Purpose
To perform the QR factorization
(U ) = Q*(R),
(x') (0)
where U and R are n-by-n upper triangular matrices, x is an
n element vector and Q is an (n+1)-by-(n+1) orthogonal matrix.
U must be supplied in the n-by-n upper triangular part of the
array A and this is overwritten by R.
Specification
SUBROUTINE MB04OX( N, A, LDA, X, INCX )
C .. Scalar Arguments ..
INTEGER INCX, LDA, N
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), X(*)
Arguments
Input/Output Parameters
N (input) INTEGER
The number of elements of X and the order of the square
matrix A. N >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading N-by-N upper triangular part of this
array must contain the upper triangular matrix U.
On exit, the leading N-by-N upper triangular part of this
array contains the upper triangular matrix R.
The strict lower triangle of A is not referenced.
LDA INTEGER
The leading dimension of the array A. LDA >= max(1,N).
X (input/output) DOUBLE PRECISION array, dimension
(1+(N-1)*INCX)
On entry, the incremented array X must contain the
vector x. On exit, the content of X is changed.
INCX (input) INTEGER.
Specifies the increment for the elements of X. INCX > 0.
Method
The matrix Q is formed as a sequence of plane rotations in planes (1, n+1), (2, n+1), ..., (n, n+1), the rotation in the (j, n+1)th plane, Q(j), being chosen to annihilate the jth element of x.Further Comments
NoneExample
Program Text
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