G 7 | Total offline memory: 0B 8 | -------------------------------------------------------------------------------- /courseworks/week1/XU_Shiqinrui/versions.txt: -------------------------------------------------------------------------------- 1 | v0.1.0 2 | v0.2.0 3 | v0.3.0 4 | v0.3.1 5 | v0.3.2 6 | v0.3.3 7 | v0.4.0 8 | v0.4.1 9 | v0.4.2 10 | v0.4.3 11 | v0.4.4 12 | v0.4.5 13 | v0.4.6 14 | v0.4.7 15 | v0.4.8 16 | v0.5.0 17 | v0.6.0 18 | v0.6.1 19 | v0.6.10 20 | v0.6.11 21 | v0.6.12 22 | v0.6.13 23 | v0.6.2 24 | v0.6.3 25 | v0.6.4 26 | v0.6.5 27 | v0.6.6 28 | v0.6.7 29 | v0.6.8 30 | v0.6.9 31 | v0.7.0 32 | v0.7.1 33 | v0.7.2 34 | -------------------------------------------------------------------------------- /courseworks/week1/XuanzhaoGao/latest-change.txt: -------------------------------------------------------------------------------- 1 | diff --git a/src/interfaces.jl b/src/interfaces.jl 2 | index 806e565..1d2303d 100644 3 | --- a/src/interfaces.jl 4 | +++ b/src/interfaces.jl 5 | @@ -157,7 +157,7 @@ function _ein_macro(ex; einsum=:einsum) 6 | righttuples = [ Tuple(indexin(ind, rightind)) for (A, ind) in rightpairs ] 7 | rightnames = [ esc(A) for (A, ind) in rightpairs ] 8 | 9 | - return :( $(esc(Z)) = $einsum( StaticEinCode(($(righttuples...),), $lefttuple), ($(rightnames...),)) ) 10 | + return :( $(esc(Z)) = $einsum( StaticEinCode{Int, ($(righttuples...),), $lefttuple}(), ($(rightnames...),)) ) 11 | end 12 | 13 | @doc raw" 14 | -------------------------------------------------------------------------------- /courseworks/week1/XuanzhaoGao/lsmem.res: -------------------------------------------------------------------------------- 1 | RANGE SIZE STATE REMOVABLE BLOCK 2 | 0x0000000000000000-0x00000000bfffffff 3G online yes 0-23 3 | 0x0000000100000000-0x000000013fffffff 1G online yes 32-39 4 | 5 | Memory block size: 128M 6 | Total online memory: 4G 7 | Total offline memory: 0B 8 | -------------------------------------------------------------------------------- /courseworks/week1/XuanzhaoGao/versions.txt: -------------------------------------------------------------------------------- 1 | v0.1.0 2 | v0.2.0 3 | v0.3.0 4 | v0.3.1 5 | v0.3.2 6 | v0.3.3 7 | v0.4.0 8 | v0.4.1 9 | v0.4.2 10 | v0.4.3 11 | v0.4.4 12 | v0.4.5 13 | v0.4.6 14 | v0.4.7 15 | v0.4.8 16 | v0.5.0 17 | v0.6.0 18 | v0.6.1 19 | v0.6.10 20 | v0.6.11 21 | v0.6.12 22 | v0.6.13 23 | v0.6.2 24 | v0.6.3 25 | v0.6.4 26 | v0.6.5 27 | v0.6.6 28 | v0.6.7 29 | v0.6.8 30 | v0.6.9 31 | v0.7.0 32 | v0.7.1 33 | v0.7.2 34 | -------------------------------------------------------------------------------- /courseworks/week1/ZhigaoXIE/latest-change.txt: -------------------------------------------------------------------------------- 1 | diff --git a/courseworks/week1/ZhigaoXIE/hello b/courseworks/week1/ZhigaoXIE/hello 2 | new file mode 100644 3 | index 0000000..4effa19 4 | --- /dev/null 5 | +++ b/courseworks/week1/ZhigaoXIE/hello 6 | @@ -0,0 +1 @@ 7 | +hello! 8 | -------------------------------------------------------------------------------- /courseworks/week1/ZhigaoXIE/lsmem.res: -------------------------------------------------------------------------------- 1 | RANGE SIZE STATE REMOVABLE BLOCK 2 | 0x0000000000000000-0x00000000bfffffff 3G online yes 0-23 3 | 0x0000000100000000-0x000000013fffffff 1G online yes 32-39 4 | 5 | Memory block size: 128M 6 | Total online memory: 4G 7 | Total offline memory: 0B 8 | -------------------------------------------------------------------------------- /courseworks/week1/ZhigaoXIE/number-of-failed-tests.txt: -------------------------------------------------------------------------------- 1 | Test Summary: | Pass Total Time 2 | OMEinsum.jl | 600 600 2m44.1s 3 | Testing OMEinsum tests passed 4 | 5 | -------------------------------------------------------------------------------- /courseworks/week1/ZhigaoXIE/versions.txt: -------------------------------------------------------------------------------- 1 | v0.1.0 2 | v0.2.0 3 | v0.3.0 4 | v0.3.1 5 | v0.3.2 6 | v0.3.3 7 | v0.4.0 8 | v0.4.1 9 | v0.4.2 10 | v0.4.3 11 | v0.4.4 12 | v0.4.5 13 | v0.4.6 14 | v0.4.7 15 | v0.4.8 16 | v0.5.0 17 | v0.6.0 18 | v0.6.1 19 | v0.6.10 20 | v0.6.11 21 | v0.6.12 22 | v0.6.13 23 | v0.6.2 24 | v0.6.3 25 | v0.6.4 26 | v0.6.5 27 | v0.6.6 28 | v0.6.7 29 | v0.6.8 30 | v0.6.9 31 | v0.7.0 32 | v0.7.1 33 | v0.7.2 34 | -------------------------------------------------------------------------------- /courseworks/week1/yanyuduan/note.md: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week1/yanyuduan/note.md -------------------------------------------------------------------------------- /courseworks/week1/yanyuduan/week1_yanyuduan.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week1/yanyuduan/week1_yanyuduan.pdf -------------------------------------------------------------------------------- /courseworks/week1/yushengzhao/hw1/ans.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week1/yushengzhao/hw1/ans.pdf -------------------------------------------------------------------------------- /courseworks/week1/yushengzhao/hw1/mem.txt: -------------------------------------------------------------------------------- 1 | RANGE SIZE STATE REMOVABLE 2 | BLOCK 3 | 0x0000000000000000-0x00000000bfffffff 3G online yes 4 | 0-2 5 | 0x0000000100000000-0x000000103fffffff 61G online yes 6 | 4-64 7 | 8 | Memory block size: 1G 9 | Total online memory: 64G 10 | Total offline memory: 0B 11 | -------------------------------------------------------------------------------- /courseworks/week1/yushengzhao/latest-change.txt: -------------------------------------------------------------------------------- 1 | diff --git a/src/interfaces.jl b/src/interfaces.jl 2 | index 806e565..1d2303d 100644 3 | --- a/src/interfaces.jl 4 | +++ b/src/interfaces.jl 5 | @@ -157,7 +157,7 @@ function _ein_macro(ex; einsum=:einsum) 6 | righttuples = [ Tuple(indexin(ind, rightind)) for (A, ind) in rightpairs ] 7 | rightnames = [ esc(A) for (A, ind) in rightpairs ] 8 | 9 | - return :( $(esc(Z)) = $einsum( StaticEinCode(($(righttuples...),), $lefttuple), ($(rightnames...),)) ) 10 | + return :( $(esc(Z)) = $einsum( StaticEinCode{Int, ($(righttuples...),), $lefttuple}(), ($(rightnames...),)) ) 11 | end 12 | 13 | @doc raw" 14 | -------------------------------------------------------------------------------- /courseworks/week1/yushengzhao/lsmem.res: -------------------------------------------------------------------------------- 1 | RANGE SIZE STATE REMOVABLE BLOCK 2 | 0x0000000000000000-0x00000000bfffffff 3G online yes 0-23 3 | 0x0000000100000000-0x000000013fffffff 1G online yes 32-39 4 | 5 | Memory block size: 128M 6 | Total online memory: 4G 7 | Total offline memory: 0B 8 | -------------------------------------------------------------------------------- /courseworks/week1/yushengzhao/versions.txt: -------------------------------------------------------------------------------- 1 | v0.1.0 2 | v0.2.0 3 | v0.3.0 4 | v0.3.1 5 | v0.3.2 6 | v0.3.3 7 | v0.4.0 8 | v0.4.1 9 | v0.4.2 10 | v0.4.3 11 | v0.4.4 12 | v0.4.5 13 | v0.4.6 14 | v0.4.7 15 | v0.4.8 16 | v0.5.0 17 | v0.6.0 18 | v0.6.1 19 | v0.6.10 20 | v0.6.11 21 | v0.6.12 22 | v0.6.13 23 | v0.6.2 24 | v0.6.3 25 | v0.6.4 26 | v0.6.5 27 | v0.6.6 28 | v0.6.7 29 | v0.6.8 30 | v0.6.9 31 | v0.7.0 32 | v0.7.1 33 | v0.7.2 34 | -------------------------------------------------------------------------------- /courseworks/week10/tianhaohu/flowchart.jpeg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week10/tianhaohu/flowchart.jpeg -------------------------------------------------------------------------------- /courseworks/week10/tianhaohu/hw10.md: -------------------------------------------------------------------------------- 1 | # 1 2 | 3 | einsum of outer product 4 | 5 | i,j -> ij 6 | 7 | # 2 8 | 9 | The einsum notation "jk,kl,lm,mj ->" can be understood as two einsum as, 10 | 11 | jk,kl,lm,mj -> jj 12 | 13 | jj -> 14 | 15 | The first one is the production of four matrix ,with the first index of the first matrix equaling to the second index of the last matrix. The result of first einsum is therefore a square matrix. 16 | 17 | The second einsum is the trace of the first matrix. 18 | 19 | So "jk,kl,lm,mj ->" is the trace of the mutiplication of four matrix. 20 | 21 | # 3 22 | 23 | ## (1) 24 | 25 | I will submit with a picture 26 | 27 | ## (2) 28 | 29 | Same as above. The different steps will be highlighted with different color. 30 | 31 | The contraction cpmlexity can be estimated for two different steps, 32 | 33 | 1. for 7 red circles, there will be $7\times n^5$. 34 | 35 | 2. for 6 red circles, there will be $6\times n^6$. Since the contraction includes two dimensions, there will be one order higher comlexity. 36 | 37 | ## (3) 38 | 39 | Refer to hw9.ipynb 40 | -------------------------------------------------------------------------------- /courseworks/week10/yushengzhao/answer.org: -------------------------------------------------------------------------------- 1 | #+TITLE: HW 10 2 | #+AUTHOR: Yusheng Zhao 3 | 4 | * P1 5 | #+begin_src julia 6 | ein"i,j->ij" (A,B) 7 | #+end_src 8 | 9 | * P2 10 | It stands for $Tr(A*B*C*D)$ where $A,B,C,D$ are rank 2 tensors. 