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Commit 48a2f685 authored by Mirko Birbaumer's avatar Mirko Birbaumer
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Adapted Numpy Pandas Intro Notebook

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%% Cell type:markdown id: tags:
## 3.2 Funktions, Conditionals, and Iteration in Python
Let us create a Python function, and call it from a loop.
%% Cell type:code id: tags:
``` python
def HelloWorldXY(x, y):
if (x < 10):
print("Hello World, x was < 10")
elif (x < 20):
print("Hello World, x was >= 10 but < 20")
else:
print("Hello World, x was >= 20")
return x + y
print(HelloWorldXY(1,2))
```
%% Cell type:markdown id: tags:
Now let us call the function `HelloWorldXY()` from a loop:
%% Cell type:code id: tags:
``` python
for i in range(8, 25, 5): # i=8, 13, 18, 23 (start, stop, step)
print("\n--- Now running with i: {}".format(i))
r = HelloWorldXY(i,i)
print("Result from HelloWorld: {}".format(r))
```
%% Output
--- Now running with i: 8
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-1-7ea2350df544> in <module>
1 for i in range(8, 25, 5): # i=8, 13, 18, 23 (start, stop, step)
2 print("\n--- Now running with i: {}".format(i))
----> 3 r = HelloWorldXY(i,i)
4 print("Result from HelloWorld: {}".format(r))
NameError: name 'HelloWorldXY' is not defined
%% Cell type:markdown id: tags:
If you want a loop starting at 0 to 2 (exclusive) you could do any of the following:
%% Cell type:code id: tags:
``` python
print("Iterate over the items. `range(2)` is like a list [0,1].")
for i in range(2):
print(i)
print("Iterate over an actual list.")
for i in [0,1]:
print(i)
print("While works")
i = 0
while i < 2:
print(i)
i += 1
print("Python supports standard key words like continue and break")
while True:
print("Entered while")
break
print("while broken")
```
%% Output
Iterate over the items. `range(2)` is like a list [0,1].
0
1
Iterate over an actual list.
0
1
While works
0
1
Python supports standard key words like continue and break
Entered while
while broken
%% Cell type:markdown id: tags:
## 3.3 Data in Numpy
%% Cell type:code id: tags:
``` python
import numpy as np
# Scalar
s = np.array(5)
# Vector
v = np.array([1, 2, 10])
# Matrix
m = np.array([[1,2,3],
[4,5,6],
[7,8,9]])
# Tensor:
t = np.array([[[[1],[2]], [[3],[4]], [[5],[6]]],
[[[7],[8]], [[9],[10]], [[11],[12]]],
[[[13],[14]], [[15],[16]], [[17],[17]]]])
# Shape
print("Shape scaler", s.shape, "\nShape vector", v.shape, "\nShape matrix", m.shape, "\nShape tensor", t.shape)
# Type
print("Type scalar or array", type(s), "\nType after addition with integer", type(s + 3))
# Slicing
print("v[1:] = ", v[1:], "\nm[1:][2:] = \n", m[1:,1:])
# Reshape arrays
x = v.reshape(1, 3)
y = v[None, :]
print(v, x, y)
print(v.shape, x.shape, y.shape)
```
%% Output
Shape scaler ()
Shape vector (3,)
Shape matrix (3, 3)
Shape tensor (3, 3, 2, 1)
Type scalar or array <class 'numpy.ndarray'>
Type after addition with integer <class 'numpy.int64'>
v[1:] = [ 2 10]
m[1:][2:] =
[[5 6]
[8 9]]
[ 1 2 10] [[ 1 2 10]] [[ 1 2 10]]
(3,) (1, 3) (1, 3)
%% Cell type:markdown id: tags:
## 3.4 Element-wise Operations
%% Cell type:code id: tags:
``` python
# The Python way:
values = [1, 2, 3, 4, 5]
for i in range(len(values)):
values[i] += 5
print(values)
# The Numpy way:
values = np.array([1, 2, 3, 4, 5])
values += 5
print(values)
# Multiplication
x = np.multiply(values, 5)
y = values * 5
print(x, "\n", y, "\n")
# Element wise matrix operations
a = np.array([[1,3],[5,7]])
b = np.array([[2,4],[6,8]])
print("a =\n", a, "\nb =\n", b)
print("a + b =\n", a + b)
print("a * b =\n", a * b)
# Shape mismatch:
print("a * values =\n", a * values)
```
%% Output
[6, 7, 8, 9, 10]
