Numpy¶

Install packages¶

You can use both pip magic as astral/uv

1 2	`!uv pip install -q numpy==2.3.0 sympy==1.14.0 # %pip install numpy==2.3.0 sympy==1.14.0`

Import packages¶

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import numpy as np
import sympy
from IPython.display import Math

Usage¶

Basic¶

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array1 = np.array([1, 2, 3, 4, 5])

Math(sympy.latex(sympy.Matrix(array1)))

\(\displaystyle \left[\begin{matrix}1\\2\\3\\4\\5\end{matrix}\right]\)

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print(array1)
print(type(array1))
print(array1.shape)

[1 2 3 4 5]

(5,)

1 2	`array2 = np.array([1, 2, 3, 4, 5]) array2.reshape(1, 5) # 1 row, 5 columns`

array([[1, 2, 3, 4, 5]])

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array3 = np.array([[1, 2, 3, 4, 5]])

Math(sympy.latex(sympy.Matrix(array3)))

\(\displaystyle \left[\begin{matrix}1 & 2 & 3 & 4 & 5\end{matrix}\right]\)

1	`array3.shape`

(1, 5)

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array4 = np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6]])

Math(sympy.latex(sympy.Matrix(array4)))

\(\displaystyle \left[\begin{matrix}1 & 2 & 3 & 4 & 5\\2 & 3 & 4 & 5 & 6\end{matrix}\right]\)

1 2	`print(array4) print(array4.shape)`

[[1 2 3 4 5]

[2 3 4 5 6]]

(2, 5)

1 2	`# 0 - 10, from 2 to 2 np.arange(0, 10, 2).reshape(5, 1)`

array([[0], [2], [4], [6], [8]])

1	`np.ones((3, 4)) # 3 rows, 4 columns of number one`

array([[1., 1., 1., 1.], [1., 1., 1., 1.], [1., 1., 1., 1.]])

1 2	`# Entity Matrix np.eye(3)`

array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])

Array attributes¶

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array5 = np.array([[1, 2, 3], [4, 5, 6]])

Math(sympy.latex(sympy.Matrix(array5)))

\(\displaystyle \left[\begin{matrix}1 & 2 & 3\\4 & 5 & 6\end{matrix}\right]\)

print(f"Array: {array5}\n")
print(f"(Rows, Columns): {array5.shape}")
print(f"Array number of dimensions: {array5.ndim}")
print(f"Array size: {array5.size}")
print(f"Data type: {array5.dtype}")
print(f"Item size (in bytes): {array5.itemsize}")

Array: [[1 2 3]

[4 5 6]]

(Rows, Columns): (2, 3)

Array number of dimensions: 2

Array size: 6

Data type: int64

Item size (in bytes): 8

Vectorized operations¶

array6 = np.array([1, 2, 3, 4, 5])
array7 = np.array([10, 20, 30, 40, 50])

print(f"Addition: {array6 + array7}")
print(f"Subtraction: {array6 - array7}")
print(f"Multiplication: {array6 * array7}")
print(f"Division: {array6 / array7}")

Addition: [11 22 33 44 55]

Subtraction: [ -9 -18 -27 -36 -45]

Multiplication: [ 10 40 90 160 250]

Division: [0.1 0.1 0.1 0.1 0.1]

Mathematical expressions¶

array8 = np.array([2, 3, 4, 5, 6])

print(f"Square root: {np.sqrt(array8)}")
print(f"Exponential: {np.exp(array8)}")
print(f"Sine: {np.sin(array8)}")
print(f"Natural log: {np.log(array8)}")

Square root: [1.41421356 1.73205081 2. 2.23606798 2.44948974]

Exponential: [ 7.3890561 20.08553692 54.59815003 148.4131591 403.42879349]

Sine: [ 0.90929743 0.14112001 -0.7568025 -0.95892427 -0.2794155 ]

Natural log: [0.69314718 1.09861229 1.38629436 1.60943791 1.79175947]

Array slicing and indexing¶

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array9 = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

Math(sympy.latex(sympy.Matrix(array9)))

\(\displaystyle \left[\begin{matrix}1 & 2 & 3 & 4\\5 & 6 & 7 & 8\\9 & 10 & 11 & 12\end{matrix}\right]\)

print(f"Array:\n {array9}")

print(f"Element in first row and first column: {array9[0][0]}")  # array9[0, 0]
print(
    "From rows from second onwards, columns from third onwards:\n "
    f" {array9[1:, 2:]}"
)

Array:

[[ 1 2 3 4]

[ 5 6 7 8]

[ 9 10 11 12]]

Element in first row and first column: 1

From rows from second onwards, columns from third onwards:

[[ 7 8]

[11 12]]

Modify Arrays¶

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array10 = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

Math(sympy.latex(sympy.Matrix(array10)))

\(\displaystyle \left[\begin{matrix}1 & 2 & 3 & 4\\5 & 6 & 7 & 8\\9 & 10 & 11 & 12\end{matrix}\right]\)

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array10[0, 0] = 15

Math(sympy.latex(sympy.Matrix(array10)))

\(\displaystyle \left[\begin{matrix}15 & 2 & 3 & 4\\5 & 6 & 7 & 8\\9 & 10 & 11 & 12\end{matrix}\right]\)

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array10[2:] = 20

Math(sympy.latex(sympy.Matrix(array10)))

\(\displaystyle \left[\begin{matrix}15 & 2 & 3 & 4\\5 & 6 & 7 & 8\\20 & 20 & 20 & 20\end{matrix}\right]\)

Statistical applications¶

Normalization¶

Mean of zero and standard deviation of 1

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array11 = np.array([1, 2, 3, 4, 5])

Math(sympy.latex(sympy.Matrix(array11)))

\(\displaystyle \left[\begin{matrix}1\\2\\3\\4\\5\end{matrix}\right]\)

mean = np.mean(array11)
std_dev = np.std(array11)

normalized_array11 = (array11 - mean) / std_dev
Math(sympy.latex(sympy.Matrix(normalized_array11)))

\(\displaystyle \left[\begin{matrix}-1.41421356237309\\-0.707106781186547\\0.0\\0.707106781186547\\1.41421356237309\end{matrix}\right]\)

Statistical methods¶

array12 = np.array([1, 2, 3, 4, 5])

print(f"Mean: {np.mean(array12)}")
print(f"Median: {np.median(array12)}")
print(f"Standard Deviation: {np.std(array12)}")
print(f"Variance: {np.var(array12)}")

Mean: 3.0

Median: 3.0

Standard Deviation: 1.4142135623730951

Variance: 2.0

Logical Operations¶

array13 = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])

print(f"Data greater than 5:\n{array13 > 5}")
print(
    f"Data greater than 5 and less than 8:\n"
    f"{array13[(array13 > 5) & (array13 < 8)]}"
)

Data greater than 5:

[False False False False False True True True True True True]

Data greater than 5 and less than 8:

[6 7]