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## Purpose

Find the local minimum of a scalar function using conjugate gradient

## Explanation

Find the local minimum of a scalar function of several variables using
the Conjugate Gradient method (Fletcher-Reeves-Polak-Ribiere algorithm).
Function may be anything with computable partial derivatives.
Each call to minF_conj_grad performs one iteration of algorithm,
and returns an N-dim point closer to the local minimum of function.
CALLING EXAMPLE:
p_min = replicate( 1, N_dim )
while (conv_factor GT 0) do begin
endwhile

## Inputs

p_min = vector of independent variables, location of minimum point
obtained from previous call to minF_conj_grad, (or first guess).

## Keywords

FUNC_NAME = function name (string)
Calling mechanism should be: F = func_name( px, gradient )
where:
F = scalar value of function at px.
px = vector of independent variables, input.
gradient = vector of partial derivatives of the function
with respect to independent variables, evaluated at px.
This is an optional output parameter:
gradient should not be calculated if parameter is not
supplied in call (Unless you want to waste some time).
/INIT must be specified on first call (whenever p_min is a guess),
to initialize the iteration scheme of algorithm.
/USE_DERIV causes the directional derivative of function to be used
in the 1-D minimization part of algorithm
(default is not to use directional derivative).
TOLERANCE = desired accuracy of minimum location, default=sqrt(1.e-7).

## Outputs

p_min = vector giving improved solution for location of minimum point.
f_min = value of function at p_min.
conv_factor = gives the current rate of convergence (change in value),
iteration should be stopped when rate gets near zero.

## External Calls

pro minF_bracket, to find 3 points which bracket the minimum in 1-D.
pro minF_parabolic, to find minimum point in 1-D.
pro minF_parabol_D, to find minimum point in 1-D, using derivatives.

## Procedure

Algorithm adapted from Numerical Recipes, sec.10.6 (p.305).
the best direction (in N-dim space) in which to proceed to find
the minimum point. The function is then minimized along
this direction of conjugate gradient (a 1-D minimization).
The algorithm is repeated starting at the new point by calling again.

## Modification History

Written, Frank Varosi NASA/GSFC 1992.
Converted to IDL V5.0 W. Landsman September 1997

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