11 | 12 | * P3 13 | 1) See the part of graph in black ink 14 | 2) The contraction order is to first contract away the 7 vertical legs. Each 15 | costs $\mathcal{O}(n^{5})$. Following that, we constract away the 6 pairs of 16 | parallel legs, each costs $\mathcal{O}(n^{6})$. In total, we require 17 | $7*n^{5} + 6 * n^{6}$ which is $\mathcal{O}(n^{6})$ 18 | 3) See code below 19 | #+begin_src julia :exports both 20 | using OMEinsum 21 | eincode = ein"abc,cde,efg,ghi,ijk,klm,mno,pbq,qdr,rfs,sht,tju,ulv,vnw->apow" 22 | optimize_code(eincode, uniformsize(eincode, 2), TreeSA()) 23 | #+end_src 24 | 25 | -------------------------------------------------------------------------------- /courseworks/week10/yushengzhao/tensor_train.jpeg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week10/yushengzhao/tensor_train.jpeg -------------------------------------------------------------------------------- /courseworks/week11/tianhaohu/week11.ipynb: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week11/tianhaohu/week11.ipynb -------------------------------------------------------------------------------- /courseworks/week11/tianhaohu/week11.md: -------------------------------------------------------------------------------- 1 | # 1 2 | 3 | Notice that $||Ax-b||_2 = \sqrt{(Ax-b)^T(Ax-b)}$ 4 | 5 | $$ 6 | \frac{\partial L}{\partial x} 7 | \\= \frac{\partial L}{\partial ||Ax-b||_2}\,\frac{\partial ||Ax-b||_2}{\partial Ax-b}\,\frac{\partial (Ax-b)}{\partial x} 8 | \\= 1 \times \frac{1}{2||Ax-b||_2}\times 2(Ax-b)^T \times A 9 | \\= \frac{(Ax-b)^TA}{||Ax-b||_2} 10 | $$ 11 | 12 | # 2 13 | 14 | The video tells the condition when the compressed sensing can work or not. 15 | 16 | 1. The first condition is incoherence. The condition is constraining the measurement matrix $C$ is incoherent with respect to $\Psi$, the basis. Or in other words, $C$ cannot be too parallel to $\Psi$. Sampling should be random instead of focusing on some columns of $\Psi$. 17 | 18 | 2. Denoting the sparsity of the signal after Fourier transforamtion by $K$, and number of measurements by $P$, there should be constraints as, 19 | 20 | $$ 21 | P \propto O(K\log(\frac{n}{K})) 22 | $$ 23 | 24 | Finally it should be noted that though the compressed sensing seems to reduce the space for storing pictures or something else, solving the optimization problem stated in the class for $x$ is in no way inexpensive. So compressed sensing may be used when measuring full resolution of the image is **really really expensive** or using it can **literally save lives** as the example of MRI of infants. 25 | -------------------------------------------------------------------------------- /courseworks/week11/yushengzhao/last_deriv.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week11/yushengzhao/last_deriv.pdf -------------------------------------------------------------------------------- /courseworks/week2/Shiqinrui_Xu/2D_brown_motion.jl: -------------------------------------------------------------------------------- 1 | using Random, Plots 2 | 3 | function simulate_brownian_motion_2d(n_steps) 4 | # Set initial position to the origin 5 | pos = [0.0, 0.0] 6 | 7 | # Initialize an array to store the particle trajectory 8 | traj = zeros(n_steps+1, 2) 9 | traj[1, :] = pos 10 | 11 | # Set the standard deviation of the step size 12 | step_size = 0.1 13 | 14 | # Loop over the specified number of steps 15 | for i in 1:n_steps 16 | # Generate a random step in x and y directions 17 | dx, dy = step_size * randn(2) 18 | 19 | # Update the position 20 | pos[1] += dx 21 | pos[2] += dy 22 | 23 | # Store the new position in the trajectory array 24 | traj[i+1, :] = pos 25 | end 26 | 27 | return traj 28 | end 29 | 30 | # Simulate Brownian motion for 10000 steps 31 | traj = simulate_brownian_motion_2d(10000) 32 | 33 | # Plot the trajectory 34 | plot(traj[:, 1], traj[:, 2], xlabel="X", ylabel="Y", title="2D Brownian Motion", legend=false) 35 | 36 | # Save the plot as a PNG file 37 | savefig("result.png") -------------------------------------------------------------------------------- /courseworks/week2/Shiqinrui_Xu/result.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week2/Shiqinrui_Xu/result.png -------------------------------------------------------------------------------- /courseworks/week2/Tinho_WHU/Brownian_Motion.jl: -------------------------------------------------------------------------------- 1 | using BenchmarkTools 2 | using Plots 3 | 4 | function simulate_brownian_motion(n::Int64) 5 | x = 0.0 6 | y = 0.0 7 | x_positions = [x] 8 | y_positions = [y] 9 | 10 | for i in 1:n 11 | dx = randn() 12 | dy = randn() 13 | x += dx 14 | y += dy 15 | push!(x_positions, x) 16 | push!(y_positions, y) 17 | end 18 | 19 | return x_positions, y_positions 20 | end 21 | 22 | n_steps = 100 23 | x_positions, y_positions = simulate_brownian_motion(n_steps) 24 | 25 | plot(x_positions, y_positions, xlabel="x", ylabel="y", legend=false,title="2D simulation of Brownian Motion") 26 | 27 | @benchmark simulate_brownian_motion($n_steps) -------------------------------------------------------------------------------- /courseworks/week2/Tinho_WHU/hw2_revised/week2_1_reviesed.md: -------------------------------------------------------------------------------- 1 | | | is concrete | is primitive | is abstract | is bits type | is mutable | 2 | | -------------------------- | ----------- | ------------ | ----------- | ------------ |:---------- | 3 | | ComplexF64 | 1 | 0 | 0 | 1 | 0 | 4 | | Complex{AbstractFloat} | 1 | 0 | 0 | 0 | 0 | 5 | | Complex{<:AbstractFloat} | 0 | 0 | 0 | 0 | 0 | 6 | | AbstractFloat | 0 | 0 | 1 | 0 | 0 | 7 | | Union{Float64, ComplexF64} | 0 | 0 | 0 | 0 | 0 | 8 | | Int32 | 1 | 1 | 0 | 1 | 0 | 9 | | Matrix{Float32} | 1 | 0 | 0 | 0 | 1 | 10 | | Base.RefValue | 0 | 0 | 0 | 0 | 1 | 11 | 12 | 1 for yes, 0 for no 13 | -------------------------------------------------------------------------------- /courseworks/week2/Tinho_WHU/week2_1.md: -------------------------------------------------------------------------------- 1 | | | is concrete | is primitive | is abstract | is bits type | is mutable | 2 | | -------------------------- | ----------- | ------------ | ----------- | ------------ |:---------- | 3 | | ComplexF64 | 1 | 0 | 0 | 1 | 1 | 4 | | Complex{AbstractFloat} | 1 | 0 | 0 | 0 | 1 | 5 | | Complex{<:AbstractFloat} | 0 | 0 | 0 | 0 | 0 | 6 | | AbstractFloat | 0 | 0 | 1 | 0 | 0 | 7 | | Union{Float64, ComplexF64} | 0 | 0 | 0 | 0 | 0 | 8 | | Int32 | 1 | 1 | 0 | 1 | 1 | 9 | | Matrix{Float32} | 1 | 0 | 0 | 0 | 1 | 10 | | Base.RefValue | 0 | 0 | 0 | 0 | 0 | 11 | 12 | 1 for yes, 0 for no 13 | -------------------------------------------------------------------------------- /courseworks/week2/XU,Chengzhen/Assignment 2.md: -------------------------------------------------------------------------------- 1 | # 1. Fill the following form 2 | 3 | 4 | ||is concrete|is primitive|is abstract|is bits type|is mutable| 5 | |--|--|--|--|--|--| 6 | |ComplexF64 |$\checkmark$|||$\checkmark$ || 7 | |Complex{AbstractFloat} |$\checkmark$||||| 8 | |Complex{<:AbstractFloat} | ||||| 9 | |AbstractFloat |||$\checkmark$ ||| 10 | |Union{Float64, ComplexF64} |||||| 11 | |Int32 |$\checkmark$|$\checkmark$ ||$\checkmark$ ||| 12 | |Matrix{Float32} | $\checkmark$ ||||$\checkmark$ | 13 | |Base.RefValue | ||||$\checkmark$ | 14 | 15 | 16 | 2. (a) repl_history.jl 17 | 18 | -------------------------------------------------------------------------------- /courseworks/week2/Xuanzhao_Gao/HW2.md: -------------------------------------------------------------------------------- 1 | #Homework2 2 | 3 | Xuanzhao Gao 4 | 5 | ## Q1 6 | 7 | |type of |is concrete|is primitive |is abstract |is bits type |is mutable| 8 | | :----: | :----: | :----: | :----: | :----: | :----: | 9 | |ComplexF64| true | false | false | true | false | 10 | |Complex{AbstractFloat}| true | false | false | false | false | 11 | |Complex{<:AbstractFloat}| false | false | false | false | false | 12 | |AbstractFloat| false | false | true | false | false | 13 | |Union{Float64, ComplexF64}| false | false | false | false | false | 14 | |Int32| true | true | false | true | false | 15 | |Matrix{Float32}| true | false | false | false | true | 16 | |Base.RefValue| false | false | false | false | true | 17 | 18 | -------------------------------------------------------------------------------- /courseworks/week2/ZhigaoXIE/Q1.jl: -------------------------------------------------------------------------------- 1 | using Printf 2 | 3 | types = [ 4 | ComplexF64, 5 | Complex{AbstractFloat}, 6 | Complex{<:AbstractFloat}, 7 | AbstractFloat, 8 | Union{Float64, ComplexF64}, 9 | Int32, 10 | Matrix{Float32}, 11 | Base.RefValue 12 | ] 13 | 14 | println("| Type | Concrete | Primitive | Abstract | Bits type | Mutable |") 15 | println("|------|----------|-----------|----------|-----------|---------|") 16 | 17 | for T in types 18 | concrete = isconcretetype(T) 19 | primitive = isprimitivetype(T) 20 | abstract = isabstracttype(T) 21 | bits_type = isbitstype(T) 22 | mutable = ismutabletype(T) 23 | 24 | @printf("| %-24s| %-8s | %-9s | %-8s | %-9s | %-7s |\n", string(T), concrete, primitive, abstract, bits_type, mutable) 25 | end 26 | 27 | -------------------------------------------------------------------------------- /courseworks/week2/ZhigaoXIE/Q1.md: -------------------------------------------------------------------------------- 1 | | Type | Concrete | Primitive | Abstract | Bits type | Mutable | 2 | |------|----------|-----------|----------|-----------|---------| 3 | | ComplexF64 | true | false | false | true | false | 4 | | Complex{AbstractFloat} | true | false | false | false | false | 5 | | Complex{<:AbstractFloat}| false | false | false | false | false | 6 | | AbstractFloat | false | false | true | false | false | 7 | | Union{Float64, ComplexF64}| false | false | false | false | false | 8 | | Int32 | true | true | false | true | false | 9 | | Matrix{Float32} | true | false | false | false | true | 10 | | Base.RefValue | false | false | false | false | true | 11 | -------------------------------------------------------------------------------- /courseworks/week2/yanyu Duan/Q1andQ2.md: -------------------------------------------------------------------------------- 1 | Question 1: 2 | Answer 1: From the definition, we can know the related condition number is 3 | $$κ(a/b) = \lim_{\epsilon → 0} max{ \frac{|(a/b) * ((\epsilon a/a)-(\epsilon b / b))|} { |\epsilon(a/b)|} }$$ 4 | If ‘a’ is a constant, define f(b) = a/b, then we have 5 | $$κ(a/b) = max{ \frac{|(a/b) * (-(\epsilon b / b))|} { |-a(εb) / b²|} } = 1$$ 6 | So when ‘b’ is constant, the relative condition number of the division operation is 1. 