Function dogleg
Given an m by n matrix A, an n by n nonsingular diagonal matrix D, an m-vector b, and a positive number delta, the problem is to determine the convex combination x of the Gauss-Newton and scaled gradient directions that minimizes (Ax-b) in the least squares sense, subject to the restriction that the Euclidean norm of Dx be at most delta.
void dogleg(Real)
(
size_t n,
Real* r,
size_t lr,
Real* diag,
Real* qtb,
Real delta,
Real* x,
Real* wa1,
Real* wa2
);
This function completes the solution of the problem if it is provided with the necessary information from the QR factorization of A. That is, if A=QR, where Q has orthogonal columns and R is an upper triangular matrix, then dogleg expects the full upper triangle of R and the first n components of (Q^T)b.
Parameters
| Name | Description |
|---|---|
| n | a positive integer variable set to the order of R. |
| r | the upper triangular matrix R. |
| lr | (not documented) |
| diag | a vector of length n which must contain the diagonal elements of the matrix D. |
| qtb | a vector of length n which must contain the first n elements of the vector (Q^T)b. |
| delta | a positive variable which specifies an upper bound on the Euclidean norm of Dx. |
| x | an output vector of length n which contains the desired convex combination of the Gauss-Newton direction and the scaled gradient direction. |
| wa1 | work array of length n. |
| wa2 | work array of length n. |