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extraplots.jl
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function GS_categories()
figure();
fst(list) = map(p -> p[1], list)
snd(list) = map(p -> p[2], list)
cat_1_0 = [
map( a2 -> (1.0, a2), 1.0:0.1:1.9),
map( a2 -> (1.1, a2), 1.4:0.1:2.0),
map( a2 -> (1.2, a2), 1.8:0.1:2.0)
]
cat_1_0_fill = [
(1.2, 1.8)
]
cat_1_1 = [
map( a2 -> (1.0, a2), 2.0:0.1:2.0),
map( a2 -> (1.1, a2), 1.0:0.1:1.3),
map( a2 -> (1.2, a2), 1.0:0.1:1.7),
map( a2 -> (1.3, a2), 1.5:0.1:2.0),
map( a2 -> (1.4, a2), 1.7:0.1:2.0),
map( a2 -> (1.5, a2), 1.9:0.1:2.0),
map( a2 -> (2.0, a2), 1.0:0.1:1.3)
]
cat_1_1_fill = [
(1.2, 1.7)
(1.2, 1.0)
]
cat_1_2 = [
map( a2 -> (1.3, a2), 1.0:0.1:1.4),
map( a2 -> (1.4, a2), 1.0:0.1:1.6),
map( a2 -> (1.5, a2), 1.0:0.1:1.8),
map( a2 -> (1.6, a2), 1.0:0.1:2.0),
map( a2 -> (1.7, a2), 1.0:0.1:2.0),
map( a2 -> (1.8, a2), 1.0:0.1:1.3),
map( a2 -> (1.8, a2), 1.6:0.1:2.0),
map( a2 -> (1.9, a2), 1.0:0.1:1.2)
]
cat_1_2_fill = [
(1.6, 1.5),
(1.6, 2.0)
]
cat_2_2 = [
map( a2 -> (1.8, a2), 1.4:0.1:1.5),
map( a2 -> (1.9, a2), 1.3:0.1:2.0),
map( a2 -> (2.0, a2), 1.4:0.1:2.0)
]
cat_2_2_fill = [
(2.0, 2.0)
]
println(length(cat_1_0) + length(cat_1_1) + length(cat_1_2) + length(cat_2_2))
s = 100;
scatter(fst(cat_1_0), snd(cat_1_0), s=s, marker="D", facecolors="none", edgecolors="g")
scatter(fst(cat_1_1), snd(cat_1_1), s=s, marker="^", facecolors="none", edgecolors="r")
scatter(fst(cat_1_2), snd(cat_1_2), s=s, marker="s", facecolors="none", edgecolors="b")
scatter(fst(cat_2_2), snd(cat_2_2), s=s, marker="8", facecolors="none", edgecolors="c")
scatter(fst(cat_1_0_fill), snd(cat_1_0_fill), s=s, marker="D", facecolors="g", edgecolors="g")
scatter(fst(cat_1_1_fill), snd(cat_1_1_fill), s=s, marker="^", facecolors="r", edgecolors="r")
scatter(fst(cat_1_2_fill), snd(cat_1_2_fill), s=s, marker="s", facecolors="b", edgecolors="b")
scatter(fst(cat_2_2_fill), snd(cat_2_2_fill), s=s, marker="8", facecolors="c", edgecolors="c")
legend([
"Links 0 golven, rechts 1 golf",
"Links 1 golf, rechts 1 golf",
"Links 2 golven, rechts 1 golf",
"Links 2 golven, rechts 2 golven"
], fontsize="small", scatterpoints=1, ncol=2,
bbox_to_anchor=(0.5, -0.12), loc="upper center", borderaxespad=0.);
subplots_adjust(bottom = 0.2)
axis([0.9, 2.1, 0.9, 2.1])
title("Classificatie van effecten")
xlabel(L"\alpha_1");
ylabel(L"\alpha_2");
end
function monomialDerivatives(;as = 1.0:0.05:3.0)
p = 3;
xs = e.^(-10:0.05:0.0); # logaritmische schaal om het stijle gedrag rond x=0 goed weer te geven
AA = maximum(as);
aa = minimum(as);
if(length(as) == 1)
colours = [(1,0,0)];
else
colours = map(a -> (0, 0.8*(1-(a-aa)/(AA-aa)), (a-aa)/(AA-aa)), as);
end
f = x -> x^p;
for i = 1:length(as)
a = as[i];
Df = x -> gamma(p+1)/gamma(p-a+1)*x^(p-a)
dudxa_exact = map(Df, xs);
plot(xs, dudxa_exact, c=colours[i]);
end
xlabel(L"x");
ylabel(L"D^\alpha x^p");
end
function monomialDerivativesMulti()
monomialDerivatives(as = [0.0])
monomialDerivatives(as = 0.05:0.05:0.95)
monomialDerivatives(as = [1.0])
monomialDerivatives(as = 1.05:0.05:1.95)
monomialDerivatives(as = [2.0])
monomialDerivatives(as = 2.05:0.05:2.95)
monomialDerivatives(as = [3.0])
end
##
# W_plotEV
# Plot eigenwaarden van W-matrix
##
function W_plotEV(W)
ev = eigvals(W)
scatter(real(ev), imag(ev))
nothing
end
function plotEV(disc::DiscMethode, dt)
cs = [
(0.0, 0.0, 1.0), (0.0, 0.5, 1.0), (0.0, 1.0, 1.0), (0.0, 1.0, 0.5),
(0.0, 1.0, 0.0), (0.5, 1.0, 0.0), (1.0, 1.0, 0.0), (1.0, 0.5, 0.0),
(1.0, 0.0, 0.0), (1.0, 0.0, 0.5), (1.0, 0.0, 1.0), (0.5, 0.0, 1.0)
];
