Title:	Interface to the 'sparseLM' Levenberg-Marquardt Library
Version:	0.5
Description:	Provides an R interface to the 'sparseLM' C library for large-scale nonlinear least squares problems with arbitrarily sparse Jacobians. The underlying solver implements a sparse variant of the Levenberg-Marquardt algorithm for minimizing sum-of-squares objective functions, supports user-supplied analytic Jacobians or finite-difference approximation, and is designed to exploit sparsity for improved memory use and performance. This package exposes the solver in R and uses sparse matrix classes and the 'CHOLMOD' sparse Cholesky factorization routines through the 'Matrix' package interface. Methods from the C library are described in Lourakis (2010) <doi:10.1007/978-3-642-15552-9_4>.
URL:	https://github.com/smith-group/sparseLM, https://smith-group.github.io/sparseLM/
Depends:	Matrix
Imports:	methods
LinkingTo:	Matrix
License:	GPL-2
Encoding:	UTF-8
NeedsCompilation:	yes
RoxygenNote:	7.3.3
Packaged:	2026-03-25 13:46:11 UTC; colin
Author:	Colin Smith [aut, cre], Manolis Lourakis [aut]
Maintainer:	Colin Smith <colin.smith@wesleyan.edu>
Repository:	CRAN
Date/Publication:	2026-03-30 09:30:08 UTC

Add values to an existing sparse column in place

Description

Adds value to the existing nonzero entries of column j at rows i. Only existing nonzeros are updated; no new nonzeros are created. add_assign_col_inplace_unsafe skips the input validation performed by add_assign_col_inplace. When validate = TRUE, the function checks that i is strictly increasing, in range, and contains no NA; that value contains no NA/NaN; and that the column pointer p is nondecreasing.

Usage

add_assign_col_inplace(x, i, j, value, validate = TRUE)

add_assign_col_inplace_unsafe(x, i, j, value)

Arguments

Value

value passed to x

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  x <- Matrix::Matrix(0, nrow = 4, ncol = 2, sparse = TRUE)
  x[1, 1] <- 1
  x[3, 1] <- 2
  # value is the same length as i
  add_assign_col_inplace(x, i = c(1L, 3L), j = 1L, value = c(10, -5))
}

Nonlinear Least Squares Fit with Sparse Levenberg-Marquardt Algorithm

Description

Nonlinear Least Squares Fit with Sparse Levenberg-Marquardt Algorithm

Usage

sparselm(
  p,
  x,
  func,
  fjac,
  Jnnz,
  nconvars = 0,
  itmax = 100,
  opts = sparselm.opts(),
  dif = FALSE,
  ...
)

Arguments

Value

list with four elements: par, niter, info, and term

Examples

set.seed(1)
t <- seq(0, 10, length.out = 80)
g <- function(A, mu, s, x) A * exp(-0.5 * ((x - mu) / s)^2)
y <- g(3, 3, 0.7, t) + g(2, 7, 1.0, t) + rnorm(length(t), sd = 0.2)
p0 <- c(2.5, 3.2, 0.8, 1.5, 6.8, 1.2)

y_obs <- y
mask1 <- abs(t - p0[2]) <= 3 * p0[3]
mask2 <- abs(t - p0[5]) <= 3 * p0[6]
mask <- mask1 | mask2
y[!mask] <- 0

idx1 <- which(mask1); idx2 <- which(mask2)
i <- c(idx1, idx1, idx1, idx2, idx2, idx2)
j <- c(rep(1, length(idx1)), rep(2, length(idx1)), rep(3, length(idx1)),
       rep(4, length(idx2)), rep(5, length(idx2)), rep(6, length(idx2)))
Jpat <- sparseMatrix(i = i, j = j, x = 1, dims = c(length(t), 6))

func <- function(p, t, ...) {
  f <- g(p[1], p[2], p[3], t) + g(p[4], p[5], p[6], t)
  f[!mask] <- 0
  f
}

fjac <- function(p, t, ...) {
  A1 <- p[1]; mu1 <- p[2]; s1 <- p[3]
  A2 <- p[4]; mu2 <- p[5]; s2 <- p[6]
  e1 <- exp(-0.5 * ((t[idx1] - mu1) / s1)^2)
  e2 <- exp(-0.5 * ((t[idx2] - mu2) / s2)^2)
  J <- Jpat
  J@x <- c(e1, A1 * e1 * ((t[idx1] - mu1) / s1^2),
           A1 * e1 * ((t[idx1] - mu1)^2 / s1^3),
           e2, A2 * e2 * ((t[idx2] - mu2) / s2^2),
           A2 * e2 * ((t[idx2] - mu2)^2 / s2^3))
  J
}

fit <- sparselm(p0, y, func, fjac,
                Jnnz = length(i),
                nconvars = 0, t = t)
Jpat
fit$par

f0 <- g(p0[1], p0[2], p0[3], t) + g(p0[4], p0[5], p0[6], t)
f1 <- g(fit$par[1], fit$par[2], fit$par[3], t) + g(fit$par[4], fit$par[5], fit$par[6], t)
plot(t, y_obs, pch = 16, cex = 0.6, col = "black", xlab = "t", ylab = "y")
lines(t, f0, col = "blue")
lines(t, f1, col = "red")

Sparse Levenberg-Marquardt Algorithm Options

Description

Sparse Levenberg-Marquardt Algorithm Options

Usage

sparselm.opts(
  mu = 0.001,
  epsilon1 = 1e-12,
  epsilon2 = 1e-12,
  epsilon3 = 1e-12,
  delta = 1e-06
)

Arguments

Value

numeric vector of length 6 with the above options and spsolver=1 (SuiteSparse CHOLMOD)