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Merge branch 'mdl_test' into 'hannes-philipp'
Add docu and validation files See merge request naaice/tug!7
This commit is contained in:
Marco De Lucia
commit
f5a59def6d
@ -536,4 +536,3 @@ left derivative becomes zero and we are left with:
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&\displaystyle =\frac{\alpha_{i-1/2}}{\Delta x^2} (C_{i-1} - C_i)
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\end{aligned}
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\end{equation}
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114
doc/ValidationHetDiff.org
Normal file
114
doc/ValidationHetDiff.org
Normal file
@ -0,0 +1,114 @@
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#+TITLE: 2D Validation Examples
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#+AUTHOR: MDL <delucia@gfz-potsdam.de>
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#+DATE: 2023-07-31
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#+STARTUP: inlineimages
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#+LATEX_CLASS_OPTIONS: [a4paper,9pt]
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#+LATEX_HEADER: \usepackage{fullpage}
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#+LATEX_HEADER: \usepackage{amsmath, systeme}
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#+LATEX_HEADER: \usepackage{graphicx}
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#+LATEX_HEADER: \usepackage{}
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#+OPTIONS: toc:nil
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* Simple setup using deSolve/ReacTran
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- Square of side 10
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- Discretization: 11 \times 11 cells
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- All boundaries closed
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- Initial state: 0 everywhere, 1 in the center (6,6)
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- Time step: 1 s, 10 iterations
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The matrix of spatially variable diffusion coefficients \alpha is
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constant in 4 quadrants:
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\alpha_{x,y} =
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| 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
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| 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
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| 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
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| 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
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| 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
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| 1 | 1 | 1 | 1 | 1 | 1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
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| 1 | 1 | 1 | 1 | 1 | 1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
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| 1 | 1 | 1 | 1 | 1 | 1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
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| 1 | 1 | 1 | 1 | 1 | 1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
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| 1 | 1 | 1 | 1 | 1 | 1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
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| 1 | 1 | 1 | 1 | 1 | 1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
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The relevant part of the R script used to produce these results is
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presented in listing 1; the whole script is at [[file:scripts/HetDiff.R]].
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A visualization of the output of the reference simulation is given in
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figure [[#fig:1][1]].
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Note: all results from this script are stored in the =outc= matrix by
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the =deSolve= function. I stored a different version into
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[[file:../scripts/gold/HetDiff1.csv]]: this file contains 11 columns (one
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for each time step including initial conditions) and 121 rows, one for
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each domain element, with no headers.
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#+caption: Result of ReacTran/deSolve solution of the above problem at 4
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[[./images/deSolve_AlphaHet1.png]]
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#+name: lst:1
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#+begin_src R :language R :frame single :caption Listing 1, generate reference simulation using R packages deSolve/ReacTran :captionpos b :label lst:1
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library(ReacTran)
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library(deSolve)
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## harmonic mean
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harm <- function(x,y) {
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if (length(x) != 1 || length(y) != 1)
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stop("x & y have different lengths")
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2/(1/x+1/y)
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}
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N <- 11 # number of grid cells
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ini <- 1 # initial value at x=0
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N2 <- ceiling(N/2)
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L <- 10 # domain side
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## Define diff.coeff per cell, in 4 quadrants
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alphas <- matrix(0, N, N)
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alphas[1:N2, 1:N2] <- 1
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alphas[1:N2, seq(N2+1,N)] <- 0.1
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alphas[seq(N2+1,N), 1:N2] <- 0.01
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alphas[seq(N2+1,N), seq(N2+1,N)] <- 0.001
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cmpharm <- function(x) {
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y <- c(0, x, 0)
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ret <- numeric(length(x)+1)
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for (i in seq(2, length(y))) {
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ret[i-1] <- harm(y[i], y[i-1])
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}
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ret
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}
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## Construction of the 2D grid
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x.grid <- setup.grid.1D(x.up = 0, L = L, N = N)
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y.grid <- setup.grid.1D(x.up = 0, L = L, N = N)
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grid2D <- setup.grid.2D(x.grid, y.grid)
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dx <- dy <- L/N
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D.grid <- list()
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## Diffusion coefs on x-interfaces
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D.grid$x.int <- apply(alphas, 1, cmpharm)
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## Diffusion coefs on y-interfaces
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D.grid$y.int <- t(apply(alphas, 2, cmpharm))
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# The model
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Diff2Dc <- function(t, y, parms) {
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CONC <- matrix(nrow = N, ncol = N, data = y)
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dCONC <- tran.2D(CONC, dx = dx, dy = dy, D.grid = D.grid)$dC
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return(list(dCONC))
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}
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## initial condition: 0 everywhere, except in central point
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y <- matrix(nrow = N, ncol = N, data = 0)
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y[N2, N2] <- ini # initial concentration in the central point...