as = [1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0];
cs = cs[1:length(as)];
Nx = 200;
figure();
grid(true);
#julia> using PyCall
#julia> @pyimport matplotlib.patches as patch
#julia> @pyimport matplotlib.pyplot as plt
c = patch.Circle((-1,0), 1, alpha=0.2);
plt.gca()[:add_patch](c)
for i = 1:length(as)
ev = eigvals(dt*berekenW(disc, Nx, as[i], 1.0, 1.0))
#Wred = berekenWReduced(disc, Nx, as[i], 1.0);
#Wimpl = berekenWimpl(disc, Wred, Nx, dt, 1.0)
#ev = eigvals(berekenW(disc, Nx, as[i], 1.0, 1.0) - Wimpl)
scatter(real(ev), imag(ev), c=cs[i])
end
loc = (typeof(disc) == L2C)?"center left":"upper left"
legend( unshift!(map( a -> string(L"$\alpha = $", a), as), "Stab."), loc=loc, fontsize="small", scatterpoints=1, labelspacing = 0.1#=, ncol = 2=#);
title("Eigenwaarden van $(disc.toString)")
xlabel("Re(z)");
ylabel("Im(z)");
if typeof(disc) == L2C
axis([-1, 0.2, -1.5, 1.5])
axis([-0.11, 0.01, -0.15, 0.15])
else
axis([-5, 1, -1, 1])
#axis([-2, 0.1, -0.5, 0.5])
end
nothing
end
function plotL2StabBound()
a = 1:0.01:2;
b = gamma(3-a)./(3-2.^(2-a))
figure();
grid(true);
plot(a, b);
xlabel(L"$\alpha$");
ylabel(L"$f(\alpha)$");
title(L"$f(\alpha) = \Gamma(3-\alpha)/(3-2^{2-\alpha})$");
axis([1, 2, 0.4, 1])
nothing
end
function plotL2StabBound2()
a = 1:0.01:2;
b = gamma(3-a)./(3-2.^(2-a));
c = 1./a;
figure();
grid(true);
plot(a, b);
plot(a, c);
xlabel(L"$\alpha$");
ylabel(L"$f$, $g$");
legend([L"f(\alpha) = \Gamma(3-\alpha)/(3-2^{2-\alpha})", L"g(\alpha) = 1/\alpha"]);
axis([1, 2, 0.4, 1])
nothing
end
function plotEVGershgorinL2()
colour = (0.5, 1.0, 0.0);
a = 1.5;
dt = 1.0;
disc = L2();
Nx = 200;
figure();
grid(true);
W = dt*berekenW(disc, Nx, a, 1.0, 1.0);
#c = patch.Circle((-1,0), 1, alpha=0.2);
#plt.gca()[:add_patch](c)
for (i, color) in [(2, "g"), (Nx-1, "b"), (1,"r")]
i = Nx-i;
ri = sumabs(W[i,:]) - abs(W[i,i]);
println(W[i,i], " ", ri);
c = patch.Circle((W[i,i],0), ri, alpha=0.4, color=color);
plt.gca()[:add_patch](c)
end
ev = eigvals(W)
scatter(real(ev), imag(ev), c=colour)
loc = (typeof(disc) == L2C)?"center left":"upper left"
legend( [L"i = 2,\ldots,N_x-2", L"i = N_x - 1", L"i = 1", "Eigenwaarden"], loc=loc, fontsize="small", scatterpoints=1, labelspacing = 0.1#=, ncol = 2=#);
title("Eigenwaarden en Gershgorin schijven van $(disc.toString)")
xlabel("Re(z)");
ylabel("Im(z)");
axis([-4, 0.5, -2, 2])
nothing
end
function plotEVGershgorinExample()
colour = (0.5, 1.0, 0.0);
Nx = 3;
W = [
3 + 3im 2 - 3im -2 + 1im
-2 + 2im -2 + 1im -1 - 2im
3 - 3im -1 - 2im 3 - 2im
];
figure();
grid(true);
for (i, color) in [(1, "r"), (2, "g"), (3,"b")]
ri = sumabs(W[i,:]) - abs(W[i,i]);
println(W[i,i], " ", ri);
c = patch.Circle((real(W[i,i]),imag(W[i,i])), ri, alpha=0.4, color=color);
plt.gca()[:add_patch](c)
end
ev = eigvals(W)
scatter(real(ev), imag(ev), c=colour)
loc = "upper left"
legend( [L"i = 1", L"i = 2", L"i = 3", "Eigenwaarden"], loc=loc, fontsize="small", scatterpoints=1, labelspacing = 0.1#=, ncol = 2=#);
title("Eigenwaarden en Gershgorin schijven")
xlabel(L"Re($\lambda$)");
ylabel(L"Im($\lambda$)");
axis([-10, 10, -10, 10])
nothing
end
function plotGS_initCond()
dx = 0.0025;
bwp = GrayScott();
xs = 0:dx:bwp.L;
u_t = beginOpl1(bwp, xs);
v_t = beginOpl2(bwp, xs);
figure();
plot(xs, u_t);
plot(xs, v_t);
xlabel(L"x");
ylabel(L"u, v");
legend([L"u(x,t=0)", L"v(x,t=0)"])
end
function plotFisher_sols()
dx = 0.025;
xs = -8:dx:5;
uA = 1./(1 + 2*exp(xs) + exp(2*xs));
uB = 1./(1 + exp(2*xs));
figure();
plot(xs, uA);
plot(xs, uB);
xlabel(L"x");
ylabel(L"u_A, u_B");
legend([L"u_A(x,t=0)", L"u_B(x,t=0)"])
axis([-8,5,-0.1, 1.1]);
nothing
end