qr

QR decomposition of a complex matrix and least squares solver

The package provides an implementation of the QR decomposition for general complex matrices for the go programming language. It uses the Householder algorithm described in this book:

Walter Gander, Martin J. Gander, Felix Kwok: Scientific Computing, an Introduction Using Maple and Matlab, Springer, April 2014, ISBN 978-3-319-04324-1 Pages 359-361.

The QR decomposition is often used to solve overdetermined linear systems of equations in the form

A x = b

where A is a complex matrix with size m x n and m >= n. b is the right hand side vector of length m and x the vector of unknowns with the same size as b.

The package is self-contained and uses only the standard library.

Example:

// Solution to the overdetermined 3x2 system: A x = b.
// import "github.com/ktye/qr"

// Matrix A (3x2).
A := [][]complex128{
        []complex128{complex(1, 2), complex(5, -1)},
        []complex128{complex(6, 8), complex(1, 0)},
        []complex128{complex(3, -2), complex(-7, 3)},
}

// Right hand side (3x1):
b := []complex128{
        complex(5, -2),
        complex(-3, 1),
        complex(3, 0),
}

// Compute the QR decomposition.
if D, err := qr.New(A); err != nil {
        panic(err)
} else {
        // Solve the system.
        if x, err := D.Solve(b); err != nil {
                panic(err)
        } else {
                // do something with x
        }
}