190 lines
4.7 KiB
XML
190 lines
4.7 KiB
XML
== Befehle
|
|
#table(columns: (0.3fr, 1fr, 0.4fr),
|
|
[Befehl], [Code], [Ausgabe],
|
|
[Betrag], [```py np.abs(-5) ``` \ ```py np.absolute(-5) ```], [5],
|
|
[Mittelwert], [```py np.mean([1, 2, 3, 4, 5]) ```], [3],
|
|
[Median \ (Zentralwert)], [```py np.median([1, 2, 4, 5, 15]) ``` \ ```py np.median([1, 2, 4, 5, 15, 16]) ```], [4 \ 4.5],
|
|
[Standardabweichung], [```py np.std([1, 2, 3, 4, 5]) ``` \ ```py np.std([1, 2, 3, 4, 5], ddof=1) ``` \ ddof = Delta Degrees of Freedom (Nicht so relevant für uns "höhere mathe" wichitg immer gleich machen!)], [1.41 \ 1.58],
|
|
[Wurzel], [```py np.sqrt(16) ```], [4],
|
|
[Integrall], [```py inter = np.trapezoid(y_data, x_data)```], [],
|
|
|
|
[Array], [```py np.linspace(2, 10, 5) ```], [\[ 2. 4. 6. 8. 10.\]],
|
|
[Array], [```py np.arange(4, 10) ``` \ ```py np.arange(0, 1, 0.2) ```], [\[4 5 6 7 8 9\] \ \[0. 0.2 0.4 0.6 0.8\]],
|
|
[ln], [```py np.log(x) ```], [],
|
|
[10er log], [```py np.log10(x) ```], [],
|
|
)
|
|
|
|
|
|
== Matrizen
|
|
#table(columns: (0.3fr, 0.9fr, 0.5fr),
|
|
[Array], [```py
|
|
A = np.array([[1, 3, -1],
|
|
[4, -2, 8]])
|
|
|
|
B = np.array([[-3, 9, 3],
|
|
[-6, 6, 3]])
|
|
```],[],
|
|
[Addition], [```py
|
|
C = A + B
|
|
```],[```
|
|
C = [[-2 12 2]
|
|
[-2 4 11]]
|
|
```],
|
|
[Multiplikation], [```py
|
|
C = A @ B
|
|
D = -2 * B
|
|
```],[```
|
|
C = [[ 15 -3 24]
|
|
[-52 92 -2]]
|
|
|
|
D = [[ 6 -18 -6]
|
|
[ -8 4 -16]
|
|
[ 12 -12 -6]]
|
|
```],
|
|
[Transposition], [```py
|
|
C = A.T
|
|
```],[```
|
|
C = [[ 1 8]
|
|
[ 3 -4]
|
|
[-1 2]]
|
|
```],
|
|
[Inverse], [```py
|
|
C = np.linalg.inv(B)
|
|
```],[```
|
|
```],
|
|
[Rodrigues-Rotationsmatrizen], [```py
|
|
def J(w):
|
|
M = np.array([[0, -w[2], w[1]],
|
|
[w[2], 0, -w[0]],
|
|
[-w[1], w[0], 0]])
|
|
return M
|
|
def R(phi, n):
|
|
nn = n/np.linalg.norm(n)
|
|
M = np.eye(3) + (1-np.cos(phi)) * J(nn)@J(nn) + np.sin(phi)*J(nn)
|
|
return M
|
|
```],[```
|
|
```],
|
|
[Spur / trace], [```py
|
|
s = np.trace(A)
|
|
```],[```
|
|
s = -3
|
|
```],
|
|
[Determinante], [```py
|
|
d = np.linalg.det(A)
|
|
```],[```
|
|
```],
|
|
[], [], [\ ],
|
|
[Zeros], [```py
|
|
A = np.zeros((2,3))
|
|
```],[```
|
|
[[0. 0. 0.]
|
|
[0. 0. 0.]]
|
|
```],
|
|
[Ones], [```py
|
|
A = np.ones((2,3))
|
|
```],[```
|
|
[[1. 1. 1.]
|
|
[1. 1. 1.]]
|
|
```],
|
|
[Eye], [```py
|
|
A = np.eye(2,3)
|
|
```],[```
|
|
[[1. 0. 0.]
|
|
[0. 1. 0.]]
