== 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],
)