(Curve Fitting): Mention plotting the curves.

(Standard Nonlinear Models): Add additional models.
(Curve fitting details): Mention the Levenberg-Marquardt method.

1 files changed, 27 insertions, 5 deletions

diff --git a/man/calc.texi b/man/calc.texi
index 9e50629a3b2..95737d6106a 100644
--- a/man/calc.texi
+++ b/man/calc.texi
@@ -23962,7 +23962,11 @@ such as @expr{y = m x + b} where @expr{m} and @expr{b} are parameters
 to be determined.  For a typical set of measured data there will be
 no single @expr{m} and @expr{b} that exactly fit the data; in this
 case, Calc chooses values of the parameters that provide the closest
-possible fit.
+possible fit.  The model formula can be entered in various ways after
+the key sequence @kbd{a F} is pressed.  If the letter @kbd{P}
+is pressed after @kbd{a F} but before the model description is entered,
+the data as well as the model formula will be plotted after the formula
+is determined.
 
 @menu
 * Linear Fits::
@@ -24454,6 +24458,18 @@ Quadratic.  @mathit{a + b (x-c)^2 + d (x-e)^2}.
 Gaussian.  
 @texline @math{{a \over b \sqrt{2 \pi}} \exp\left( -{1 \over 2} \left( x - c \over b \right)^2 \right)}.
 @infoline @mathit{(a / b sqrt(2 pi)) exp(-0.5*((x-c)/b)^2)}.
+@item s
+Logistic @emph{s} curve.
+@texline @math{a/(1+e^{b(x-c)})}.
+@infoline @mathit{a/(1 + exp(b (x - c)))}.
+@item b
+Logistic bell curve.
+@texline @math{ae^{b(x-c)}/(1+e^{b(x-c)})^2}.
+@infoline @mathit{a exp(b (x - c))/(1 + exp(b (x - c)))^2}.
+@item o
+Hubbert linearization.
+@texline @math{{y \over x} = a(1-x/b)}.
+@infoline @mathit{(y/x) = a (1 - x/b)}.
 @end table
 
 All of these models are used in the usual way; just press the appropriate
@@ -24462,8 +24478,9 @@ result will be a formula as shown in the above table, with the best-fit
 values of the parameters substituted.  (You may find it easier to read
 the parameter values from the vector that is placed in the trail.)
 
-All models except Gaussian and polynomials can generalize as shown to any
-number of independent variables.  Also, all the built-in models have an
+All models except Gaussian, logistics, Hubbert and polynomials can
+generalize as shown to any number of independent variables.  Also, all
+the built-in models except for the logistic and Hubbert curves have an 
 additive or multiplicative parameter shown as @expr{a} in the above table
 which can be replaced by zero or one, as appropriate, by typing @kbd{h}
 before the model key.
@@ -24603,7 +24620,7 @@ to convert the model into this form.  For example, if the model
 is @expr{a + b x + c x^2}, then @expr{f(x) = 1}, @expr{g(x) = x},
 and @expr{h(x) = x^2} are suitable functions.
 
-For other models, Calc uses a variety of algebraic manipulations
+For most other models, Calc uses a variety of algebraic manipulations
 to try to put the problem into the form
 
 @smallexample
@@ -24662,7 +24679,12 @@ The Gaussian model looks quite complicated, but a closer examination
 shows that it's actually similar to the quadratic model but with an
 exponential that can be brought to the top and moved into @expr{Y}.
 
-An example of a model that cannot be put into general linear
+The logistic models cannot be put into general linear form.  For these
+models, and the Hubbert linearization, Calc computes a rough
+approximation for the parameters, then uses the Levenberg-Marquardt
+iterative method to refine the approximations.
+
+Another model that cannot be put into general linear
 form is a Gaussian with a constant background added on, i.e.,
 @expr{d} + the regular Gaussian formula.  If you have a model like
 this, your best bet is to replace enough of your parameters with