ApCoCoA-1:Num.QR

From ApCoCoAWiki
This article is about a function from ApCoCoA-1.

Num.QR

Computes the QR-decomposition of a matrix.

Syntax

Num.QR(A:MAT):[Q:MAT,R:MAT]

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

This command computes the QR-decomposition of a matrix using the external library Lapack, i.e. the matrix A will be decomposed into the product of an orthogonal matrix Q and an upper-right triangular matrix R.

  • @param A The matrix to decompose.

  • @return An orthogonal matrix Q and an upper-right triangular matrix R such that Q*R=A.

Example

Points:=Mat([[1,2,3],[2,3,4],[3,4,5]]);
QR := Num.QR(Points);
Dec(QR[1]*QR[2],3);

-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Mat([
  ["0.999", "1.999", "2.999"],
  ["1.999", "2.999", "3.999"],
  ["2.999", "3.999", "4.999"]
])
-------------------------------

See also

Introduction to CoCoAServer

Num.SVD

Num.EigenValues

Num.EigenValuesAndVectors

Num.EigenValuesAndAllVectors