human
Say we have an equation we want to get coefficients of, f(x)=sum(c_i * phi(abs(x - s_i))) for phi(r)=r^2 * log(r), where s_i is a source color vector (L_s_i a_s_i b_s_i) and we want f(s_i)=t_i, where t_i is a target color vector (L_t_i a_t_i b_t_i). The way to solve this is in the linear system (A P 0)*(c d)^T=t, where A is an array of the phi(r_ij) between various source/target colors (this is defined as CIE 76 Delta E between Lab colors), P is an array of the Lab components of each source color such that it looks like (L_s_0 a_s_0 b_s_0 1 L_s_1 a_s_1 b_s_1 1 ...), c is the array of the coefficients we want to solve (c_0 c_1 ...) and d is the array (1 1 1 0). Can you write python code using numpy, scikit-learn, and other libraries as needed to solve the linear system using SVD? Note that we don't know c_0, c_1, etc in advance and are trying to solve for those.
gpt
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