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Tnnls
Purpose
MEX interface for Tnnls, TOMLAB
NNLS solver
For solving linearly constrained least squares problems with both equality and inequality constraints.
Syntax
[x, rNorm, mode, w] = Tnnls ( A, b, E, f, L, ColScale, D, epsRank, epsBlow);
Description
Tnnls solves a linearly constrained least squares
problem with both equality and inequality constraints.
May return a covariance matrix of the solution parameters.
Given dense matrices E, A and G of
respective
dimensions mE by N, mA by N
and mG by N, and vectors f, b
and h of
respective lengths ME, MA and MG.
This subroutine solves the
linearly constrained least squares problem formulated as:
min || A x - b || subject to
E x = f Equations to be exactly satisfied
x >= 0 Nonnegativitiy constraints
In case the equality constraints cannot be satisfied, a
generalized inverse solution residual vector length is obtained
for f-Ex. This is the minimal length possible for
f-Ex.
Any number of rows in A and E are permitted.
Input Parameters
At least 2 input parameters needed.
A mA x n dense matrix
b mA x 1 dense vector
E mE x n dense matrix
f mE x 1 dense vector
L Variable 1:L are unconstrained. Variable L+1:N non-negative
ColScale If > 0 column scaling of full matrix [A,b;E,f]. Default 0
D If nonempty, n x 1 dense vector with diagonal scaling of columns
epsRank Rank tolerance in least squares part
epsBlow Blow-up parameter, default value SQRT(eps), must be > eps
The reciprocal of this parameter is used in rejecting solution
components as too large when a variable is first brought into the
active set. Too large means that the proposed component times the
reciprocal of the parameter is not less than the ratio of the
norms of the right-side vector and the data matrix.
Output Parameters
x Solution x
rNorm || [Ax-b;Ex-f] ||
mode Exit status:
0 Success
1 Max. number of iterations (equal to 3*(N-L)) exceeded.
Nearly all problems should complete in fewer than this
number of iterations. An approximate solution and its
corresponding residual vector length are in x and rNorm.
2 Usage error occurred. Should not be possible.
w Dual solution vector, Lagrange multipliers
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