7 | Question 2: 8 | Answer 2: 9 | ill=conditioned: (a), (d) 10 | well-conditioned: (b), (c) 11 | -------------------------------------------------------------------------------- /courseworks/week2/yanyu Duan/Q1andQ2yanyuduan.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week2/yanyu Duan/Q1andQ2yanyuduan.pdf -------------------------------------------------------------------------------- /courseworks/week2/yanyu Duan/Q3yanyuduan.jl: -------------------------------------------------------------------------------- 1 | using LinearAlgebra 2 | 3 | function gauss_jordan(A_in) 4 | A = copy(A_in) 5 | n = size(A,1) 6 | B = Matrix{Float64}(I, n, n) 7 | for i = 1:n 8 | for j = 1:n 9 | if j != i 10 | c_ji = A[j, i] / A[i, i] 11 | for k = 1 : i 12 | B[j, k] -= B[i, k] * c_ji 13 | end 14 | for k = i : n 15 | A[j, k] -= A[i, k] * c_ji 16 | end 17 | end 18 | end 19 | end 20 | 21 | for i = 1:n 22 | for j in 1:n 23 | B[i, j] = B[i, j] / A[i, i] 24 | end 25 | end 26 | return B 27 | end 28 | 29 | #gauss_jordan (generic function with 1 method) 30 | 31 | 32 | A_example = [1. 2 2; 4 4 2; 4 6 4] 33 | B = gauss_jordan(A_example) 34 | 35 | B * Matrix(A_example) 36 | 37 | 38 | using Test 39 | @testset "Gauss Jordan" begin 40 | n = 10 41 | A = randn(n, n) 42 | @test gauss_jordan(A) * A ≈ Matrix{Float64}(I, n, n) 43 | end 44 | 45 | #= 46 | 47 | Test Summary: | Pass Total Time 48 | Gauss Jordan | 1 1 0.7s 49 | 50 | =# -------------------------------------------------------------------------------- /courseworks/week2/yanyu Duan/Week2_hw.md: -------------------------------------------------------------------------------- 1 | ## Fill the following form 2 | | | is concrete | is primitive | is abstract | is bits | is mutable | 3 | |----------------------------|-------------|--------------|-------------|---------|------------| 4 | | ComplexF64 | T | F | F | T | F | 5 | | Complex{AbstractFloat} | T | F | F | F | F | 6 | | Complex{<:AbstractFloat} | F | F | F | F | F | 7 | | AbstractFloat | F | F | T | F | F | 8 | | Union{Float64, ComplexF64} | F | F | F | F | F | 9 | | Int32 | T | T | F | T | F | 10 | | Matrix{Float32} | T | F | F | F | T | 11 | | Base.RefValue | F | F | F | F | T | 12 | 13 | T means true and F means false. 14 | -------------------------------------------------------------------------------- /courseworks/week2/yanyuduan/week2.md: -------------------------------------------------------------------------------- 1 | ## Fill the following form 2 | | | is concrete | is primitive | is abstract | is bits | is mutable | 3 | |----------------------------|-------------|--------------|-------------|---------|------------| 4 | | ComplexF64 | T | F | F | T | T | 5 | | Complex{AbstractFloat} | T | F | F | F | T | 6 | | Complex{<:AbstractFloat} | F | F | F | F | F | 7 | | AbstractFloat | F | F | T | F | F | 8 | | Union{Float64, ComplexF64} | F | F | F | F | F | 9 | | Int32 | T | T | F | T | T | 10 | | Matrix{Float32} | T | F | F | F | T | 11 | | Base.RefValue | F | F | F | F | F | 12 | 13 | T means true and F means false. -------------------------------------------------------------------------------- /courseworks/week3/TianhaoHu/hw_3.md: -------------------------------------------------------------------------------- 1 | # 1 2 | 3 | $\Delta y_{rel} = \frac{a/(b+\epsilon)-a/b}{a/b}=\frac{\frac{1}{b+\epsilon}-\frac{1}{b}}{\frac{1}{b}}=\frac{-\epsilon}{b+\epsilon} 4 | $ 5 | 6 | $\Delta x_{rel}=\frac{\epsilon}{b}$ 7 | 8 | $\frac{\Delta y_{rel}}{\Delta _{rel}}=\frac{1}{1+\frac{\epsilon}{b}} $ 9 | 10 | $\lim_{\epsilon \to 0} \frac{\Delta y_{rel}}{\Delta _{rel}} =1$ for any b given 11 | 12 | So the condition number of division operation is 1 13 | 14 | # 2 15 | 16 | (a) ill=conditioned 17 | 18 | (b) well-conditioned 19 | 20 | (c) well-conditioned 21 | 22 | (d) well-conditioned 23 | 24 | # 3 25 | -------------------------------------------------------------------------------- /courseworks/week3/ZhigaoXIE/Q1.txt: -------------------------------------------------------------------------------- 1 | using LinearAlgebra 2 | 3 | a = 5.0 4 | b = 3.0 5 | 6 | cond(a/b) = 1.0 7 | -------------------------------------------------------------------------------- /courseworks/week3/ZhigaoXIE/Q1_revised.md: -------------------------------------------------------------------------------- 1 | 2 | As the definition, the related condition number is: 3 | $$κ(a/b) = \lim_{\epsilon → 0} max{ \frac{|(a/b) * ((\epsilon a/a)-(\epsilon b / b))|} { |\epsilon(a/b)|} }$$ 4 | 5 | If 'a' is constant, let f(b) = a/b 6 | $$κ(a/b) = max{ \frac{|(a/b) * (-(\epsilon b / b))|} { |-a(εb) / b²|} } = 1$$ 7 | 8 | So as when 'b' is constant. 9 | 10 | The relative condition number of the division operation is 1. 11 | 12 | 13 | 14 | -------------------------------------------------------------------------------- /courseworks/week3/ZhigaoXIE/Q3.jl: -------------------------------------------------------------------------------- 1 | using LinearAlgebra 2 | using Test 3 | 4 | function gauss_jordan_inverse(A::Matrix{Float64}) 5 | n = size(A, 1) 6 | I = LinearAlgebra.I(n) 7 | aug = [A I] 8 | 9 | # Perform row operations to get A on the left side 10 | for i in 1:n 11 | # Swap rows if necessary 12 | if aug[i,i] == 0 13 | for j in (i+1):n 14 | if aug[j,i] != 0 15 | aug[[i,j],:] = aug[[j,i],:] 16 | break 17 | end 18 | end 19 | end 20 | 21 | # Divide row i by the pivot to make it 1 22 | pivot = aug[i,i] 23 | if pivot != 1 24 | aug[i,:] /= pivot 25 | end 26 | 27 | # Subtract a multiple of row i from all other rows to make their entries 0 28 | for j in 1:n 29 | if j != i 30 | factor = aug[j,i] 31 | aug[j,:] -= factor * aug[i,:] 32 | end 33 | end 34 | end 35 | # The inverse of A is on the right side of the augmented matrix 36 | A_inv = aug[:, (n+1):end] 37 | 38 | return A_inv 39 | end 40 | 41 | #gauss_jordan_inverse (generic function with 1 method) 42 | @testset "Gauss-Jordan inverse" begin 43 | n = 10 44 | A = randn(n, n) 45 | @test gauss_jordan_inverse(A) * A ≈ Matrix{Float64}(I, n, n) 46 | end 47 | 48 | 49 | -------------------------------------------------------------------------------- /courseworks/week3/xuanzhaogao/hw.md: -------------------------------------------------------------------------------- 1 | # Assignments 2 | 1. Get the relative condition number of division operation $a/b$. 3 | 4 | 2. Classify each of the following matrices as well-conditioned or ill-conditioned: 5 | ```math 6 | (a). ~~\left(\begin{matrix}10^{10} & 0\\ 0 & 10^{-10}\end{matrix}\right) 7 | ``` 8 | ```math 9 | (b). ~~\left(\begin{matrix}10^{10} & 0\\ 0 & 10^{10}\end{matrix}\right) 10 | ``` 11 | ```math 12 | (c). ~~\left(\begin{matrix}10^{-10} & 0\\ 0 & 10^{-10}\end{matrix}\right) 13 | ``` 14 | ```math 15 | (d). ~~\left(\begin{matrix}1 & 2\\ 2 & 4\end{matrix}\right) 16 | ``` 17 | 3. Implement the Gauss-Jordan elimination algorithm to compute matrix inverse. In the following example, we first create an augmented matrix $(A | I)$. Then we apply the Gauss-Jordan elimination matrices on the left. The final result is stored in the augmented matrix as $(I, A^{-1})$. 18 | ![](https://user-images.githubusercontent.com/6257240/222182865-c2a1aa28-946a-4acb-8df8-f5d7da93c3ee.png) 19 | 20 | Task: Please implement a function `gauss_jordan` that computes the inverse for a matrix at any size. Please also include the following test in your submission. 21 | ```julia 22 | @testset "Gauss Jordan" begin 23 | n = 10 24 | A = randn(n, n) 25 | @test gauss_jordan(A) * A ≈ Matrix{Float64}(I, n, n) 26 | end -------------------------------------------------------------------------------- /courseworks/week3/yushengzhao/period.jl: -------------------------------------------------------------------------------- 1 | ### A Pluto.jl notebook ### 2 | # v0.19.19 3 | 4 | using Markdown 5 | using InteractiveUtils 6 | 7 | # ╔═╡ a653e170-b753-11ed-0e5c-5f5fef2e5fee 8 | 9 | 10 | # ╔═╡ Cell order: 11 | # ╠═a653e170-b753-11ed-0e5c-5f5fef2e5fee 12 | -------------------------------------------------------------------------------- /courseworks/week4/TianhaoHu/hw4.md: -------------------------------------------------------------------------------- 1 | # 1. Review 2 | 3 | Q1 4 | 5 | 3 Householder transformations are required 6 | 7 | Q2 8 | 9 |  $v=[1,1,1,1]$ 10 | 11 | $|| v || = 2$ 12 | 13 | $u=[1;1;1;1]-2\times[1;0;0;0]=[-1;1;1;1] $ 14 | 15 | $u = \frac{u}{||u||}=\frac{u}{2}$ 16 | 17 | $H1 = I - 2\times u \times u^T$ 18 | 19 | $H1 \cdot v = [2;0;0;0]$ 20 | 21 | Q3 22 | 23 | The second householder transfomation only affect the element below the diagnol, so it should still be $[2;0;0;0]$ 24 | 25 | Q4 26 | 27 | 6 Givens transformations are required. 28 | 29 | # 2. Coding 30 | 31 | I write the code based on the version as shown in the class. The major change is, 32 | 33 | 1. Givens rotation do not start from the last row,but the first and second row, since elements in lower suddiaganol is zero 34 | 35 | 2. Givens rotation only acts on the first three columns instead of all columns,since elements in upper subdiagnol is zero 36 | 37 | While the modification of H in each iteration is not changed. 38 | 39 | The FLOPS can be computed as followed, 40 | 41 | $compute_A = 3 \times 6 \times n \approx 18n$ 42 | 43 | $compute_H \approx \sum_{k=1}^{n} 6\times k^2 = (2n+1)(n+1)n = 2n^3+3n^2 + n$ 44 | 45 | $FLOPS = compute_A + compute_H \approx 2n^3+ 3n^2 + 19n$ 46 | -------------------------------------------------------------------------------- /courseworks/week4/ZhigaoXIE/Q1.md: -------------------------------------------------------------------------------- 1 | 2 | (1) 3 Householder transformations. Because min(m-1, n) Householder transformations is needed for a m $\time$ n matrix. 