Matlab
qr
compute the QR orthogonal-triangular decomposition of a MapleMatrix or MatlabMatrix in MATLAB(R), where X*P = Q*R
Calling Sequence
Parameters
Description
Examples
qr(X, output=R)
qr(X, output=QR)
qr(X, output=QRP)
X
-
MapleMatrix or MatlabMatrix
output
specify the form of the output (optional)
R
return the upper triangular matrix R
QR
return unitary matrix Q and upper triangular R matrix
QRP
return Q, R, and permutation matrix P
The qr command computes the QR orthogonal-triangular decomposition of a matrix (either a Maple matrix or a MatlabMatrix) in MATLAB®. When output=QRP, the result is computed where XP=QR. When output=QR, the result is computed where X=QR.
The matrix X can be either square or rectangular.
The matrix X is expressed as product of an upper triangular matrix and either a real orthonormal matrix or a complex unitary matrix.
The default if no output option is specified is to return the matrices Q and R.
Define the Maple matrix
withMatlab:
maplematrix_a≔Matrix3,1,3,1,6,4,6,7,8,3,3,7
maplematrix_a≔313164678337
The QR decomposition of this MapleMatrix is computed and returns Q and R, as follows:
Q,R≔Matlabqrmaplematrix_a
Q, R :=
[-0.404519917477945468 , 0.418121005003545431 , -0.120768607347027060 , -0.804334137667873206]
[-0.134839972492648424 , -0.903141370807658106 , 0.0315048540905287777 , -0.406400406400609482]
[-0.809039834955890602 , -0.0836242010007090253 , -0.399061485146697980 , 0.423333756667301608]
[-0.404519917477945301 , 0.0501745206004254873 , 0.908389959610246600 , 0.0931334264668064182]
[-7.41619848709566209 -8.09039834955890668 -11.0568777443971715]
[ ]
[ 0. -5.43557306504609006 -2.67597443202269013]
[ 0. 0. 2.92995143041917760 ]
[ 0. 0. 0. ]
The QR decomposition returning only the R matrix is as follows:
M≔Matlabqrmaplematrix_a,output=R
[-7.41619848709566209 , -8.09039834955890668 , -11.0568777443971715]
[0.0960043149368622339 , -5.43557306504609006 , -2.67597443202269013]
[0.576025889621173404 , 0.166971439413840017 , 2.92995143041917760]
[0.288012944810586701 , 0.0361500352119390120 , -0.704436674263540508]
To force the lower triangle entries to zero, use
MatrixM,shape=triangularupper
Note that the R in output=R is surrounded by quotation marks, since the variable R was assigned previously. QR decomposition returning Q, R, and P matrices is as follows:
Q,R,P≔Matlabqrmaplematrix_a,output=QRP
See Also
LinearAlgebra[QRDecomposition]
Matlab[chol]
Matlab[det]
Matlab[evalM]
Matlab[inv]
Matlab[lu]
MatlabMatrix
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