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## solve for 10 time units
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times <- 0:10
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outc <- ode.2D(y = y, func = Diff2Dc, t = times, parms = NULL,
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dim = c(N, N), lrw = 1860000)
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#+end_src
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BIN
doc/images/deSolve_AlphaHet1.png
Normal file
BIN
doc/images/deSolve_AlphaHet1.png
Normal file
Binary file not shown.
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After Width: | Height: | Size: 19 KiB |
@ -2,13 +2,14 @@ add_executable(first_example first_example.cpp)
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add_executable(second_example second_example.cpp)
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add_executable(boundary_example1D boundary_example1D.cpp)
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add_executable(FTCS_2D_proto_example FTCS_2D_proto_example.cpp)
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add_executable(FTCS_2D_proto_example_mdl FTCS_2D_proto_example_mdl.cpp)
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add_executable(FTCS_1D_proto_example FTCS_1D_proto_example.cpp)
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add_executable(reference-FTCS_2D_closed reference-FTCS_2D_closed.cpp)
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target_link_libraries(first_example tug)
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target_link_libraries(second_example tug)
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target_link_libraries(boundary_example1D tug)
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target_link_libraries(FTCS_2D_proto_example tug)
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target_link_libraries(FTCS_2D_proto_example_mdl tug)
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target_link_libraries(FTCS_1D_proto_example tug)
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target_link_libraries(reference-FTCS_2D_closed tug)
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# target_link_libraries(FTCS_2D_proto_example easy_profiler)
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# target_link_libraries(FTCS_2D_proto_example easy_profiler)
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77
examples/FTCS_2D_proto_closed_mdl.cpp
Normal file
77
examples/FTCS_2D_proto_closed_mdl.cpp
Normal file
@ -0,0 +1,77 @@
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/**
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* @file FTCS_2D_proto_example.cpp
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* @author Hannes Signer, Philipp Ungrund
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* @brief Creates a prototypical standard TUG simulation in 2D with FTCS approach
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* and constant boundary condition
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*
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*/
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#include <tug/Simulation.hpp>
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int main(int argc, char *argv[]) {
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// **************
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// **** GRID ****
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// **************
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// create a grid with a 20 x 20 field
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int row = 64;
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int col = 64;
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int n2 = row/2-1;
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Grid grid = Grid(row,col);
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// (optional) set the domain, e.g.:
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// grid.setDomain(20, 20);
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// (optional) set the concentrations, e.g.:
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// MatrixXd concentrations = MatrixXd::Constant(20,20,1000); // #row,#col,value
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MatrixXd concentrations = MatrixXd::Constant(row,col,0);
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concentrations(n2,n2) = 1;
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concentrations(n2,n2+1) = 1;
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concentrations(n2+1,n2) = 1;
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concentrations(n2+1,n2+1) = 1;
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grid.setConcentrations(concentrations);
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// (optional) set alphas of the grid, e.g.:
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MatrixXd alphax = MatrixXd::Constant(row, col, 1E-4); // row,col,value
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MatrixXd alphay = MatrixXd::Constant(row, col, 1E-6); // row,col,value
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grid.setAlpha(alphax, alphay);
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// ******************
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// **** BOUNDARY ****
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// ******************
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// create a boundary with constant values
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Boundary bc = Boundary(grid);
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// (optional) set boundary condition values for one side, e.g.:
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bc.setBoundarySideClosed(BC_SIDE_LEFT); // side,values
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bc.setBoundarySideClosed(BC_SIDE_RIGHT);
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bc.setBoundarySideClosed(BC_SIDE_TOP);
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bc.setBoundarySideClosed(BC_SIDE_BOTTOM);
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// ************************
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// **** SIMULATION ENV ****
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// ************************
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// set up a simulation environment
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Simulation simulation = Simulation(grid, bc, FTCS_APPROACH); // grid,boundary,simulation-approach
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// (optional) set the timestep of the simulation
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simulation.setTimestep(1000); // timestep
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// (optional) set the number of iterations
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simulation.setIterations(5);
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// (optional) set kind of output [CSV_OUTPUT_OFF (default), CSV_OUTPUT_ON, CSV_OUTPUT_VERBOSE]
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simulation.setOutputCSV(CSV_OUTPUT_OFF);