3 | 4 | (2) [2; 0; 0; 0] 5 | 6 | (3) [2; 0; 0; 0] 7 | 8 | (4) 6 Givens rotations. 9 | -------------------------------------------------------------------------------- /courseworks/week4/ZhigaoXIE/code.jl: -------------------------------------------------------------------------------- 1 | using LinearAlgebra 2 | using Test 3 | 4 | function givens_rotation(a, b) 5 | if abs(b) < 1e-15 6 | c = copysign(1.0, a) 7 | s = 0.0 8 | else 9 | r = hypot(a, b) 10 | c = a / r 11 | s = b / r 12 | end 13 | return c, s 14 | end 15 | 16 | function symmetric_triangular_qr(T) 17 | m, n = size(T) 18 | Q = Matrix{Float64}(I, m, m) 19 | R = copy(T) 20 | 21 | for j = 1:n 22 | for i = m:-1:(j + 1) 23 | c, s = givens_rotation(R[i - 1, j], R[i, j]) 24 | 25 | # Update R 26 | R[i - 1:i, j:n] = [c s; -s c] * R[i - 1:i, j:n] 27 | 28 | # Update Q 29 | Q[:, i - 1:i] = Q[:, i - 1:i] * [c -s; s c] 30 | end 31 | end 32 | 33 | return Q, R 34 | end 35 | 36 | 37 | # Test 38 | using Random 39 | 40 | function rand_A(n) 41 | A = Matrix(Tridiagonal(rand(n - 1), rand(n), rand(n - 1))) 42 | return A 43 | end 44 | 45 | 46 | using Test 47 | 48 | @testset "Givens Rotation" begin 49 | for i in 1:100 50 | n = rand(1:100) 51 | A = rand_A(n) 52 | Q, R = symmetric_triangular_qr(A) 53 | @test Q * R ≈ A 54 | end 55 | end 56 | -------------------------------------------------------------------------------- /courseworks/week4/yanyu duan/Q1yanyuduan.md: -------------------------------------------------------------------------------- 1 | 1.There are four householder transformations required. 2 | 3 | 2.After transformation, the first column *A* of will be (2,0,0,0). 4 | 5 | 3.The second transformation will not be affected by the first column. 6 | 7 | 4.Six times of Givens rotations would be required. 8 | -------------------------------------------------------------------------------- /courseworks/week4/yushengzhao/gauss_jordan.jl: -------------------------------------------------------------------------------- 1 | using LinearAlgebra, Test, BenchmarkTools 2 | 3 | 4 | function gauss_jordan(M::AbstractMatrix{T}) where T <: Number 5 | m,n = size(M) 6 | @assert m == n 7 | MI = hcat(M,Matrix{eltype(M)}(I,m,m)) 8 | return _gauss_jordan_helper!(MI) 9 | end 10 | 11 | function _gauss_jordan_helper!(MI_partial::AbstractMatrix{T}) where T <: Number 12 | m,n = size(MI_partial) 13 | fct = 0.0 14 | if n == m 15 | return MI_partial 16 | else 17 | cur_idx = 2 * m - n + 1 18 | fct = MI_partial[cur_idx,1] 19 | 20 | @inbounds for j in 1:n 21 | MI_partial[cur_idx,j] /= fct 22 | end 23 | 24 | @inbounds for i in 1:m 25 | if i != cur_idx 26 | fct = MI_partial[i,1] 27 | @inbounds for j in 1:n 28 | MI_partial[i,j] -= fct * MI_partial[cur_idx,j] 29 | end 30 | end 31 | end 32 | return _gauss_jordan_helper!(view(MI_partial,:,2:n)) 33 | end 34 | 35 | end 36 | 37 | @testset "Gauss Jordan" begin 38 | n = 10 39 | A = randn(n, n) 40 | @test gauss_jordan(A) * A ≈ Matrix{Float64}(I, n, n) 41 | end 42 | 43 | # begin 44 | # n = 10 45 | # A = randn(n, n) 46 | # @benchmark gauss_jordan(A) 47 | # @benchmark inv(A) 48 | # end 49 | -------------------------------------------------------------------------------- /courseworks/week5/TianhaoHu/hw5.md: -------------------------------------------------------------------------------- 1 | Q1: 2 | 3 | The sparse matrix can be written in the dense form, 4 | 5 | $$ 6 | \begin{array}{c} 7 | \cdot& 0.942&0.848 & \cdot& \cdot\\ 8 | & & & & \\ 9 | 0.799 & \cdot& \cdot & \cdot & \cdot \\ 10 | \cdot& \cdot& 0.164 & \cdot & \cdot\\ 11 | \cdot & \cdot & \cdot & 0.637 & \cdot 12 | \end{array} \cdot 13 | $$ 14 | 15 | rowindices:[1 1 3 4 5 ] 16 | 17 | colindices:[2 3 1 3 4] 18 | 19 | data: [0.799 0.942 0.848 0.164 0.637] 20 | 21 | 22 | -------------------------------------------------------------------------------- /courseworks/week5/ZhigaoXIE/Q1.jl: -------------------------------------------------------------------------------- 1 | using SparseArrays 2 | 3 | using LinearAlgebra 4 | begin 5 | sp = sparse([3, 1, 1, 4, 5],[1, 2, 3, 3, 5],[0.799, 0.942, 0.848, 0.164, 0.637]) 6 | 7 | println(Matrix(sp)) 8 | print("sp.colptr = ") 9 | println( sp.colptr) 10 | print("sp.rowval = ") 11 | println(sp.rowval) 12 | print("sp.nzval = ") 13 | println(sp.nzval) 14 | end 15 | -------------------------------------------------------------------------------- /courseworks/week5/ZhigaoXIE/Q2.jl: -------------------------------------------------------------------------------- 1 | # Q2.jl 2 | 3 | using SparseArrays, Test 4 | using LinearAlgebra 5 | 6 | function my_spv(A::SparseMatrixCSC{T1}, x::AbstractVector{T2}) where {T1, T2} 7 | T = promote_type(T1, T2) 8 | @assert size(A, 2) == length(x) 9 | y = spzeros(T, size(A, 1)) 10 | for j in 1:size(A, 2) 11 | for k in nzrange(A, j) 12 | y[A.rowval[k]] += A.nzval[k] * x[j] 13 | end 14 | end 15 | return y 16 | end 17 | 18 | @testset "sparse matrix - vector multiplication" begin 19 | for k = 1:100 20 | m, n = rand(1:100, 2) 21 | density = rand() 22 | sp = sprand(m, n, density) 23 | v = randn(n) 24 | @test Matrix(sp) * v ≈ my_spv(sp, v) 25 | end 26 | end 27 | 28 | -------------------------------------------------------------------------------- /courseworks/week5/ZhigaoXIE/Q2_revised.jl: -------------------------------------------------------------------------------- 1 | # Q2.jl 2 | 3 | using SparseArrays, Test 4 | using LinearAlgebra 5 | 6 | function my_spv(A::SparseMatrixCSC{T1}, x::AbstractVector{T2}) where {T1, T2} 7 | T = promote_type(T1, T2) 8 | @assert size(A, 2) == length(x) 9 | y = zeros(T, size(A,1)) 10 | for j in 1:size(A, 2) 11 | for k in nzrange(A, j) 12 | y[A.rowval[k]] += A.nzval[k] * x[j] 13 | end 14 | end 15 | return y 16 | end 17 | 18 | @testset "sparse matrix - vector multiplication" begin 19 | for k = 1:100 20 | m, n = rand(1:100, 2) 21 | density = rand() 22 | sp = sprand(m, n, density) 23 | v = randn(n) 24 | @test Matrix(sp) * v ≈ my_spv(sp, v) 25 | end 26 | end 27 | 28 | -------------------------------------------------------------------------------- /courseworks/week5/yuanyu Duan/Q1.jl: -------------------------------------------------------------------------------- 1 | using SparseArrays 2 | 3 | using LinearAlgebra 4 | begin 5 | sp = sparse([3, 1, 1, 4, 5],[1, 2, 3, 3, 5],[0.799, 0.942, 0.848, 0.164, 0.637]) 6 | 7 | println(Matrix(sp)) 8 | print("sp.colptr = ") 9 | println( sp.colptr) 10 | print("sp.rowval = ") 11 | println(sp.rowval) 12 | print("sp.nzval = ") 13 | println(sp.nzval) 14 | end 15 | 16 | #julia "e:\HKUSTgz\courses\Julia\week5\tempCodeRunnerFile.jl" 17 | #[0.0 0.942 0.848 0.0 0.0; 0.0 0.0 0.0 0.0 0.0; 0.799 0.0 0.0 0.0 0.0; 0.0 0.0 0.164 0.0 0.0; 0.0 0.0 0.0 0.0 0.637] 18 | #sp.colptr = [1, 2, 3, 5, 5, 6] 19 | #sp.rowval = [3, 1, 1, 4, 5] 20 | #sp.nzval = [0.799, 0.942, 0.848, 0.164, 0.637] 21 | -------------------------------------------------------------------------------- /courseworks/week5/yuanyu Duan/Q2.jl: -------------------------------------------------------------------------------- 1 | using SparseArrays, Test 2 | 3 | function my_spv(sp::SparseMatrixCSC{T1},v::AbstractVector{T2}) where {T1,T2} 4 | T = promote_type(T1,T2) 5 | @assert size(sp,2) == size(v,1) 6 | rowval, colval, nzval = Int[], Int[], T[] 7 | @inbounds for j in 1:size(sp,2) 8 | @inbounds for i in nzrange(sp,j) 9 | push!(rowval,sp.rowval[i]) 10 | push!(colval,1) 11 | push!(nzval,sp.nzval[i]*v[j]) 12 | end 13 | end 14 | return sparse(rowval,colval,nzval,size(sp,1),size(v,2)) 15 | end 16 | 17 | @testset "sparse matrix - vector multiplication" begin 18 | for k = 1:100 19 | m, n = rand(1:100, 2) 20 | density = rand() 21 | sp = sprand(m, n, density) 22 | v = randn(n) 23 | @test Matrix(sp) * v ≈ my_spv(sp, v) 24 | end 25 | 26 | #Test Summary: | Pass Total Time 27 | #sparse matrix - vector multiplication | 100 100 0.8s 28 | 29 | -------------------------------------------------------------------------------- /courseworks/week6/ZhigaoXIE/wavelet-2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week6/ZhigaoXIE/wavelet-2.png -------------------------------------------------------------------------------- /courseworks/week6/ZhigaoXIE/wavelet.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week6/ZhigaoXIE/wavelet.png -------------------------------------------------------------------------------- /courseworks/week6/shiqinruixu/wavelet.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week6/shiqinruixu/wavelet.png -------------------------------------------------------------------------------- /courseworks/week6/xuanzhaogao/wavelet.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week6/xuanzhaogao/wavelet.png -------------------------------------------------------------------------------- /courseworks/week6/yushengzhao/ans.org: -------------------------------------------------------------------------------- 1 | #+TITLE: Homework 5 2 | #+AUTHOR: Yusheng Zhao 3 | 4 | * Problem 1 5 | #+begin_src julia :exports both :results output 6 | begin 7 | using SparseArrays 8 | colindices = [1; 2; 3; 3; 4] 9 | rowindices = [3; 1; 1; 4; 5] 10 | m,n = 5,5 11 | data = [0.799; 0.942; 0.848; 0.164; 0.637] 12 | sp = sparse(rowindices, colindices, data,m,n); 13 | @assert sp.colptr == [1; 2; 3; 5; 6; 6] 14 | @assert sp.rowval == [3; 1; 1; 4; 5] 15 | @assert sp.nzval == [0.799; 0.942; 0.848; 0.164; 0.637] 16 | @assert sp.m == 5 17 | @assert sp.n == 5 18 | println("Yeah, everything works!") 19 | end 20 | #+end_src 21 | 22 | #+RESULTS: 23 | : Yeah, everything works! 