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Calling Sequence
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qr(X, output=R)
qr(X, output=QR)
qr(X, output=QRP)
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Parameters
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X
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MapleMatrix or MatlabMatrix
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output
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specify the form of the output (optional)
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R
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return the upper triangular matrix R
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QR
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return unitary matrix Q and upper triangular R matrix
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QRP
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return Q, R, and permutation matrix P
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Description
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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 . When output=QR, the result is computed where .
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The matrix X can be either square or rectangular.
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The matrix X is expressed as product of an upper triangular matrix and either a real orthonormal matrix or a complex unitary matrix.
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The default if no output option is specified is to return the matrices Q and R.
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Examples
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Define the Maple matrix
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The QR decomposition of this MapleMatrix is computed and returns Q and R, as follows:
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Q, R :=
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[-0.404519917477945468 , 0.418121005003545431 , -0.120768607347027060 , -0.804334137667873206]
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[-0.134839972492648424 , -0.903141370807658106 , 0.0315048540905287777 , -0.406400406400609482]
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[-0.809039834955890602 , -0.0836242010007090253 , -0.399061485146697980 , 0.423333756667301608]
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[-0.404519917477945301 , 0.0501745206004254873 , 0.908389959610246600 , 0.0931334264668064182]
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[-7.41619848709566209 -8.09039834955890668 -11.0568777443971715]
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[ ]
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[ 0. -5.43557306504609006 -2.67597443202269013]
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[ ]
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[ 0. 0. 2.92995143041917760 ]
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[ ]
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[ 0. 0. 0. ]
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The QR decomposition returning only the R matrix is as follows:
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[-7.41619848709566209 , -8.09039834955890668 , -11.0568777443971715]
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[ ]
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[0.0960043149368622339 , -5.43557306504609006 , -2.67597443202269013]
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[ ]
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[0.576025889621173404 , 0.166971439413840017 , 2.92995143041917760]
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[0.288012944810586701 , 0.0361500352119390120 , -0.704436674263540508]
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To force the lower triangle entries to zero, use
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[-7.41619848709566209 -8.09039834955890668 -11.0568777443971715]
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[ ]
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[ 0. -5.43557306504609006 -2.67597443202269013]
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[ ]
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[ 0. 0. 2.92995143041917760 ]
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[ ]
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[ 0. 0. 0. ]
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Note that the R in is surrounded by quotation marks, since the variable R was assigned previously. QR decomposition returning Q, R, and P matrices is as follows:
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