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      integer jpvt(*)
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      integer jpvt(*)
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      double precision x(ldx,*),qraux(*),work(*)
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      double precision x(ldx,*),qraux(*),work(*)
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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 j,jp,l,lp1,lup,maxj,pl,pu
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      integer j,jp,jj, l,lp1,lup,maxj,pl,pu
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      double precision maxnrm,dnrm2,tt
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      double precision maxnrm,dnrm2,tt
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      double precision ddot,nrmxl,t
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      double precision ddot,nrmxl,t
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      logical negj,swapj
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      logical negj,swapj
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c
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c
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c
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c