24 | 25 | 26 | * Problem 2 27 | ** Section A 28 | - See [[./csc.jl]] 29 | ** Section B 30 | - See [[./lanczos.jl]] 31 | -------------------------------------------------------------------------------- /courseworks/week6/yushengzhao/csc.jl: -------------------------------------------------------------------------------- 1 | using SparseArrays, Test 2 | 3 | function my_spv(sp::SparseMatrixCSC{T1},v::AbstractVector{T2}) where {T1,T2} 4 | T = promote_type(T1,T2) 5 | @assert size(sp,2) == size(v,1) 6 | rowval, colval, nzval = Int[], Int[], T[] 7 | @inbounds for j in 1:size(sp,2) 8 | @inbounds for i in nzrange(sp,j) 9 | push!(rowval,sp.rowval[i]) 10 | push!(colval,1) 11 | push!(nzval,sp.nzval[i]*v[j]) 12 | end 13 | end 14 | return sparse(rowval,colval,nzval,size(sp,1),size(v,2)) 15 | end 16 | 17 | @testset "sparse matrix - vector multiplication" begin 18 | for k = 1:100 19 | m, n = rand(1:100, 2) 20 | density = rand() 21 | sp = sprand(m, n, density) 22 | v = randn(n) 23 | @test Matrix(sp) * v ≈ my_spv(sp, v) 24 | end 25 | end 26 | -------------------------------------------------------------------------------- /courseworks/week7/ZhigaoXIE/unit_disk_embedding.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week7/ZhigaoXIE/unit_disk_embedding.png -------------------------------------------------------------------------------- /courseworks/week7/xuanzhaogao/HW7.pdf: -------------------------------------------------------------------------------- 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| (7,9), (8, 9), (8, 10), (9, 10)] 13 | 14 | theta = np.linspace(0, 2 * np.pi, 100) 15 | x_0 = np.cos(theta) 16 | y_0 = np.sin(theta) 17 | 18 | plt.figure(dpi = 150) 19 | for i in range(10): 20 | plt.scatter(best_x[2 * i], best_x[2 * i + 1]) 21 | x_i = best_x[2 * i] + x_0 22 | y_i = best_x[2 * i + 1] + y_0 23 | plt.plot(x_i, y_i, label = str(i + 1)) 24 | 25 | for i in range(10): 26 | for j in range(i, 10): 27 | if (i + 1, j + 1) in E: 28 | plt.plot([best_x[2 * i], best_x[2 * j]], [best_x[2 * i + 1], best_x[2 * j + 1]], 'black') 29 | 30 | plt.legend(ncol = 2) 31 | plt.gca().set_aspect(1) 32 | plt.savefig('unit_disk_py.png') 33 | -------------------------------------------------------------------------------- /courseworks/week7/xuanzhaogao/unit_disk_py.png: -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- /courseworks/week9/tianhaohu/HW9.md: -------------------------------------------------------------------------------- 1 | # HW8 2 | 3 | ## 1. 4 | 5 | $$ 6 | \eta(\tau,\delta)-\sum_{k=0}^{\delta}\eta(\tau-1,k) 7 | $$ 8 | 9 | $$ 10 | = \frac{(\tau+\delta)!}{\tau! \delta!} - \sum_{k=0}^{\delta}\frac{((\tau-1)+k)!}{(\tau-1)! k!} 11 | $$ 12 | 13 | $$ 14 | = (\frac{1}{(\tau-1)!})(\frac{(\tau+\delta)!}{\tau \delta!}-\sum_{k=0}^{\delta}\frac{((\tau-1)+k)!}{ k!}) 15 | $$ 16 | 17 | $$ 18 | = \frac{(\tau+\delta)...\tau}{\tau \cdot \delta!} - 1 - \frac{\tau}{1!}- ...-\frac{\tau...(\tau+\delta-1)}{\delta !} 19 | $$ 20 | 21 | $$ 22 | = \frac{(\tau+\delta)...\tau}{\tau \cdot \delta!} - \sum_{k=0}^{\delta}\frac{(k+\tau-1)...\tau}{k!} 23 | $$ 24 | 25 | Notice that, 26 | 27 | $$ 28 | \frac{(\tau+k)...\tau}{\tau \cdot k!} - \frac{\tau...(\tau+k-1)}{k!} 29 | $$ 30 | 31 | $$ 32 | = \frac{k \cdot(\tau + k -1)...\tau }{\tau \cdot k !} = \frac{(\tau + k -1)...\tau }{\tau \cdot (k-1) !} 33 | $$ 34 | 35 | The above Eqn holds for $k$ from $\delta$ to 0. So $\eta(\tau,\delta)-\sum_{k=0}^{\delta}\eta(\tau-1,k)$ can be recursively proved to be zero. 36 | 37 | 38 | 39 | ## 2. 40 | 41 | 42 | -------------------------------------------------------------------------------- /courseworks/week9/xuanzhaogao/tensors.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/courseworks/week9/xuanzhaogao/tensors.jpg -------------------------------------------------------------------------------- /lib/CUDATutorial/Project.toml: -------------------------------------------------------------------------------- 1 | [deps] 2 | CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" 3 | -------------------------------------------------------------------------------- /lib/CUDATutorial/libraries.jl: -------------------------------------------------------------------------------- 1 | import SparseArrays, FFTW, LinearAlgebra, Random 2 | using CUDA; CUDA.allowscalar(false) 3 | using Test 4 | 5 | @testset "CUSOLVER" begin 6 | A = randn(10, 10) 7 | v = randn(10) 8 | # operations 9 | @test Array(CuArray(A) \ CuArray(v)) ≈ A \ Array(v) 10 | end 11 | 12 | @testset "CUSPARSE" begin 13 | Random.seed!(2) 14 | # initialize a CUDA sparse array 15 | A = SparseArrays.sprand(10, 10, 0.2) 16 | cuA = CUSPARSE.CuSparseMatrixCSC(A) 17 | 18 | @show SparseArrays.nnz(cuA) 19 | 20 | # operations 21 | v = randn(10) 22 | cuv = CuArray(v) 23 | # matrix vector 24 | @test Array(cuA * cuv) ≈ A * v 25 | 26 | # matrix matrix 27 | @test Array(cuA * cuA) ≈ A * A 28 | 29 | # gaussian eliminatjion 30 | cuA += Diagonal(CUDA.randn(10)) 31 | A = Array(cuA) 32 | @show CuArray(LinearAlgebra.UpperTriangular(cuA) \ cuv) 33 | @test Array(LinearAlgebra.UpperTriangular(cuA) \ cuv) ≈ LinearAlgebra.UpperTriangular(A) \ v 34 | end 35 | 36 | @testset "CUFFT" begin 37 | v = randn(10) 38 | @test Array(CUFFT.fft(CuArray(v))) ≈ FFTW.fft(v) 39 | 40 | # 2D fft 41 | A = randn(10, 10) 42 | @test Array(CUFFT.fft(CuArray(A))) ≈ FFTW.fft(A) 43 | end 44 | -------------------------------------------------------------------------------- /lib/CompressedSensingTutorial/.github/workflows/CI.yml: -------------------------------------------------------------------------------- 1 | name: CI 2 | on: 3 | push: 4 | branches: 5 | - main 6 | tags: ['*'] 7 | pull_request: 8 | concurrency: 9 | # Skip intermediate builds: always. 10 | # Cancel intermediate builds: only if it is a pull request build. 11 | group: ${{ github.workflow }}-${{ github.ref }} 12 | cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }} 13 | jobs: 14 | test: 15 | name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }} 16 | runs-on: ${{ matrix.os }} 17 | strategy: 18 | fail-fast: false 19 | matrix: 20 | version: 21 | - '1.0' 22 | - 'nightly' 23 | os: 24 | - ubuntu-latest 25 | arch: 26 | - x64 27 | steps: 28 | - uses: actions/checkout@v2 29 | - uses: julia-actions/setup-julia@v1 30 | with: 31 | version: ${{ matrix.version }} 32 | arch: ${{ matrix.arch }} 33 | - uses: julia-actions/cache@v1 34 | - uses: julia-actions/julia-buildpkg@v1 35 | - uses: julia-actions/julia-runtest@v1 36 | - uses: julia-actions/julia-processcoverage@v1 37 | - uses: codecov/codecov-action@v2 38 | with: 39 | files: lcov.info 40 | -------------------------------------------------------------------------------- /lib/CompressedSensingTutorial/.github/workflows/CompatHelper.yml: -------------------------------------------------------------------------------- 1 | name: CompatHelper 2 | on: 3 | schedule: 4 | - cron: 0 0 * * * 5 | workflow_dispatch: 6 | jobs: 7 | CompatHelper: 8 | runs-on: ubuntu-latest 9 | steps: 10 | - name: Pkg.add("CompatHelper") 11 | run: julia -e 'using Pkg; Pkg.add("CompatHelper")' 12 | - name: CompatHelper.main() 13 | env: 14 | GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} 15 | COMPATHELPER_PRIV: ${{ secrets.DOCUMENTER_KEY }} 16 | run: julia -e 'using CompatHelper; CompatHelper.main()' 17 | -------------------------------------------------------------------------------- /lib/CompressedSensingTutorial/.github/workflows/TagBot.yml: -------------------------------------------------------------------------------- 1 | name: TagBot 2 | on: 3 | issue_comment: 4 | types: 5 | - created 6 | workflow_dispatch: 7 | jobs: 8 | TagBot: 9 | if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot' 10 | runs-on: ubuntu-latest 11 | steps: 12 | - uses: JuliaRegistries/TagBot@v1 13 | with: 14 | token: ${{ secrets.GITHUB_TOKEN }} 15 | ssh: ${{ secrets.DOCUMENTER_KEY }} 16 | -------------------------------------------------------------------------------- /lib/CompressedSensingTutorial/.gitignore: -------------------------------------------------------------------------------- 1 | *.jl.*.cov 2 | *.jl.cov 3 | *.jl.mem 4 | /Manifest.toml 5 | .vscode/ -------------------------------------------------------------------------------- /lib/CompressedSensingTutorial/LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2023 GiggleLiu and contributors 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /lib/CompressedSensingTutorial/Project.toml: -------------------------------------------------------------------------------- 1 | name = "CompressedSensingTutorial" 2 | uuid = "3ab334c4-b558-47f6-9400-74651b19301f" 3 | authors = ["GiggleLiu and contributors"] 4 | version = "1.0.0-DEV" 5 | 6 | [deps] 7 | FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341" 8 | FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000" 9 | Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0" 10 | LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 11 | NLSolversBase = "d41bc354-129a-5804-8e4c-c37616107c6c" 12 | Optim = "429524aa-4258-5aef-a3af-852621145aeb" 13 | Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" 14 | StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" 15 | 16 | [compat] 17 | julia = "1" 18 | 19 | [extras] 20 | Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" 21 | 22 | [targets] 23 | test = ["Test"] 24 | -------------------------------------------------------------------------------- /lib/CompressedSensingTutorial/README.md: -------------------------------------------------------------------------------- 1 | # CompressedSensingTutorial 2 | 3 | [![Build Status](https://github.com/GiggleLiu/CompressedSensingTutorial.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/GiggleLiu/CompressedSensingTutorial.jl/actions/workflows/CI.yml?query=branch%3Amain) 4 | [![Coverage](https://codecov.io/gh/GiggleLiu/CompressedSensingTutorial.