linalg[QRdecomp] - QR decomposition of a matrix
|
Calling Sequence
|
|
QRdecomp(A)
QRdecomp(A, arg2, arg3, ...)
QRdecomp(A, Q='q', rank='r', fullspan=value)
|
|
Parameters
|
|
A
|
-
|
rectangular matrix
|
arg.i
|
-
|
(optional) is of the form name=val
|
rank='r'
|
-
|
(optional) for returning the rank of A
|
Q='q'
|
-
|
(optional) for returning the Q factor of A
|
fullspan=value
|
-
|
(optional) include null span in Q
|
|
|
|
|
Description
|
|
•
|
The routine QRdecomp computes the QR decomposition of the matrix A.
|
•
|
For matrices of floating-point entries, the numerically stable Householder-transformations are used. For symbolic computation, the Gram-Schmidt process is applied.
|
•
|
The result is an upper triangular matrix R. The orthonormal (unitary) factor Q is passed back to the Q parameter.
|
•
|
The default factorization is the full QR where R will have the same dimension as A. Q will be a full rank square matrix whose first n columns span the column space of A and whose last m-n columns span the null space of A.
|
•
|
If the (optional) fullspan arg is set to false, a Q1R1 factorization will be given where the Q1 factor will have the same dimension as A and, assuming A has full column rank, the columns of Q will span the column space of A. The R factor will be square and agree in dimension with Q. The default for fullspan is true.
|
•
|
If A is an n by n matrix then .
|
•
|
If A contains complex entries, the Q factor will be unitary.
|
•
|
The command with(linalg,QRdecomp) allows the use of the abbreviated form of this command.
|
|
|
Examples
|
|
Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.
>
|
|
>
|
|
| (1) |
>
|
|
| (2) |
>
|
|
Warning, unable to find a provably non-zero pivot
| |
| (3) |
>
|
|
| (4) |
>
|
|
| (5) |
>
|
|
| (6) |
>
|
|
Warning, unable to find a provably non-zero pivot
| |
| (7) |
>
|
|
| (8) |
|
|
Download Help Document
Was this information helpful?