Function r1updt
Given an m by n lower trapezoidal matrix S, an m-vector u, and an n-vector v, the problem is to determine an orthogonal matrix Q such that
void r1updt(Real)
(
size_t m,
size_t n,
Real* s,
size_t ls,
Real* u,
Real* v,
Real* w,
out bool sing
);
t
(S + u v ) Qis again lower trapezoidal.
This subroutine determines Q as the product of 2*(n - 1) transformations
gv(n-1)*...*gv(1)*gw(1)*...*gw(n-1)where gv(i), gw(i) are Givens rotations in the (i,n) plane which eliminate elements in the i-th and n-th planes, respectively. Q itself is not accumulated, rather the information to recover the gv, gw rotations is returned.
Parameters
| Name | Description |
|---|---|
| m | a positive integer input variable set to the number of rows of S. |
| n | a positive integer input variable set to the number of columns of S. n must not exceed m. |
| s | an array of length ls. on input s must contain the lower trapezoidal matrix S stored by columns. on output s contains the lower trapezoidal matrix produced as described above. |
| ls | a positive integer input variable not less than (n*(2*m-n+1))/2. |
| u | an input array of length m which must contain the vector u. |
| v | an array of length n. on input v must contain the vector v. on output v(i) contains the information necessary to recover the Givens rotation gv(i) described above. |
| w | an output array of length m. w(i) contains information necessary to recover the Givens rotation gw(i) described above. |
| sing | a logical output variable. sing is set true if any of the diagonal elements of the output s are zero. otherwise sing is set false. |