Plotte-opgaver

%matplotlib inline
import matplotlib.pyplot as plt
fig, ax = plt.subplots()

ax.plot([1, 0.5, -0.5, -1, -0.5, 0.5, 1],[0, 0.866, 0.866, 0, -0.866, -0.866, 0])
ax.plot([0,1],[0,0])
ax.plot([0,0.5],[0,0.866])
ax.plot([0,-.5],[0,0.866])
ax.plot([0,-1],[0,0])
ax.plot([0,-.5],[0,-0.866])
ax.plot([0,0.5],[0,-0.866])

ax.set_title('Title')
ax.set_xlabel('horizontal-x')
ax.set_ylabel('vertical-y')
ax.text(-0.15,0.5,'triangle')

ax.set_aspect('equal')

fig.tight_layout()
fig.savefig('nice_fig.png')

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

plt.rc('font', size=18)
fig, ax = plt.subplots()
ax.set_aspect('equal')
ax.grid()

thetas = np.linspace(-np.pi/2,np.pi/4)
x1 = np.cos(thetas)
y1 = np.sin(thetas)


x2 = [(1+np.sqrt(2)),0]
y2 = [-1, -1]
xs = np.concatenate((x1,x2))
ys = np.concatenate((y1,y2))

ax.fill(xs,ys,linewidth=3,edgecolor='k')
ax.fill(ys,xs,linewidth=3,edgecolor='k')

thetas = np.linspace(np.pi,np.pi*3/2)
x1 = np.cos(thetas)
y1 = np.sin(thetas)
x2 = [-1]
y2 = [-1]
xt = np.concatenate((x1,x2))
yt = np.concatenate((y1,y2))

ax.fill(xt,yt,linewidth=3,edgecolor='k')

ax.arrow((1+np.sqrt(2)),0.2,0,-1.15,width=.05,length_includes_head=True,facecolor='w')
ax.text(2,0.5,'$x=1+\sqrt{2}$')

ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
fig.tight_layout()
fig.savefig('jupyter21_exercise3_triangular_hole_01.png')

fig, ax = plt.subplots()
ax.set_aspect('equal')
ax.grid()

ax.fill(xs+1,ys,linewidth=3,edgecolor='k')
ax.fill(ys,xs+1,linewidth=3,edgecolor='k')
ax.fill(xt+1,yt+1,linewidth=3,edgecolor='k')

ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
fig.tight_layout()
fig.savefig('jupyter21_exercise3_triangular_hole_02.png')

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

plt.rc('font', size=18)

thetas = np.linspace(np.pi,np.pi/2)
xs = 2 * np.cos(thetas) + 2
ys = 2 * np.sin(thetas) + 0

thetas = np.linspace(np.pi/2,np.pi)
x1 = np.cos(thetas) + 2
y1 = np.sin(thetas) + 1

xs = np.concatenate((xs,x1))
ys = np.concatenate((ys,y1))

thetas = np.linspace(-np.pi/2,0)
x1 = 2 * np.cos(thetas) + 1
y1 = 2 * np.sin(thetas) + 3

xs = np.concatenate((xs,x1))
ys = np.concatenate((ys,y1))

thetas = np.linspace(0,-np.pi/2)
x1 = 3 * np.cos(thetas) + 0
y1 = 3 * np.sin(thetas) + 3

xs = np.concatenate((xs,x1))
ys = np.concatenate((ys,y1))

fig, ax = plt.subplots()
ax.set_aspect('equal')
ax.grid()
ax.set_yticks([0,1,2,3])

ax.fill(xs,ys,linewidth=3,edgecolor='k')

ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
fig.tight_layout()
fig.savefig('jupyter21_exercise_claw.png')

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

plt.rc('font', size=18)

ts = [(np.pi,np.pi/2),
     (np.pi/2,np.pi),
     (-np.pi/2,0),
     (0,-np.pi/2)]

cs = [(2,0),(2,1),(1,3),(0,3)]
rs = [2, 1, 2, 3]

xs = []
ys = []

for (t1,t2),(cx,cy),r in zip(ts,cs,rs):

    thetas = np.linspace(t1,t2)
    x1 = r * np.cos(thetas) + cx
    y1 = r * np.sin(thetas) + cy

    xs = np.concatenate((xs,x1))
    ys = np.concatenate((ys,y1))

fig, ax = plt.subplots()
ax.set_aspect('equal')
ax.grid()
ax.set_yticks([0,1,2,3])

ax.fill(xs,ys,linewidth=3,edgecolor='k')

ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
fig.tight_layout()
fig.savefig('jupyter21_exercise_claw.png')

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
plt.rc('font', size=18)

fig, axs = plt.subplots(3,1,sharex=True,figsize=(6,10))
fig.suptitle('Smooth cutoff functions')

