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as we learned in class, an important component of non-linear least squares is the jacobian matrix, the set of partial derivatives with respect to parameters at each data point. in def calc jacobian(x,p), you will need to implement the calculation of the jacobian matrix for the function: where 'a' is the first parameter (p[0,0]), 'b' is the second (p[1,0]), an so on...

Respuesta :

To calculate the Jacobian matrix for the function given in the problem, you can follow these steps:

Define the function and its parameters. The function is given as:

f(x, p) = aexp(bx) + cexp(dx)

where a, b, c, and d are the parameters of the function, represented as p[0], p[1], p[2], and p[3] respectively.

Write a function to calculate the partial derivatives of the function with respect to each parameter. The Jacobian matrix is a matrix of partial derivatives, so you will need to calculate the partial derivative of the function with respect to each parameter.

The partial derivative of the function with respect to a parameter is the derivative of the function with respect to that parameter, holding all other parameters constant.

For example, the partial derivative of f(x, p) with respect to a is:

df/da = exp(b*x)

The partial derivatives of the function with respect to the other parameters can be calculated in a similar manner.

Calculate the Jacobian matrix at each data point. To calculate the Jacobian matrix at a given data point (x, y), you will need to evaluate the partial derivatives of the function at that point.

For example, to calculate the Jacobian matrix at the data point (x, y), you would evaluate the partial derivatives at x and p[0], p[1], p[2], and p[3], and place the results in the appropriate positions in the Jacobian matrix.

Return the Jacobian matrix. Once you have calculated the Jacobian matrix at each data point, you can return the matrix as the result of the function

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