Restructuring, moved KS demo to 2-numeric-like-matlab.ipynb

1-introduction.ipynb

@@ -15,12 +15,12 @@
    "source": [
     "## Julia \n",
     "\n",
-    "  * a new open-source scientific programming language\n",
-    "  * does interactive numerics and graphics like Matlab\n",
-    "  * runs as fast as C, Fortran\n",
-    "  * modern, dynamic, high-level, general-purpose like Python\n",
+    "  * new open-source scientific programming language\n",
+    "  * interactive numerics and graphics like Matlab\n",
+    "  * as fast as C, Fortran\n",
+    "  * extensible, dynamic, general-purpose like Python\n",
     "  * metaprogramming power of LISP\n",
-    "  * open-ended innovation"
+    "  * potential game-changer in scientific computing"
    ]
   },
   {

3-fast-as-C.ipynb

@@ -4,10 +4,28 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Julia is as fast as C or Fortran\n",
+    "# Julia is fast"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "## Performance benchmarks, general algorithms\n",
+    "\n",
+    "Micro-benchmark codes testing iteration, recursion, matrix operations, and I/O, \n",
+    "using identical algorithms in 11 languages. Smaller is better. Results normalized so C = 1.\n",
     "\n",
     "\n",
-    "## Case study: simulation of the Kuramoto-Sivashinksy equation\n",
+    "![language benchmarks plot](figs/benchmarks.svg)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Performance benchmark, Kuramoto-Sivashinksy equation\n",
     "\n",
     "The Kuramoto-Sivashinsky (KS) equation is a nonlinear time-evolving partial differential equation (PDE) on a 1d spatial domain.\n",
     "\n",
@@ -18,18 +36,26 @@
     "where $x$ is space, $t$ is time, and subscripts indicate differentiation. We assume a spatial domain $x \\in [0, L_x]$ with periodic boundary conditions and initial condition $u(x,0) = u_0(x)$. \n",
     "\n",
     "A simulation for $u_0 = \\cos(x) + 0.1 \\sin x/8  + 0.01 \\cos x/32$ and $L_x = 64\\pi$.\n",
-    "![alternative text](figs/ksdynamics.svg)\n",
+    "![Kuramoto-Sivashinsky u(x,t)](figs/ksdynamics.svg)\n",
     "\n",
     "## The benchmark algorithm: KS-CNAB2\n",
     "\n",
-    "We implemented the same numerical integration method for the KS equation in six languages. The method uses finite Fourier expansions to discretize space and semi-implicit finite-differencing to discretize time, specifically the 2nd-order rank-Nicolson/Adams-Bashforth (CNAB2) timestepping formula. All languages use the same FFTW library for the Fourier transforms. \n"
+    "We implemented the same numerical integration method for the KS equation in six languages. The method uses finite Fourier expansions to discretize space and semi-implicit finite-differencing to discretize time, specifically the 2nd-order Crank-Nicolson/Adams-Bashforth (CNAB2) time-stepping formula. This transforms the above PDE to the following iterated linear algebra problem\n",
+    "\n",
+    "\n",
+    "\\begin{equation*}\n",
+    "A \\, u^{n+1} = B \\, u^n + \\frac{3 \\Delta t}{2} N^n -  \\frac{\\Delta t}{2}N^{n-1}\n",
+    "\\end{equation*}\n",
+    "\n",
+    "where $u^n$ is a vector of Fourier coefficients at time $t = n \\Delta t$, $A$ and $B$ are diagonal matrices related to the linear terms in the PDE, and $N^n$ is the Fourier transform of the nonlinear term $u u_x$ at $t = n \\Delta t$. \n",
+    "See my [julia-pde-benchmark talk](https://github.com/johnfgibson/julia-pde-benchmark/blob/master/1-Kuramoto-Sivashinksy-benchmark.ipynb) talk for mathematical details. All languages use the same FFTW library for the Fourier transforms."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Benchmark results: execution time versus simulation size $N_x$\n",
+    "## Benchmark results: execution time versus number of gridpoints $N_x$\n",
     "\n",
     "![alternate text](figs/cputime_vs_size.svg)\n",
     "\n",
@@ -4673,28 +4699,14 @@
     "collapsed": true
    },
    "source": [
-    "## Benchmark codes\n",
+    "## KS-CNAB2 benchmark codes\n",
     "\n",
-    "  * [ksbenchmark.py](codes/ksbenchmark.py), Python\n",
-    "  * [ksbenchmark.m](codes/ksbenchmark.m), Matlab\n",
-    "  * [ksbenchmark.jl](codes/ksbenchmark.jl), Julia \n",
-    "  * [ksbenchmark.c](codes/ksbenchmark.c), C\n",
-    "  * [ksbenchmark.cpp](codes/ksbenchmark.cpp), C++ \n",
-    "  * [ksbenchmark.f90](codes/ksbenchmark.f90), Fortran\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "\n",
-    "# Julia performance benchmarks\n",
-    "\n",
-    "Micro-benchmark codes testing iteration, recursion, matrix operations, and I/O, \n",
-    "using identical algorithms in 11 languages. Smaller is better. Results normalized so C = 1.\n",
-    "\n",
-    "\n",
-    "![language benchmarks plot](figs/benchmarks.svg)\n"
+    "  * [ksbenchmark.py](ks-codes/ksbenchmark.py), Python\n",
+    "  * [ksbenchmark.m](ks-codes/ksbenchmark.m), Matlab\n",
+    "  * [ksbenchmark.jl](ks-codes/ksbenchmark.jl), Julia \n",
+    "  * [ksbenchmark.c](ks-codes/ksbenchmark.c), C\n",
+    "  * [ksbenchmark.cpp](ks-codes/ksbenchmark.cpp), C++ \n",
+    "  * [ksbenchmark.f90](ks-codes/ksbenchmark.f90), Fortran\n"
    ]
   },
   {

