Weighted L.S. conjugate-direction template

The pseudocode for minimizing the weighted residual $\bold 0\approx \bold r = \bold W (\bold F \bold m - \bold d)$by conjugate-direction method, is effectively like that for the unweighted method except that the initial residual is weighted and the operator $\bold F$ has the premultiplier $\bold W$.Naturally, the adjoint operator $\bold F'$has the postmultiplier $\bold W'$.In some applications the weighting operator $\bold W$is simply a weighting function or diagonal matrix (so then $\bold W = \bold W'$)and in other applications, the weighting operator $\bold W$may be an operator, like the derivative along a data recording trajectory (so then $\bold W \ne \bold W'$).

		 $\bold r \quad\longleftarrow\quad\bold W (\bold F \bold m - \bold d)$ 
		 iterate { 
		 		  $\Delta\bold m \quad\longleftarrow\quad\bold F'\bold W'\ \bold r$ 
		 		  $\Delta\bold r\ \quad\longleftarrow\quad\bold W \bold F \ \Delta \bold m$ 
		 		  $(\bold m,\bold r) \quad\longleftarrow\quad{\rm cgstep}
 (\bold m,\bold r, \Delta\bold m,\Delta\bold r )$ 
		 		 }