# lsq

linear least square solution of A*X=B with minimal norm(X)

### Syntax

X = lsq(A, B) X = lsq(A, B, tol)

### 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 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

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