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// **** RUN SIMULATION ****
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// run the simulation
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simulation.run();
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return 0;
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}
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77
examples/FTCS_2D_proto_example_mdl.cpp
Normal file
77
examples/FTCS_2D_proto_example_mdl.cpp
Normal file
@ -0,0 +1,77 @@
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/**
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* @file FTCS_2D_proto_example.cpp
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* @author Hannes Signer, Philipp Ungrund
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* @brief Creates a prototypical standard TUG simulation in 2D with FTCS approach
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* and constant boundary condition
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*
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*/
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#include <tug/Simulation.hpp>
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int main(int argc, char *argv[]) {
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// **************
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// **** GRID ****
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// **************
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// create a grid with a 20 x 20 field
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int row = 64;
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int col = 64;
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int n2 = row/2-1;
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Grid grid = Grid(row,col);
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// (optional) set the domain, e.g.:
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// grid.setDomain(20, 20);
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// (optional) set the concentrations, e.g.:
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// MatrixXd concentrations = MatrixXd::Constant(20,20,1000); // #row,#col,value
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MatrixXd concentrations = MatrixXd::Constant(row,col,0);
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concentrations(n2,n2) = 1;
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concentrations(n2,n2+1) = 1;
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concentrations(n2+1,n2) = 1;
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concentrations(n2+1,n2+1) = 1;
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grid.setConcentrations(concentrations);
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// (optional) set alphas of the grid, e.g.:
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MatrixXd alphax = MatrixXd::Constant(row, col, 1E-4); // row,col,value
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MatrixXd alphay = MatrixXd::Constant(row, col, 1E-6); // row,col,value
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grid.setAlpha(alphax, alphay);
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// ******************
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// **** BOUNDARY ****
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// ******************
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// create a boundary with constant values
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Boundary bc = Boundary(grid);
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// (optional) set boundary condition values for one side, e.g.:
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bc.setBoundarySideConstant(BC_SIDE_LEFT, 0); // side,values
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bc.setBoundarySideConstant(BC_SIDE_RIGHT, 0);
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bc.setBoundarySideConstant(BC_SIDE_TOP, 0);
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bc.setBoundarySideConstant(BC_SIDE_BOTTOM, 0);
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// ************************
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// **** SIMULATION ENV ****
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// ************************
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// set up a simulation environment
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Simulation simulation = Simulation(grid, bc, FTCS_APPROACH); // grid,boundary,simulation-approach
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// (optional) set the timestep of the simulation
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simulation.setTimestep(1000); // timestep
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// (optional) set the number of iterations
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simulation.setIterations(5);
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// (optional) set kind of output [CSV_OUTPUT_OFF (default), CSV_OUTPUT_ON, CSV_OUTPUT_VERBOSE]
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simulation.setOutputCSV(CSV_OUTPUT_OFF);
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// **** RUN SIMULATION ****
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// run the simulation
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simulation.run();
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return 0;
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}
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@ -458,7 +458,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.4"
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"version": "3.9.7"
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},
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"orig_nbformat": 4
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},
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@ -1,4 +1,4 @@
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## Time-stamp: "Last modified 2023-05-11 17:31:41 delucia"
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## Time-stamp: "Last modified 2023-07-31 14:26:49 delucia"
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## Brutal implementation of 2D ADI scheme
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## Square NxN grid with dx=dy=1
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237
scripts/HetDiff.R
Normal file
237
scripts/HetDiff.R
Normal file
@ -0,0 +1,237 @@
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## Time-stamp: "Last modified 2023-07-31 16:28:48 delucia"
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library(ReacTran)
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library(deSolve)
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options(width=114)
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## harmonic mean
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harm <- function(x,y) {
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if (length(x) != 1 || length(y) != 1)
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stop("x & y have different lengths")
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2/(1/x+1/y)
