Changes

* Got rid of the inner evolution of the magnetization. If the looping over the number of CPMG elements is given by the index l, and the initial magnetization has been formed, then the number of times for propagation of magnetization is l = power_si_mi_di-1. If the magnetization matrix "Mint" has the index Mint_(i,k) and the evolution matrix has the index Evol_(k,j), i=1, k=7, j=7 then the dot product is given by: Sum_{k=1}^{k} Mint_(1,k) * Evol_(k,j) = D_(1, j). The numpy einsum formula for this would be: einsum('ik,kj -> ij', Mint, Evol). Following evolution will be: Sum_{k=1}^{k} D_(1, j) * Evol_(k,j) = Mint_(1,k) * Evol_(k,j) * Evol_(k,j). We can then realize, that the evolution matrix can be raised to the power l. Evol_P = Evol**^l. It will then be: einsum('ik,kj -> ij', Mint, Evol_P). Get which power to raise the matrix to. l = power_si_mi_di-1. Raise the square evolution matrix to the power l. evolution_matrix_T_pwer_i = matrix_power(evolution_matrix_T_i, l), Mint_T_i = dot(Mint_T_i, evolution_matrix_T_pwer_i) or Mint_T_i = einsum('ik,kj -> ij', Mint_T_i, evolution_matrix_T_pwer_i). [https://gna.org/task/?7807 Task #7807]: Speed-up of dispersion models for clustered analysis.

* Implemented the zooming grid search. If the zoom level is set to any value other than 0, then the grid width will be divided by 2**^zoom_level and centred at the current parameter values. If the new grid is outside of the bounds of the original grid, the entire grid will be translated so that it lies entirely within the original.

* Bug fix for the chi-squared gradient calculation in the C module. The definition of the square() function needed extra brackets so that the 1/error**² calculation would be 1/(error*error) rather than the incorrect 1/error*error form.

* Got the method of 'Steepest descent' to work properly, by specifying the Jacobian correctly. The Jacobian was derived according to the χ² function. The key point was to evaluate the two derivative arrays for all times points, and then sum each of the two arrays together, before constructing the Jacobian. This clearly shows the difference between minfx and scipy.optimize.leastsq. scipy.optimize.leastsq takes as input a function F(x0), which should return the array of weighted differences between function value and measured values: "1. / self.errors * (self.calc_exp(self.times, *params) - self.values)". This will be an array with number of elements 'i' corresponding to number of elements. scipy.optimize.leastsq then internally evaluates the sum of squares -> sum[ (O - E)**² ], and minimises this. This is the χ². Minfx requires the function to minimise before hand. So, the "func" should be χ². Then the dfunc, and d2func, should be derivative of χ², but all elements in the array should still be summed together. [https://gna.org/task/?7822 Task #7822]: Implement user function to estimate R_2eff and associated errors for exponential curve fitting.

* By using minfx, and the reported Jacobian, it is now possible to get the exact same error estimation as scipy.optimize.leastsq. The fatal error was to set the weighting matrix with diagonal elements as the error. There weights are 1/errors**². There is though some unanswered questions left. The Jacobian used, is the direct derivative of the function. It is not the χ² derivative Jacobian. [https://gna.org/task/?7822 Task #7822]: Implement user function to estimate R_2eff and associated errors for exponential curve fitting.