NAME

constrained_least_squares - Solves Ax=b in the least squares sense with linear constraints.

SYNOPSIS

#include "n2/n2_quadratic.h"

Example compile flags (system dependent):
  -DLINUX_X86_64 -DLINUX_X86_64_OPTERON  -DGNU_COMPILER 
   -I/home/kobus/include
   -L/home/kobus/misc/load/linux_x86_64_opteron -L/usr/lib/x86_64-linux-gnu
  -lKJB                               -lfftw3  -lgsl -lgslcblas -ljpeg  -lSVM -lstdc++                    -lpthread -lSLATEC -lg2c    -lacml -lacml_mv -lblas -lg2c      -lncursesw 


int constrained_least_squares
(
	Vector **result_vpp,
	const Matrix *A_mp,
	const Vector *b_vp,
	const Matrix *le_constraint_mp,
	const Vector *le_constraint_vp,
	const Matrix *eq_constraint_mp,
	const Vector *eq_constraint_vp,
	const Vector *lb_vp,
	const Vector *ub_vp
);

DESCRIPTION

This routine solves Ax=b in the least squares sense subject to linear constraints. Put differently, this routine calculates


  MIN { || Ax - b ||  }
   x                2

  Subject to:

     Lx <= m
     Ex  = e
      x <= u
      x >= l

Note that it is generally easy to convert a basic sum of squared error objective function into Ax=0, least squares sense. The result is put into the vector pointed to by *result_vpp, which is created if it is NULL, resized if it is the wrong sized, and reused otherwise. The number of rows in the matrix pointed to by the argument "A_mp" (i.e, A, above) must be the same as the length of the vector pointed to by the argument "b_vp" (i.e. b, above). In addition, the number of columns of of *A_mp (i.e, number of unknowns) cannot exceed the number of rows of *A_mp (number of equations). With respect to the above formulation, the parameter le_constraint_mp corresponds to L, le_constraint_vp to m, eq_constraint_mp to E, eq_constraint_vp to e, lb_row_arg_vp corresponds to l, and ub_row_arg_vp corresponds to u. Any of these constraint arguments can be set to NULL if there are no constraints of the corresponding type.

RETURNS

NO_ERROR on success, and ERROR on failure, with an appropriate error message being set.

DISCLAIMER

This software is not adequatedly tested. It is recomended that results are checked independantly where appropriate.

AUTHOR

Kobus Barnard

DOCUMENTER

Kobus Barnard