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}
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## harm(0, 1) ## 0
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## harm(1, 2) ## 0
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############# Providing coeffs on the interfaces
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N <- 11 # number of grid cells
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ini <- 1 # initial value at x=0
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N2 <- ceiling(N/2)
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L <- 10 # domain side
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|
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## Define diff.coeff per cell, in 4 quadrants
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alphas <- matrix(0, N, N)
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alphas[1:N2, 1:N2] <- 1
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alphas[1:N2, seq(N2+1,N)] <- 0.1
|
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alphas[seq(N2+1,N), 1:N2] <- 0.01
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alphas[seq(N2+1,N), seq(N2+1,N)] <- 0.001
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image(log10(alphas), col=heat.colors(4))
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|
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r180 <- function(x) {
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xx <- rev(x)
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dim(xx) <- dim(x)
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xx
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}
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mirror <- function (x) {
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xx <- as.data.frame(x)
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xx <- rev(xx)
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xx <- as.matrix(xx)
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xx
|
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}
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array_to_LaTeX <- function(arr) {
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rows <- apply(arr, MARGIN=1, paste, collapse = " & ")
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matrix_string <- paste(rows, collapse = " \\\\ ")
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return(paste("\\begin{bmatrix}", matrix_string, "\\end{bmatrix}"))
|
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}
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|
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|
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cat(array_to_LaTeX(mirror(r180(alphas))))
|
||||
|
||||
|
||||
|
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r180(alphas)
|
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|
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filled.contour(log10(alphas), col=terrain.colors(4), nlevels=4)
|
||||
|
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cmpharm <- function(x) {
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y <- c(0, x, 0)
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ret <- numeric(length(x)+1)
|
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for (i in seq(2, length(y))) {
|
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ret[i-1] <- harm(y[i], y[i-1])
|
||||
}
|
||||
ret
|
||||
}
|
||||
|
||||
## Construction of the 2D grid
|
||||
x.grid <- setup.grid.1D(x.up = 0, L = L, N = N)
|
||||
y.grid <- setup.grid.1D(x.up = 0, L = L, N = N)
|
||||
grid2D <- setup.grid.2D(x.grid, y.grid)
|
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|
||||
D.grid <- list()
|
||||
|
||||
# Diffusion on x-interfaces
|
||||
D.grid$x.int <- apply(alphas, 1, cmpharm)
|
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|
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# Diffusion on y-interfaces
|
||||
## matrix(nrow = N, ncol = N+1, data = rep(c(rep(1E-1, 50),5.E-1,rep(1., 50)), 100) )
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D.grid$y.int <- t(apply(alphas, 2, cmpharm))
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||||
|
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dx <- L/N
|
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dy <- L/N
|
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|
||||
# The model equations
|
||||
Diff2Dc <- function(t, y, parms) {
|
||||
CONC <- matrix(nrow = N, ncol = N, data = y)
|
||||
dCONC <- tran.2D(CONC, dx = dx, dy = dy, D.grid = D.grid)$dC
|
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return(list(dCONC))
|
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}
|
||||
|
||||
## initial condition: 0 everywhere, except in central point
|
||||
y <- matrix(nrow = N, ncol = N, data = 0)
|
||||
y[N2, N2] <- ini # initial concentration in the central point...
|
||||
|
||||
## solve for 10 time units
|
||||
times <- 0:10
|
||||
outc <- ode.2D(y = y, func = Diff2Dc, t = times, parms = NULL,
|
||||
dim = c(N, N), lrw = 1860000)
|
||||
|
||||
outtimes <- c(0, 4, 7, 10)
|
||||
|
||||
## NB: assuming current working dir is "tug"
|
||||
cairo_pdf("doc/images/deSolve_AlphaHet1.pdf", family="serif", width=12, height=12)
|
||||
image(outc, ask = FALSE, mfrow = c(2, 2), main = paste("time", outtimes),
|
||||
legend = TRUE, add.contour = FALSE, subset = time %in% outtimes,
|
||||
xlab="",ylab="", axes=FALSE, asp=1)
|
||||
dev.off()
|
||||
|
||||
## outc is a matrix with 11 rows and 122 columns (first column is
|
||||
## simulation time);
|
||||
str(outc)
|
||||
|
||||
## extract only the results and transpose the matrix for storage
|
||||
ret <- data.matrix(t(outc[ , -1]))
|
||||
rownames(ret) <- NULL
|
||||
|
||||
## NB: assuming current working dir is "tug"
|
||||
data.table::fwrite(ret, file="scripts/gold/HetDiff1.csv", col.names=FALSE)
|
||||
|
||||
|
||||
|
||||
|
||||
#################### 2D visualization
|
||||
|
||||
## Version of Rmufits::PlotCartCellData with the ability to fix the
|
||||
## "breaks" for color coding of 2D simulations
|
||||
Plot2DCellData <- function(data, grid, nx, ny, contour = TRUE,
|
||||
nlevels = 12, breaks, palette = "heat.colors",
|
||||
rev.palette = TRUE, scale = TRUE, plot.axes=TRUE, ...) {
|
||||
if (!missing(grid)) {
|
||||
xc <- unique(sort(grid$cell$XCOORD))
|
||||
yc <- unique(sort(grid$cell$YCOORD))
|
||||
nx <- length(xc)
|
||||
ny <- length(yc)
|
||||
if (!length(data) == nx * ny)
|
||||
stop("Wrong nx, ny or grid")
|
||||
} else {
|
||||
xc <- seq(1, nx)
|
||||
yc <- seq(1, ny)
|
||||
}
|
||||
z <- matrix(round(data, 6), ncol = nx, nrow = ny, byrow = TRUE)
|
||||
pp <- t(z[rev(seq(1, nrow(z))), ])
|
||||
|
||||
if (missing(breaks)) {
|
||||
breaks <- pretty(data, n = nlevels)
|
||||
}
|
||||
|
||||
breakslen <- length(breaks)
|
||||
colors <- do.call(palette, list(n = breakslen - 1))
|
||||
if (rev.palette)
|
||||
colors <- rev(colors)
|
||||
if (scale) {
|
||||
par(mfrow = c(1, 2))
|
||||
nf <- layout(matrix(c(1, 2), 1, 2, byrow = TRUE), widths = c(4,
|
||||
1))
|
||||
}
|
||||
par(las = 1, mar = c(5, 5, 3, 1))
|
||||
image(xc, yc, pp, xlab = "X [m]", ylab = "Y[m]", las = 1, asp = 1,
|
||||
breaks = breaks, col = colors, axes = FALSE, ann=plot.axes,
|
||||
...)
