README.md

Author: MWillettM

README.md

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+This is a Python implementation of the Faul-Goodsen-Powell algorithm which produces an interpolant for d-dimensional data using the multiquadric radial basis functions. It works well for even very high dimensional data.
+
+INSTALLATION/REQUIREMENTS:
+Python > 3.11.8
+Numpy
+
+ALGORITHM DESCRIPTION - inputs - FGP(data, values, q, c, error)
+Data centers (x_i) and values at those points (f_i)
+Error
+Two parameters for the algorithm - q and c:
+c>0, using a smaller value (O(10^-1) or smaller) is advised. This is the 'shape parameter' for the multiquadric.
+q>0, using a value of q=30 is standard - feel free to go between 5 and 50. A rule of thumb is that smaller q means each iteration is quicker, but we may need more iterations for convergence overally. 
+
+ALGORITHM DESCRIPTION - outputs
+Iteration count - k
+
+
+The interpolant, s(x) is of the form 
+
+s(x) = sum_i^n lambda_i phi(x-x_i) + alpha
+
+where the x_i are the data centers and phi(x) = (x^2+c^2)^0.5 is the multiquadric radial basis function.
+
+The algorithm returns the coefficients lambda_i and the value of alpha.
+
+You can try the DEMO version or use the FULL IMPLEMENTATION version as well.
+
+The DEMO version lets you vary the distribution that the test data is drawn from:
+The unit d-ball
+The unit d-cube
+The unit d-Normal
+The integer grid in d-dimensions.