6-conclusions.ipynb

@@ -6,32 +6,30 @@
    "source": [
     "# Conclusions\n",
     "\n",
-    "### Julia \n",
-    "  * well-designed open-source scientific programming language \n",
-    "  * great numeric types, libraries\n",
-    "  * great general-purpose types, libraries\n",
-    "  * modern, dynamic, flexible\n",
-    "  * roughly as fast as compiled C\n",
-    "  * easy learning curve\n",
-    "  * dynamism and metaprogramming make new things possible\n",
-    "  * **solves the two-language problem:** from tinkering to HPC\n",
+    "  \n",
+    "### *Julia solves the two-language problem*\n",
+    "   * from interactive exploration to high-performance computing\n",
+    "   \n",
+    "### *Julia opens new doors*\n",
+    "   * exact and high-precision calculations \n",
+    "   * higher-level abstraction of parallelism   \n",
+    "   * numerics and general-purpose computing\n",
+    "   * scientific computing and computer science\n",
+    "   \n",
+    "### *Openness fosters innovation* \n",
     "\n",
-    "\n",
-    "### Didn't cover\n",
-    "  * [parallel computing](http://docs.julialang.org/en/release-0.5/manual/parallel-computing/)\n",
-    "  * [general-purpose libraries:](http://docs.julialang.org/en/release-0.5/#stdlib) Strings, Sets, Arrays, Tuples, Dicts, Time, Streams, Network, Tasks,...\n",
-    "  * [documentation](http://docs.julialang.org/en/release-0.5/)\n",
-    "  * [installation](http://julialang.org/downloads/)\n",
-    "  * required libraries: LLVM, OpenBLAS, LAPACK, ARPACK, FFTW, GNU arb-size int & float, ...\n",
-    "  * [calling C and Fortran](http://docs.julialang.org/en/stable/manual/calling-c-and-fortran-code/)\n",
+    "#### Didn't cover\n",
+    "  * [installation](http://julialang.org/downloads/), [documentation](http://docs.julialang.org/en/stable/)  \n",
+    "  * [Juno](http://junolab.org/) integrated development environment, [Gallium](https://github.com/Keno/Gallium.jl) debugger.\n",
+    "  * [parallel computing](http://docs.julialang.org/en/stable/manual/parallel-computing/)\n",
+    "  * [interoperability](http://docs.julialang.org/en/stable/manual/calling-c-and-fortran-code/) with other languages\n",
     "  * [modules](ocs.julialang.org/en/stable/manual/modules/) and [package manager](http://docs.julialang.org/en/stable/manual/packages/)\n",
-    "  * [documentation](http://docs.julialang.org/en/stable/)\n",
-    "  * [code hosting on git](https://github.com/JuliaLang/juliasource)\n",
-    "  * running Julia on [JuliaBox](https://juliabox.com/) or from command-line\n",
-    " \n",
-    "### Acknowledgements\n",
+    "  * Julia community: [language development](https://github.com/JuliaLang/juliasource), [discussion forum](https://discourse.julialang.org)\n",
+    "  * running Julia on [JuliaBox](https://juliabox.com/)\n",
+    "\n",
+    "#### Acknowledgements\n",
     "  * [David Sanders](http://sistemas.fciencias.unam.mx/~dsanders/), Physics, Universidad Nacional Autónoma de México \n",
-    "  * [Andreas Noack](http://andreasnoack.github.io/academiccv.html), CS and AI Lab, MIT\n",
+    "  * [Andreas Noack](http://andreasnoack.github.io/academiccv.html), Julia Computing\n",
     "  * The Julia team\n",
     "  * NSF grant #1554149"
    ]
@@ -48,9 +46,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Julia 0.5.0",
+   "display_name": "Julia 0.6.0",
    "language": "julia",
-   "name": "julia-0.5"
+   "name": "julia-0.6"
   },
   "language_info": {
    "file_extension": ".jl",