|
|
```],
|
|
[Diag], [```py
|
|
d = np.array([1.,2.,3.])
|
|
A = np.diag(d)
|
|
```],[```
|
|
[[1. 0. 0.]
|
|
[0. 2. 0.]
|
|
[0. 0. 3.]]
|
|
```],
|
|
[Diag rev.], [```py
|
|
A = np.array([[1. 0. 0.],
|
|
[0. 2. 0.],
|
|
[0. 0. 3.]]
|
|
B = np.diag(A)
|
|
```],[```
|
|
B = [1. 2. 3.]
|
|
```],
|
|
|
|
)
|
|
|
|
|
|
== Matplotlib
|
|
#table(columns: (0.3fr, 0.9fr, 0.5fr),
|
|
[Linien], [```py
|
|
x = [1, 2, 3, 4]
|
|
y = [1, 4, 9, 16]
|
|
|
|
plt.plot(x, y)
|
|
plt.xlabel('Zeit (s)')
|
|
plt.ylabel('Amplitude')
|
|
plt.grid()
|
|
plt.show()
|
|
```], [#image("../img/python/matplotlib_linie.png", width: 100%)],
|
|
|
|
[Kreis], [```py
|
|
labels = 'Frogs', 'Hogs', 'Dogs', 'Logs'
|
|
sizes = [15, 30, 45, 10]
|
|
|
|
plt.pie(sizes, labels=labels)
|
|
plt.show()
|
|
```], [#image("../img/python/matplotlib_kreis.png", width: 100%)],
|
|
[Punktwolke / Scatterplot], [```py
|
|
n = 100
|
|
x = np.random.normal(0,1,n)
|
|
y = np.random.normal(0,1,n)
|
|
|
|
plt.scatter(x, y)
|
|
plt.title('Scatter Plot')
|
|
plt.xlabel('x')
|
|
plt.ylabel('y')
|
|
plt.show()
|
|
```], [#image("../img/python/matplotlib_punktewolke.png", width: 100%)],
|
|
|
|
[Säulendiagramme], [```py
|
|
fruits = ['apple', 'blueberry', 'cherry', 'orange']
|
|
counts = [40, 100, 30, 55]
|
|
|
|
bar_labels = ['red', 'blue', '_red', 'orange']
|
|
bar_colors = ['tab:red', 'tab:blue', 'tab:red', 'tab:orange']
|
|
|
|
plt.bar(fruits, counts, label=bar_labels, color=bar_colors)
|
|
plt.ylabel('fruit supply')
|
|
plt.title('Fruit supply by kind and color')
|
|
plt.show()
|
|
```], [#image("../img/python/matplotlib_säulendiagramme.png", width: 100%)],
|
|
|
|
[Säulendiagramme wagerecht], [```py
|
|
fruits = ['apple', 'blueberry', 'cherry', 'orange']
|
|
counts = [40, 100, 30, 55]
|
|
|
|
bar_labels = ['red', 'blue', '_red', 'orange']
|
|
bar_colors = ['tab:red', 'tab:blue', 'tab:red', 'tab:orange']
|
|
|
|
plt.barh(fruits, counts, label=bar_labels, color=bar_colors)
|
|
plt.ylabel('fruit supply')
|
|
plt.title('Fruit supply by kind and color')
|
|
plt.show()
|
|
```], [#image("../img/python/matplotlib_säulendiagramme_wagerecht.png", width: 100%)],
|
|
|
|
[Ausgabe als png], [```py
|
|
plt.savefig("test.png", transparent=True) # transparent nur für png
|
|
plt.savefig("test.png")
|
|
plt.show() # savefig muss zwingend vor show()!
|
|
```], [#image("../img/python/matplotlib_savefig.png", width: 100%)],
|
|
[Ausgabe als pdf], [```py
|
|
plt.savefig("test.pdf", pad_inches=0.1, bbox_inches="tight")
|
|
# so ist der Rand um den plot schmaller.
|
|
plt.savefig("test.pdf")
|
|
plt.show() # savefig muss zwingend vor show()!
|
|
```], [#image("../img/python/matplotlib_savefig_tight.png", width: 100%)],
|
|
[Ausgabe als svg], [```py
|
|
plt.savefig("test.svg")
|
|
plt.show() # savefig muss zwingend vor show()!
|
|
```], [svg ist eine Vektorgrafik],
|
|
)
|
|
|