|
||||
|
||||
if (plot.axes) {
|
||||
axis(1)
|
||||
axis(2)
|
||||
}
|
||||
if (contour)
|
||||
contour(unique(sort(xc)), unique(sort(yc)), pp, breaks = breaks,
|
||||
add = TRUE)
|
||||
if (scale) {
|
||||
par(las = 1, mar = c(5, 1, 5, 5))
|
||||
PlotImageScale(data, breaks = breaks, add.axis = FALSE,
|
||||
axis.pos = 4, col = colors)
|
||||
axis(4, at = breaks)
|
||||
}
|
||||
invisible(pp)
|
||||
}
|
||||
|
||||
PlotImageScale <- function(z, zlim, col = grDevices::heat.colors(12), breaks,
|
||||
axis.pos = 1, add.axis = TRUE, ...) {
|
||||
if (!missing(breaks)) {
|
||||
if (length(breaks) != (length(col) + 1)) {
|
||||
stop("must have one more break than colour")
|
||||
}
|
||||
}
|
||||
if (missing(breaks) & !missing(zlim)) {
|
||||
breaks <- seq(zlim[1], zlim[2], length.out = (length(col) + 1))
|
||||
}
|
||||
if (missing(breaks) & missing(zlim)) {
|
||||
zlim <- range(z, na.rm = TRUE)
|
||||
zlim[2] <- zlim[2] + c(zlim[2] - zlim[1]) * (0.001)
|
||||
zlim[1] <- zlim[1] - c(zlim[2] - zlim[1]) * (0.001)
|
||||
breaks <- seq(zlim[1], zlim[2], length.out = (length(col) + 1))
|
||||
}
|
||||
|
||||
poly <- vector(mode = "list", length(col))
|
||||
for (i in seq(poly)) {
|
||||
poly[[i]] <- c(breaks[i], breaks[i + 1], breaks[i + 1],
|
||||
breaks[i])
|
||||
}
|
||||
if (axis.pos %in% c(1, 3)) {
|
||||
ylim <- c(0, 1)
|
||||
xlim <- range(breaks)
|
||||
}
|
||||
if (axis.pos %in% c(2, 4)) {
|
||||
ylim <- range(breaks)
|
||||
xlim <- c(0, 1)
|
||||
}
|
||||
plot(1, 1, t = "n", ylim = ylim, xlim = xlim, axes = FALSE,
|
||||
xlab = "", ylab = "", xaxs = "i", yaxs = "i", ...)
