bspline - B-Spline Interpolation and Regression

Build and use B-splines for interpolation and regression. In case of regression, equality constraints as well as monotonicity and/or positivity of B-spline weights can be imposed. Moreover, knot positions (not only spline weights) can be part of optimized parameters too. For this end, 'bspline' is able to calculate Jacobian of basis vectors as function of knot positions. User is provided with functions calculating spline values at arbitrary points. These functions can be differentiated and integrated to obtain B-splines calculating derivatives/integrals at any point. B-splines of this package can simultaneously operate on a series of curves sharing the same set of knots. 'bspline' is written with concern about computing performance that's why the basis and Jacobian calculation is implemented in C++. The rest is implemented in R but without notable impact on computing speed.

Last updated 20 days ago

openblascpp

3.48 score 3 stars 1 scripts 609 downloads

nlsic - Non Linear Least Squares with Inequality Constraints

We solve non linear least squares problems with optional equality and/or inequality constraints. Non linear iterations are globalized with back-tracking method. Linear problems are solved by dense QR decomposition from 'LAPACK' which can limit the size of treated problems. On the other side, we avoid condition number degradation which happens in classical quadratic programming approach. Inequality constraints treatment on each non linear iteration is based on 'NNLS' method (by Lawson and Hanson). We provide an original function 'lsi_ln' for solving linear least squares problem with inequality constraints in least norm sens. Thus if Jacobian of the problem is rank deficient a solution still can be provided. However, truncation errors are probable in this case. Equality constraints are treated by using a basis of Null-space. User defined function calculating residuals must return a list having residual vector (not their squared sum) and Jacobian. If Jacobian is not in the returned list, package 'numDeriv' is used to calculated finite difference version of Jacobian. The 'NLSIC' method was fist published in Sokol et al. (2012) <doi:10.1093/bioinformatics/btr716>.

Last updated 8 months ago

2.78 score 1 stars 1 dependents 4 scripts 264 downloads