function positivity, x, DERIVATIVE=deriv, EPSILON=epsilon ;+ ; NAME: ; POSITIVITY ; PURPOSE: ; Map an image uniquely and smoothly into all positive values. ; EXPLANATION: ; Take unconstrained x (usually an image), and map it uniquely and ; smoothly into positive values. Negative values of x get mapped to ; interval ( 0, sqrt( epsilon )/2 ], positive values go to ; ( sqrt( epsilon )/2, oo ) with deriv approaching 1. Derivative is ; always 1/2 at x=0. Derivative is used by the MRL deconvolution ; algorithm. ; ; CALLING SEQUENCE: ; result = POSITIVITY( x, [ /DERIVATIVE, EPSILON = ) ; ; INPUTS: ; x - input array, unconstrained ; ; OUTPUT: ; result = output array = ((x + sqrt(x^2 + epsilon))/2 ; if the /DERIV keyword is set then instead the derivative of ; the above expression with respect to X is returned ; ; OPTIONAL INPUT KEYWORDS: ; DERIV - if this keyword set, then the derivative of the positivity ; mapping is returned, rather than the mapping itself ; EPSILON - real scalar specifying the interval into which to map ; negative values. If EPSILON EQ 0 then the mapping reduces to ; positive truncation. If EPSILON LT then the mapping reduces to ; an identity (no change). Default is EPSILON = 1e-9 ; ; REVISION HISTORY: ; F.Varosi NASA/GSFC 1992, as suggested by R.Pina UCSD. ; Converted to IDL V5.0 W. Landsman September 1997 ;- if N_elements( epsilon ) NE 1 then epsilon = 1.e-9 if keyword_set( deriv ) then begin if (epsilon GT 0) then return,(1 + x/sqrt( x^2 + epsilon ))/2 \$ else if (epsilon LT 0) then return,(1) \$ else return,( x GT 0 ) endif else begin if (epsilon GT 0) then return,( x + sqrt( x^2 + epsilon ) )/2 \$ else if (epsilon LT 0) then return, x \$ else return,( x > 0 ) endelse end