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/GiggleLiu/CompressedSensingTutorial.jl) 5 | -------------------------------------------------------------------------------- /lib/CompressedSensingTutorial/src/CompressedSensingTutorial.jl: -------------------------------------------------------------------------------- 1 | module CompressedSensingTutorial 2 | using FFTW, StatsBase, LinearAlgebra, Optim 3 | 4 | export sensing_image, sample_image_pixels, ImageSamples 5 | export SimpleLinesearch 6 | 7 | include("owlqn.jl") 8 | include("compressed_sensing_2d.jl") 9 | 10 | end 11 | -------------------------------------------------------------------------------- /lib/CompressedSensingTutorial/test/runtests.jl: -------------------------------------------------------------------------------- 1 | using Test 2 | 3 | @testset "compressed sensing 2d" begin 4 | include("compressed_sensing_2d.jl") 5 | end 6 | 7 | @testset "owlqn" begin 8 | include("owlqn.jl") 9 | end -------------------------------------------------------------------------------- /lib/CompressedSensingTutorial/test/waterfall.jpeg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/lib/CompressedSensingTutorial/test/waterfall.jpeg -------------------------------------------------------------------------------- /lib/KernelPCA/.github/workflows/CI.yml: -------------------------------------------------------------------------------- 1 | name: CI 2 | on: 3 | push: 4 | branches: 5 | - main 6 | tags: ['*'] 7 | pull_request: 8 | concurrency: 9 | # Skip intermediate builds: always. 10 | # Cancel intermediate builds: only if it is a pull request build. 11 | group: ${{ github.workflow }}-${{ github.ref }} 12 | cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }} 13 | jobs: 14 | test: 15 | name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }} 16 | runs-on: ${{ matrix.os }} 17 | strategy: 18 | fail-fast: false 19 | matrix: 20 | version: 21 | - '1.0' 22 | - 'nightly' 23 | os: 24 | - ubuntu-latest 25 | arch: 26 | - x64 27 | steps: 28 | - uses: actions/checkout@v2 29 | - uses: julia-actions/setup-julia@v1 30 | with: 31 | version: ${{ matrix.version }} 32 | arch: ${{ matrix.arch }} 33 | - uses: julia-actions/cache@v1 34 | - uses: julia-actions/julia-buildpkg@v1 35 | - uses: julia-actions/julia-runtest@v1 36 | - uses: julia-actions/julia-processcoverage@v1 37 | - uses: codecov/codecov-action@v2 38 | with: 39 | files: lcov.info 40 | -------------------------------------------------------------------------------- /lib/KernelPCA/.github/workflows/CompatHelper.yml: -------------------------------------------------------------------------------- 1 | name: CompatHelper 2 | on: 3 | schedule: 4 | - cron: 0 0 * * * 5 | workflow_dispatch: 6 | jobs: 7 | CompatHelper: 8 | runs-on: ubuntu-latest 9 | steps: 10 | - name: Pkg.add("CompatHelper") 11 | run: julia -e 'using Pkg; Pkg.add("CompatHelper")' 12 | - name: CompatHelper.main() 13 | env: 14 | GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} 15 | COMPATHELPER_PRIV: ${{ secrets.DOCUMENTER_KEY }} 16 | run: julia -e 'using CompatHelper; CompatHelper.main()' 17 | -------------------------------------------------------------------------------- /lib/KernelPCA/.github/workflows/TagBot.yml: -------------------------------------------------------------------------------- 1 | name: TagBot 2 | on: 3 | issue_comment: 4 | types: 5 | - created 6 | workflow_dispatch: 7 | jobs: 8 | TagBot: 9 | if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot' 10 | runs-on: ubuntu-latest 11 | steps: 12 | - uses: JuliaRegistries/TagBot@v1 13 | with: 14 | token: ${{ secrets.GITHUB_TOKEN }} 15 | ssh: ${{ secrets.DOCUMENTER_KEY }} 16 | -------------------------------------------------------------------------------- /lib/KernelPCA/.gitignore: -------------------------------------------------------------------------------- 1 | *.jl.*.cov 2 | *.jl.cov 3 | *.jl.mem 4 | /Manifest.toml 5 | -------------------------------------------------------------------------------- /lib/KernelPCA/LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2023 GiggleLiu and contributors 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /lib/KernelPCA/Project.toml: -------------------------------------------------------------------------------- 1 | name = "KernelPCA" 2 | uuid = "659736db-e33a-4d97-a2b7-5a5dcfea6c5b" 3 | authors = ["GiggleLiu and contributors"] 4 | version = "1.0.0-DEV" 5 | 6 | [deps] 7 | LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 8 | 9 | [compat] 10 | julia = "1" 11 | 12 | [extras] 13 | Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" 14 | 15 | [targets] 16 | test = ["Test"] 17 | -------------------------------------------------------------------------------- /lib/KernelPCA/README.md: -------------------------------------------------------------------------------- 1 | # KernelPCA 2 | 3 | [![Build Status](https://github.com/GiggleLiu/KernelPCA.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/GiggleLiu/KernelPCA.jl/actions/workflows/CI.yml?query=branch%3Amain) 4 | [![Coverage](https://codecov.io/gh/GiggleLiu/KernelPCA.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/GiggleLiu/KernelPCA.jl) 5 | -------------------------------------------------------------------------------- /lib/KernelPCA/src/KernelPCA.jl: -------------------------------------------------------------------------------- 1 | module KernelPCA 2 | 3 | using LinearAlgebra 4 | 5 | export RBFKernel, PolyKernel, LinearKernel, kernelf, matrix, Point 6 | export kpca, KPCAResult, ϕ 7 | 8 | include("kernels.jl") 9 | include("kpca.jl") 10 | include("dataset.jl") 11 | 12 | end 13 | -------------------------------------------------------------------------------- /lib/KernelPCA/src/dataset.jl: -------------------------------------------------------------------------------- 1 | module DataSets 2 | 3 | using KernelPCA: Point 4 | export quadratic, linear, curve, rings 5 | 6 | function quadratic(n::Int; xspan=1, noise=0.1) 7 | xs = randn(n) .* xspan 8 | ys = xs .^ 2 .+ noise .* randn(n) 9 | return Point{2, Float64}[Point(x, y) for (x, y) in zip(xs, ys)] 10 | end 11 | 12 | function linear(n::Int; xspan=1, noise=0.1, offsety=0.0) 13 | xs = randn(n) .* xspan 14 | ys = xs .+ noise .* randn(n) .+ offsety 15 | return Point{2, Float64}[Point(x, y) for (x, y) in zip(xs, ys)] 16 | end 17 | 18 | function curve(n::Int; xspan=1, noise=0.1) 19 | xs = randn(n) .* xspan 20 | ys = (xs .- 1) .^ 2 .+ noise .* randn(n) 21 | return Point{2, Float64}[Point(x, y) for (x, y) in zip(xs, ys)] 22 | end 23 | 24 | function rings(n::Int; radius=1.0, width=0.1) 25 | vcat([let 26 | angles = rand(n) * 2π 27 | radis = radi .+ randn(n) * width 28 | [Point(r*cos(angle), r*sin(angle)) for (r, angle) in zip(radis, angles)] 29 | end for radi in radius]...) 30 | end 31 | end -------------------------------------------------------------------------------- /lib/KernelPCA/test/kernels.jl: -------------------------------------------------------------------------------- 1 | using KernelPCA, Test, LinearAlgebra 2 | 3 | @testset "rbf" begin 4 | ker = RBFKernel(0.56) 5 | m = matrix(ker, 0:0.01:0.99) 6 | @test m isa Matrix && size(m) == (100, 100) 7 | @test diag(m) ≈ ones(100) 8 | end 9 | 10 | @testset "poly" begin 11 | ker = PolyKernel{2}() 12 | x, y = Point(0.2, 0.5), Point(0.4, 0.9) 13 | @test ker(x, y) == ϕ(ker, x)' * ϕ(ker, y) 14 | 15 | ker = PolyKernel{3}() 16 | x, y = Point(0.2, 0.5), Point(0.4, 0.9) 17 | @test ker(x, y) == ϕ(ker, x)' * ϕ(ker, y) 18 | 19 | # linear kernel 20 | ker = LinearKernel() 21 | @test ker(x, y) == ϕ(ker, x)' * ϕ(ker, y) 22 | @test ker(x, y) == collect(x)' * collect(y) 23 | end -------------------------------------------------------------------------------- /lib/KernelPCA/test/runtests.jl: -------------------------------------------------------------------------------- 1 | using KernelPCA 2 | using Test 3 | 4 | @testset "KernelPCA.jl" begin 5 | # Write your tests here. 6 | end 7 | -------------------------------------------------------------------------------- /lib/LatticeGasCA/.github/workflows/CompatHelper.yml: -------------------------------------------------------------------------------- 1 | name: CompatHelper 2 | on: 3 | schedule: 4 | - cron: 0 0 * * * 5 | workflow_dispatch: 6 | jobs: 7 | CompatHelper: 8 | runs-on: ubuntu-latest 9 | steps: 10 | - name: Pkg.add("CompatHelper") 11 | run: julia -e 'using Pkg; Pkg.add("CompatHelper")' 12 | - name: CompatHelper.main() 13 | env: 14 | GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} 15 | COMPATHELPER_PRIV: ${{ secrets.DOCUMENTER_KEY }} 16 | run: julia -e 'using CompatHelper; CompatHelper.main()' 17 | -------------------------------------------------------------------------------- /lib/LatticeGasCA/.github/workflows/TagBot.yml: -------------------------------------------------------------------------------- 1 | name: TagBot 2 | on: 3 | issue_comment: 4 | types: 5 | - created 6 | workflow_dispatch: 7 | jobs: 8 | TagBot: 9 | if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot' 10 | runs-on: ubuntu-latest 11 | steps: 12 | - uses: JuliaRegistries/TagBot@v1 13 | with: 14 | token: ${{ secrets.GITHUB_TOKEN }} 15 | ssh: ${{ secrets.DOCUMENTER_KEY }} 16 | -------------------------------------------------------------------------------- /lib/LatticeGasCA/.gitignore: -------------------------------------------------------------------------------- 1 | *.jl.