/* ************************************************************
PROCEDURE qtxq - computes tril(Qb' * X * Qb)
Here, Qb = Q_1*Q_2*..*Q_{m-1}, where each Q_i is a Householder reflection.
(Qb is from a Qb * R decomposition.)
INPUT
beta - length m vector
c - m x m matrix, lower triangular gives Householder reflections
m - order
UPDATED
x - m x m. On output, Xnew = Qb' * X * Qb
This means: start with order m reflection, up to order 2 reflection.
WORK
fwork - length m working vector.
************************************************************ */
void qtxq(double *x, const double *beta, const double *c,
const int m, double *fwork)
{
int k, inz;
inz = 0;
/* ------------------------------------------------------------
For each k, c[inz] = c(k,k), the top of the lower-right block,
x[k] is start of k-th row in k.
------------------------------------------------------------ */
for(k = 0; k < m-1; k++, inz += m+1)
elqxq(x + k, -beta[k], c + inz, k, m, fwork);
}
/* ************************************************************
PROCEDURE qxqt - computes tril(Qb * X * Qb')
Here, Qb = Q_1*Q_2*..*Q_{m-1}, where each Q_i is a Householder reflection.
(Qb is from a Qb * R decomposition.)
INPUT
beta - length m vector
c - m x m matrix, lower triangular gives Householder reflections
m - order
UPDATED
x - m x m. On output, Xnew = Qb * X * Qb'
This means: start with order 2 reflection, up to order m reflection.
WORK
fwork - length m working vector.
************************************************************ */
void qxqt(double *x, const double *beta, const double *c,
const int m, double *fwork)
{
int k, inz;
inz = SQR(m) - (m+2);
/* ------------------------------------------------------------
For each k, c[inz] = c(k,k), the top of the lower-right block,
x[k] is start of k-th row in k.
------------------------------------------------------------ */
for(k = m-2; k >= 0; k--, inz -= m+1)
elqxq(x + k, -beta[k], c + inz, k, m, fwork);
}
/* ************************************************************
PROCEDURE qxqt - computes tril(Qb * X * Qb')
Here, Qb = Q_1*Q_2*..*Q_{m-1}, where each Q_i is a Householder reflection.
(Qb is from a Qb * R decomposition.)
INPUT
beta - length m vector
c - m x m matrix, lower triangular gives Householder reflections
m - order
UPDATED
x - m x m. On output, Xnew = Qb * X * Qb'
This means: start with order 2 reflection, up to order m reflection.
WORK
fwork - length m working vector.
************************************************************ */
void qxqt(double *x, const double *beta, const double *c,
const mwIndex m, double *fwork)
{
mwIndex k, inz;
mxAssert(m>1,"");
inz = SQR(m) - (m+2);
/* ------------------------------------------------------------
For each k, c[inz] = c(k,k), the top of the lower-right block,
x[k] is start of k-th row in k.
------------------------------------------------------------ */
for(k = m-1; k > 0; k--, inz -= m+1) {
elqxq(x + k-1, -beta[k-1], c + inz, k-1, m, fwork);
}
/*elqxq(x , -beta[0], c , 0, m, fwork);*/
}