|
||||
for (i in seq(poly)) {
|
||||
if (axis.pos %in% c(1, 3)) {
|
||||
polygon(poly[[i]], c(0, 0, 1, 1), col = col[i], border = NA)
|
||||
}
|
||||
if (axis.pos %in% c(2, 4)) {
|
||||
polygon(c(0, 0, 1, 1), poly[[i]], col = col[i], border = NA)
|
||||
}
|
||||
}
|
||||
box()
|
||||
if (add.axis) {
|
||||
axis(axis.pos)
|
||||
}
|
||||
}
|
||||
|
||||
cairo_pdf("AlphaHet1.pdf", family="serif", width=8)
|
||||
par(mar = c(1,1,1,1))
|
||||
Plot2DCellData(log10(mirror(alphas)), nx=N, ny=N, nlevels=5, palette = terrain.colors, contour=FALSE, plot.axes=FALSE,
|
||||
scale = F,
|
||||
main=expression(log[10](alpha)))
|
||||
text(3,8,"1")
|
||||
text(8,8,"0.1")
|
||||
text(3,3,"0.01")
|
||||
text(8,3,"0.001")
|
||||
# title("Diff. Coefficients (log10)")
|
||||
dev.off()
|
||||
|
||||
121
scripts/gold/HetDiff1.csv
Normal file
121
scripts/gold/HetDiff1.csv
Normal file
@ -0,0 +1,121 @@
|
||||
0,1.15723009391899e-05,0.000573422585977779,0.00271483227696389,0.00592017488450261,0.00919024372055321,0.0119992110381186,0.01421611640169,0.0158871549414673,0.0171115136326332,0.0179901833258047
|
||||
0,4.32496365970161e-05,0.00110003761455522,0.0038588402926536,0.00723956931728921,0.0103665385368182,0.0129275133140941,0.0149018727052112,0.0163722917415511,0.0174425542133075,0.0182067473313329
|
||||
0,0.000156410551955808,0.0022501860978233,0.00596846775043427,0.00951979828485079,0.0123439077799255,0.0144650737976258,0.0160242190667615,0.0171550743320483,0.0179654704632021,0.0185369538227271
|
||||
0,0.000449900131743341,0.00397802650798475,0.0085351147388942,0.0120552559726064,0.0144482796517419,0.0160547847343675,0.0171511707942764,0.0179099936829702,0.0184375120234885,0.0188001645647094
|
||||
0,0.00096247784605253,0.00575161551352107,0.0106416083625011,0.0139078265679269,0.0158706072121663,0.0170493964826529,0.0177834857154376,0.0182584391833927,0.018573228563985,0.0187811039627322
|
||||
0,0.00139148060908994,0.00653728609085073,0.0112226963812925,0.0141895931925161,0.0159026822227563,0.0168925530607027,0.0174883152516615,0.017865325174865,0.0181135647391488,0.0182789062492789
|
||||
0,7.88755181655377e-05,0.000890855516524495,0.0025489601065516,0.00451888907818989,0.00640234215109739,0.00803400181298965,0.00938380805959316,0.0104782803692741,0.0113602330285538,0.0120715601783272
|
||||
0,1.96835046894113e-06,5.20032828635902e-05,0.000248131836356188,0.000630746867714403,0.00117274437938983,0.00182064447664627,0.00252211668991391,0.00323643607872941,0.00393564702867779,0.00460249317726503
|
||||
0,4.05263620284678e-08,2.41553600349545e-06,1.87665958722685e-05,6.74081501157623e-05,0.000163264089823103,0.000313023273063137,0.000515631508985307,0.000764816320228696,0.00105167332970099,0.00136658044925295
|
||||
0,7.12888460576857e-10,9.36408593803959e-08,1.16671799220012e-06,5.86484773654181e-06,1.84017858631692e-05,4.34716444970184e-05,8.51739231661631e-05,0.000146375097555955,0.000228524220562364,0.000331765311847696
|
||||
0,1.11266213313442e-11,3.21569209939452e-09,6.45997582539074e-08,4.58674913815976e-07,1.88637915450085e-06,5.56437226690733e-06,1.31531030829188e-05,2.6577288329037e-05,4.78110315422556e-05,7.86848274922097e-05
|
||||
0,4.35985871981009e-05,0.0011173013784839,0.00393465640259938,0.00738648425859891,0.0105643563174128,0.0131485926879987,0.0151246465122267,0.016583690239707,0.0176362908990393,0.0183809352240671
|
||||
0,0.000162940275870536,0.00214415472789055,0.0055971341202626,0.00904266600518215,0.0119317484324307,0.01418453738493,0.0158744170951516,0.0171103507405317,0.0179967639568099,0.0186199630282087
|
||||
0,0.000589272728343116,0.00438867743664915,0.00866893626959719,0.0119151946783314,0.0142428604635392,0.0159134847420158,0.0171142649822806,0.0179721981758363,0.0185775454158148,0.0189955063245207
|
||||
0,0.00169526769334991,0.00776694628989879,0.0124247154337811,0.0151382671118746,0.0167367107498905,0.0177366662921586,0.0183940071716407,0.0188368236363926,0.0191342578330509,0.0193277227804878
|
||||