*.cov 2 | *.jl.cov 3 | *.jl.mem 4 | /Manifest.toml 5 | /docs/build/ 6 | .vscode/ -------------------------------------------------------------------------------- /lib/LatticeGasCA/LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2023 GiggleLiu and contributors 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /lib/LatticeGasCA/Project.toml: -------------------------------------------------------------------------------- 1 | name = "LatticeGasCA" 2 | uuid = "38b09334-5df9-4e03-8969-f8217d04990c" 3 | authors = ["GiggleLiu and contributors"] 4 | version = "1.0.0-DEV" 5 | 6 | [deps] 7 | CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" 8 | Requires = "ae029012-a4dd-5104-9daa-d747884805df" 9 | UnicodePlots = "b8865327-cd53-5732-bb35-84acbb429228" 10 | 11 | [compat] 12 | CUDA = "4.2" 13 | UnicodePlots = "3.5" 14 | julia = "1" 15 | 16 | [extras] 17 | Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" 18 | 19 | [targets] 20 | test = ["Test"] 21 | -------------------------------------------------------------------------------- /lib/LatticeGasCA/README.md: -------------------------------------------------------------------------------- 1 | # LatticeGasCA 2 | 3 | [![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://GiggleLiu.github.io/LatticeGasCA.jl/stable/) 4 | [![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://GiggleLiu.github.io/LatticeGasCA.jl/dev/) 5 | [![Build Status](https://github.com/GiggleLiu/LatticeGasCA.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/GiggleLiu/LatticeGasCA.jl/actions/workflows/CI.yml?query=branch%3Amain) 6 | [![Coverage](https://codecov.io/gh/GiggleLiu/LatticeGasCA.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/GiggleLiu/LatticeGasCA.jl) 7 | -------------------------------------------------------------------------------- /lib/LatticeGasCA/docs/Project.toml: -------------------------------------------------------------------------------- 1 | [deps] 2 | Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" 3 | LatticeGasCA = "38b09334-5df9-4e03-8969-f8217d04990c" 4 | -------------------------------------------------------------------------------- /lib/LatticeGasCA/docs/make.jl: -------------------------------------------------------------------------------- 1 | using LatticeGasCA 2 | using Documenter 3 | 4 | DocMeta.setdocmeta!(LatticeGasCA, :DocTestSetup, :(using LatticeGasCA); recursive=true) 5 | 6 | makedocs(; 7 | modules=[LatticeGasCA], 8 | authors="GiggleLiu and contributors", 9 | repo="https://github.com/GiggleLiu/LatticeGasCA.jl/blob/{commit}{path}#{line}", 10 | sitename="LatticeGasCA.jl", 11 | format=Documenter.HTML(; 12 | prettyurls=get(ENV, "CI", "false") == "true", 13 | canonical="https://GiggleLiu.github.io/LatticeGasCA.jl", 14 | edit_link="main", 15 | assets=String[], 16 | ), 17 | pages=[ 18 | "Home" => "index.md", 19 | ], 20 | ) 21 | 22 | deploydocs(; 23 | repo="github.com/GiggleLiu/LatticeGasCA.jl", 24 | devbranch="main", 25 | ) 26 | -------------------------------------------------------------------------------- /lib/LatticeGasCA/docs/src/index.md: -------------------------------------------------------------------------------- 1 | ```@meta 2 | CurrentModule = LatticeGasCA 3 | ``` 4 | 5 | # LatticeGasCA 6 | 7 | Documentation for [LatticeGasCA](https://github.com/GiggleLiu/LatticeGasCA.jl). 8 | 9 | ```@index 10 | ``` 11 | 12 | ```@autodocs 13 | Modules = [LatticeGasCA] 14 | ``` 15 | -------------------------------------------------------------------------------- /lib/LatticeGasCA/project/visualize.jl: -------------------------------------------------------------------------------- 1 | using WGLMakie 2 | using LatticeGasCA 3 | 4 | function make_video(lg::AbstractLatticeGas; filename::String="lattice-gas.mp4", nframes::Int=120) 5 | lattice_data = Observable(LatticeGasCA.density(lg)) 6 | fig, axis, plt = Makie.heatmap(lattice_data) 7 | 8 | Makie.record(fig, filename, 1:nframes) do frame 9 | notify.((lattice_data,)) 10 | lattice_data[] = LatticeGasCA.density(update!(lg)) 11 | end 12 | end 13 | 14 | 15 | hpp = hpp_center_square(200, 200, 0.01); 16 | make_video(hpp) -------------------------------------------------------------------------------- /lib/LatticeGasCA/src/LatticeGasCA.jl: -------------------------------------------------------------------------------- 1 | module LatticeGasCA 2 | 3 | import UnicodePlots 4 | 5 | export hpp_center_square, hpp_singledot, HPPLatticeGas, simulate, update!, AbstractLatticeGas, density 6 | 7 | include("hpp.jl") 8 | include("cuda.jl") 9 | 10 | # using Requires 11 | # function __init__() 12 | # @require CUDA="052768ef-5323-5732-b1bb-66c8b64840ba" include("cuda.jl") 13 | # end 14 | 15 | end 16 | -------------------------------------------------------------------------------- /lib/LatticeGasCA/src/cuda.jl: -------------------------------------------------------------------------------- 1 | using CUDA 2 | using CUDA.GPUArrays: gpu_call, @cartesianidx 3 | 4 | export cpu 5 | 6 | function update!(lg::HPPLatticeGas{ET, <:CuArray{ET}}) where ET 7 | @inline function kernel(ctx, lattice::AbstractArray{T}, cache) where T 8 | i, j = (@cartesianidx lattice).I 9 | nx, ny = size(lattice) 10 | @inbounds state = (i == nx ? zero(T) : left(lattice[i+1, j])) + 11 | (i == 1 ? zero(T) : right(lattice[i-1, j])) + 12 | (j == ny ? zero(T) : down(lattice[i, j+1])) + 13 | (j == 1 ? zero(T) : up(lattice[i, j-1])) 14 | newstate = hpp_state_transfer_rule(state, i, j, nx, ny) 15 | @inbounds cache[i, j] = newstate 16 | return 17 | end 18 | gpu_call(kernel, lg.lattice, lg.cache) 19 | CUDA.synchronize() 20 | copyto!(lg.lattice, lg.cache) 21 | return lg 22 | end 23 | 24 | function CUDA.cu(lg::HPPLatticeGas) 25 | HPPLatticeGas(CuArray(lg.lattice), CuArray(lg.cache)) 26 | end 27 | 28 | function cpu(lg::HPPLatticeGas) 29 | HPPLatticeGas(Array(lg.lattice), Array(lg.cache)) 30 | end -------------------------------------------------------------------------------- /lib/LatticeGasCA/test/cuda.jl: -------------------------------------------------------------------------------- 1 | using LatticeGasCA, Test, CUDA 2 | CUDA.allowscalar(false) 3 | 4 | @testset "hpp" begin 5 | hpp = cu(hpp_singledot()) 6 | hpp2 = simulate(hpp, 76; verbose=true) 7 | @test !(hpp === hpp2) && hpp == hpp2 8 | end -------------------------------------------------------------------------------- /lib/LatticeGasCA/test/hpp.jl: -------------------------------------------------------------------------------- 1 | using LatticeGasCA, Test 2 | 3 | @testset "hpp" begin 4 | hpp = hpp_singledot() 5 | hpp2 = simulate(hpp, 76; verbose=true) 6 | @test !(hpp === hpp2) && hpp == hpp2 7 | end -------------------------------------------------------------------------------- /lib/LatticeGasCA/test/runtests.jl: -------------------------------------------------------------------------------- 1 | using LatticeGasCA 2 | using Test, CUDA 3 | 4 | @testset "hpp" begin 5 | include("hpp.jl") 6 | end 7 | 8 | if CUDA.functional() 9 | include("cuda.jl") 10 | end -------------------------------------------------------------------------------- /lib/PlutoLecturing/.gitignore: -------------------------------------------------------------------------------- 1 | *.jl.*.cov 2 | *.jl.cov 3 | *.jl.mem 4 | /Manifest.toml 5 | -------------------------------------------------------------------------------- /lib/PlutoLecturing/LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2023 GiggleLiu and contributors 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /lib/PlutoLecturing/Project.toml: -------------------------------------------------------------------------------- 1 | name = "PlutoLecturing" 2 | uuid = "3e1d68ed-7204-4e43-84e1-610205b9583d" 3 | authors = ["GiggleLiu and contributors"] 4 | version = "0.1.0" 5 | 6 | [deps] 7 | AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c" 8 | InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240" 9 | Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" 10 | Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" 11 | PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" 12 | Reexport = "189a3867-3050-52da-a836-e630ba90ab69" 13 | 14 | [compat] 15 | AbstractTrees = "0.4" 16 | PlutoUI = "0.7" 17 | Reexport = "1" 18 | julia = "1" 19 | 20 | [extras] 21 | Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" 22 | 23 | [targets] 24 | test = ["Test"] 25 | -------------------------------------------------------------------------------- /lib/PlutoLecturing/README.md: -------------------------------------------------------------------------------- 1 | # PlutoLecturing 2 | 3 | [![Build Status](https://github.com/GiggleLiu/PlutoLecturing.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/GiggleLiu/PlutoLecturing.jl/actions/workflows/CI.yml?query=branch%3Amain) 4 | [![Coverage](https://codecov.io/gh/GiggleLiu/PlutoLecturing.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/GiggleLiu/PlutoLecturing.jl) 5 | -------------------------------------------------------------------------------- /lib/PlutoLecturing/src/PlutoLecturing.jl: -------------------------------------------------------------------------------- 1 | module PlutoLecturing 2 | 3 | using AbstractTrees, Pkg 4 | using InteractiveUtils 5 | using Reexport: @reexport 6 | @reexport using PlutoUI 7 | using Markdown: html 8 | 9 | include("functions.jl") 10 | include("xbind.jl") 11 | include("trees.jl") 12 | 13 | end 14 | -------------------------------------------------------------------------------- /lib/PlutoLecturing/src/xbind.jl: -------------------------------------------------------------------------------- 1 | export @xbind 2 | 3 | struct BondWrapper 4 | content 5 | end 6 | 7 | function Base.show(io::IO, mime::MIME"text/html", b::BondWrapper) 8 | print(io, 9 | """$(b.content.defines) = """) 10 | Base.show(io, mime, b.content) 11 | end 12 | 13 | macro xbind(args...) 14 | esc(quote 15 | let 16 | bond = @bind $(args...) 17 | $BondWrapper(bond) 18 | end 19 | end) 20 | end 21 | 22 | -------------------------------------------------------------------------------- /lib/PlutoLecturing/test/runtests.jl: -------------------------------------------------------------------------------- 1 | using PlutoLecturing 2 | using Test 3 | 4 | @testset "PlutoLecturing.jl" begin 5 | # Write your tests here. 6 | end 7 | 8 | @testset "trees" begin 9 | @test print_dependency_tree(PlutoLecturing) isa HTML 10 | @test print_dir_tree(".") isa Text 11 | @test print_type_tree(".") isa Text 12 | end 13 | -------------------------------------------------------------------------------- /notebooks/1.understanding-our-computing-devices.