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May 18th, 2017
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  1. for i = 1:n
  2.       for j = i+1:n
  3.          println(r)
  4.          sinA = r[j][i] / sqrt(r[i][i] * r[i][i] + r[j][i] * r[j][i])
  5.          cosA = (sinA * r[i][i] / r[j][i])
  6.          println(sinA)
  7.          println(cosA)
  8.          for k = i:n
  9.             rj = r[j][k]
  10.             r[j][k] = - cosA * r[j][k] + sinA * r[i][k]
  11.             r[i][k] = cosA * r[i][k] + sinA * rj
  12.          end    
  13.          for k = 1:n
  14.             qj = q[j][k]
  15.             q[j][k] = - cosA * q[j][k] + sinA * q[i][k]
  16.             q[i][k] = cosA * q[i][k] + sinA * qj
  17.          end    
  18.       end
  19.    end
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