Linear Least-Squares Fitting
Solves linearly constrained linear least-squares problems.
lsqlin(A, b, C, d, tol = 1e-13)
A |
|
b |
vector or colum matrix with |
C |
|
d |
vector or |
tol |
tolerance to be passed to |
lsqlin(A, b, C, d) minimizes ||A*x - b|| (i.e., in the
least-squares sense) subject to C*x = d.
Returns a least-squares solution as column vector, or a matrix of solutions
in the columns if b is a matrix with several columns.
The Matlab function lsqlin solves a more general problem, allowing
additional linear inequalities and bound constraints. In pracma this
task is solved applying function lsqlincon.
HwB email: <hwborchers@googlemail.com>
Trefethen, L. N., and D. Bau III. (1997). Numerical Linear Algebra. SIAM, Society for Industrial and Applied Mathematics, Philadelphia.
A <- matrix(c(
0.8147, 0.1576, 0.6557,
0.9058, 0.9706, 0.0357,
0.1270, 0.9572, 0.8491,
0.9134, 0.4854, 0.9340,
0.6324, 0.8003, 0.6787,
0.0975, 0.1419, 0.7577,
0.2785, 0.4218, 0.7431,
0.5469, 0.9157, 0.3922,
0.9575, 0.7922, 0.6555,
0.9649, 0.9595, 0.1712), 10, 3, byrow = TRUE)
b <- matrix(c(
0.7060, 0.4387,
0.0318, 0.3816,
0.2769, 0.7655,
0.0462, 0.7952,
0.0971, 0.1869,
0.8235, 0.4898,
0.6948, 0.4456,
0.3171, 0.6463,
0.9502, 0.7094,
0.0344, 0.7547), 10, 2, byrow = TRUE)
C <- matrix(c(
1.0000, 1.0000, 1.0000,
1.0000, -1.0000, 0.5000), 2, 3, byrow = TRUE)
d <- as.matrix(c(1, 0.5))
# With a full rank constraint system
(L <- lsqlin(A, b, C, d))
# 0.10326838 0.3740381
# 0.03442279 0.1246794
# 0.86230882 0.5012825
C %*% L
# 1.0 1.0
# 0.5 0.5
## Not run:
# With a rank deficient constraint system
C <- str2num('[1 1 1;1 1 1]')
d <- str2num('[1;1]')
(L <- lsqlin(A, b[, 1], C, d))
# 0.2583340
# -0.1464215
# 0.8880875
C %*% L # 1 1 as column vector
# Where both A and C are rank deficient
A2 <- repmat(A[, 1:2], 1, 2)
C <- ones(2, 4) # d as above
(L <- lsqlin(A2, b[, 2], C, d))
# 0.2244121
# 0.2755879
# 0.2244121
# 0.2755879
C %*% L # 1 1 as column vector
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.