Fix Exp/Power fit docs to match returned log-space intercept (closes #110)

README.md

@@ -26,8 +26,8 @@ CurveFit.jl provides the following fitting algorithms:
 
 - **Linear fitting**: `LinearCurveFitAlgorithm` - General linear fits with customizable transformations
 - **Log fitting**: `LogCurveFitAlgorithm` - Fits `y = a*log(x) + b`
-- **Power fitting**: `PowerCurveFitAlgorithm` - Fits `y = b*x^a`
-- **Exponential fitting**: `ExpCurveFitAlgorithm` - Fits `y = b*exp(a*x)`
+- **Power fitting**: `PowerCurveFitAlgorithm` - Fits `y = exp(a*log(x) + b)` (returns `(a, b)`; scale factor is `exp(b)`)
+- **Exponential fitting**: `ExpCurveFitAlgorithm` - Fits `y = exp(a*x + b)` (returns `(a, b)`; scale factor is `exp(b)`)
 - **Polynomial fitting**: `PolynomialFitAlgorithm` - Fits polynomials of arbitrary degree
 - **Rational polynomial fitting**: `RationalPolynomialFitAlgorithm` - Fits rational functions p(x)/q(x)
 - **Sum of exponentials**: `ExpSumFitAlgorithm` - Fits `y = k + p1*exp(λ1*t) + p2*exp(λ2*t) + ...`

docs/src/tutorials/getting_started.md

@@ -112,7 +112,10 @@ println("Prediction at x=5: ", sol(5.0))
 
 ## Exponential Fitting
 
-Fit an exponential function `y = b * exp(a * x)`:
+Fit an exponential function `y = exp(a * x + b)`. The fit is performed in
+log-linear space, so `sol.u = (a, b)` returns the log-space intercept `b`; the
+multiplicative scale factor of the equivalent form `y = B * exp(a * x)` is
+`B = exp(b)`:
 
 ```@example exponential
 using CurveFit
@@ -132,7 +135,10 @@ println("Scale factor (b): ", exp(sol.u[2]))
 
 ## Power Law Fitting
 
-Fit a power law `y = b * x^a`:
+Fit a power law `y = exp(a * log(x) + b)`. The fit is performed in log-log
+space, so `sol.u = (a, b)` returns the log-space intercept `b`; the
+multiplicative scale factor of the equivalent form `y = B * x^a` is
+`B = exp(b)`:
 
 ```@example power
 using CurveFit

src/common_interface.jl

@@ -254,14 +254,18 @@ to fit. This algorithm does not support passing weights through `sigma` in
 We want to solve for `a` and `b` such that:
 
 ```math
-y = b x^a
+y = \exp(a \log(x) + b) = \exp(b)\, x^a
 ```
 
-This is equivalent to a linear fit in log-log space, i.e.,
+This is a linear fit in log-log space, i.e.,
 
 ```math
-\log(y) = a \log(x) + \log(b)
+\log(y) = a \log(x) + b
 ```
+
+The returned parameters are `(a, b)`, where `b` is the intercept in log space.
+The multiplicative scale factor `B` of the equivalent form ``y = B x^a`` is
+recovered as ``B = \exp(b)``.
 """
 PowerCurveFitAlgorithm() = LinearCurveFitAlgorithm(; xfun = log, yfun = log)
 
@@ -274,14 +278,18 @@ fit. This algorithm does not support passing weights through `sigma` in
 We want to solve for `a` and `b` such that:
 
 ```math
-y = b \exp(a x)
+y = \exp(a x + b)
 ```
 
-This is equivalent to a linear fit in log-linear space, i.e.,
+This is a linear fit in log-linear space, i.e.,
 
 ```math
-\log(y) = a x + \log(b)
+\log(y) = a x + b
 ```
+
+The returned parameters are `(a, b)`, where `b` is the intercept in log space.
+The multiplicative scale factor `B` of the equivalent form ``y = B \exp(a x)``
+is recovered as ``B = \exp(b)``.
 """
 ExpCurveFitAlgorithm() = LinearCurveFitAlgorithm(; xfun = identity, yfun = log)