The Matrix component of the NAG output object contains R in the upper triangle if m >= n, and in the lower triangle if m Ī ≔ 2, 3, 1 | 4, 6, − 1 | − 1, − 3 2, − 2 The NAG object is an expression sequence whose first item is a Matrix and whose second item is a Vector.
It may not be requested with either of the other Matrix output objects, Q or R. The output object NAG may only be requested if the input Matrix contains floating-point data.
#Qr algorithm symbolic calculator software#
If R contains hardware floating-point entries, then e is taken to be 10^(1-evalhf(Digits)), else e is taken to be 10^(1-Digits) in the case of software floating-point entries. If rank is included in the output option along with R or NAG and A contains floating-point entries, then the rank is computed by counting the number of diagonal entries in the R (or NAG ) factor which exceed a certain tolerance, equal to the product of e and c, where c is equal to the maximum absolute diagonal element of R. The objects are returned in the same order as specified in the output list. If A contains floating-point entries, Householder transformations are used to compute the factorization.ĭepending on what is included in the output option ( out ), an expression sequence containing Q, R, rank or an expression sequence containing NAG, rank, can be returned. If conjugate=false is specified in the calling sequence, no conjugations are performed. Thus the rank is an optional output object.īy default, elements are conjugated during the Gram-Schmidt process. Otherwise, at some point a 0 column (on and below the diagonal) will be encountered.
#Qr algorithm symbolic calculator full#
If the QR decomposition is successful, then the Matrix is full rank. If the fullspan option is specified as just the symbol fullspan or as fullspan=true, or A has full rank, then a full QR factorization is performed. The columns of the Q1 factor span the column space of A. If the fullspan option ( fs ) is omitted or entered as fullspan=false, and A does not have full rank or has more rows than columns, a Q1R1 factorization is performed. If A contains symbolic entries, a Gram-Schmidt process is used to generate the factorization of A. The QRDecomposition function computes the QR decomposition of the Matrix A. (optional) equation of the form outputoptions = list where o is one of 'Q', 'R', or 'NAG' constructor options for the specified result object (optional) constructor options for the result object(s) (optional) equation of the form conjugate=true or false selects whether conjugations are performed in the Gram-Schmidt process (optional) equation of the form output = obj where obj is one of 'Q', R', 'NAG', or 'rank', or a list containing one or more of these names selects result objects to compute (optional) equation of the form fullspan=true or false selects whether a full QR factorization is performed QRDecomposition( A, fs, out, c, options, outopts )
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