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See the recommended documentation of this function

# lsq

linear least square problems.

### Calling Sequence

`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 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```

• backslash — (\) левое матричное деление.
• inv — matrix inverse
• pinv — pseudoinverse
• rank — rank