0,0.00362839452566188,0.0112526737744286,0.0155521246084951,0.0175590393037948,0.0184985843185778,0.0189571544442947,0.0191923705608016,0.0193168273546316,0.0193791769704849,0.0194019806796609
|
||||
0,0.00525177970919126,0.0128429513741672,0.0165189505188843,0.0180778870279157,0.0187197075826292,0.018968965691842,0.0190518322037241,0.0190652772723224,0.0190482483782045,0.019016041284815
|
||||
0,0.000385153961868949,0.00229577940499986,0.00480460165448024,0.00711204718132809,0.0089909576548431,0.0104472162269959,0.0115548772926463,0.0123946614477843,0.0130350658282232,0.013528343285464
|
||||
0,1.16858258297074e-05,0.000164584714174317,0.000570116218846185,0.00119271144355875,0.00194723110061389,0.00275621955267251,0.00356441433332025,0.00433765719695555,0.00505760032168857,0.00571654514201105
|
||||
0,2.81208380577636e-07,8.97423573740115e-06,5.03422264992399e-05,0.000147427646174569,0.000310274427544454,0.000536832367026033,0.000817602280027168,0.00113989443932459,0.00149069663261676,0.00185828031564749
|
||||
0,5.63399964199174e-09,3.96964588417007e-07,3.55564115271452e-06,1.44716592579598e-05,3.91537025779409e-05,8.28348829677685e-05,0.000148977185800308,0.000239043494747069,0.00035275053097983,0.000488513445484224
|
||||
0,9.84398346768558e-11,1.5293568296117e-08,2.20334810416761e-07,1.26108145384204e-06,4.44865566281344e-06,1.16871019830672e-05,2.52195633384727e-05,4.73253788486059e-05,8.00591501276681e-05,0.000125072519296284
|
||||
0,0.00015939225040812,0.00233357034425003,0.00625562530069953,0.0100135877171516,0.0129676882444301,0.0151374162693059,0.0166874294020243,0.0177764984876221,0.0185308441084237,0.0190433426894296
|
||||
0,0.000595680647430986,0.0044801608514742,0.00890743169921897,0.0122772025886856,0.0146734676860174,0.0163633416618241,0.0175504470842378,0.0183769265178609,0.018943746718196,0.019322547574371
|
||||
0,0.00215448195385171,0.0091767592756406,0.0138199838635887,0.0162232592499362,0.0175799863177681,0.0184333811027871,0.0190005234819769,0.0193808295698239,0.0196287328140203,0.01977995018463
|
||||
0,0.00619992143295609,0.0162622253524985,0.0198667054266907,0.0207089785376823,0.0207820327860086,0.0206824193920932,0.0205605370395911,0.0204471756023412,0.0203412141522796,0.0202389042951594
|
||||
0,0.0132779136133337,0.0236231555894036,0.0250044710521133,0.0242144479160946,0.0231938485225262,0.0223380815152074,0.0216793603038312,0.0211797341820616,0.020794392809717,0.0204895366674834
|
||||
0,0.0192489696423083,0.0271184370488408,0.026840217635384,0.0252838506050641,0.023849962885927,0.0227245048675836,0.0218698389880889,0.0212219274277141,0.0207240679736698,0.020334308600127
|
||||
0,0.00188379770767293,0.00657190925731914,0.0104892667525962,0.0130700680836906,0.0146349533533907,0.015535980568487,0.0160269602381333,0.0162728756742906,0.0163767130755721,0.016400710298742
|
||||
0,7.01829175866307e-05,0.000581093706531354,0.00153370940121776,0.00269094081762158,0.00386803514667116,0.00496316154582596,0.00593261862345271,0.00676642929553236,0.0074719703393928,0.00806413175855109
|
||||
0,1.97847089603411e-06,3.69925955384929e-05,0.000157406497985584,0.000384860592255597,0.000709846476804252,0.0011079382186538,0.00155170108970297,0.00201681216519113,0.00248426641823041,0.00294058581228933
|
||||
0,4.51078087575571e-08,1.85104501980116e-06,1.25057013282593e-05,4.22892094350572e-05,9.98395815944757e-05,0.000189787308802236,0.000312690644970973,0.000466034643916367,0.000645463690913993,0.000845828528229199
|
||||
0,8.80252798763183e-10,7.92215439962928e-08,8.56765592551646e-07,4.05803525996784e-06,1.2449180396882e-05,2.9295973763362e-05,5.7746988001425e-05,0.0001003733295813,0.000158928915289496,0.00023429575744269
|
||||
0,0.000466368704740309,0.00424791180746615,0.00926944539909274,0.0131713216643424,0.0157625616947689,0.0174133722552654,0.0184577152890545,0.0191156877417616,0.0195250042740468,0.0197700479556243
|
||||
0,0.00174300015594418,0.00815930380362134,0.0132116161354557,0.016172754442502,0.0178696343095053,0.0188636958720877,0.0194550603754561,0.0198042367684176,0.0200009359043926,0.0200979478510297
