lsq

Arguments

A

Real or complex (m x n) matrix

B

real or complex (m x p) matrix

tol

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).

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 ZGELSY 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 — (\) left matrix division.
• inv — matrix inverse
• pinv — pseudoinverse
• rank — rank