Scilab Website | Contribute with GitLab | Mailing list archives | ATOMS toolboxes
Scilab Online Help
5.5.0 - English

Change language to:
Français - 日本語 - Português - Русский

Please note that the recommended version of Scilab is 2024.0.0. This page might be outdated.
See the recommended documentation of this function

Scilab Help >> Linear Algebra > Linear Equations > lsq

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

See Also

Report an issue
<< linsolve Linear Equations lu >>

Copyright (c) 2022-2023 (Dassault Systèmes)
Copyright (c) 2017-2022 (ESI Group)
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Fri Apr 11 14:06:50 CEST 2014