lsq - linear least square problems.

Calling Sequence

X=lsq(A,B)

Parameters

• A : Real or complex (m x n) matrix
• B : real or complex (m x p) matrix
• X : real or complex (n x p) matrix

Description

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.

REFERENCES

lsq function is based on the LApack functions DGELSY for real matrices and WGELSY for complex matrices.

EXAMPLES

//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
   

See Also

backslash  inv  pinv  rank