lsq — linear least square problems.
X=lsq(A,B [,tol])
Real or complex (m x n) matrix
real or complex (m x p) matrix
positive scalar, used to determine the effective rank of A
(defined as the order of the largest leading triangular
submatrix R11 in the QR factorization with pivoting of A,
whose estimated condition number <= 1/tol. The tol default value is
set to sqrt(%eps).
real or complex (n x p) matrix
X=lsq(A,B) computes the minimum norm least square solution of
the equation A*X=B, while X=A \ B compute a least square
solution with at at most rank(A) nonzero components per column.
lsq function is based on the LApack functions DGELSY for
real matrices and ZGELSY for complex matrices.
//Build the data x=(1:10)'; y1=3*x+4.5+3*rand(x,'normal'); y2=1.8*x+0.5+2*rand(x,'normal'); plot2d(x,[y1,y2],[-2,-3]) //Find the linear regression A=[x,ones(x)];B=[y1,y2]; X=lsq(A,B); y1e=X(1,1)*x+X(2,1); y2e=X(1,2)*x+X(2,2); plot2d(x,[y1e,y2e],[2,3]) //Difference between lsq(A,b) and A\b A=rand(4,2)*rand(2,3);//a rank 2 matrix b=rand(4,1); X1=lsq(A,b) X2=A\b [A*X1-b, A*X2-b] //the residuals are the same