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lines changed Original file line number Diff line number Diff line change @@ -102,24 +102,28 @@ two calls to ``f`` to evaluate the gradient:
102102 x_3 \\
103103 x_4
104104 \end{bmatrix}
105-
106- \vec{x}_{\epsilon} = \begin{bmatrix}
105+ ```
106+ 1st call:
107+ ``` math
108+ \to \vec{x}_{\epsilon} = \begin{bmatrix}
107109 x_1 + \epsilon_1 \\
108110 x_2 + \epsilon_2 \\
109111 x_3 \\
110112 x_4
111113 \end{bmatrix}
112114\to
113- f(\vec{x}_{\epsilon}) = f(\vec{x}) + \frac{\delta f(\vec{x})}{\delta x_1} \epsilon_1 + \frac{\delta f(\vec{x})}{\delta x_2} \epsilon_2
114-
115- \vec{x}_{\epsilon} = \begin{bmatrix}
115+ f(\vec{x}_{\epsilon}) = f(\vec{x}) + \frac{\delta f(\vec{x})}{\delta x_1} \epsilon_1 + \frac{\delta f(\vec{x})}{\delta x_2} \epsilon_2,
116+ ```
117+ 2nd call:
118+ ``` math
119+ \to \vec{x}_{\epsilon} = \begin{bmatrix}
116120 x_1 \\
117121 x_2 \\
118122 x_3 + \epsilon_1 \\
119123 x_4 + \epsilon_2
120124 \end{bmatrix}
121125\to
122- f(\vec{x}_{\epsilon}) = f(\vec{x}) + \frac{\delta f(\vec{x})}{\delta x_3} \epsilon_1 + \frac{\delta f(\vec{x})}{\delta x_4} \epsilon_2
126+ f(\vec{x}_{\epsilon}) = f(\vec{x}) + \frac{\delta f(\vec{x})}{\delta x_3} \epsilon_1 + \frac{\delta f(\vec{x})}{\delta x_4} \epsilon_2.
123127```
124128
125129This seeding process is similar for Jacobians, so we won't rehash it here.
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