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/notebooks/1.understanding-our-computing-devices.pdf -------------------------------------------------------------------------------- /notebooks/10.inference.pdf: -------------------------------------------------------------------------------- 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27 | ~~~ 28 | -------------------------------------------------------------------------------- /website/Project.toml: -------------------------------------------------------------------------------- 1 | [deps] 2 | Franklin = "713c75ef-9fc9-4b05-94a9-213340da978e" 3 | NodeJS = "2bd173c7-0d6d-553b-b6af-13a54713934c" 4 | PlutoLecturing = "3e1d68ed-7204-4e43-84e1-610205b9583d" 5 | PlutoSliderServer = "2fc8631c-6f24-4c5b-bca7-cbb509c42db4" 6 | Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" 7 | -------------------------------------------------------------------------------- /website/README.md: -------------------------------------------------------------------------------- 1 | # To deploy 2 | 3 | ```bash 4 | julia -e 'using Franklin; Franklin.serve()' 5 | ``` 6 | 7 | Logo is generate by [Surreal Graphics Generator API](https://deepai.org/machine-learning-model/surreal-graphics-generator) 8 | 9 | ![](_assets/favicon.jpg) 10 | -------------------------------------------------------------------------------- /website/_assets/favicon.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/website/_assets/favicon.jpg -------------------------------------------------------------------------------- /website/_assets/images/arch.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/website/_assets/images/arch.png -------------------------------------------------------------------------------- /website/_assets/images/gnu.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/website/_assets/images/gnu.png -------------------------------------------------------------------------------- /website/_assets/msc2.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/GiggleLiu/ModernScientificComputing/e9051873755364160d4f650beb6104021052ba59/website/_assets/msc2.jpg -------------------------------------------------------------------------------- /website/_ignore/2017-12-14-slackapp.md: -------------------------------------------------------------------------------- 1 | --- 2 | layout: post 3 | title: Create your own slack AI with python 4 | --- 5 | 6 | Before reading this page, please go through [tutorial](https://www.fullstackpython.com/blog/build-first-slack-bot-python.html). 7 | 8 | 9 | -------------------------------------------------------------------------------- /website/_ignore/2018-01-02-rbmmps.md: -------------------------------------------------------------------------------- 1 | --- 2 | 75layout: post 3 | title: RBM-MPO ansatz 4 | --- 5 | ## Definition of RBM-MPO ansatz 6 | $$\langle\sigma\vert\psi\rangle=\sum\limits_{\{b_i\},\{\sigma_i'\}}\prod\limits_i O^{\sigma_i,\sigma'_i}_{b_{i-1},b_{i}}f(W,\sigma_i')$$. 7 | 8 | ## Training 9 | 10 | $$\frac{\partial}{\partial W}=\frac{\partial}{\partial\psi}\frac{\partial \psi}{\partial f}\frac{\partial f}{\partial W}$$ is in general not accessable because we have infinitely many $\{\sigma_i'\}$. However, we can sample over $\{\sigma_i'\}$ instead of $\{\sigma_i\}$ and train it with VMC (so called Heisenberg picture). This time, the exploding Hilbert space problem is transformed into how to optimize $O$. 11 | 12 | Impose translational invariance on $O​$, and resort to VUMPO approach to optimize it. -------------------------------------------------------------------------------- /website/_ignore/2018-01-31-qv.md: -------------------------------------------------------------------------------- 1 | --- 2 | layout: post 3 | title: Quantum Representation Power 4 | --- 5 | 6 | Notice the following facts 7 | * The representation power of a noisy quantum device is restricted. 8 | * The representation power of a shallow quantum circuit is restricted. 9 | 10 | I want to give a measure of representation power from measurement results. 11 | Here, I'd like to introduce the concept of "volume of reduced density matrixs (RDM)". 12 | * If the circuit is noisy enough, that fully coupled with environment, its RDM is $-$. 13 | 14 | Questions: 15 | * any one come up with similar idea? 16 | 17 | ### Why this is important 18 | The reason I came up 19 | -------------------------------------------------------------------------------- /website/_ignore/diff.md: -------------------------------------------------------------------------------- 1 | Back-Propagation 2 | 3 | we have a data $x$ 4 | 5 | go through operations $f_1, f_2, f_3 \rightarrow L = f_3(f_2(f_1(x)))$ 6 | 7 | the gradient for $x$ is $\frac{\partial L}{\partial x} = \frac{\partial L}{\partial y_2}\cdot \frac{\partial y_2}{\partial y_1}\cdot \frac{\partial y_1}{\partial x}$ 8 | 9 | so we just remember the input and output of every function, for $y=f_i(x)$, we know $f_i'= g(x, y)$. 10 | 11 | when $x\rightarrow \vec x$, $y\rightarrow \vec y$, 12 | 13 | $\frac{\partial L}{\partial x} = \sum\limits_{y_2}\left(\frac{\partial L}{\partial y_2}\cdot\sum\limits_{\partial y_1}\left(\frac{\partial y_2}{\partial y_1}\cdot \frac{\partial y_1}{\partial x}\right)\right)$ 14 | 15 | Notice $\frac{\partial y_2}{\partial y_1}$ is a matrix, called Jacobian matrix. 16 | 17 | e.g. y = Wx+b 18 | 19 | 20 | 21 | Back-Propagation for RBM 22 | 23 | $$E(x) = x^T\mathbf Wh + b^Th +x^Ta$$ 24 | 25 | $\frac{\partial E}{\partial W_{ij}}=x_ih_j$ 26 | 27 | -------------------------------------------------------------------------------- /website/_layout/foot.html: -------------------------------------------------------------------------------- 1 | 2 | {{ if hasmath }} 3 | {{ insert foot_katex.html }} 4 | {{ end }} 5 | {{ if hascode }} 6 | {{ insert foot_highlight.html }} 7 | {{ end }} 8 | 9 | 10 | -------------------------------------------------------------------------------- /website/_layout/foot_highlight.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | -------------------------------------------------------------------------------- /website/_layout/foot_katex.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | -------------------------------------------------------------------------------- /website/_layout/head.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | {{if hasmath}} {{insert head_katex.html }} {{end}} 7 | {{if hascode}} {{insert head_highlight.html }} {{end}} 8 | 9 | 10 | 11 | {{isdef title}} {{fill title}} {{end}} 12 | 13 | 14 | {{insert header.html}} 15 | 16 | 17 | -------------------------------------------------------------------------------- /website/_layout/head_highlight.html: -------------------------------------------------------------------------------- 1 | 2 | -------------------------------------------------------------------------------- /website/_layout/head_katex.html: -------------------------------------------------------------------------------- 1 | 2 | -------------------------------------------------------------------------------- /website/_layout/header.html: -------------------------------------------------------------------------------- 1 |
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mintoclevel = 2 7 | 8 | # Add here files or directories that should be ignored by Franklin, otherwise 9 | # these files might be copied and, if markdown, processed by Franklin which 10 | # you might not want. Indicate directories by ending the name with a `/`. 11 | # Base files such as LICENSE.md and README.md are ignored by default. 12 | ignore = ["node_modules/", "_ignore/"] 13 | 14 | # RSS (the website_{title, descr, url} must be defined to get RSS) 15 | generate_rss = true 16 | website_title = "Course AMAT5315" 17 | website_descr = "The modern way of learning scientific computing" 18 | prepath = "ModernScientificComputing" 19 | website_url = "https://giggleliu.github.io/ModernScientificComputing" 20 | +++ 21 | 22 | 25 | \newcommand{\R}{\mathbb R} 26 | \newcommand{\scal}[1]{\langle #1 \rangle} 27 | -------------------------------------------------------------------------------- /website/index.md: -------------------------------------------------------------------------------- 1 | @def title = "Modern Scientific Computing" 2 | @def tags = ["jinguo liu", "scientific computing", "julia"] 3 | 4 | # Modern Scientific Computing 5 | 6 | ~~~ 7 |

The modern way of learning scientific computing ☞ github repo

8 |
9 | {{msc}} 10 | ~~~ 11 | -------------------------------------------------------------------------------- /website/msc.md: -------------------------------------------------------------------------------- 1 | @def title = "Modern Scientific Computing" 2 | 3 | # Modern Scientific Computing 4 | ~~~ 5 | {{msc}} 6 | ~~~ 7 | -------------------------------------------------------------------------------- /website/package-lock.json: -------------------------------------------------------------------------------- 1 | { 2 | "requires": true, 3 | "lockfileVersion": 1, 4 | "dependencies": { 5 | "highlight.js": { 6 | "version": "11.7.0", 7 | "resolved": "https://registry.npmjs.org/highlight.js/-/highlight.js-11.7.0.tgz", 8 | "integrity": "sha512-1rRqesRFhMO/PRF+G86evnyJkCgaZFOI+Z6kdj15TA18funfoqJXvgPCLSf0SWq3SRfg1j3HlDs8o4s3EGq1oQ==" 9 | } 10 | } 11 | } 12 | --------------------------------------------------------------------------------