|
||||
0,0.00630533087106852,0.0167264504542955,0.0205352907522532,0.021433296617797,0.0214908287288404,0.021342901494693,0.0211590163834043,0.0209808421912509,0.020813382900871,0.0206559438303523
|
||||
0,0.0181516683021334,0.0296877506877057,0.0296188711707772,0.0274991387847508,0.0255697170579367,0.0241218925670229,0.0230708035427124,0.0223012794968431,0.0217225548818433,0.0212745536462067
|
||||
0,0.0389067518217964,0.0432743493327086,0.037525495598965,0.0324527348417642,0.0288543692365208,0.0263663031569143,0.0246230583185604,0.0233728213888174,0.0224524193870472,0.0217568092848378
|
||||
0,0.0565396239160925,0.0500897261990562,0.0408387347867424,0.0344846493850116,0.0302543240032215,0.0273643802632421,0.0253287379325492,0.0238539136707014,0.0227584403765214,0.02192583980509
|
||||
0,0.00794755170946868,0.0172628249510397,0.0219912124473273,0.0237906919799591,0.0240591222673087,0.0235982544067714,0.0228369786001951,0.021996032718532,0.0211823304839058,0.0204423856134907
|
||||
0,0.000373684524467729,0.00190283496658901,0.00395283626547245,0.00595433814031928,0.00766198835968331,0.0090150942497423,0.0100370905098692,0.0107818312810106,0.0113083452714233,0.0116697843722264
|
||||
0,1.24794246503553e-05,0.000141270114233274,0.000466648605475989,0.000969170133300241,0.00158727378005724,0.00225743530947124,0.00292973311195242,0.00357075743939607,0.00416127927601125,0.00469265749237697
|
||||
0,3.25056776407433e-07,7.95461921640221e-06,4.12089493515841e-05,0.000117250753288648,0.00024402042254145,0.000420314286347587,0.000638908995931823,0.000889809192557268,0.00116261453581859,0.00144792147140295
|
||||
0,7.0854379238238e-09,3.75524392933622e-07,3.08321489667331e-06,1.21925554449326e-05,3.27749649029249e-05,6.95563221553643e-05,0.000126018794389096,0.000204052811537285,0.000304018569398211,0.000425019521621274
|
||||
0,0.00102836224521133,0.0064274670666241,0.0121491816508084,0.015968397765568,0.0181492003638804,0.019314880428558,0.0199102032969297,0.0201928751968812,0.0203044557297043,0.020320071184116
|
||||
0,0.00384385388740204,0.0123515070854559,0.0173313777131353,0.0196324133235912,0.0206081184457373,0.0209612687545928,0.0210258040457677,0.0209599611581841,0.0208374482363417,0.0206927731773186
|
||||
0,0.0139084634226096,0.0253420008838306,0.0269858208570455,0.0260863431776468,0.0248662406090429,0.023805495300228,0.0229587141516884,0.0222941985053244,0.0217679373130175,0.021344966099159
|
||||
0,0.0400577489259572,0.0450598366852064,0.0390556903095381,0.0336304680408348,0.0297597604093353,0.0270807237205804,0.0252035706273644,0.0238573134643687,0.0228662562144913,0.0221177566182138
|
||||
0,0.0859596622787531,0.0659645822190159,0.0498440895724295,0.0400638374763904,0.0339433683852068,0.0299353070092985,0.0272039578032914,0.0252772077773997,0.0238777953326208,0.0228341669415018
|
||||
0,0.125398084679699,0.0772427043755313,0.0551767906604444,0.0434193651923798,0.0363278914606691,0.0317025734216055,0.0285266548704347,0.0262622056865752,0.0246012510386757,0.0233529211513904
|
||||
0,0.0279719026476077,0.0399912836159061,0.041824217737992,0.0399960375533372,0.0370306079722165,0.0339334669014817,0.0310904350363235,0.0286238301128732,0.0265419722346029,0.0248094228214593
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|
||||
0,3.40393634256781e-22,6.53632617070714e-20,1.31310268914671e-18,1.05893998255463e-17,5.20829887103865e-17,1.87956724398352e-16,5.48951609054929e-16,1.3751099157628e-15,3.06669713938502e-15,6.2447989892164e-15
|
||||
0,4.00278935798164e-24,1.50166583042231e-21,4.40866620105182e-20,4.60970828253607e-19,2.75310436445269e-18,1.15735040672427e-17,3.82669184362989e-17,1.06268988633135e-16,2.58592708871164e-16,5.67426085674954e-16
|
||||
0,4.89860423986417e-26,3.68055944030794e-23,1.6212071379999e-21,2.25639400694407e-20,1.6800782168471e-19,8.44489572108405e-19,3.24448865148392e-18,1.02486142861079e-17,2.79143092738667e-17,6.76923776023426e-17
|
||||
|
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Reference in New Issue
Block a user