Difference between revisions of "ApCoCoA-1:Num.QR"
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<short_description>QR-decomposition of a matrix</short_description> | <short_description>QR-decomposition of a matrix</short_description> | ||
<syntax> | <syntax> | ||
| − | $numerical.QR(A:Matrix):Matrix; | + | $numerical.QR(A:Matrix):[Matrix,Matrix]; |
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | This function returns | + | This function returns an orthogonal matrix Q and an upper-right triangular matrix matrix R such that Q*R=A. |
| − | |||
| − | |||
<example> | <example> | ||
| Line 14: | Line 12: | ||
$numerical.QR(Points); | $numerical.QR(Points); | ||
------------------------------- | ------------------------------- | ||
| − | Mat([ | + | [Mat([ |
| − | [- | + | [-601818814743685/2251799813685248, 11221204152260750623490098342212473544619072342960407833413029/12855504354071922204335696738729300820177623950262342682411008, 47271922480373450167411707109523238704832584221077416524231372166340777774771/115792089237316195423570985008687907853269984665640564039457584007913129639936], |
| − | [- | + | [-21682807918593711888147761857797/40564819207303340847894502572032, 50535810838769898760508425874290037828518802391596092889928280803858452207141/231584178474632390847141970017375815706539969331281128078915168015826259279872, -1703150499741573022389535271505216648161852967701209661846360168011288983405834487511405397453/2085924839766513752338888384931203236916703635113918720651407820138886450957656787131798913024], |
| − | [-7823644591667907/1125899906842624, 5896596054914343/4503599627370496, | + | [-16262105938945284629515478500581/20282409603651670423947251286016, -50535810838769832038494686341702987883818294138398199855497298160515307568635/115792089237316195423570985008687907853269984665640564039457584007913129639936, 425787624935393028634420116827871332361842515189763323298971758853897488257161264158457298771/1042962419883256876169444192465601618458351817556959360325703910069443225478828393565899456512] |
| − | ]) | + | ]), Mat([ |
| + | [-8425463406411593/2251799813685248, -1504547036859213/281474976710656, -7823644591667907/1125899906842624], | ||
| + | [0, 5896596054914343/9007199254740992, 5896596054914343/4503599627370496], | ||
| + | [0, 0, 1197/9223372036854775808] | ||
| + | ])] | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
Revision as of 21:55, 21 June 2008
Numerical.QR
QR-decomposition of a matrix
Syntax
$numerical.QR(A:Matrix):[Matrix,Matrix];
Description
This function returns an orthogonal matrix Q and an upper-right triangular matrix matrix R such that Q*R=A.
Example
Points:=Mat([[1,2,3],[2,3,4],[3,4,5]]); $numerical.QR(Points); ------------------------------- [Mat([ [-601818814743685/2251799813685248, 11221204152260750623490098342212473544619072342960407833413029/12855504354071922204335696738729300820177623950262342682411008, 47271922480373450167411707109523238704832584221077416524231372166340777774771/115792089237316195423570985008687907853269984665640564039457584007913129639936], [-21682807918593711888147761857797/40564819207303340847894502572032, 50535810838769898760508425874290037828518802391596092889928280803858452207141/231584178474632390847141970017375815706539969331281128078915168015826259279872, -1703150499741573022389535271505216648161852967701209661846360168011288983405834487511405397453/2085924839766513752338888384931203236916703635113918720651407820138886450957656787131798913024], [-16262105938945284629515478500581/20282409603651670423947251286016, -50535810838769832038494686341702987883818294138398199855497298160515307568635/115792089237316195423570985008687907853269984665640564039457584007913129639936, 425787624935393028634420116827871332361842515189763323298971758853897488257161264158457298771/1042962419883256876169444192465601618458351817556959360325703910069443225478828393565899456512] ]), Mat([ [-8425463406411593/2251799813685248, -1504547036859213/281474976710656, -7823644591667907/1125899906842624], [0, 5896596054914343/9007199254740992, 5896596054914343/4503599627370496], [0, 0, 1197/9223372036854775808] ])] -------------------------------
See also
Numerical.EigenValuesAndVectors
Numerical.EigenValuesAndAllVectors
