wolffd@0: wolffd@0: wolffd@0: wolffd@0: Netlab Reference Manual conjgrad wolffd@0: wolffd@0: wolffd@0: wolffd@0:

conjgrad wolffd@0:

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wolffd@0: Purpose wolffd@0:

wolffd@0: Conjugate gradients optimization. wolffd@0: wolffd@0:

wolffd@0: Description wolffd@0:

wolffd@0: [x, options, flog, pointlog] = conjgrad(f, x, options, gradf) uses a wolffd@0: conjugate gradients wolffd@0: algorithm to find the minimum of the function f(x) whose wolffd@0: gradient is given by gradf(x). Here x is a row vector wolffd@0: and f returns a scalar value. wolffd@0: The point at which f has a local minimum wolffd@0: is returned as x. The function value at that point is returned wolffd@0: in options(8). A log of the function values wolffd@0: after each cycle is (optionally) returned in flog, and a log wolffd@0: of the points visited is (optionally) returned in pointlog. wolffd@0: wolffd@0:

conjgrad(f, x, options, gradf, p1, p2, ...) allows wolffd@0: additional arguments to be passed to f() and gradf(). wolffd@0: wolffd@0:

The optional parameters have the following interpretations. wolffd@0: wolffd@0:

options(1) is set to 1 to display error values; also logs error wolffd@0: values in the return argument errlog, and the points visited wolffd@0: in the return argument pointslog. If options(1) is set to 0, wolffd@0: then only warning messages are displayed. If options(1) is -1, wolffd@0: then nothing is displayed. wolffd@0: wolffd@0:

options(2) is a measure of the absolute precision required for the value wolffd@0: of x at the solution. If the absolute difference between wolffd@0: the values of x between two successive steps is less than wolffd@0: options(2), then this condition is satisfied. wolffd@0: wolffd@0:

options(3) is a measure of the precision required of the objective wolffd@0: function at the solution. If the absolute difference between the wolffd@0: objective function values between two successive steps is less than wolffd@0: options(3), then this condition is satisfied. wolffd@0: Both this and the previous condition must be wolffd@0: satisfied for termination. wolffd@0: wolffd@0:

options(9) is set to 1 to check the user defined gradient function. wolffd@0: wolffd@0:

options(10) returns the total number of function evaluations (including wolffd@0: those in any line searches). wolffd@0: wolffd@0:

options(11) returns the total number of gradient evaluations. wolffd@0: wolffd@0:

options(14) is the maximum number of iterations; default 100. wolffd@0: wolffd@0:

options(15) is the precision in parameter space of the line search; wolffd@0: default 1e-4. wolffd@0: wolffd@0:

wolffd@0: Examples wolffd@0:

wolffd@0: An example of wolffd@0: the use of the additional arguments is the minimization of an error wolffd@0: function for a neural network: wolffd@0:

wolffd@0: 
wolffd@0: w = quasinew('neterr', w, options, 'netgrad', net, x, t);
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wolffd@0: Algorithm wolffd@0:

wolffd@0: wolffd@0: The conjugate gradients algorithm constructs search wolffd@0: directions di that are conjugate: i.e. di*H*d(i-1) = 0, wolffd@0: where H is the Hessian matrix. This means that minimising along wolffd@0: di does not undo the effect of minimising along the previous wolffd@0: direction. The Polak-Ribiere formula is used to calculate new search wolffd@0: directions. The Hessian is not calculated, so there is only an wolffd@0: O(W) storage requirement (where W is the number of wolffd@0: parameters). However, relatively accurate line searches must be used wolffd@0: (default is 1e-04). wolffd@0: wolffd@0:

wolffd@0: See Also wolffd@0:

wolffd@0: graddesc, linemin, minbrack, quasinew, scg

wolffd@0: Pages: wolffd@0: Index wolffd@0:

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