Rs = [2, 4, 6]
gammas = [1, 2, 3]

for ax,R in zip(axs,Rs):
    rs1 = np.linspace(0,R,100)
    rs2 = np.linspace(R,10,100)
    rs = np.concatenate((rs1,rs2))
    ys2 = np.zeros(100)
    for gamma in gammas:
        f = lambda r: 1 + gamma * np.power(r/R,gamma + 1) - (gamma + 1) * np.power(r/R,gamma)
        ys1 = f(rs1)
        ys = np.concatenate((ys1,ys2))
        ax.plot(rs,ys)
    
    ax.grid()
    ax.legend(['$\gamma={}$'.format(g) for g in gammas])
    ax.set_ylabel('$y$')
    ax.set_title('$R={}$'.format(R))
    
ax.set_xlabel('$r$')
fig.tight_layout()
fig.subplots_adjust(top=0.9)
fig.savefig('loesning_funktioner_01.png')

Figure 1

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
plt.rc('font', size=16)
fig, ax = plt.subplots()
ax.set_aspect('equal')
ax.grid()
ax.set_xlim([-1,7])
ax.set_ylim([-1,4])
ax.set_xticks(range(7))
ax.set_yticks(range(4))

xs = np.array([0, 1, 1, 0])
ys = np.array([0, 0, 1, 1])

def plot_square_more_compact(x,y,col):
    return ax.fill(x + xs,
                   y + ys,
                   linewidth=3,
                   facecolor=col,
                   edgecolor='k')[0]     # note the [0]

my_square = plot_square_more_compact(1,0,'pink')
fig.savefig('pyth21_manipulating_square_01.png')

def move_square(square,dx,dy,col):
    square.set(facecolor=col)
    xy_vals = square.get_xy()
    new_xy_vals = xy_vals + [dx,dy]
    square.update({'xy': new_xy_vals})

move_square(my_square,1,0,'pink')
fig.savefig('pyth21_manipulating_square_02.png')
fig

p = 3
dxs = (4 * [1] + 4 * [-1]) * p
dys = [0] * len(dxs)
cols = (3 * ['pink'] + ['white']) * 2 * p

# move back to start
move_square(my_square,-1,0,'pink')
i = 0
for dx, dy, col in zip(dxs,dys,cols):
    move_square(my_square,dx,0,col)
    fig.savefig('pyth21_manipulating_square_{:02d}.png'.format(i))
    i += 1

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
np.set_printoptions(precision=3)
plt.rc('font', size=16)

fig, ax = plt.subplots()
ax.grid()
ax.set_xlim(-4,4)

f = lambda x0,x: np.exp(-np.power(x-x0,2))
xs = np.linspace(-5,5,100)
ys = f(-2,xs)

gauss = ax.plot(xs,ys)[0]
fig.savefig('pyth21_moving_gauss_01.png')

from matplotlib import animation
plt.rc('animation', html='jshtml')

N = 50
x0s = np.linspace(-2,2,N)

def update(i):
    x0 = x0s[i]
    ys = f(x0,xs)
    gauss.set_data((xs,ys))

    return [gauss]

anim = animation.FuncAnimation(fig,
                               update,
                               frames=N,
                               interval=10,
                               blit=True)
anim

writer = animation.writers['pillow'](fps=10) # frames per second
anim.save('moving_gauss.gif', writer=writer)

import numpy as np
import matplotlib.pyplot as plt
plt.rc('font', size=16)
fig, ax = plt.subplots()
ax.set_aspect('equal')
ax.grid()

# ramp
N =44
xramp = np.linspace(0,10,N)
yramp = (10 - xramp) * 0.2
xramp = np.concatenate(([0],xramp))
yramp = np.concatenate(([0],yramp))

ax.fill(xramp,yramp,linewidth=3,facecolor='darkorange',edgecolor='k')

# box
v1 = np.array([10,-2])/np.sqrt(10**2 + (-2)**2)
v2 = [-v1[1],v1[0]]
xs = [0, v1[0], v1[0]+v2[0], v2[0]]
ys = [0, v1[1], v1[1]+v2[1], v2[1]]
ys = np.array(ys) + 2

box = ax.fill(xs,ys,linewidth=3,facecolor='steelblue',edgecolor='k')[0]
fig.savefig('pyth21_sliding_box_01.png')

from matplotlib import animation
plt.rc('animation', html='jshtml')

def update(i):
    xy = box.get_xy()
    box.update({'xy': xy + v1/5})
    return [box]

anim = animation.FuncAnimation(fig,
                               update,
                               frames=N,
                               interval=10,
                               blit=True)
anim