function [A, tau] = alst2c(A)
% to obtain the QR factorization of the matrix A using Householder
% transformations. Use LAPACK's CGEQRF routine storage.
% function [A,tau] = alst2c(A)
% (c) 2020 Alain Hebert, Polytechnique Montreal
  [m, n] = size(A);
  if(n < 1), error('n < 1'), end
  if(n > m), error(['n > m (',num2str(n),num2str(m),')']), end
  tau = zeros(1,n);
  for j = 1:n
    m1 = m-j+1; w = A(j:m,j); x1 = w(1);
    ax = sqrt(w(1:m1)'*w(1:m1));
    a1 = abs(x1); s = sign(w(1));
    ssss = -ax*s; a1 = a1+ax;
    w(1) = a1*s;
    dd2 = a1*ax;
    if dd2 == 0, error('singular reflection'), end
    w = w/sqrt(dd2);
    A(j:m,j) = w;
    if j < n
      A(j:m,j+1:n) = A(j:m,j+1:n)-w*(w'*A(j:m,j+1:n));
    end
    diag = A(j,j);
    A(j:m,j) = A(j:m,j)/diag;
    A(j,j) = ssss;
    tau(j) = -diag'*diag;
  end