following the formulation in the link:
Householder matrix and QR factorization.PDF
the code is as follows:
x=matrix(RDF,5,1,[1,2,3,4,5])
x1_=-sgn(x[0,0])*sqrt((x.transpose()*x)[0,0])
u=matrix(RDF,x.nrows(),1)
u[0,0]=sqrt((x1_-x[0,0])/(2*x1_))
for i in range(1,x.nrows()):
u[i]=x[i,0]/(-2*u[0,0]*x1_)
H=matrix(RDF,x.nrows(),x.nrows(),1)-2*u*u.transpose()
ndigits = 5
html('$%s$'%LatexExpr(r"x = "))
show((x).round(ndigits))
html('$%s$'%LatexExpr(r"\hat{x_1} = "))
show((x1_))
html('$%s$'%LatexExpr(r"u^{T}u = "))
show((u.transpose()*u).round(ndigits))
html('$%s$'%LatexExpr(r"u = "))
show((u).round(ndigits))
html('$%s$'%LatexExpr(r"H^{T}H = "))
show((H.transpose()*H).round(ndigits))
html('$%s$'%LatexExpr(r"H = "))
show((H).round(ndigits))
html('$%s$'%LatexExpr(r"Hx = "))
show((H*x).round(ndigits))
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