# Generate a gradient function from a nonlinear model expression and a vector of named parameters.

### Description

Given a nonlinear model expressed as an expression of the form
lhs ~ formula_for_rhs
and a start vector where parameters used in the model formula are named,
attempts to build the the `R`

function for the gradient of the
residual sum of squares.
As a side effect, a text file with the program code is generated.

### Usage

1 | ```
model2grfun(modelformula, pvec, funname="mygr", filename=NULL)
``` |

### Arguments

`modelformula` |
This is a modeling formula of the form (as in |

`pvec` |
A named parameter vector. For our example, we could use start=c(b1=1, b2=2.345, b3=0.123) WARNING: the parameters in the output function will be used in the order presented in this vector. Names are NOT respected in the output function. |

`funname` |
The (optional) name for the function that is generated in the file named in the next argument. The default name is 'mygr'. |

`filename` |
The (optional) name of a file that is written containing the (text) program code for the function. If NULL, no file is written. |

### Details

None.

### Value

An `R`

function object that computes the gradient of the sum of
squared residuals of a nonlinear model at a set of parameters.

### Author(s)

John C Nash <nashjc@uottawa.ca>

### References

Nash, J. C. (1979, 1990) _Compact Numerical Methods for Computers. Linear Algebra and Function Minimisation._ Adam Hilger./Institute of Physics Publications

### See Also

Function `nls()`

, packages `optim`

and `optimx`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | ```
cat("See also examples in nlmrt-package.Rd\n")
require(numDeriv)
y <- c(5.308, 7.24, 9.638, 12.866, 17.069, 23.192, 31.443, 38.558,
50.156, 62.948, 75.995, 91.972) # for testing
tt <- seq_along(y) # for testing
f <- y ~ b1/(1 + b2 * exp(-1 * b3 * tt))
p <- c(b1 = 1, b2 = 1, b3 = 1)
mygr <- model2grfun(f, p)
myss <- model2ssfun(f, p) # for check
cat("mygr:\n")
print(mygr)
ans <- mygr(p, tt = tt, y = y)
print(ans)
gnum <- grad(myss, p, tt = tt, y = y)
cat("Max(abs(ans-gnum)) = ",max(abs(ans-gnum)),"\n")
bnew <- c(b1 = 200, b2 = 50, b3 = 0.3)
ans <- mygr(prm = bnew, tt = tt, y = y)
print(ans)
gnum <- grad(myss, bnew, tt = tt, y = y)
cat("Max(abs(ans-gnum)) = ",max(abs(ans-gnum)),"\n")
cat("Test with un-named vector\n") # At 20120424 should fail
bthree <- c(100, 40, 0.1)
ans <- mygr(prm = bthree, tt = tt, y = y)
print(ans)
gnum <- grad(myss, bthree, tt = tt, y = y)
cat("Max(abs(ans-gnum)) = ",max(abs(ans-gnum)),"\n")
``` |