➗ Math tools

Summary

• Interpolate
• Resample
• Matrix multiply
• Matrix determinant
• Matrix linear equation solution



Formula variable names

x:
x₁:
x₂:
i₁:
i₂:
f:
lambda:
n_samples:

Interpolate

f_interpolate(x, x₁, x₂) = f(x₁) * (1 - 𝜆_x) + f(x₂) * 𝜆_x
𝜆_x = (x - x₁) / (x₂ - x₁) if x₁ ≠ x₂, else 0.

Code:

Resample

Resample x:
f_resample(x, x₁, x₂, n_samples) = [x_i1... x_insamples] = [x₁... x₂]

Code:

Matrix multiply

Matrix multiply:
M[i_row][i_col] = ∑_iprod M₁[i_row][i_prod] * M₂[i_prod][i_col]

Code:

Matrix determinant

Matrix determinant:
det(M) = ∑_icol (-1)^{i_row + i_col} * M[i_row][i_col] * det(M[i_row][i_col])

Code:

Matrix linear equation solution

Matrix linear equation solution:
X[i] = det(M_i) / det(M)
M_i[i_row][i] = B[i_row]
M_i[i_row][i_col != i] = M[i_row][i_col]

Code: