Data Array Worked Examples

When learning about new topics in maths or related fields, by far the best approach is practice solving problems yourself. In my introduction to multidimensional arrays I set a few little problems that I wanted you to have a go at. On this page I will provide some answers, as well as a method for generating new problems that you can tackle!

Linear Index Conversion

def get_array_element(data, size, cartesian_indices):
    linear_index = 0
    for i, cartesian_index in enumerate(cartesian_indices):
        section_size = np.prod(size[i + 1:])
        linear_index += section_size * cartesian_index

    return data[linear_index]

Data Array Practice

array = np.zeros((2, 4, 3))
array[:, :, 0] = [
    [0.7, 0.9, 0.2, 0.6],
    [0.3, 0.0, 0.2, 0.7],
]
array[:, :, 1] = [
    [0.1, 0.5, 0.5, 0.2],
    [0.0, 0.4, 0.7, 0.8],
]
array[:, :, 2] = [
    [0.8, 0.8, 0.1, 0.4],
    [0.4, 0.9, 0.8, 0.7],
]

\[ \begin{aligned}A_{i,j,0} & = { \begin{pmatrix} 0.7 & 0.9 & 0.2 & 0.6 \\ 0.3 & 0.0 & 0.2 & 0.7 \end{pmatrix} }_{i,j} \\ A_{i,j,1} & = { \begin{pmatrix} 0.1 & 0.5 & 0.5 & 0.2 \\ 0.4 & 0.9 & 0.7 & 0.8 \end{pmatrix} }_{i,j} \\ A_{i,j,2} & = { \begin{pmatrix} 0.8 & 0.8 & 0.1 & 0.4 \\ 0.4 & 0.9 & 0.8 & 0.7 \end{pmatrix} }_{i,j}\end{aligned} \] \[ \mathbf{d} = ( \underset{i = 0}{\underbrace{ \underset{j = 0}{\underbrace{\underset{0}{0.7},\, \underset{1}{0.1},\, \underset{2}{0.8}}},\: \underset{j = 1}{\underbrace{\underset{0}{0.9},\, \underset{1}{0.5},\, \underset{2}{0.8}}},\: \underset{j = 2}{\underbrace{\underset{0}{0.2},\, \underset{1}{0.5},\, \underset{2}{0.1}}},\: \underset{j = 3}{\underbrace{\underset{0}{0.6},\, \underset{1}{0.2},\, \underset{2}{0.4}}} }},\; \underset{i = 1}{\underbrace{ \underset{j = 0}{\underbrace{\underset{0}{0.3},\, \underset{1}{0.0},\, \underset{2}{0.4}}},\: \underset{j = 1}{\underbrace{\underset{0}{0.0},\, \underset{1}{0.4},\, \underset{2}{0.9}}},\: \underset{j = 2}{\underbrace{\underset{0}{0.2},\, \underset{1}{0.7},\, \underset{2}{0.8}}},\: \underset{j = 3}{\underbrace{\underset{0}{0.7},\, \underset{1}{0.8},\, \underset{2}{0.7}}} }} ) \]

array = np.zeros((2, 4, 3))
array[:, 0, :] = [
    [0.4, 0.9, 0.1],
    [0.0, 0.4, 0.4],
]
array[:, 1, :] = [
    [0.3, 0.9, 0.1],
    [0.7, 0.8, 0.1],
]
array[:, 2, :] = [
    [0.5, 0.9, 0.4],
    [1.0, 0.4, 0.5],
]
array[:, 3, :] = [
    [0.2, 0.7, 0.3],
    [0.0, 0.9, 0.7],
]

\[ \begin{aligned}A_{i,0,k} & = { \begin{pmatrix} 0.4 & 0.9 & 0.1 \\ 0.0 & 0.4 & 0.4 \end{pmatrix} }_{i,k} \\ A_{i,1,k} & = { \begin{pmatrix} 0.3 & 0.9 & 0.1 \\ 0.7 & 0.8 & 0.1 \end{pmatrix} }_{i,k} \\ A_{i,2,k} & = { \begin{pmatrix} 0.5 & 0.9 & 0.4 \\ 1.0 & 0.4 & 0.5 \end{pmatrix} }_{i,k} \\ A_{i,3,k} & = { \begin{pmatrix} 0.2 & 0.7 & 0.3 \\ 0.0 & 0.9 & 0.7 \end{pmatrix} }_{i,k}\end{aligned} \] \[ \mathbf{d} = ( \underset{i = 0}{\underbrace{ \underset{j = 0}{\underbrace{\underset{0}{0.4},\, \underset{1}{0.9},\, \underset{2}{0.1}}},\: \underset{j = 1}{\underbrace{\underset{0}{0.3},\, \underset{1}{0.9},\, \underset{2}{0.1}}},\: \underset{j = 2}{\underbrace{\underset{0}{0.5},\, \underset{1}{0.9},\, \underset{2}{0.4}}},\: \underset{j = 3}{\underbrace{\underset{0}{0.2},\, \underset{1}{0.7},\, \underset{2}{0.3}}} }},\; \underset{i = 1}{\underbrace{ \underset{j = 0}{\underbrace{\underset{0}{0.0},\, \underset{1}{0.4},\, \underset{2}{0.4}}},\: \underset{j = 1}{\underbrace{\underset{0}{0.7},\, \underset{1}{0.8},\, \underset{2}{0.1}}},\: \underset{j = 2}{\underbrace{\underset{0}{1.0},\, \underset{1}{0.4},\, \underset{2}{0.5}}},\: \underset{j = 3}{\underbrace{\underset{0}{0.0},\, \underset{1}{0.9},\, \underset{2}{0.7}}} }} ) \]

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