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      integer jpvt(*)
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      integer jpvt(*)
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      double precision x(ldx,*),qraux(*),work(p,2),tol
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      double precision x(ldx,*),qraux(*),work(p,2),tol
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c
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c
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c     internal variables
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c     internal variables
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c
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c
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      integer i,j,l,lp1,lup
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      integer i,j,l,lp1,lup,k
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      double precision dnrm2,tt,ttt
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      double precision dnrm2,tt,ttt
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      double precision ddot,nrmxl,t
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      double precision ddot,nrmxl,t
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c
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c
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c
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c
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c     compute the norms of the columns of x.
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c     compute the norms of the columns of x.