ApCoCoA-1:Num.QR: Difference between revisions

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Updated example. Use Dec to make result human readable.
Line 17: Line 17:
<example>
<example>
Points:=Mat([[1,2,3],[2,3,4],[3,4,5]]);
Points:=Mat([[1,2,3],[2,3,4],[3,4,5]]);
Num.QR(Points);
QR := Num.QR(Points);
Dec(QR[1]*QR[2],3);
 
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
-------------------------------
[Mat([
Mat([
   [-601818814743685/2251799813685248, 11221204152260750623490098342212473544619072342960407833413029/12855504354071922204335696738729300820177623950262342682411008, 47271922480373450167411707109523238704832584221077416524231372166340777774771/115792089237316195423570985008687907853269984665640564039457584007913129639936],
   [<quote>0.999</quote>, <quote>1.999</quote>, <quote>2.999</quote>],
   [-21682807918593711888147761857797/40564819207303340847894502572032, 50535810838769898760508425874290037828518802391596092889928280803858452207141/231584178474632390847141970017375815706539969331281128078915168015826259279872, -1703150499741573022389535271505216648161852967701209661846360168011288983405834487511405397453/2085924839766513752338888384931203236916703635113918720651407820138886450957656787131798913024],
   [<quote>1.999</quote>, <quote>2.999</quote>, <quote>3.999</quote>],
   [-16262105938945284629515478500581/20282409603651670423947251286016, -50535810838769832038494686341702987883818294138398199855497298160515307568635/115792089237316195423570985008687907853269984665640564039457584007913129639936, 425787624935393028634420116827871332361842515189763323298971758853897488257161264158457298771/1042962419883256876169444192465601618458351817556959360325703910069443225478828393565899456512]
   [<quote>2.999</quote>, <quote>3.999</quote>, <quote>4.999</quote>]
]), Mat([
])
  [-8425463406411593/2251799813685248, -1504547036859213/281474976710656, -7823644591667907/1125899906842624],
  [0, 5896596054914343/9007199254740992, 5896596054914343/4503599627370496],
  [0, 0, 1197/9223372036854775808]
])]
-------------------------------
-------------------------------
</example>
</example>

Revision as of 08:12, 7 July 2009

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.

Calculates the QR decomposition of a matrix using Lapack.

  • @param A Matrix A

  • @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([
  [<quote>0.999</quote>, <quote>1.999</quote>, <quote>2.999</quote>],
  [<quote>1.999</quote>, <quote>2.999</quote>, <quote>3.999</quote>],
  [<quote>2.999</quote>, <quote>3.999</quote>, <quote>4.999</quote>]
])
-------------------------------

See also

Introduction to CoCoAServer

Num.SVD

Num.EigenValues

Num.EigenValuesAndVectors

Num.EigenValuesAndAllVectors




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