[ 6 7 8 9 10]
[30 35 40 45 50]
[30 35 40 45 50]
a =
[[1 3]
[5 7]]
b =
[[2 4]
[6 8]]
a + b =
[[ 3 7]
[11 15]]
a * b =
[[ 2 12]
[30 56]]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-4-7ddd6b5f4e75> in <module>
24 print("a * b =\n", a * b)
25 # Shape mismatch:
---> 26 print("a * values =\n", a * values)
ValueError: operands could not be broadcast together with shapes (2,2) (5,)
%% Cell type:markdown id: tags:
## Numpy Matrix Multiplication
Recap element-wise multiplication:
%% Cell type:code id: tags:
``` python
# Elementwise recap:
m = np.array([[1,2,3],[4,5,6]])
# Scalar multiplication
n = m * 0.25
# Python Elementwise matrix multiplication
x = m * n
# Numpy Elementwise matrix multiplication
y = np.multiply(m, n)
print("m =\n", m, "\nn =\n", n)
print("x =\n", x, "\ny =\n", y)
```
%% Output
m =
[[1 2 3]
[4 5 6]]
n =
[[0.25 0.5 0.75]
[1. 1.25 1.5 ]]
x =
[[0.25 1. 2.25]
[4. 6.25 9. ]]
y =
[[0.25 1. 2.25]
[4. 6.25 9. ]]
%% Cell type:markdown id: tags:
Matrix Product:
%% Cell type:code id: tags:
``` python
""" Using np.matmul """
a = np.array([[1,2,3,4],[5,6,7,8]])
b = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])
print("a =\n", a, "\na.shape =\n", a.shape, "\nb =\n", b, "\nb.shape =\n", b.shape)
# Matrix product
c = np.matmul(a, b)
print("c = \n", c, "\nc.shape =\n", c.shape)
# Dimension mismatch:
# print(np.matmul(b, a))
""" Using np.dot """
d = np.dot(a, b)
print("d = \n", d, "\nd.shape =\n", d.shape)
```
%% Output
a =
[[1 2 3 4]
[5 6 7 8]]
a.shape =
(2, 4)
b =
[[ 1 2 3]
[ 4 5 6]
[ 7 8 9]
[10 11 12]]
b.shape =
(4, 3)
c =
[[ 70 80 90]
[158 184 210]]
c.shape =
(2, 3)
d =
[[ 70 80 90]
[158 184 210]]
d.shape =
(2, 3)
%% Cell type:markdown id: tags:
## Transpose
%% Cell type:code id: tags:
``` python
m = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
print("m = \n", m,"\nm.T = \n", m.T)
# note how the transposed matrix is not a copy of the original:
m_t = m.T
m_t[3][1] = 200
print("m = \n", m, "\nm_t = \n", m_t)
print("entries [3][1], [1][3], respectively are edited in both matrices")
```
%% Output
m =
[[ 1 2 3 4]
[ 5 6 7 8]
[ 9 10 11 12]]
m.T =
[[ 1 5 9]
[ 2 6 10]
[ 3 7 11]
[ 4 8 12]]
m =
[[ 1 2 3 4]
[ 5 6 7 200]
[ 9 10 11 12]]
m_t =
[[ 1 5 9]
[ 2 6 10]
[ 3 7 11]
[ 4 200 12]]
entries [3][1], [1][3], respectively are edited in both matrices
%% Cell type:markdown id: tags:
## A real use case
%% Cell type:code id: tags:
``` python
inputs = np.array([[-0.27, 0.45, 0.64, 0.31]])
print(inputs, inputs.shape)
weights = np.array([[0.02, 0.001, -0.03, 0.036],
[0.04, -0.003, 0.025, 0.009],
[0.012, -0.045, 0.28, -0.067]])
print(weights, weights.shape)
print("Matrix multiplication gives:\n", np.matmul(inputs, weights.T), "\nor, equivalently:\n", np.matmul(weights, inputs.T))
```
%% Output
[[-0.27 0.45 0.64 0.31]] (1, 4)
[[ 0.02 0.001 -0.03 0.036]
[ 0.04 -0.003 0.025 0.009]
[ 0.012 -0.045 0.28 -0.067]] (3, 4)
Matrix multiplication gives:
[[-0.01299 0.00664 0.13494]]
or, equivalently:
[[-0.01299]
[ 0.00664]
[ 0.13494]]
%% Cell type:markdown id: tags:
## Some more useful Numpy methods
%% Cell type:code id: tags:
``` python
print("\nShowing some basic math on arrays")
b = np.array([0,1,4,3,2])
print("Max: {}".format(np.max(b)))
print("Average: {}".format(np.average(b)))
print("Max index: {}".format(np.argmax(b)))
print("\nUse numpy to create a [3,3] dimension array with random number")
c = np.random.rand(3, 3)
print(c)
```
%% Output
Showing some basic math on arrays
Max: 4
Average: 2.0
Max index: 2
Use numpy to create a [3,3] dimension array with random number
[[0.92371879 0.58999086 0.76979433]
[0.48733651 0.44698554 0.91494542]
[0.59130531 0.69632003 0.32785335]]
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